Make test/ a standalone project

2025-12-06 08:18:51 -06:00 · 2023-05-19 15:27:54 -05:00
56 changed files with 184 additions and 4842 deletions
--- a/.zenodo.json
+++ b/.zenodo.json
@@ -1,27 +0,0 @@
 {
    "creators": [
      {
        "orcid": "0000-0002-5022-9802",
        "affiliation": "Argonne National Laboratory",
        "name": "Santos Xavier, Alinson"
      },
      {
        "affiliation": "University of Florida",
        "name": "Kazachkov, Aleksandr M."
      },
      {
        "affiliation": "Technische Universität Berlin",
        "name": "Yurdakul, Ogün"
      },
      {
        "affiliation": "Purdue University",
        "name": "He, Jun"
      },
      {
        "affiliation": "Argonne National Laboratory",
        "name": "Qiu, Feng"
      }
    ],
    "title": "UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment",
    "description": "<b>UnitCommitment.jl</b> (UC.jl) is an optimization package for the Security-Constrained Unit Commitment Problem (SCUC), a fundamental optimization problem in power systems used, for example, to clear the day-ahead electricity markets. The package provides benchmark instances for the problem and Julia/JuMP implementations of state-of-the-art mixed-integer programming formulations."
  }
--- a/Project.toml
+++ b/Project.toml
@@ -13,15 +13,11 @@ JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
 MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
 MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
 PackageCompiler = "9b87118b-4619-50d2-8e1e-99f35a4d4d9d"
 Printf = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 [compat]
 DataStructures = "0.18"
@@ -29,8 +25,6 @@ Distributions = "0.25"
 GZip = "0.5"
 JSON = "0.21"
 JuMP = "1"
 MPI = "0.20"
 MathOptInterface = "1"
 PackageCompiler = "1"
 TimerOutputs = "0.5"
 julia = "1"
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -1,9 +1,5 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Glob = "c27321d9-0574-5035-807b-f59d2c89b15c"
 HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b"
 JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
 Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
 UnitCommitment = "64606440-39ea-11e9-0f29-3303a1d3d877"
--- a/docs/example/out.json
+++ b/docs/example/out.json
--- a/docs/example/s1.json
+++ b/docs/example/s1.json
@@ -1,495 +0,0 @@
 {
    "Parameters": {
 	"Version": "0.3",
        "Time horizon (h)": 4
    },
    "Generators": {
        "g1": {
            "Bus": "b1",
            "Production cost curve (MW)": [
                100,
                110,
                130,
                135
            ],
            "Production cost curve ($)": [
                1400,
                1600,
                2200,
                2400
            ],
            "Startup delays (h)": [
                1,
                2,
                3
            ],
            "Startup costs ($)": [
                1000.0,
                1500.0,
                2000.0
            ],
            "Initial status (h)": -100,
            "Initial power (MW)": 0
        },
        "g2": {
            "Bus": "b2",
            "Production cost curve (MW)": [
                0,
                47,
                94,
                140
            ],
            "Production cost curve ($)": [
                0,
                2256.00,
                4733.37,
                7395.39
            ],
            "Startup delays (h)": [
                1,
                4
            ],
            "Startup costs ($)": [
                3000.0,
                4000.0
            ],
            "Ramp up limit (MW)": 98.0,
            "Ramp down limit (MW)": 98.0,
            "Startup limit (MW)": 98.0,
            "Shutdown limit (MW)": 98.0,
            "Minimum uptime (h)": 4,
            "Minimum downtime (h)": 4,
            "Maximum daily energy (MWh)": null,
            "Maximum daily starts": null,
            "Initial status (h)": -8,
            "Initial power (MW)": 0,
            "Reserve eligibility": [
                "r1"
            ]
        },
        "g3": {
            "Bus": "b3",
            "Production cost curve (MW)": [
                0,
                33,
                66,
                100
            ],
            "Production cost curve ($)": [
                0,
                1113.75,
                2369.07,
                3891.54
            ],
            "Startup delays (h)": [
                1,
                4,
                8
            ],
            "Startup costs ($)": [
                1000.0,
                2000.0,
                3000.0
            ],
            "Ramp up limit (MW)": 70.0,
            "Ramp down limit (MW)": 70.0,
            "Startup limit (MW)": 70.0,
            "Shutdown limit (MW)": 70.0,
            "Must run?": true,
            "Minimum uptime (h)": 1,
            "Minimum downtime (h)": 1,
            "Maximum daily energy (MWh)": null,
            "Maximum daily starts": null,
            "Initial status (h)": -6,
            "Initial power (MW)": 0,
            "Reserve eligibility": [
                "r1"
            ]
        },
        "g4": {
            "Bus": "b6",
            "Production cost curve (MW)": [
                33,
                66,
                100
            ],
            "Production cost curve ($)": [
                1113.75,
                2369.07,
                3891.54
            ],
            "Initial status (h)": -100,
            "Initial power (MW)": 0,
            "Reserve eligibility": [
                "r1"
            ]
        },
        "g5": {
            "Bus": "b8",
            "Production cost curve (MW)": [
                33,
                66,
                100
            ],
            "Production cost curve ($)": [
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                2369.07,
                3891.54
            ],
            "Initial status (h)": -100,
            "Initial power (MW)": 0,
            "Reserve eligibility": [
                "r1"
            ]
        },
        "g6": {
            "Bus": "b8",
            "Production cost curve (MW)": [
                100
            ],
            "Production cost curve ($)": [
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            ],
            "Initial status (h)": -100,
            "Initial power (MW)": 0,
            "Reserve eligibility": [
                "r1"
            ]
        }
    },
    "Buses": {
        "b1": {
            "Load (MW)": 0.0
        },
        "b2": {
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        },
        "b3": {
            "Load (MW)": [
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        },
        "b4": {
            "Load (MW)": [
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        "b5": {
            "Load (MW)": [
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        "b6": {
            "Load (MW)": [
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        },
        "b7": {
            "Load (MW)": 0.0
        },
        "b8": {
            "Load (MW)": 0.0
        },
        "b9": {
            "Load (MW)": [
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        },
        "b10": {
            "Load (MW)": [
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        },
        "b11": {
            "Load (MW)": [
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        },
        "b12": {
            "Load (MW)": [
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        },
        "b13": {
            "Load (MW)": [
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        },
        "b14": {
            "Load (MW)": [
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        }
    },
    "Transmission lines": {
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            "Susceptance (S)": 29.496860773945063,
            "Normal flow limit (MW)": 300.0,
            "Emergency flow limit (MW)": 400.0,
            "Flow limit penalty ($/MW)": 1000.0
        },
        "l2": {
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        },
        "l3": {
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            "Susceptance (S)": 8.816129979261149
        },
        "l4": {
            "Source bus": "b2",
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            "Reactance (ohms)": 0.17632,
            "Susceptance (S)": 9.898645939169292
        },
        "l5": {
            "Source bus": "b2",
            "Target bus": "b5",
            "Reactance (ohms)": 0.17388,
            "Susceptance (S)": 10.037550333530765
        },
        "l6": {
            "Source bus": "b3",
            "Target bus": "b4",
            "Reactance (ohms)": 0.17103,
            "Susceptance (S)": 10.204813494675376
        },
        "l7": {
            "Source bus": "b4",
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            "Susceptance (S)": 41.44690695783257
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        "l8": {
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            "Reactance (ohms)": 0.20911999999999997,
            "Susceptance (S)": 8.346065665619404
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        "l9": {
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            "Target bus": "b9",
            "Reactance (ohms)": 0.55618,
            "Susceptance (S)": 3.1380654680037567
        },
        "l10": {
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            "Target bus": "b6",
            "Reactance (ohms)": 0.25201999999999997,
            "Susceptance (S)": 6.92536009838239
        },
        "l11": {
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            "Susceptance (S)": 8.774908255376218
        },
        "l12": {
            "Source bus": "b6",
            "Target bus": "b12",
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            "Susceptance (S)": 6.8227561549365925
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        "l13": {
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            "Susceptance (S)": 13.397783465067395
        },
        "l14": {
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            "Susceptance (S)": 9.908198989465395
        },
        "l15": {
            "Source bus": "b7",
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            "Reactance (ohms)": 0.11001,
            "Susceptance (S)": 15.865187273832648
        },
        "l16": {
            "Source bus": "b9",
            "Target bus": "b10",
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            "Susceptance (S)": 20.65478404727017
        },
        "l17": {
            "Source bus": "b9",
            "Target bus": "b14",
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            "Susceptance (S)": 6.4550974628091184
        },
        "l18": {
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            "Susceptance (S)": 9.08694357262628
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        "l19": {
            "Source bus": "b12",
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            "Susceptance (S)": 8.73188539120637
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        "l20": {
            "Source bus": "b13",
            "Target bus": "b14",
            "Reactance (ohms)": 0.34802,
            "Susceptance (S)": 5.0150257226433235
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    },
    "Contingencies": {
        "c1": {
            "Affected lines": [
                "l1"
            ]
        },
        "c2": {
            "Affected lines": [
                "l2"
            ]
        },
        "c3": {
            "Affected lines": [
                "l3"
            ]
        },
        "c4": {
            "Affected lines": [
                "l4"
            ]
        },
        "c5": {
            "Affected lines": [
                "l5"
            ]
        },
        "c6": {
            "Affected lines": [
                "l6"
            ]
        },
        "c7": {
            "Affected lines": [
                "l7"
            ]
        },
        "c8": {
            "Affected lines": [
                "l8"
            ]
        },
        "c9": {
            "Affected lines": [
                "l9"
            ]
        },
        "c10": {
            "Affected lines": [
                "l10"
            ]
        },
        "c11": {
            "Affected lines": [
                "l11"
            ]
        },
        "c12": {
            "Affected lines": [
                "l12"
            ]
        },
        "c13": {
            "Affected lines": [
                "l13"
            ]
        },
        "c15": {
            "Affected lines": [
                "l15"
            ]
        },
        "c16": {
            "Affected lines": [
                "l16"
            ]
        },
        "c17": {
            "Affected lines": [
                "l17"
            ]
        },
        "c18": {
            "Affected lines": [
                "l18"
            ]
        },
        "c19": {
            "Affected lines": [
                "l19"
            ]
        },
        "c20": {
            "Affected lines": [
                "l20"
            ]
        }
    },
    "Price-sensitive loads": {
        "ps1": {
            "Bus": "b3",
            "Revenue ($/MW)": 100.0,
            "Demand (MW)": 50.0
        }
    },
    "Reserves": {
        "r1": {
            "Type": "Spinning",
            "Amount (MW)": 100.0,
            "Shortfall penalty ($/MW)": 1000.0
        }
    }
 }
--- a/docs/example/s2.json
+++ b/docs/example/s2.json
@@ -1,495 +0,0 @@
 {
    "Parameters": {
 	"Version": "0.3",
        "Time horizon (h)": 4
    },
    "Generators": {
        "g1": {
            "Bus": "b1",
            "Production cost curve (MW)": [
                100,
                110,
                130,
                135
            ],
            "Production cost curve ($)": [
                1400,
                1600,
                2200,
                2400
            ],
            "Startup delays (h)": [
                1,
                2,
                3
            ],
            "Startup costs ($)": [
                1000.0,
                1500.0,
                2000.0
            ],
            "Initial status (h)": -100,
            "Initial power (MW)": 0
        },
        "g2": {
            "Bus": "b2",
            "Production cost curve (MW)": [
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                140
            ],
            "Production cost curve ($)": [
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            ],
            "Startup delays (h)": [
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                4
            ],
            "Startup costs ($)": [
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                4000.0
            ],
            "Ramp up limit (MW)": 98.0,
            "Ramp down limit (MW)": 98.0,
            "Startup limit (MW)": 98.0,
            "Shutdown limit (MW)": 98.0,
            "Minimum uptime (h)": 4,
            "Minimum downtime (h)": 4,
            "Maximum daily energy (MWh)": null,
            "Maximum daily starts": null,
            "Initial status (h)": -8,
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            "Reserve eligibility": [
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        },
        "g3": {
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            "Production cost curve ($)": [
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            "Startup delays (h)": [
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            "Startup costs ($)": [
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            "Ramp up limit (MW)": 70.0,
            "Ramp down limit (MW)": 70.0,
            "Startup limit (MW)": 70.0,
            "Shutdown limit (MW)": 70.0,
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        "g4": {
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            "Production cost curve ($)": [
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        "g5": {
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            "Load (MW)": [
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        "b14": {
            "Load (MW)": [
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    },
    "Transmission lines": {
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            "Target bus": "b2",
            "Reactance (ohms)": 0.05917000000000001,
            "Susceptance (S)": 29.496860773945063,
            "Normal flow limit (MW)": 300.0,
            "Emergency flow limit (MW)": 400.0,
            "Flow limit penalty ($/MW)": 1000.0
        },
        "l2": {
            "Source bus": "b1",
            "Target bus": "b5",
            "Reactance (ohms)": 0.22304000000000002,
            "Susceptance (S)": 7.825184953346168
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        "l3": {
            "Source bus": "b2",
            "Target bus": "b3",
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            "Susceptance (S)": 8.816129979261149
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        "l4": {
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        "l5": {
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            "Susceptance (S)": 10.037550333530765
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        "l6": {
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            "Susceptance (S)": 10.204813494675376
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        "l7": {
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            "Susceptance (S)": 41.44690695783257
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        "l8": {
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            "Susceptance (S)": 8.346065665619404
        },
        "l9": {
            "Source bus": "b4",
            "Target bus": "b9",
            "Reactance (ohms)": 0.55618,
            "Susceptance (S)": 3.1380654680037567
        },
        "l10": {
            "Source bus": "b5",
            "Target bus": "b6",
            "Reactance (ohms)": 0.25201999999999997,
            "Susceptance (S)": 6.92536009838239
        },
        "l11": {
            "Source bus": "b6",
            "Target bus": "b11",
            "Reactance (ohms)": 0.1989,
            "Susceptance (S)": 8.774908255376218
        },
        "l12": {
            "Source bus": "b6",
            "Target bus": "b12",
            "Reactance (ohms)": 0.25581,
            "Susceptance (S)": 6.8227561549365925
        },
        "l13": {
            "Source bus": "b6",
            "Target bus": "b13",
            "Reactance (ohms)": 0.13027,
            "Susceptance (S)": 13.397783465067395
        },
        "l14": {
            "Source bus": "b7",
            "Target bus": "b8",
            "Reactance (ohms)": 0.17615,
            "Susceptance (S)": 9.908198989465395
        },
        "l15": {
            "Source bus": "b7",
            "Target bus": "b9",
            "Reactance (ohms)": 0.11001,
            "Susceptance (S)": 15.865187273832648
        },
        "l16": {
            "Source bus": "b9",
            "Target bus": "b10",
            "Reactance (ohms)": 0.0845,
            "Susceptance (S)": 20.65478404727017
        },
        "l17": {
            "Source bus": "b9",
            "Target bus": "b14",
            "Reactance (ohms)": 0.27038,
            "Susceptance (S)": 6.4550974628091184
        },
        "l18": {
            "Source bus": "b10",
            "Target bus": "b11",
            "Reactance (ohms)": 0.19207,
            "Susceptance (S)": 9.08694357262628
        },
        "l19": {
            "Source bus": "b12",
            "Target bus": "b13",
            "Reactance (ohms)": 0.19988,
            "Susceptance (S)": 8.73188539120637
        },
        "l20": {
            "Source bus": "b13",
            "Target bus": "b14",
            "Reactance (ohms)": 0.34802,
            "Susceptance (S)": 5.0150257226433235
        }
    },
    "Contingencies": {
        "c1": {
            "Affected lines": [
                "l1"
            ]
        },
        "c2": {
            "Affected lines": [
                "l2"
            ]
        },
        "c3": {
            "Affected lines": [
                "l3"
            ]
        },
        "c4": {
            "Affected lines": [
                "l4"
            ]
        },
        "c5": {
            "Affected lines": [
                "l5"
            ]
        },
        "c6": {
            "Affected lines": [
                "l6"
            ]
        },
        "c7": {
            "Affected lines": [
                "l7"
            ]
        },
        "c8": {
            "Affected lines": [
                "l8"
            ]
        },
        "c9": {
            "Affected lines": [
                "l9"
            ]
        },
        "c10": {
            "Affected lines": [
                "l10"
            ]
        },
        "c11": {
            "Affected lines": [
                "l11"
            ]
        },
        "c12": {
            "Affected lines": [
                "l12"
            ]
        },
        "c13": {
            "Affected lines": [
                "l13"
            ]
        },
        "c15": {
            "Affected lines": [
                "l15"
            ]
        },
        "c16": {
            "Affected lines": [
                "l16"
            ]
        },
        "c17": {
            "Affected lines": [
                "l17"
            ]
        },
        "c18": {
            "Affected lines": [
                "l18"
            ]
        },
        "c19": {
            "Affected lines": [
                "l19"
            ]
        },
        "c20": {
            "Affected lines": [
                "l20"
            ]
        }
    },
    "Price-sensitive loads": {
        "ps1": {
            "Bus": "b3",
            "Revenue ($/MW)": 100.0,
            "Demand (MW)": 50.0
        }
    },
    "Reserves": {
        "r1": {
            "Type": "Spinning",
            "Amount (MW)": 100.0,
            "Shortfall penalty ($/MW)": 1000.0
        }
    }
 }
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -1,18 +1,16 @@
 using Documenter, UnitCommitment, JuMP
-function make()
+makedocs(
-    makedocs(
+    sitename="UnitCommitment.jl",
-        sitename="UnitCommitment.jl",
+    pages=[
-        pages=[
+        "Home" => "index.md",
-            "Home" => "index.md",
+        "usage.md",
-            "usage.md",
+        "format.md",
-            "format.md",
+        "instances.md",
-            "instances.md",
+        "model.md",
-            "model.md",
+        "api.md",
-            "api.md",
+    ],
-        ],
+    format = Documenter.HTML(
-        format = Documenter.HTML(
+        assets=["assets/custom.css"],
            assets=["assets/custom.css"],
        )
    )
-end
+)
--- a/docs/src/format.md
+++ b/docs/src/format.md
@@ -4,12 +4,11 @@ Data Format
 Input Data Format
 -----------------
-An instance of the stochastic security-constrained unit commitment (SCUC) problem is composed multiple scenarios. Each scenario should be described in an individual JSON file containing the main section belows. For deterministic instances, a single scenario file, following the same format below, may also be provided. Fields that are allowed to differ among scenarios are marked as "uncertain". Fields that are allowed to be time-dependent are marked as "time series".
+Instances are specified by JSON files containing the following main sections:
 * [Parameters](#Parameters)
 * [Buses](#Buses)
 * [Generators](#Generators)
 * [Storage units](#Storage-units)
 * [Price-sensitive loads](#Price-sensitive-loads)
 * [Transmission lines](#Transmission-lines)
 * [Reserves](#Reserves)
@@ -21,14 +20,12 @@ Each section is described in detail below. See [case118/2017-01-01.json.gz](http
 This section describes system-wide parameters, such as power balance penalty, and optimization parameters, such as the length of the planning horizon and the time.
-| Key                            | Description                                       | Default  | Time series? | Uncertain?
+| Key                            | Description                                       | Default  | Time series?
-| :----------------------------- | :------------------------------------------------ | :------: | :------------:| :----------:
+| :----------------------------- | :------------------------------------------------ | :------: | :------------:
-| `Version` | Version of UnitCommitment.jl this file was written for. Required to ensure that the file remains readable in future versions of the package. If you are following this page to construct the file, this field should equal `0.4`. | Required | No | No
+| `Version` | Version of UnitCommitment.jl this file was written for. Required to ensure that the file remains readable in future versions of the package. If you are following this page to construct the file, this field should equal `0.3`. | Required | N
-| `Time horizon (min)` or  `Time horizon (h)` | Length of the planning horizon (in minutes or hours). Either `Time horizon (min)` or `Time horizon (h)` is required, but not both.  | Required | No | No
+| `Time horizon (h)` | Length of the planning horizon (in hours). | Required | N
-| `Time step (min)` | Length of each time step (in minutes). Must be a divisor of 60 (e.g. 60, 30, 20, 15, etc). | `60` | No | No
+| `Time step (min)` | Length of each time step (in minutes). Must be a divisor of 60 (e.g. 60, 30, 20, 15, etc). | `60` | N
-| `Power balance penalty ($/MW)` | Penalty for system-wide shortage or surplus in production (in $/MW). This is charged per time step. For example, if there is a shortage of 1 MW for three time steps, three times this amount will be charged. | `1000.0` | No | Yes
+| `Power balance penalty ($/MW)` | Penalty for system-wide shortage or surplus in production (in $/MW). This is charged per time step. For example, if there is a shortage of 1 MW for three time steps, three times this amount will be charged. | `1000.0` | Y
 | `Scenario name` | Name of the scenario. | `"s1"` | No | ---
 | `Scenario weight` | Weight of the scenario. The scenario weight can be any positive real number, that is, it does not have to be between zero and one. The package normalizes the weights to ensure that the probability of all scenarios sum up to one. | 1.0 | No | ---
 #### Example
@@ -37,9 +34,7 @@ This section describes system-wide parameters, such as power balance penalty, an
    "Parameters": {
        "Version": "0.3",
        "Time horizon (h)": 4,
-        "Power balance penalty ($/MW)": 1000.0,
+        "Power balance penalty ($/MW)": 1000.0
        "Scenario name": "s1",
        "Scenario weight": 0.5
    }
 }
 ```
@@ -48,9 +43,9 @@ This section describes system-wide parameters, such as power balance penalty, an
 This section describes the characteristics of each bus in the system. 
-| Key                | Description                                                   | Default | Time series? | Uncertain?
+| Key                | Description                                                   | Default | Time series?
-| :----------------- | :------------------------------------------------------------ | ------- | :-----------: | :---:
+| :----------------- | :------------------------------------------------------------ | ------- | :-------------:
-| `Load (MW)`        | Fixed load connected to the bus (in MW).                      | Required | Yes | Yes
+| `Load (MW)`        | Fixed load connected to the bus (in MW).                      | Required | Y
 #### Example
@@ -82,33 +77,33 @@ This section describes all generators in the system. Two types of units can be s
 #### Thermal Units
-| Key                       | Description                                      | Default | Time series? | Uncertain?
+| Key                       | Description                                      | Default | Time series?
-| :------------------------ | :------------------------------------------------| ------- | :-----------: | :---:
+| :------------------------ | :------------------------------------------------| ------- | :-----------:
-| `Bus`                     | Identifier of the bus where this generator is located (string). | Required | No | Yes
+| `Bus`                     | Identifier of the bus where this generator is located (string). | Required | N
-| `Type`                     | Type of the generator (string). For thermal generators, this must be `Thermal`.  | Required | No | No
+| `Type`                     | Type of the generator (string). For thermal generators, this must be `Thermal`.  | Required | N
-| `Production cost curve (MW)` and `Production cost curve ($)` | Parameters describing the piecewise-linear production costs. See below for more details. | Required | Yes | Yes
+| `Production cost curve (MW)` and `Production cost curve ($)` | Parameters describing the piecewise-linear production costs. See below for more details. | Required | Y
-| `Startup costs ($)` and `Startup delays (h)` | Parameters describing how much it costs to start the generator after it has been shut down for a certain amount of time. If `Startup costs ($)` and `Startup delays (h)` are set to `[300.0, 400.0]` and `[1, 4]`, for example, and the generator is shut down at time `00:00` (h:min), then it costs \$300 to start up the generator at any time between `01:00` and `03:59`, and \$400 to start the generator at time `04:00` or any time after that.  The number of startup cost points is unlimited, and may be different for each generator. Startup delays must be strictly increasing and the first entry must equal `Minimum downtime (h)`. | `[0.0]` and `[1]` | No | Yes
+| `Startup costs ($)` and `Startup delays (h)` | Parameters describing how much it costs to start the generator after it has been shut down for a certain amount of time. If `Startup costs ($)` and `Startup delays (h)` are set to `[300.0, 400.0]` and `[1, 4]`, for example, and the generator is shut down at time `00:00` (h:min), then it costs \$300 to start up the generator at any time between `01:00` and `03:59`, and \$400 to start the generator at time `04:00` or any time after that.  The number of startup cost points is unlimited, and may be different for each generator. Startup delays must be strictly increasing and the first entry must equal `Minimum downtime (h)`. | `[0.0]` and `[1]` | N
-| `Minimum uptime (h)`      | Minimum amount of time the generator must stay operational after starting up (in hours). For example, if the generator starts up at time `00:00` (h:min) and `Minimum uptime (h)` is set to 4, then the generator can only shut down at time `04:00`. | `1` | No | Yes
+| `Minimum uptime (h)`      | Minimum amount of time the generator must stay operational after starting up (in hours). For example, if the generator starts up at time `00:00` (h:min) and `Minimum uptime (h)` is set to 4, then the generator can only shut down at time `04:00`. | `1` | N
-| `Minimum downtime (h)`    | Minimum amount of time the generator must stay offline after shutting down (in hours). For example, if the generator shuts down at time `00:00` (h:min) and `Minimum downtime (h)` is set to 4, then the generator can only start producing power again at time `04:00`. | `1` | No | Yes
+| `Minimum downtime (h)`    | Minimum amount of time the generator must stay offline after shutting down (in hours). For example, if the generator shuts down at time `00:00` (h:min) and `Minimum downtime (h)` is set to 4, then the generator can only start producing power again at time `04:00`. | `1` | N
-| `Ramp up limit (MW)`      | Maximum increase in production from one time step to the next (in MW). For example, if the generator is producing 100 MW at time step 1 and if this parameter is set to 40 MW, then the generator will produce at most 140 MW at time step 2. | `+inf` | No | Yes
+| `Ramp up limit (MW)`      | Maximum increase in production from one time step to the next (in MW). For example, if the generator is producing 100 MW at time step 1 and if this parameter is set to 40 MW, then the generator will produce at most 140 MW at time step 2. | `+inf` | N
-| `Ramp down limit (MW)`    | Maximum decrease in production from one time step to the next (in MW). For example, if the generator is producing 100 MW at time step 1 and this parameter is set to 40 MW, then the generator will produce at least 60 MW at time step 2. | `+inf` | No | Yes
+| `Ramp down limit (MW)`    | Maximum decrease in production from one time step to the next (in MW). For example, if the generator is producing 100 MW at time step 1 and this parameter is set to 40 MW, then the generator will produce at least 60 MW at time step 2. | `+inf` | N
-| `Startup limit (MW)`   | Maximum amount of power a generator can produce immediately after starting up (in MW). For example, if `Startup limit (MW)` is set to 100 MW and the unit is off at time step 1, then it may produce at most 100 MW at time step 2.| `+inf` | No | Yes
+| `Startup limit (MW)`   | Maximum amount of power a generator can produce immediately after starting up (in MW). For example, if `Startup limit (MW)` is set to 100 MW and the unit is off at time step 1, then it may produce at most 100 MW at time step 2.| `+inf` | N
-| `Shutdown limit (MW)`     | Maximum amount of power a generator can produce immediately before shutting down (in MW). Specifically, the generator can only shut down at time step `t+1` if its production at time step `t` is below this limit.  | `+inf` | No | Yes
+| `Shutdown limit (MW)`     | Maximum amount of power a generator can produce immediately before shutting down (in MW). Specifically, the generator can only shut down at time step `t+1` if its production at time step `t` is below this limit.  | `+inf` | N
-| `Initial status (h)`  | If set to a positive number, indicates the amount of time (in hours) the generator has been on at the beginning of the simulation, and if set to a negative number, the amount of time the generator has been off. For example, if `Initial status (h)` is `-2`, this means that the generator was off since `-02:00` (h:min). The simulation starts at time `00:00`. If `Initial status (h)` is `3`, this means that the generator was on since `-03:00`. A value of zero is not acceptable. | Required | No | No
+| `Initial status (h)`  | If set to a positive number, indicates the amount of time (in hours) the generator has been on at the beginning of the simulation, and if set to a negative number, the amount of time the generator has been off. For example, if `Initial status (h)` is `-2`, this means that the generator was off since `-02:00` (h:min). The simulation starts at time `00:00`. If `Initial status (h)` is `3`, this means that the generator was on since `-03:00`. A value of zero is not acceptable. | Required | N
-| `Initial power (MW)`  | Amount of power the generator at time step `-1`, immediately before the planning horizon starts. | Required | No | No
+| `Initial power (MW)`  | Amount of power the generator at time step `-1`, immediately before the planning horizon starts. | Required | N
-| `Must run?`               | If `true`, the generator should be committed, even if that is not economical (Boolean). | `false` | Yes | Yes
+| `Must run?`               | If `true`, the generator should be committed, even if that is not economical (Boolean). | `false` | Y
-| `Reserve eligibility` | List of reserve products this generator is eligibe to provide. By default, the generator is not eligible to provide any reserves. | `[]` | No | Yes
+| `Reserve eligibility` | List of reserve products this generator is eligibe to provide. By default, the generator is not eligible to provide any reserves. | `[]` | N
-| `Commitment status` | List of commitment status over the time horizon. At time `t`, if `true`, the generator must be commited at that time period; if `false`, the generator must not be commited at that time period. If `null` at time `t`, the generator's commitment status is then decided by the model. By default, the status is a list of `null` values. | `null` | Yes | Yes
+| `Commitment status` | List of commitment status over the time horizon. At time `t`, if `true`, the generator must be commited at that time period; if `false`, the generator must not be commited at that time period. If `null` at time `t`, the generator's commitment status is then decided by the model. By default, the status is a list of `null` values. | `null` | Y
 #### Profiled Units
-| Key               | Description                                       | Default  | Time series? | Uncertain?
+| Key               | Description                                       | Default  | Time series?
-| :---------------- | :------------------------------------------------ | :------: | :------------: | :---:
+| :---------------- | :------------------------------------------------ | :------: | :------------:
-| `Bus`             | Identifier of the bus where this generator is located (string). | Required | No | Yes
+| `Bus`             | Identifier of the bus where this generator is located (string). | Required | N
-| `Type`            | Type of the generator (string). For profiled generators, this must be `Profiled`.  | Required | No | No
+| `Type`            | Type of the generator (string). For profiled generators, this must be `Profiled`.  | Required | N
-| `Cost ($/MW)`     | Cost incurred for serving each MW of power by this generator. | Required | Yes | Yes
+| `Cost ($/MW)`     | Cost incurred for serving each MW of power by this generator. | Required | Y
-| `Minimum power (MW)` | Minimum amount of power this generator may supply. | `0.0` | Yes | Yes
+| `Minimum power (MW)` | Minimum amount of power this generator may supply. | `0.0` | Y
-| `Maximum power (MW)` | Maximum amount of power this generator may supply. | Required | Yes | Yes
+| `Maximum power (MW)` | Maximum amount of power this generator may supply. | Required | Y
 #### Production costs and limits
@@ -174,90 +169,15 @@ Note that this curve also specifies the production limits. Specifically, the fir
 }
 ```
 ### Storage units
 This section describes energy storage units in the system which charge and discharge power. The storage units consume power while charging, and generate power while discharging. 
 | Key               | Description                                       | Default  | Time series? | Uncertain?
 | :---------------- | :------------------------------------------------ | :------: | :------------: | :----: 
 | `Bus`             | Bus where the storage unit is located. Multiple storage units may be placed at the same bus. | Required | No | Yes
 | `Minimum level (MWh)`  | Minimum of energy level this storage unit may contain. | `0.0` | Yes | Yes
 | `Maximum level (MWh)`  | Maximum of energy level this storage unit may contain. | Required | Yes | Yes
 | `Allow simultaneous charging and discharging`  | If `false`, the storage unit is not allowed to charge and discharge at the same time (Boolean). | `true` | Yes | Yes
 | `Charge cost ($/MW)`  | Cost incurred for charging each MW of power into this storage unit. | Required | Yes | Yes
 | `Discharge cost ($/MW)`  | Cost incurred for discharging each MW of power from this storage unit. | Required | Yes | Yes
 | `Charge efficiency`  | Efficiency rate to charge power into this storage unit. This value must be greater than or equal to `0.0`, and less than or equal to `1.0`. | `1.0` | Yes | Yes
 | `Discharge efficiency`  | Efficiency rate to discharge power from this storage unit. This value must be greater than or equal to `0.0`, and less than or equal to `1.0`. | `1.0` | Yes | Yes
 | `Loss factor`  | The energy dissipation rate of this storage unit. This value must be greater than or equal to `0.0`, and less than or equal to `1.0`. | `0.0` | Yes | Yes
 | `Minimum charge rate (MW)`  | Minimum amount of power rate this storage unit may charge. | `0.0` | Yes | Yes
 | `Maximum charge rate (MW)`  | Maximum amount of power rate this storage unit may charge. | Required | Yes | Yes
 | `Minimum discharge rate (MW)`  | Minimum amount of power rate this storage unit may discharge. | `0.0` | Yes | Yes
 | `Maximum discharge rate (MW)`  | Maximum amount of power rate this storage unit may discharge. | Required | Yes | Yes
 | `Initial level (MWh)`  | Amount of energy this storage unit at time step `-1`, immediately before the planning horizon starts. | `0.0` | No | Yes
 | `Last period minimum level (MWh)`  | Minimum of energy level this storage unit may contain in the last time step. By default, this value is the same as the last value of `Minimum level (MWh)`. | `Minimum level (MWh)` | No | Yes
 | `Last period maximum level (MWh)`  | Maximum of energy level this storage unit may contain in the last time step. By default, this value is the same as the last value of `Maximum level (MWh)`. | `Maximum level (MWh)` | No | Yes
 #### Example
 ```json
 {
    "Storage units": {
        "su1": {
            "Bus": "b2",
            "Maximum level (MWh)": 100.0,
            "Charge cost ($/MW)": 2.0,
            "Discharge cost ($/MW)": 2.5,
            "Maximum charge rate (MW)": 10.0,
            "Maximum discharge rate (MW)": 8.0
        },
        "su2": {
            "Bus": "b2",
            "Minimum level (MWh)": 10.0,
            "Maximum level (MWh)": 100.0,
            "Allow simultaneous charging and discharging": false,
            "Charge cost ($/MW)": 3.0,
            "Discharge cost ($/MW)": 3.5,
            "Charge efficiency": 0.8,
            "Discharge efficiency": 0.85,
            "Loss factor": 0.01,
            "Minimum charge rate (MW)": 5.0,
            "Maximum charge rate (MW)": 10.0,
            "Minimum discharge rate (MW)": 2.0,
            "Maximum discharge rate (MW)": 10.0,
            "Initial level (MWh)": 70.0,
            "Last period minimum level (MWh)": 80.0,
            "Last period maximum level (MWh)": 85.0
        },
        "su3": {
            "Bus": "b9",
            "Minimum level (MWh)": [10.0, 11.0, 12.0, 13.0],
            "Maximum level (MWh)": [100.0, 110.0, 120.0, 130.0],
            "Allow simultaneous charging and discharging": [false, false, true, true],
            "Charge cost ($/MW)": [2.0, 2.1, 2.2, 2.3],
            "Discharge cost ($/MW)": [1.0, 1.1, 1.2, 1.3],
            "Charge efficiency": [0.8, 0.81, 0.82, 0.82],
            "Discharge efficiency": [0.85, 0.86, 0.87, 0.88],
            "Loss factor": [0.01, 0.01, 0.02, 0.02],
            "Minimum charge rate (MW)": [5.0, 5.1, 5.2, 5.3],
            "Maximum charge rate (MW)": [10.0, 10.1, 10.2, 10.3],
            "Minimum discharge rate (MW)": [4.0, 4.1, 4.2, 4.3],
            "Maximum discharge rate (MW)": [8.0, 8.1, 8.2, 8.3],
            "Initial level (MWh)": 20.0,
            "Last period minimum level (MWh)": 21.0,
            "Last period maximum level (MWh)": 22.0
        }
    }
 }
 ```
 ### Price-sensitive loads
 This section describes components in the system which may increase or reduce their energy consumption according to the energy prices. Fixed loads (as described in the `buses` section) are always served, regardless of the price, unless there is significant congestion in the system or insufficient production capacity. Price-sensitive loads, on the other hand, are only served if it is economical to do so. 
-| Key               | Description                                       | Default  | Time series? | Uncertain?
+| Key               | Description                                       | Default  | Time series?
-| :---------------- | :------------------------------------------------ | :------: | :------------: | :----: 
+| :---------------- | :------------------------------------------------ | :------: | :------------:
-| `Bus`             | Bus where the load is located. Multiple price-sensitive loads may be placed at the same bus. | Required | No | Yes
+| `Bus`             | Bus where the load is located. Multiple price-sensitive loads may be placed at the same bus. | Required | N
-| `Revenue ($/MW)`  | Revenue obtained for serving each MW of power to this load. | Required | Yes | Yes
+| `Revenue ($/MW)`  | Revenue obtained for serving each MW of power to this load. | Required | Y
-| `Demand (MW)`     | Maximum amount of power required by this load. Any amount lower than this may be served. | Required | Yes | Yes
+| `Demand (MW)`     | Maximum amount of power required by this load. Any amount lower than this may be served. | Required | Y
 #### Example
@@ -277,14 +197,15 @@ This section describes components in the system which may increase or reduce the
 This section describes the characteristics of transmission system, such as its topology and the susceptance of each transmission line.
-| Key                    | Description                                      | Default | Time series? | Uncertain?
+| Key                    | Description                                      | Default | Time series?
-| :--------------------- | :----------------------------------------------- | ------- | :------------: | :---:
+| :--------------------- | :----------------------------------------------- | ------- | :------------:
-| `Source bus`           | Identifier of the bus where the transmission line originates. | Required | No | Yes
+| `Source bus`           | Identifier of the bus where the transmission line originates. | Required | N
-| `Target bus`           | Identifier of the bus where the transmission line reaches. | Required | No | Yes
+| `Target bus`           | Identifier of the bus where the transmission line reaches. | Required | N
-| `Susceptance (S)`      | Susceptance of the transmission line (in siemens). | Required | No | Yes
+| `Reactance (ohms)`     | Reactance of the transmission line (in ohms). | Required | N
-| `Normal flow limit (MW)` | Maximum amount of power (in MW) allowed to flow through the line when the system is in its regular, fully-operational state. | `+inf` | Yes | Yes
+| `Susceptance (S)`      | Susceptance  of the transmission line (in siemens). | Required | N
-| `Emergency flow limit (MW)` | Maximum amount of power (in MW) allowed to flow through the line when the system is in degraded state (for example, after the failure of another transmission line). | `+inf` | Y | Yes
+| `Normal flow limit (MW)` | Maximum amount of power (in MW) allowed to flow through the line when the system is in its regular, fully-operational state. | `+inf` | Y
-| `Flow limit penalty ($/MW)` | Penalty for violating the flow limits of the transmission line (in $/MW). This is charged per time step. For example, if there is a thermal violation of 1 MW for three time steps, then three times this amount will be charged. | `5000.0` | Yes | Yes
+| `Emergency flow limit (MW)` | Maximum amount of power (in MW) allowed to flow through the line when the system is in degraded state (for example, after the failure of another transmission line). | `+inf` | Y
 | `Flow limit penalty ($/MW)` | Penalty for violating the flow limits of the transmission line (in $/MW). This is charged per time step. For example, if there is a thermal violation of 1 MW for three time steps, then three times this amount will be charged. | `5000.0` | Y
 #### Example
@@ -294,6 +215,7 @@ This section describes the characteristics of transmission system, such as its t
        "l1": {
            "Source bus": "b1",
            "Target bus": "b2",
            "Reactance (ohms)": 0.05917,
            "Susceptance (S)": 29.49686,
            "Normal flow limit (MW)": 15000.0,
            "Emergency flow limit (MW)": 20000.0,
@@ -309,11 +231,11 @@ This section describes the characteristics of transmission system, such as its t
 This section describes the hourly amount of reserves required.
-| Key                   | Description                                        | Default   | Time series? | Uncertain?
+| Key                   | Description                                        | Default   |  Time series?
-| :-------------------- | :------------------------------------------------- | --------- | :----: | :---:
+| :-------------------- | :------------------------------------------------- | --------- |  :----:
-| `Type` | Type of reserve product. Must be either "spinning" or "flexiramp". | Required | No | No
+| `Type` | Type of reserve product. Must be either "spinning" or "flexiramp". | Required | N
-| `Amount (MW)` | Amount of reserves required. | Required | Yes | Yes
+| `Amount (MW)` | Amount of reserves required. | Required | Y
-| `Shortfall penalty ($/MW)` | Penalty for shortage in meeting the reserve requirements (in $/MW). This is charged per time step. Negative value implies reserve constraints must always be satisfied. | `-1` | Yes | Yes
+| `Shortfall penalty ($/MW)` | Penalty for shortage in meeting the reserve requirements (in $/MW). This is charged per time step. Negative value implies reserve constraints must always be satisfied. | `-1` | Y
 #### Example 1
@@ -347,10 +269,10 @@ This section describes the hourly amount of reserves required.
 This section describes credible contingency scenarios in the optimization, such as the loss of a transmission line or generator.
-| Key                   | Description                                      | Default | Uncertain?
+| Key                   | Description                                      | Default
-| :-------------------- | :----------------------------------------------- | :--------: | :---:
+| :-------------------- | :----------------------------------------------- | ----------
-| `Affected generators` | List of generators affected by this contingency. May be omitted if no generators are affected. | `[]` | Yes
+| `Affected generators`      | List of generators affected by this contingency. May be omitted if no generators are affected. | `[]`
-| `Affected lines`      | List of transmission lines affected by this contingency. May be omitted if no lines are affected. | `[]` | Yes
+| `Affected lines`      | List of transmission lines affected by this contingency. May be omitted if no lines are affected. | `[]`
 #### Example
@@ -401,8 +323,8 @@ The output data format is also JSON-based, but it is not currently documented si
 Current limitations
 -------------------
-* Network topology must remain the same for all time periods.
+* Network topology remains the same for all time periods
 * Only N-1 transmission contingencies are supported. Generator contingencies are not currently supported.
 * Time-varying minimum production amounts are not currently compatible with ramp/startup/shutdown limits.
 * Flexible ramping products can only be acquired under the `WanHob2016` formulation, which does not support spinning reserves. 
-* The set of generators must be the same in all scenarios.
+
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -1,12 +1,12 @@
 # UnitCommitment.jl
-**UnitCommitment.jl** (UC.jl) is an optimization package for the Security-Constrained Unit Commitment Problem (SCUC), a fundamental optimization problem in power systems used, for example, to clear the day-ahead electricity markets. Both deterministic and two-stage stochastic versions of the problem are supported. The package provides benchmark instances for the problem, a flexible and well-documented data format for the problem, as well as Julia/JuMP implementations of state-of-the-art mixed-integer programming formulations and solution methods.
+**UnitCommitment.jl** (UC.jl) is a Julia/JuMP optimization package for the Security-Constrained Unit Commitment Problem (SCUC), a fundamental optimization problem in power systems used, for example, to clear the day-ahead electricity markets. The package provides benchmark instances for the problem and Julia/JuMP implementations of state-of-the-art mixed-integer programming formulations.
 ## Package Components
-* **Data Format:** The package proposes an extensible and fully-documented JSON-based data specification format for SCUC, developed in collaboration with Independent System Operators (ISOs), which describes the most important aspects of the problem. The format supports all the most common thermal generator characteristics (including ramping, piecewise-linear production cost curves and time-dependent startup costs), as well as profiled generators, reserves, price-sensitive loads, battery storage, transmission, and contingencies.
+* **Data Format:** The package proposes an extensible and fully-documented JSON-based data specification format for SCUC, developed in collaboration with Independent System Operators (ISOs), which describes the most important aspects of the problem. The format supports all the most common generator characteristics (including ramping, piecewise-linear production cost curves and time-dependent startup costs), as well as operating reserves, price-sensitive loads, transmission networks and contingencies.
 * **Benchmark Instances:** The package provides a diverse collection of large-scale benchmark instances collected from the literature, converted into a common data format, and extended using data-driven methods to make them more challenging and realistic.
-* **Model Implementation**: The package provides a Julia/JuMP implementations of state-of-the-art formulations and solution methods for the deterministic and stochastic SCUC, including multiple ramping formulations ([ArrCon2000](https://doi.org/10.1109/59.871739), [MorLatRam2013](https://doi.org/10.1109/TPWRS.2013.2251373), [DamKucRajAta2016](https://doi.org/10.1007/s10107-015-0919-9), [PanGua2016](https://doi.org/10.1287/opre.2016.1520)), piecewise-linear costs formulations ([Gar1962](https://doi.org/10.1109/AIEEPAS.1962.4501405), [CarArr2006](https://doi.org/10.1109/TPWRS.2006.876672), [KnuOstWat2018](https://doi.org/10.1109/TPWRS.2017.2783850)), contingency screening methods ([XavQiuWanThi2019](https://doi.org/10.1109/TPWRS.2019.2892620)) and decomposition methods. Our goal is to keep these implementations up-to-date as new methods are proposed in the literature.
+* **Model Implementation**: The package provides a Julia/JuMP implementations of state-of-the-art formulations and solution methods for SCUC, including multiple ramping formulations ([ArrCon2000](https://doi.org/10.1109/59.871739), [MorLatRam2013](https://doi.org/10.1109/TPWRS.2013.2251373), [DamKucRajAta2016](https://doi.org/10.1007/s10107-015-0919-9), [PanGua2016](https://doi.org/10.1287/opre.2016.1520)), multiple piecewise-linear costs formulations ([Gar1962](https://doi.org/10.1109/AIEEPAS.1962.4501405), [CarArr2006](https://doi.org/10.1109/TPWRS.2006.876672), [KnuOstWat2018](https://doi.org/10.1109/TPWRS.2017.2783850)) and contingency screening methods ([XavQiuWanThi2019](https://doi.org/10.1109/TPWRS.2019.2892620)). Our goal is to keep these implementations up-to-date as new methods are proposed in the literature.
 * **Benchmark Tools:** The package provides automated benchmark scripts to accurately evaluate the performance impact of proposed code changes.
 ## Table of Contents
@@ -35,7 +35,7 @@ Depth = 3
 If you use UnitCommitment.jl in your research (instances, models or algorithms), we kindly request that you cite the package as follows:
-* **Alinson S. Xavier, Aleksandr M. Kazachkov, Ogün Yurdakul, Jun He, Feng Qiu**, "UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment (Version 0.4)". Zenodo (2023). [DOI: 10.5281/zenodo.4269874](https://doi.org/10.5281/zenodo.4269874).
+* **Alinson S. Xavier, Aleksandr M. Kazachkov, Ogün Yurdakul, Feng Qiu**, "UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment (Version 0.3)". Zenodo (2022). [DOI: 10.5281/zenodo.4269874](https://doi.org/10.5281/zenodo.4269874).
 If you use the instances, we additionally request that you cite the original sources, as described in the [instances page](instances.md).
@@ -43,7 +43,7 @@ If you use the instances, we additionally request that you cite the original sou
 ```text
 UnitCommitment.jl: A Julia/JuMP Optimization Package for Security-Constrained Unit Commitment
-Copyright © 2020-2023, UChicago Argonne, LLC. All Rights Reserved.
+Copyright © 2020-2022, UChicago Argonne, LLC. All Rights Reserved.
 Redistribution and use in source and binary forms, with or without modification, are permitted
 provided that the following conditions are met:
--- a/docs/src/model.md
+++ b/docs/src/model.md
@@ -1,69 +1,57 @@
 JuMP Model
 ==========
-In this page, we describe the JuMP optimization model produced by the function `build_model`. A detailed understanding of this model is not necessary if you are just interested in using the package to solve some standard unit commitment cases, but it may be useful, for example, if you need to solve a slightly different problem, with additional variables and constraints. The notation in this page generally follows [KnOsWa20].
+In this page, we describe the JuMP optimization model produced by the function `UnitCommitment.build_model`. A detailed understanding of this model is not necessary if you are just interested in using the package to solve some standard unit commitment cases, but it may be useful, for example, if you need to solve a slightly different problem, with additional variables and constraints. The notation in this page generally follows [KnOsWa20].
 Decision variables
 ------------------
 UC.jl models the security-constrained unit commitment problem as a two-stage stochastic program. In this approach, some of the decision variables are *first-stage decisions*, which are taken before the uncertainty is realized and must therefore be the same across all scenarios, while the remaining variables are *second-stage decisions*, which can attain a different values in each scenario. In the current version of the package, all binary variables (which model commitment decisions of thermal units) are first-stage decisions and all continuous variables are second-stage decisions.
 !!! note
    UC.jl treats deterministic SCUC instances as a special case of the stochastic problem in which there is only one scenario, named `"s1"` by default. To access second-stage decisions, therefore, you must provide this scenario name as the value for `sn`. For example, `model[:prod_above]["s1", g, t]`. 
 ### Generators
 In this section, we describe the decision variables associated with the generators, which include both thermal units (e.g., natural gas-fired power plant) and profiled units (e.g., wind turbine). 
 #### Thermal Units
-Name |  Description | Unit | Stage
+Name | Symbol | Description | Unit
-:-----|:-------------|:------: | :------:
+:-----|:--------:|:-------------|:------:
-`is_on[g,t]` | True if generator `g` is on at time `t`. | Binary | 1
+`is_on[g,t]` | $u_{g}(t)$ | True if generator `g` is on at time `t`. | Binary
-`switch_on[g,t]` | True is generator `g` switches on at time `t`. | Binary| 1
+`switch_on[g,t]` | $v_{g}(t)$ | True is generator `g` switches on at time `t`. | Binary
-`switch_off[g,t]` | True if generator `g` switches off at time `t`. | Binary| 1
+`switch_off[g,t]` | $w_{g}(t)$ | True if generator `g` switches off at time `t`. | Binary
-`startup[g,t,s]` | True if generator `g` switches on at time `t` incurring start-up costs from start-up category `s`. | Binary| 1
+`prod_above[g,t]` |$p'_{g}(t)$ | Amount of power produced by generator `g` above its minimum power output at time `t`. For example, if the minimum power of generator `g` is 100 MW and `g` is producing 115 MW of power at time `t`, then `prod_above[g,t]` equals `15.0`. | MW
-`prod_above[sn,g,t]` | Amount of power produced by generator `g` above its minimum power output at time `t` in scenario `sn`. For example, if the minimum power of generator `g` is 100 MW and `g` is producing 115 MW of power at time `t` in scenario `sn`, then `prod_above[sn,g,t]` equals `15.0`. | MW | 2
+`segprod[g,t,k]` | $p^k_g(t)$ | Amount of power from piecewise linear segment `k` produced by generator `g` at time `t`. For example, if cost curve for generator `g` is defined by the points `(100, 1400)`, `(110, 1600)`, `(130, 2200)` and `(135, 2400)`, and if the generator is producing 115 MW of power at time `t`, then `segprod[g,t,:]` equals `[10.0, 5.0, 0.0]`.| MW
-`segprod[sn,g,t,k]` | Amount of power from piecewise linear segment `k` produced by generator `g` at time `t` in scenario `sn`. For example, if cost curve for generator `g` is defined by the points `(100, 1400)`, `(110, 1600)`, `(130, 2200)` and `(135, 2400)`, and if the generator is producing 115 MW of power at time `t` in scenario `sn`, then `segprod[sn,g,t,:]` equals `[10.0, 5.0, 0.0]`.| MW | 2
+`reserve[r,g,t]` | $r_g(t)$ | Amount of reserve `r` provided by unit `g` at time `t`. | MW
-`reserve[sn,r,g,t]` | Amount of reserve `r` provided by unit `g` at time `t` in scenario `sn`. | MW | 2
+`startup[g,t,s]` | $\delta^s_g(t)$ | True if generator `g` switches on at time `t` incurring start-up costs from start-up category `s`. | Binary
 !!! warning
    The first-stage decision variables of the JuMP model are `is_on[g,t]`, `switch_on[g,t]`, `switch_off[g,t]`, and `startup[g,t,s]`. As such, the dictionaries corresponding to these variables do not include the scenario index in their keys. In contrast, all other variables of the created JuMP model are allowed to obtain a different value in each scenario and are thus modeled as second-stage decision variables. Accordingly, the dictionaries of all second-stage decision variables have the scenario index in their keys. This is true even if the model is created to solve the deterministic SCUC, in which case the default scenario index `s1` is included in the dictionary key.
 #### Profiled Units
-Name | Description | Unit | Stage
+Name | Symbol | Description | Unit
-:-----|:-------------|:------: | :------:
+:-----|:------:|:-------------|:------:
-`prod_profiled[s,t]` | Amount of power produced by profiled unit `g` at time `t`. | MW | 2
+`prod_profiled[s,t]` | $p^{\dagger}_{g}(t)$ | Amount of power produced by profiled unit `g` at time `t`. | MW
 ### Buses
-Name | Description | Unit | Stage
+Name | Symbol | Description | Unit
-:-----|:-------------|:------:| :------:
+:-----|:------:|:-------------|:------:
-`net_injection[sn,b,t]` | Net injection at bus `b` at time `t` in scenario `sn`. | MW | 2
+`net_injection[b,t]` | $n_b(t)$ | Net injection at bus `b` at time `t`. | MW
-`curtail[sn,b,t]` | Amount of load curtailed at bus `b` at time `t` in scenario `sn`. | MW | 2
+`curtail[b,t]` | $s^+_b(t)$ | Amount of load curtailed at bus `b` at time `t` | MW
 ### Price-sensitive loads
-Name |  Description | Unit | Stage
+Name | Symbol | Description | Unit
-:-----|:-------------|:------:| :------:
+:-----|:------:|:-------------|:------:
-`loads[sn,s,t]` | Amount of power served to price-sensitive load `s` at time `t` in scenario `sn`. | MW | 2
+`loads[s,t]` | $d_{s}(t)$ | Amount of power served to price-sensitive load `s` at time `t`. | MW
 ### Transmission lines
-Name |  Description | Unit | Stage 
+Name | Symbol | Description | Unit
-:-----|:-------------|:------:| :------:
+:-----|:------:|:-------------|:------:
-`flow[sn,l,t]` |  Power flow on line `l` at time `t` in scenario `sn`. | MW | 2
+`flow[l,t]` | $f_l(t)$ | Power flow on line `l` at time `t`. | MW
-`overflow[sn,l,t]` | Amount of flow above the limit for line `l` at time `t` in scenario `sn`. | MW | 2
+`overflow[l,t]` | $f^+_l(t)$ | Amount of flow above the limit for line `l` at time `t`. | MW
 !!! warning
-    Since transmission and N-1 security constraints are enforced in a lazy way, most of the `flow[l,t]` variables are never added to the model. Accessing `model[:flow][sn,l,t]` without first checking that the variable exists will likely generate an error.
+    Since transmission and N-1 security constraints are enforced in a lazy way, most of the `flow[l,t]` variables are never added to the model. Accessing `model[:flow][l,t]` without first checking that the variable exists will likely generate an error.
 Objective function
 ------------------
@@ -118,12 +106,7 @@ end
 ### Fixing variables, modifying objective function and adding constraints
-Since we now have a direct reference to the JuMP decision variables, it is possible to fix variables, change the coefficients in the objective function, or even add new constraints to the model before solving it. 
+Since we now have a direct reference to the JuMP decision variables, it is possible to fix variables, change the coefficients in the objective function, or even add new constraints to the model before solving it. The script below shows how can this be accomplished. For more information on modifying an existing model, [see the JuMP documentation](https://jump.dev/JuMP.jl/stable/manual/variables/).
 !!! warning
    It is important to take into account the stage of the decision variables in modifying the optimization model. In changing a deterministic SCUC model, modifying the second-stage decision variables requires adding the term `s1`, which is the default scenario name assigned to the second-stage decision variables in the SCUC model. For an SUC model, the package permits the modification of the second-stage decision variables individually for each scenario. 
 The script below shows how the JuMP model can be modified after it is created. For more information on modifying an existing model, [see the JuMP documentation](https://jump.dev/JuMP.jl/stable/manual/variables/).
 ```julia
 using Cbc
@@ -139,29 +122,13 @@ model = UnitCommitment.build_model(
    optimizer=Cbc.Optimizer,
 )
-# Fix the commitment status of the generator "g1" in time period 1 to 1.0
+# Fix a decision variable to 1.0
 JuMP.fix(
    model[:is_on]["g1",1],
    1.0,
    force=true,
 )
 # Fix the production level of the generator "g1" above its minimum level in time period 1 and 
 # in scenario "s1" to 20.0 MW. Observe that the three-tuple dictionary key involves the scenario 
 # index "s1", as production above minimum is a second-stage decision variable.
 JuMP.fix(
    model[:prod_above]["s1", "g1", 1],
    20.0,
    force=true,
 )
 # Enforce the curtailment of 20.0 MW of load at bus "b2" in time period 4 in scenario "s1".
 JuMP.fix(
    curtail["s1", "b2", 4] =
    20.0,
    force=true,
 )
 # Change the objective function
 JuMP.set_objective_coefficient(
    model,
@@ -211,10 +178,10 @@ for t in 1:T
    # In this example, we assume a cost of $5/MW.
    set_objective_coefficient(model, x[t], 5.0)
-    # Attach the new component to bus b1 in scenario s1, by modifying the
+    # Attach the new component to bus b1, by modifying the
    # constraint `eq_net_injection`.
    set_normalized_coefficient(
-        model[:eq_net_injection]["s1", "b1", t],
+        model[:eq_net_injection]["b1", t],
        x[t],
        1.0,
    )
--- a/docs/src/usage.md
+++ b/docs/src/usage.md
@@ -4,33 +4,41 @@ Usage
 Installation
 ------------
-UnitCommitment.jl was tested and developed with [Julia 1.9](https://julialang.org/). To install Julia, please follow the [installation guide on the official Julia website](https://julialang.org/downloads/). To install UnitCommitment.jl, run the Julia interpreter, type `]` to open the package manager, then type:
+UnitCommitment.jl was tested and developed with [Julia 1.7](https://julialang.org/). To install Julia, please follow the [installation guide on the official Julia website](https://julialang.org/downloads/). To install UnitCommitment.jl, run the Julia interpreter, type `]` to open the package manager, then type:
 ```text
-pkg> add UnitCommitment@0.4
+pkg> add UnitCommitment@0.3
 ```
-To solve the optimization models, a mixed-integer linear programming (MILP) solver is also required. Please see the [JuMP installation guide](https://jump.dev/JuMP.jl/stable/installation/) for more instructions on installing a solver. Typical open-source choices are [HiGHS](https://github.com/jump-dev/HiGHS.jl), [Cbc](https://github.com/JuliaOpt/Cbc.jl) and [GLPK](https://github.com/JuliaOpt/GLPK.jl). In the instructions below, HiGHS will be used, but any other MILP solver listed in JuMP installation guide should also be compatible.
+To test that the package has been correctly installed, run:
 ```text
 pkg> test UnitCommitment
 ```
 If all tests pass, the package should now be ready to be used by any Julia script on the machine.
 To solve the optimization models, a mixed-integer linear programming (MILP) solver is also required. Please see the [JuMP installation guide](https://jump.dev/JuMP.jl/stable/installation/) for more instructions on installing a solver. Typical open-source choices are [Cbc](https://github.com/JuliaOpt/Cbc.jl) and [GLPK](https://github.com/JuliaOpt/GLPK.jl). In the instructions below, Cbc will be used, but any other MILP solver listed in JuMP installation guide should also be compatible.
 Typical Usage
 -------------
 ### Solving user-provided instances
-The first step to use UC.jl is to construct JSON files that describe each scenario of your deterministic or stochastic unit commitment instance. See [Data Format](format.md) for a complete description of the data format UC.jl expects. The next steps, as shown below, are to: (1) read the scenario files; (2) build the optimization model; (3) run the optimization; and (4) extract the optimal solution.
+The first step to use UC.jl is to construct a JSON file describing your unit commitment instance. See [Data Format](format.md) for a complete description of the data format UC.jl expects. The next steps, as shown below, are to: (1) read the instance from file; (2) construct the optimization model; (3) run the optimization; and (4) extract the optimal solution.
 ```julia
-using HiGHS
+using Cbc
-using JuMP
+using JSON
 using UnitCommitment
 # 1. Read instance
-instance = UnitCommitment.read(["example/s1.json", "example/s2.json"])
+instance = UnitCommitment.read("/path/to/input.json")
 # 2. Construct optimization model
 model = UnitCommitment.build_model(
    instance=instance,
-    optimizer=HiGHS.Optimizer,
+    optimizer=Cbc.Optimizer,
 )
 # 3. Solve model
@@ -38,39 +46,16 @@ UnitCommitment.optimize!(model)
 # 4. Write solution to a file
 solution = UnitCommitment.solution(model)
-UnitCommitment.write("example/out.json", solution)
+UnitCommitment.write("/path/to/output.json", solution)
 ```
 To read multiple files from a given folder, the [Glob](https://github.com/vtjnash/Glob.jl) package can be used:
 ```jldoctest usage1; output = false
 using Glob
 using UnitCommitment
 instance = UnitCommitment.read(glob("s*.json", "example/"))
 # output
 UnitCommitmentInstance(2 scenarios, 6 thermal units, 0 profiled units, 14 buses, 20 lines, 19 contingencies, 1 price sensitive loads, 4 time steps)
 ```
 To solve deterministic instances, a single scenario file may be provided.
 ```jldoctest usage1; output = false
 instance = UnitCommitment.read("example/s1.json")
 # output
 UnitCommitmentInstance(1 scenarios, 6 thermal units, 0 profiled units, 14 buses, 20 lines, 19 contingencies, 1 price sensitive loads, 4 time steps)
 ```
 ### Solving benchmark instances
-UnitCommitment.jl contains a large number of deterministic benchmark instances collected from the literature and converted into a common data format. To solve one of these instances individually, instead of constructing your own, the function `read_benchmark` can be used, as shown below. See [Instances](instances.md) for the complete list of available instances.
+UnitCommitment.jl contains a large number of benchmark instances collected from the literature and converted into a common data format. To solve one of these instances individually, instead of constructing your own, the function `read_benchmark` can be used, as shown below. See [Instances](instances.md) for the complete list of available instances.
-```jldoctest usage1; output = false
+```julia
 using UnitCommitment
 instance = UnitCommitment.read_benchmark("matpower/case3375wp/2017-02-01")
 # output
 UnitCommitmentInstance(1 scenarios, 590 thermal units, 0 profiled units, 3374 buses, 4161 lines, 3245 contingencies, 0 price sensitive loads, 36 time steps)
 ```
 ## Customizing the formulation
@@ -78,7 +63,7 @@ UnitCommitmentInstance(1 scenarios, 590 thermal units, 0 profiled units, 3374 bu
 By default, `build_model` uses a formulation that combines modeling components from different publications, and that has been carefully tested, using our own benchmark scripts, to provide good performance across a wide variety of instances. This default formulation is expected to change over time, as new methods are proposed in the literature. You can, however, construct your own formulation, based on the modeling components that you choose, as shown in the next example.
 ```julia
-using HiGHS
+using Cbc
 using UnitCommitment
 import UnitCommitment:
@@ -93,7 +78,7 @@ instance = UnitCommitment.read_benchmark(
 model = UnitCommitment.build_model(
    instance = instance,
-    optimizer = HiGHS.Optimizer,
+    optimizer = Cbc.Optimizer,
    formulation = Formulation(
        pwl_costs = KnuOstWat2018.PwlCosts(),
        ramping = MorLatRam2013.Ramping(),
@@ -108,24 +93,24 @@ model = UnitCommitment.build_model(
 ## Generating initial conditions
-When creating random unit commitment instances for benchmark purposes, it is often hard to compute, in advance, sensible initial conditions for all thermal generators. Setting initial conditions naively (for example, making all generators initially off and producing no power) can easily cause the instance to become infeasible due to excessive ramping. Initial conditions can also make it hard to modify existing instances. For example, increasing the system load without carefully modifying the initial conditions may make the problem infeasible or unrealistically challenging to solve.
+When creating random unit commitment instances for benchmark purposes, it is often hard to compute, in advance, sensible initial conditions for all generators. Setting initial conditions naively (for example, making all generators initially off and producing no power) can easily cause the instance to become infeasible due to excessive ramping. Initial conditions can also make it hard to modify existing instances. For example, increasing the system load without carefully modifying the initial conditions may make the problem infeasible or unrealistically challenging to solve.
 To help with this issue, UC.jl provides a utility function which can generate feasible initial conditions by solving a single-period optimization problem, as shown below:
 ```julia
-using HiGHS
+using Cbc
 using UnitCommitment
 # Read original instance
-instance = UnitCommitment.read("example/s1.json")
+instance = UnitCommitment.read("instance.json")
 # Generate initial conditions (in-place)
-UnitCommitment.generate_initial_conditions!(instance, HiGHS.Optimizer)
+UnitCommitment.generate_initial_conditions!(instance, Cbc.Optimizer)
 # Construct and solve optimization model
 model = UnitCommitment.build_model(
    instance=instance,
-    optimizer=HiGHS.Optimizer,
+    optimizer=Cbc.Optimizer,
 )
 UnitCommitment.optimize!(model)
 ```
@@ -136,76 +121,22 @@ UnitCommitment.optimize!(model)
 ## Verifying solutions
-When developing new formulations, it is very easy to introduce subtle errors in the model that result in incorrect solutions. To help avoiding this, UC.jl includes a utility function that verifies if a given solution is feasible, and, if not, prints all the validation errors it found. The implementation of this function is completely independent from the implementation of the optimization model, and therefore can be used to validate it.
+When developing new formulations, it is very easy to introduce subtle errors in the model that result in incorrect solutions. To help with this, UC.jl includes a utility function that verifies if a given solution is feasible, and, if not, prints all the validation errors it found. The implementation of this function is completely independent from the implementation of the optimization model, and therefore can be used to validate it. The function can also be used to verify solutions produced by other optimization packages, as long as they follow the [UC.jl data format](format.md).
-```jldoctest; output = false
+```julia
 using JSON
 using UnitCommitment
 # Read instance
-instance = UnitCommitment.read("example/s1.json")
+instance = UnitCommitment.read("instance.json")
 # Read solution (potentially produced by other packages) 
-solution = JSON.parsefile("example/out.json")
+solution = JSON.parsefile("solution.json")
 # Validate solution and print validation errors
 UnitCommitment.validate(instance, solution)
 # output
 true
 ```
 ## Progressive Hedging
 By default, UC.jl uses the Extensive Form (EF) when solving stochastic instances. This approach involves constructing a single JuMP model that contains data and decision variables for all scenarios. Although EF has optimality guarantees and performs well with small test cases, it can become computationally intractable for large instances or substantial number of scenarios.
 Progressive Hedging (PH) is an alternative (heuristic) solution method provided by UC.jl in which the problem is decomposed into smaller scenario-based subproblems, which are then solved in parallel in separate Julia processes, potentially across multiple machines. Quadratic penalty terms are used to enforce convergence of first-stage decision variables. The method is closely related to the Alternative Direction Method of Multipliers (ADMM) and can handle larger instances, although it is not guaranteed to converge to the optimal solution. Our implementation of PH relies on Message Passing Interface (MPI) for communication. We refer to [MPI.jl Documentation](https://github.com/JuliaParallel/MPI.jl) for more details on installing MPI.
 The following example shows how to solve SCUC instances using progressive hedging. The script should be saved in a file, say `ph.jl`, and executed using `mpiexec -n <num-scenarios> julia ph.jl`.
 ```julia
 using HiGHS
 using MPI
 using UnitCommitment
 using Glob
 # 1. Initialize MPI
 MPI.Init()
 # 2. Configure progressive hedging method
 ph = UnitCommitment.ProgressiveHedging()
 # 3. Read problem instance
 instance = UnitCommitment.read(["example/s1.json", "example/s2.json"], ph)
 # 4. Build JuMP model
 model = UnitCommitment.build_model(
    instance = instance,
    optimizer = HiGHS.Optimizer,
 )
 # 5. Run the decentralized optimization algorithm
 UnitCommitment.optimize!(model, ph)
 # 6. Fetch the solution
 solution = UnitCommitment.solution(model, ph)
 # 7. Close MPI
 MPI.Finalize()
 ```
 When using PH, the model can be customized as usual, with different formulations or additional user-provided constraints. Note that `read`, in this case, takes `ph` as an argument. This allows each Julia process to read only the instance files that are relevant to it. Similarly, the `solution` function gathers the optimal solution of each processes and returns a combined dictionary. 
 Each process solves a sub-problem with $\frac{s}{p}$ scenarios, where $s$ is the total number of scenarios and $p$ is the number of MPI processes. For instance, if we have 15 scenario files and 5 processes, then each process will solve a JuMP model that contains data for 3 scenarios. If the total number of scenarios is not divisible by the number of processes, then an error will be thrown.
 !!! warning
    Currently, PH can handle only equiprobable scenarios. Further, `solution(model, ph)` can only handle cases where only one scenario is modeled in each process.
 ## Computing Locational Marginal Prices
 Locational marginal prices (LMPs) refer to the cost of supplying electricity at a particular location of the network. Multiple methods for computing LMPs have been proposed in the literature. UnitCommitment.jl implements two commonly-used methods: conventional LMPs and Approximated Extended LMPs (AELMPs). To compute LMPs for a given unit commitment instance, the `compute_lmp` function can be used, as shown in the examples below. The function accepts three arguments -- a solved SCUC model, an LMP method, and a linear optimizer -- and it returns a dictionary mapping `(bus_name, time)` to the marginal price.
@@ -292,90 +223,4 @@ aelmp = UnitCommitment.compute_lmp(
 # Example: "s1" is the scenario name, "b1" is the bus name, 1 is the first time slot
 # Note: although scenario is supported, the query still keeps the scenario keys for consistency.
@show aelmp["s1", "b1", 1]
-```
+```
 ## Time Decomposition
 Solving unit commitment instances that have long time horizons (for example, year-long 8760-hour instances) requires a substantial amount of computational power. To address this issue, UC.jl offers a time decomposition method, which breaks the instance down into multiple overlapping subproblems, solves them sequentially, then reassembles the solution.
 When solving a unit commitment instance with a dense time slot structure, computational complexity can become a significant challenge. For instance, if the instance contains hourly data for an entire year (8760 hours), solving such a model can require a substantial amount of computational power. To address this issue, UC.jl provides a time_decomposition method within the `optimize!` function. This method decomposes the problem into multiple sub-problems, solving them sequentially.
 The `optimize!` function takes 5 parameters: a unit commitment instance, a `TimeDecomposition` method, an optimizer, and two optional functions `after_build` and `after_optimize`. It returns a solution dictionary. The `TimeDecomposition` method itself requires four arguments: `time_window`, `time_increment`, `inner_method` (optional), and `formulation` (optional). These arguments define the time window for each sub-problem, the time increment to move to the next sub-problem, the method used to solve each sub-problem, and the formulation employed, respectively. The two functions, namely `after_build` and `after_optimize`, are invoked subsequent to the construction and optimization of each sub-model, respectively. It is imperative that the `after_build` function requires its two arguments to be consistently mapped to `model` and `instance`, while the `after_optimize` function necessitates its three arguments to be consistently mapped to `solution`, `model`, and `instance`.
 The code snippet below illustrates an example of solving an instance by decomposing the model into multiple 36-hour sub-problems using the `XavQiuWanThi2019` method. Each sub-problem advances 24 hours at a time. The first sub-problem covers time steps 1 to 36, the second covers time steps 25 to 60, the third covers time steps 49 to 84, and so on. The initial power levels and statuses of the second and subsequent sub-problems are set based on the results of the first 24 hours from each of their immediate prior sub-problems. In essence, this approach addresses the complexity of solving a large problem by tackling it in 24-hour intervals, while incorporating an additional 12-hour buffer to mitigate the closing window effect for each sub-problem. Furthermore, the `after_build` function imposes the restriction that `g3` and `g4` cannot be activated simultaneously during the initial time slot of each sub-problem. On the other hand, the `after_optimize` function is invoked to calculate the conventional Locational Marginal Prices (LMPs) for each sub-problem, and subsequently appends the computed values to the `lmps` vector.
 > **Warning** 
 > Specifying `TimeDecomposition` as the value of the `inner_method` field of another `TimeDecomposition` causes errors when calling the `optimize!` function due to the different argument structures between the two `optimize!` functions.
 ```julia
 using UnitCommitment, JuMP, Cbc, HiGHS
 import UnitCommitment: 
    TimeDecomposition,
    ConventionalLMP,
    XavQiuWanThi2019,
    Formulation
 # specifying the after_build and after_optimize functions
 function after_build(model, instance)
    @constraint(
        model,
        model[:is_on]["g3", 1] + model[:is_on]["g4", 1] <= 1,
    )
 end
 lmps = []
 function after_optimize(solution, model, instance)
    lmp = UnitCommitment.compute_lmp(
        model,
        ConventionalLMP(),
        optimizer = HiGHS.Optimizer,
    )
    return push!(lmps, lmp)
 end
 # assume the instance is given as a 120h problem
 instance = UnitCommitment.read("instance.json")
 solution = UnitCommitment.optimize!(
    instance,
    TimeDecomposition(
        time_window = 36,  # solve 36h problems
        time_increment = 24,  # advance by 24h each time
        inner_method = XavQiuWanThi2019.Method(),
        formulation = Formulation(),
    ),
    optimizer = Cbc.Optimizer,
    after_build = after_build,
    after_optimize = after_optimize,
 )
 ```
 ## Day-ahead (DA) Market to Real-time (RT) Markets
 The UC.jl package offers a comprehensive set of functions for solving marketing problems. The primary function, `solve_market`, facilitates the solution of day-ahead (DA) markets, which can be either deterministic or stochastic in nature. Subsequently, it sequentially maps the commitment status obtained from the DA market to all the real-time (RT) markets, which are deterministic instances. It is essential to ensure that the time span of the DA market encompasses all the RT markets, and the file paths for the RT markets must be specified in chronological order. Each RT market should represent a single time slot, and it is recommended to include a few additional time slots to mitigate the closing window effect.
 The `solve_market` function accepts several parameters, including the file path (or a list of file paths in the case of stochastic markets) for the DA market, a list of file paths for the RT markets, the market settings specified by the `MarketSettings` structure, and an optimizer. The `MarketSettings` structure itself requires three optional arguments: `inner_method`, `lmp_method`, and `formulation`. If the computation of Locational Marginal Prices (LMPs) is not desired, the `lmp_method` can be set to `nothing`. Additional optional parameters include a linear programming optimizer for solving LMPs (if a different optimizer than the required one is desired), callback functions `after_build_da` and `after_optimize_da`, which are invoked after the construction and optimization of the DA market, and callback functions `after_build_rt` and `after_optimize_rt`, which are invoked after the construction and optimization of each RT market. It is crucial to note that the `after_build` function requires its two arguments to consistently correspond to `model` and `instance`, while the `after_optimize` function requires its three arguments to consistently correspond to `solution`, `model`, and `instance`.
 As an illustrative example, suppose the DA market predicts hourly data for a 24-hour period, while the RT markets represent 5-minute intervals. In this scenario, each RT market file corresponds to a specific 5-minute interval, with the first RT market representing the initial 5 minutes, the second RT market representing the subsequent 5 minutes, and so on. Consequently, there should be 12 RT market files for each hour. To mitigate the closing window effect, except for the last few RT markets, each RT market should contain three time slots, resulting in a total time span of 15 minutes. However, only the first time slot is considered in the final solution. The last two RT markets should only contain 2 and 1 time slot(s), respectively, to ensure that the total time covered by all RT markets does not exceed the time span of the DA market. The code snippet below demonstrates a simplified example of how to utilize the `solve_market` function. Please note that it only serves as a simplified example and may require further customization based on the specific requirements of your use case.
 ```julia
 using UnitCommitment, Cbc, HiGHS
 import UnitCommitment: 
    MarketSettings,
    XavQiuWanThi2019,
    ConventionalLMP,
    Formulation
 solution = UnitCommitment.solve_market(
    "da_instance.json",
    ["rt_instance_1.json", "rt_instance_2.json", "rt_instance_3.json"],
    MarketSettings(
        inner_method = XavQiuWanThi2019.Method(),
        lmp_method = ConventionalLMP(),
        formulation = Formulation(),
    ),
    optimizer = Cbc.Optimizer,
    lp_optimizer = HiGHS.Optimizer,
 )
 ```
--- a/src/UnitCommitment.jl
+++ b/src/UnitCommitment.jl
@@ -4,15 +4,12 @@
 module UnitCommitment
 using Requires
 using Base: String
 include("instance/structs.jl")
 include("model/formulations/base/structs.jl")
 include("solution/structs.jl")
 include("lmp/structs.jl")
 include("market/structs.jl")
 include("model/formulations/ArrCon2000/structs.jl")
 include("model/formulations/CarArr2006/structs.jl")
@@ -22,9 +19,7 @@ include("model/formulations/KnuOstWat2018/structs.jl")
 include("model/formulations/MorLatRam2013/structs.jl")
 include("model/formulations/PanGua2016/structs.jl")
 include("solution/methods/XavQiuWanThi2019/structs.jl")
 include("solution/methods/ProgressiveHedging/structs.jl")
 include("model/formulations/WanHob2016/structs.jl")
 include("solution/methods/TimeDecomposition/structs.jl")
 include("import/egret.jl")
 include("instance/read.jl")
@@ -38,7 +33,6 @@ include("model/formulations/base/sensitivity.jl")
 include("model/formulations/base/system.jl")
 include("model/formulations/base/unit.jl")
 include("model/formulations/base/punit.jl")
 include("model/formulations/base/storage.jl")
 include("model/formulations/CarArr2006/pwlcosts.jl")
 include("model/formulations/DamKucRajAta2016/ramp.jl")
 include("model/formulations/Gar1962/pwlcosts.jl")
@@ -55,10 +49,6 @@ include("solution/methods/XavQiuWanThi2019/enforce.jl")
 include("solution/methods/XavQiuWanThi2019/filter.jl")
 include("solution/methods/XavQiuWanThi2019/find.jl")
 include("solution/methods/XavQiuWanThi2019/optimize.jl")
 include("solution/methods/TimeDecomposition/optimize.jl")
 include("solution/methods/ProgressiveHedging/optimize.jl")
 include("solution/methods/ProgressiveHedging/read.jl")
 include("solution/methods/ProgressiveHedging/solution.jl")
 include("solution/optimize.jl")
 include("solution/solution.jl")
 include("solution/warmstart.jl")
@@ -72,13 +62,5 @@ include("validation/repair.jl")
 include("validation/validate.jl")
 include("lmp/conventional.jl")
 include("lmp/aelmp.jl")
 include("market/market.jl")
 function __init__()
    @require MIPLearn = "2b1277c3-b477-4c49-a15e-7ba350325c68" begin
        include("solution/methods/MIPLearn/structs.jl")
        include("solution/methods/MIPLearn/miplearn.jl")
    end
 end
 end
--- a/src/instance/read.jl
+++ b/src/instance/read.jl
@@ -136,35 +136,22 @@ function _from_json(json; repair = true)::UnitCommitmentScenario
    loads = PriceSensitiveLoad[]
    reserves = Reserve[]
    profiled_units = ProfiledUnit[]
    storage_units = StorageUnit[]
    function scalar(x; default = nothing)
        x !== nothing || return default
        return x
    end
-    time_horizon = json["Parameters"]["Time horizon (min)"]
+    time_horizon = json["Parameters"]["Time (h)"]
    if time_horizon === nothing
-        time_horizon = json["Parameters"]["Time (h)"]
+        time_horizon = json["Parameters"]["Time horizon (h)"]
        if time_horizon === nothing
            time_horizon = json["Parameters"]["Time horizon (h)"]
        end
        if time_horizon !== nothing
            time_horizon *= 60
        end
    end
-    time_horizon !== nothing || error("Missing parameter: Time horizon (min)")
+    time_horizon !== nothing || error("Missing parameter: Time horizon (h)")
    isinteger(time_horizon) ||
        error("Time horizon must be an integer in minutes")
    time_horizon = Int(time_horizon)
    time_step = scalar(json["Parameters"]["Time step (min)"], default = 60)
    (60 % time_step == 0) ||
        error("Time step $time_step is not a divisor of 60")
    (time_horizon % time_step == 0) || error(
        "Time step $time_step is not a divisor of time horizon $time_horizon",
    )
    time_multiplier = 60 ÷ time_step
-    T = time_horizon ÷ time_step
+    T = time_horizon * time_multiplier
    probability = json["Parameters"]["Scenario weight"]
    probability !== nothing || (probability = 1)
@@ -197,7 +184,6 @@ function _from_json(json; repair = true)::UnitCommitmentScenario
            ThermalUnit[],
            PriceSensitiveLoad[],
            ProfiledUnit[],
            StorageUnit[],
        )
        name_to_bus[bus_name] = bus
        push!(buses, bus)
@@ -354,6 +340,7 @@ function _from_json(json; repair = true)::UnitCommitmentScenario
                length(lines) + 1,
                name_to_bus[dict["Source bus"]],
                name_to_bus[dict["Target bus"]],
                scalar(dict["Reactance (ohms)"]),
                scalar(dict["Susceptance (S)"]),
                timeseries(
                    dict["Normal flow limit (MW)"],
@@ -406,52 +393,6 @@ function _from_json(json; repair = true)::UnitCommitmentScenario
        end
    end
    # Read storage units 
    if "Storage units" in keys(json)
        for (storage_name, dict) in json["Storage units"]
            bus = name_to_bus[dict["Bus"]]
            min_level =
                timeseries(scalar(dict["Minimum level (MWh)"], default = 0.0))
            max_level = timeseries(dict["Maximum level (MWh)"])
            storage = StorageUnit(
                storage_name,
                bus,
                min_level,
                max_level,
                timeseries(
                    scalar(
                        dict["Allow simultaneous charging and discharging"],
                        default = true,
                    ),
                ),
                timeseries(dict["Charge cost (\$/MW)"]),
                timeseries(dict["Discharge cost (\$/MW)"]),
                timeseries(scalar(dict["Charge efficiency"], default = 1.0)),
                timeseries(scalar(dict["Discharge efficiency"], default = 1.0)),
                timeseries(scalar(dict["Loss factor"], default = 0.0)),
                timeseries(
                    scalar(dict["Minimum charge rate (MW)"], default = 0.0),
                ),
                timeseries(dict["Maximum charge rate (MW)"]),
                timeseries(
                    scalar(dict["Minimum discharge rate (MW)"], default = 0.0),
                ),
                timeseries(dict["Maximum discharge rate (MW)"]),
                scalar(dict["Initial level (MWh)"], default = 0.0),
                scalar(
                    dict["Last period minimum level (MWh)"],
                    default = min_level[T],
                ),
                scalar(
                    dict["Last period maximum level (MWh)"],
                    default = max_level[T],
                ),
            )
            push!(bus.storage_units, storage)
            push!(storage_units, storage)
        end
    end
    scenario = UnitCommitmentScenario(
        name = scenario_name,
        probability = probability,
@@ -467,13 +408,10 @@ function _from_json(json; repair = true)::UnitCommitmentScenario
        reserves = reserves,
        reserves_by_name = name_to_reserve,
        time = T,
        time_step = time_step,
        thermal_units_by_name = Dict(g.name => g for g in thermal_units),
        thermal_units = thermal_units,
        profiled_units_by_name = Dict(pu.name => pu for pu in profiled_units),
        profiled_units = profiled_units,
        storage_units_by_name = Dict(su.name => su for su in storage_units),
        storage_units = storage_units,
        isf = spzeros(Float64, length(lines), length(buses) - 1),
        lodf = spzeros(Float64, length(lines), length(lines)),
    )
--- a/src/instance/structs.jl
+++ b/src/instance/structs.jl
@@ -9,7 +9,6 @@ mutable struct Bus
    thermal_units::Vector
    price_sensitive_loads::Vector
    profiled_units::Vector
    storage_units::Vector
 end
 mutable struct CostSegment
@@ -56,6 +55,7 @@ mutable struct TransmissionLine
    offset::Int
    source::Bus
    target::Bus
    reactance::Float64
    susceptance::Float64
    normal_flow_limit::Vector{Float64}
    emergency_flow_limit::Vector{Float64}
@@ -83,26 +83,6 @@ mutable struct ProfiledUnit
    cost::Vector{Float64}
 end
 mutable struct StorageUnit
    name::String
    bus::Bus
    min_level::Vector{Float64}
    max_level::Vector{Float64}
    simultaneous_charge_and_discharge::Vector{Bool}
    charge_cost::Vector{Float64}
    discharge_cost::Vector{Float64}
    charge_efficiency::Vector{Float64}
    discharge_efficiency::Vector{Float64}
    loss_factor::Vector{Float64}
    min_charge_rate::Vector{Float64}
    max_charge_rate::Vector{Float64}
    min_discharge_rate::Vector{Float64}
    max_discharge_rate::Vector{Float64}
    initial_level::Float64
    min_ending_level::Float64
    max_ending_level::Float64
 end
 Base.@kwdef mutable struct UnitCommitmentScenario
    buses_by_name::Dict{AbstractString,Bus}
    buses::Vector{Bus}
@@ -123,10 +103,7 @@ Base.@kwdef mutable struct UnitCommitmentScenario
    reserves::Vector{Reserve}
    thermal_units_by_name::Dict{AbstractString,ThermalUnit}
    thermal_units::Vector{ThermalUnit}
    storage_units_by_name::Dict{AbstractString,StorageUnit}
    storage_units::Vector{StorageUnit}
    time::Int
    time_step::Int
 end
 Base.@kwdef mutable struct UnitCommitmentInstance
--- a/src/market/market.jl
+++ b/src/market/market.jl
@@ -1,220 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 """
    solve_market(
        da_path::Union{String, Vector{String}}, 
        rt_paths::Vector{String},
        settings::MarketSettings;
        optimizer,
        lp_optimizer = nothing,
        after_build_da = nothing,
        after_optimize_da = nothing,
        after_build_rt = nothing,
        after_optimize_rt = nothing,
    )::OrderedDict
 Solve the day-ahead and the real-time markets by the means of commitment status mapping.
 The method firstly acquires the commitment status outcomes through the resolution of the day-ahead market; 
 and secondly resolves each real-time market based on the corresponding results obtained previously.
 Arguments
 ---------
 - `da_path`:
    the data file path of the day-ahead market, can be stochastic.
 - `rt_paths`:
    the list of data file paths of the real-time markets, must be deterministic for each market.
 - `settings`:
    the MarketSettings which include the problem formulation, the solving method, and LMP method.
 - `optimizer`:
    the optimizer for solving the problem.
 - `lp_optimizer`:
    the linear programming optimizer for solving the LMP problem, defaults to `nothing`.
    If not specified by the user, the program uses `optimizer` instead.
 - `after_build_da`:
    a user-defined function that allows modifying the DA model after building,
    must have 2 arguments `model` and `instance` in order.
 - `after_optimize_da`:
    a user-defined function that allows handling additional steps after optimizing the DA model,
    must have 3 arguments `solution`, `model` and `instance` in order.
 - `after_build_rt`:
    a user-defined function that allows modifying each RT model after building,
    must have 2 arguments `model` and `instance` in order.
 - `after_optimize_rt`:
    a user-defined function that allows handling additional steps after optimizing each RT model,
    must have 3 arguments `solution`, `model` and `instance` in order.
 Examples
 --------
 ```julia
 using UnitCommitment, Cbc, HiGHS
 import UnitCommitment: 
    MarketSettings,
    XavQiuWanThi2019,
    ConventionalLMP,
    Formulation
 solution = UnitCommitment.solve_market(
    "da_instance.json",
    ["rt_instance_1.json", "rt_instance_2.json", "rt_instance_3.json"],
    MarketSettings(
        inner_method = XavQiuWanThi2019.Method(),
        lmp_method = ConventionalLMP(),
        formulation = Formulation(),
    ),
    optimizer = Cbc.Optimizer,
    lp_optimizer = HiGHS.Optimizer,
 )
 """
 function solve_market(
    da_path::Union{String,Vector{String}},
    rt_paths::Vector{String},
    settings::MarketSettings;
    optimizer,
    lp_optimizer = nothing,
    after_build_da = nothing,
    after_optimize_da = nothing,
    after_build_rt = nothing,
    after_optimize_rt = nothing,
 )::OrderedDict
    # solve da instance as usual
    @info "Solving the day-ahead market with file $da_path..."
    instance_da = UnitCommitment.read(da_path)
    # LP optimizer is optional: if not specified, use optimizer
    lp_optimizer = lp_optimizer === nothing ? optimizer : lp_optimizer
    # build and optimize the DA market
    model_da, solution_da = _build_and_optimize(
        instance_da,
        settings,
        optimizer = optimizer,
        lp_optimizer = lp_optimizer,
        after_build = after_build_da,
        after_optimize = after_optimize_da,
    )
    # prepare the final solution 
    solution = OrderedDict()
    solution["Day-ahead market"] = solution_da
    solution["Real-time markets"] = OrderedDict()
    # count the time, sc.time = n-slots, sc.time_step = slot-interval
    # sufficient to look at only one scenario
    sc = instance_da.scenarios[1]
    # max time (min) of the DA market
    max_time = sc.time * sc.time_step
    # current time increments through the RT market list
    current_time = 0
    # DA market time slots in (min)
    da_time_intervals = [sc.time_step * ts for ts in 1:sc.time]
    # get the uc status and set each uc fixed
    solution_rt = OrderedDict()
    prev_initial_status = OrderedDict()
    for rt_path in rt_paths
        @info "Solving the real-time market with file $rt_path..."
        instance_rt = UnitCommitment.read(rt_path)
        # check instance time 
        sc = instance_rt.scenarios[1]
        # check each time slot in the RT model
        for ts in 1:sc.time
            slot_t_end = current_time + ts * sc.time_step
            # ensure this RT's slot time ub never exceeds max time of DA
            slot_t_end <= max_time || error(
                "The time of the real-time market cannot exceed the time of the day-ahead market.",
            )
            # get the slot start time to determine commitment status
            slot_t_start = slot_t_end - sc.time_step
            # find the index of the first DA time slot that covers slot_t_start
            da_time_slot = findfirst(ti -> slot_t_start < ti, da_time_intervals)
            # update thermal unit commitment status
            for g in sc.thermal_units
                g.commitment_status[ts] =
                    value(model_da[:is_on][g.name, da_time_slot]) == 1.0
            end
        end
        # update current time by ONE slot only
        current_time += sc.time_step
        # set initial status for all generators in all scenarios
        if !isempty(solution_rt) && !isempty(prev_initial_status)
            for g in sc.thermal_units
                g.initial_power =
                    solution_rt["Thermal production (MW)"][g.name][1]
                g.initial_status = UnitCommitment._determine_initial_status(
                    prev_initial_status[g.name],
                    [solution_rt["Is on"][g.name][1]],
                )
            end
        end
        # build and optimize the RT market
        _, solution_rt = _build_and_optimize(
            instance_rt,
            settings,
            optimizer = optimizer,
            lp_optimizer = lp_optimizer,
            after_build = after_build_rt,
            after_optimize = after_optimize_rt,
        )
        prev_initial_status =
            OrderedDict(g.name => g.initial_status for g in sc.thermal_units)
        # rt_name = first(split(last(split(rt_path, "/")), "."))
        solution["Real-time markets"][rt_path] = solution_rt
    end # end of for-loop that checks each RT market
    return solution
 end
 function _build_and_optimize(
    instance::UnitCommitmentInstance,
    settings::MarketSettings;
    optimizer,
    lp_optimizer,
    after_build = nothing,
    after_optimize = nothing,
 )::Tuple{JuMP.Model,OrderedDict}
    # build model with after build
    model = UnitCommitment.build_model(
        instance = instance,
        optimizer = optimizer,
        formulation = settings.formulation,
    )
    if after_build !== nothing
        after_build(model, instance)
    end
    # optimize model
    UnitCommitment.optimize!(model, settings.inner_method)
    solution = UnitCommitment.solution(model)
    # compute lmp and add to solution 
    if settings.lmp_method !== nothing
        lmp = UnitCommitment.compute_lmp(
            model,
            settings.lmp_method,
            optimizer = lp_optimizer,
        )
        if length(instance.scenarios) == 1
            solution["Locational marginal price"] = lmp
        else
            for sc in instance.scenarios
                solution[sc.name]["Locational marginal price"] = OrderedDict(
                    key => val for (key, val) in lmp if key[1] == sc.name
                )
            end
        end
    end
    # run after optimize with solution
    if after_optimize !== nothing
        after_optimize(solution, model, instance)
    end
    return model, solution
 end
--- a/src/market/structs.jl
+++ b/src/market/structs.jl
@@ -1,33 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 import ..SolutionMethod
 import ..PricingMethod
 import ..Formulation
 """
    struct MarketSettings
        inner_method::SolutionMethod = XavQiuWanThi2019.Method()
        lmp_method::Union{PricingMethod, Nothing} = ConventionalLMP()
        formulation::Formulation = Formulation()
    end
 Market setting struct, typically used to map a day-ahead market to real-time markets.
 Arguments
 ---------
 - `inner_method`: 
    method to solve each marketing problem.
 - `lmp_method`:
    a PricingMethod method to calculate the locational marginal prices.
    If it is set to `nothing`, the LMPs will not be calculated.
 - `formulation`:
    problem formulation.
 """
 Base.@kwdef struct MarketSettings
    inner_method::SolutionMethod = XavQiuWanThi2019.Method()
    lmp_method::Union{PricingMethod,Nothing} = ConventionalLMP()
    formulation::Formulation = Formulation()
 end
--- a/src/model/build.jl
+++ b/src/model/build.jl
@@ -99,9 +99,6 @@ function build_model(;
            for pu in sc.profiled_units
                _add_profiled_unit!(model, pu, sc)
            end
            for su in sc.storage_units
                _add_storage_unit!(model, su, sc)
            end
            _add_system_wide_eqs!(model, sc)
        end
        @objective(model, Min, model[:obj])
--- a/src/model/formulations/KnuOstWat2018/pwlcosts.jl
+++ b/src/model/formulations/KnuOstWat2018/pwlcosts.jl
@@ -99,7 +99,7 @@ function _add_production_piecewise_linear_eqs!(
            add_to_expression!(
                model[:obj],
                segprod[sc.name, gn, t, k],
-                sc.probability * g.cost_segments[k].cost[t],
+                g.cost_segments[k].cost[t],
            )
            # Also add an explicit upper bound on segprod to make the solver's
--- a/src/model/formulations/base/sensitivity.jl
+++ b/src/model/formulations/base/sensitivity.jl
@@ -10,8 +10,8 @@ using SparseArrays, Base.Threads, LinearAlgebra, JuMP
 Returns a (B-1)xL matrix M, where B is the number of buses and L is the number
 of transmission lines. For a given bus b and transmission line l, the entry
 M[l.offset, b.offset] indicates the amount of power (in MW) that flows through
-transmission line l when 1 MW of power is injected at b and withdrawn from the
+transmission line l when 1 MW of power is injected at the slack bus (the bus
-slack bus (the bus that has offset zero).
+that has offset zero) and withdrawn from b.
 """
 function _injection_shift_factors(;
    buses::Array{Bus},
--- a/src/model/formulations/base/storage.jl
+++ b/src/model/formulations/base/storage.jl
@@ -1,125 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 function _add_storage_unit!(
    model::JuMP.Model,
    su::StorageUnit,
    sc::UnitCommitmentScenario,
 )::Nothing
    # Initialize variables
    storage_level = _init(model, :storage_level)
    charge_rate = _init(model, :charge_rate)
    discharge_rate = _init(model, :discharge_rate)
    is_charging = _init(model, :is_charging)
    is_discharging = _init(model, :is_discharging)
    eq_min_charge_rate = _init(model, :eq_min_charge_rate)
    eq_max_charge_rate = _init(model, :eq_max_charge_rate)
    eq_min_discharge_rate = _init(model, :eq_min_discharge_rate)
    eq_max_discharge_rate = _init(model, :eq_max_discharge_rate)
    # Initialize constraints
    net_injection = _init(model, :expr_net_injection)
    eq_storage_transition = _init(model, :eq_storage_transition)
    eq_ending_level = _init(model, :eq_ending_level)
    # time in hours
    time_step = sc.time_step / 60
    for t in 1:model[:instance].time
        # Decision variable
        storage_level[sc.name, su.name, t] = @variable(
            model,
            lower_bound = su.min_level[t],
            upper_bound = su.max_level[t]
        )
        charge_rate[sc.name, su.name, t] = @variable(model)
        discharge_rate[sc.name, su.name, t] = @variable(model)
        is_charging[sc.name, su.name, t] = @variable(model, binary = true)
        is_discharging[sc.name, su.name, t] = @variable(model, binary = true)
        # Objective function terms ##### CHECK & FIXME
        add_to_expression!(
            model[:obj],
            charge_rate[sc.name, su.name, t],
            su.charge_cost[t] * sc.probability,
        )
        add_to_expression!(
            model[:obj],
            discharge_rate[sc.name, su.name, t],
            su.discharge_cost[t] * sc.probability,
        )
        # Net injection
        add_to_expression!(
            net_injection[sc.name, su.bus.name, t],
            discharge_rate[sc.name, su.name, t],
            1.0,
        )
        add_to_expression!(
            net_injection[sc.name, su.bus.name, t],
            charge_rate[sc.name, su.name, t],
            -1.0,
        )
        # Simultaneous charging and discharging
        if !su.simultaneous_charge_and_discharge[t]
            # Initialize the model dictionary
            eq_simultaneous_charge_and_discharge =
                _init(model, :eq_simultaneous_charge_and_discharge)
            # Constraints
            eq_simultaneous_charge_and_discharge[sc.name, su.name, t] =
                @constraint(
                    model,
                    is_charging[sc.name, su.name, t] +
                    is_discharging[sc.name, su.name, t] <= 1.0
                )
        end
        # Charge and discharge constraints
        eq_min_charge_rate[sc.name, su.name, t] = @constraint(
            model,
            charge_rate[sc.name, su.name, t] >=
            is_charging[sc.name, su.name, t] * su.min_charge_rate[t]
        )
        eq_max_charge_rate[sc.name, su.name, t] = @constraint(
            model,
            charge_rate[sc.name, su.name, t] <=
            is_charging[sc.name, su.name, t] * su.max_charge_rate[t]
        )
        eq_min_discharge_rate[sc.name, su.name, t] = @constraint(
            model,
            discharge_rate[sc.name, su.name, t] >=
            is_discharging[sc.name, su.name, t] * su.min_discharge_rate[t]
        )
        eq_max_discharge_rate[sc.name, su.name, t] = @constraint(
            model,
            discharge_rate[sc.name, su.name, t] <=
            is_discharging[sc.name, su.name, t] * su.max_discharge_rate[t]
        )
        # Storage energy transition constraint 
        prev_storage_level =
            t == 1 ? su.initial_level : storage_level[sc.name, su.name, t-1]
        eq_storage_transition[sc.name, su.name, t] = @constraint(
            model,
            storage_level[sc.name, su.name, t] ==
            (1 - su.loss_factor[t]) * prev_storage_level +
            charge_rate[sc.name, su.name, t] *
            time_step *
            su.charge_efficiency[t] -
            discharge_rate[sc.name, su.name, t] * time_step /
            su.discharge_efficiency[t]
        )
        # Storage ending level constraint 
        if t == sc.time
            eq_ending_level[sc.name, su.name] = @constraint(
                model,
                su.min_ending_level <=
                storage_level[sc.name, su.name, t] <=
                su.max_ending_level
            )
        end
    end
    return
 end
--- a/src/solution/methods/MIPLearn/miplearn.jl
+++ b/src/solution/methods/MIPLearn/miplearn.jl
@@ -1,71 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using .MIPLearn
 using Suppressor
 using JuMP
 function _build_ucjl_model(instance, method)
    if instance isa String
        instance = UnitCommitment.read(instance)
    end
    model = UnitCommitment.build_model(
        instance = instance,
        optimizer = method.optimizer,
        variable_names = true,
    )
    write_to_file(model, "/tmp/model.lp")
    return JumpModel(model)
 end
 function _set_default_collectors!(method::MIPLearnMethod)
    method.collectors = [BasicCollector()]
    return
 end
 function _set_default_solver!(method::MIPLearnMethod)
    KNN = MIPLearn.pyimport("sklearn.neighbors").KNeighborsClassifier
    method.solver = LearningSolver(
        components = [
            MemorizingPrimalComponent(
                clf = KNN(n_neighbors = 30),
                extractor = H5FieldsExtractor(
                    instance_fields = ["static_var_obj_coeffs"],
                ),
                constructor = MergeTopSolutions(30, [0.0, 1.0]),
                action = FixVariables(),
            ),
        ],
    )
    return
 end
 function collect!(filenames::Vector, method::MIPLearnMethod)
    build(x) = _build_ucjl_model(x, method)
    if method.collectors === nothing
        _set_default_collectors!(method)
    end
    for c in method.collectors
        c.collect(filenames, build)
    end
 end
 function fit!(filenames::Vector, method::MIPLearnMethod)
    if method.solver === nothing
        _set_default_solver!(method)
    end
    return method.solver.fit(filenames)
 end
 function optimize!(filename::AbstractString, method::MIPLearnMethod)
    build(x) = _build_ucjl_model(x, method)
    method.solver.optimize(filename, build)
    return
 end
 function optimize!(instance::UnitCommitmentInstance, method::MIPLearnMethod)
    model = _build_ucjl_model(instance, method)
    method.solver.optimize(model)
    return
 end
--- a/src/solution/methods/MIPLearn/structs.jl
+++ b/src/solution/methods/MIPLearn/structs.jl
@@ -1,11 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using Suppressor
 Base.@kwdef mutable struct MIPLearnMethod
    optimizer::Any
    collectors::Any = nothing
    solver::Any = nothing
 end
--- a/src/solution/methods/ProgressiveHedging/optimize.jl
+++ b/src/solution/methods/ProgressiveHedging/optimize.jl
@@ -1,230 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using MPI, Printf
 using TimerOutputs
 import JuMP
 const to = TimerOutput()
 function optimize!(model::JuMP.Model, method::ProgressiveHedging)::Nothing
    mpi = MpiInfo(MPI.COMM_WORLD)
    iterations = PHIterationInfo[]
    consensus_vars = [var for var in all_variables(model) if is_binary(var)]
    nvars = length(consensus_vars)
    weights = ones(nvars)
    if method.initial_weights !== nothing
        weights = copy(method.initial_weights)
    end
    target = zeros(nvars)
    if method.initial_target !== nothing
        target = copy(method.initial_target)
    end
    params = PHSubProblemParams(
        ρ = method.ρ,
        λ = [method.λ for _ in 1:nvars],
        target = target,
    )
    sp = PHSubProblem(model, model[:obj], consensus_vars, weights)
    while true
        iteration_time = @elapsed begin
            solution = solve_subproblem(sp, params, method.inner_method)
            MPI.Barrier(mpi.comm)
            global_obj = compute_global_objective(mpi, solution)
            target = compute_target(mpi, solution)
            update_λ_and_residuals!(solution, params, target)
            global_infeas = compute_global_infeasibility(solution, mpi)
            global_residual = compute_global_residual(mpi, solution)
            if has_numerical_issues(target)
                break
            end
        end
        total_elapsed_time =
            compute_total_elapsed_time(iteration_time, iterations)
        current_iteration = PHIterationInfo(
            global_infeas = global_infeas,
            global_obj = global_obj,
            global_residual = global_residual,
            iteration_number = length(iterations) + 1,
            iteration_time = iteration_time,
            sp_vals = solution.vals,
            sp_obj = solution.obj,
            target = target,
            total_elapsed_time = total_elapsed_time,
        )
        push!(iterations, current_iteration)
        print_progress(mpi, current_iteration, method.print_interval)
        if should_stop(mpi, iterations, method.termination)
            break
        end
    end
    return
 end
 function compute_total_elapsed_time(
    iteration_time::Float64,
    iterations::Array{PHIterationInfo,1},
 )::Float64
    length(iterations) > 0 ?
    current_total_time = last(iterations).total_elapsed_time :
    current_total_time = 0
    return current_total_time + iteration_time
 end
 function compute_global_objective(
    mpi::MpiInfo,
    s::PhSubProblemSolution,
 )::Float64
    global_obj = MPI.Allreduce(s.obj, MPI.SUM, mpi.comm)
    global_obj /= mpi.nprocs
    return global_obj
 end
 function compute_target(mpi::MpiInfo, s::PhSubProblemSolution)::Array{Float64,1}
    sp_vals = s.vals
    target = MPI.Allreduce(sp_vals, MPI.SUM, mpi.comm)
    target = target / mpi.nprocs
    return target
 end
 function compute_global_residual(mpi::MpiInfo, s::PhSubProblemSolution)::Float64
    n_vars = length(s.vals)
    local_residual_sum = abs.(s.residuals)
    global_residual_sum = MPI.Allreduce(local_residual_sum, MPI.SUM, mpi.comm)
    return sum(global_residual_sum) / n_vars
 end
 function compute_global_infeasibility(
    solution::PhSubProblemSolution,
    mpi::MpiInfo,
 )::Float64
    local_infeasibility = norm(solution.residuals)
    global_infeas = MPI.Allreduce(local_infeasibility, MPI.SUM, mpi.comm)
    return global_infeas
 end
 function solve_subproblem(
    sp::PHSubProblem,
    params::PHSubProblemParams,
    method::SolutionMethod,
 )::PhSubProblemSolution
    G = length(sp.consensus_vars)
    if norm(params.λ) < 1e-3
        @objective(sp.mip, Min, sp.obj)
    else
        @objective(
            sp.mip,
            Min,
            sp.obj +
            sum(
                sp.weights[g] *
                params.λ[g] *
                (sp.consensus_vars[g] - params.target[g]) for g in 1:G
            ) +
            (params.ρ / 2) * sum(
                sp.weights[g] * (sp.consensus_vars[g] - params.target[g])^2 for
                g in 1:G
            )
        )
    end
    optimize!(sp.mip, method)
    obj = objective_value(sp.mip)
    sp_vals = value.(sp.consensus_vars)
    return PhSubProblemSolution(obj = obj, vals = sp_vals, residuals = zeros(G))
 end
 function update_λ_and_residuals!(
    solution::PhSubProblemSolution,
    params::PHSubProblemParams,
    target::Array{Float64,1},
 )::Nothing
    n_vars = length(solution.vals)
    params.target = target
    for n in 1:n_vars
        solution.residuals[n] = solution.vals[n] - params.target[n]
        params.λ[n] += params.ρ * solution.residuals[n]
    end
 end
 function print_header(mpi::MpiInfo)::Nothing
    if !mpi.root
        return
    end
    @info "Solving via Progressive Hedging:"
    @info @sprintf(
        "%8s %20s %20s %14s %8s %8s",
        "iter",
        "obj",
        "infeas",
        "consensus",
        "time-it",
        "time"
    )
 end
 function print_progress(
    mpi::MpiInfo,
    iteration::PHIterationInfo,
    print_interval,
 )::Nothing
    if !mpi.root
        return
    end
    if iteration.iteration_number % print_interval != 0
        return
    end
    @info @sprintf(
        "%8d %20.6e %20.6e %12.2f %% %8.2f %8.2f",
        iteration.iteration_number,
        iteration.global_obj,
        iteration.global_infeas,
        iteration.global_residual * 100,
        iteration.iteration_time,
        iteration.total_elapsed_time
    )
 end
 function has_numerical_issues(target::Array{Float64,1})::Bool
    if target == NaN
        @warn "Numerical issues detected. Stopping."
        return true
    end
    return false
 end
 function should_stop(
    mpi::MpiInfo,
    iterations::Array{PHIterationInfo,1},
    termination::PHTermination,
 )::Bool
    if length(iterations) >= termination.max_iterations
        if mpi.root
            @info "Iteration limit reached. Stopping."
        end
        return true
    end
    if length(iterations) < termination.min_iterations
        return false
    end
    if last(iterations).total_elapsed_time > termination.max_time
        if mpi.root
            @info "Time limit reached. Stopping."
        end
        return true
    end
    curr_it = last(iterations)
    prev_it = iterations[length(iterations)-1]
    if curr_it.global_infeas < termination.min_feasibility
        obj_change = abs(prev_it.global_obj - curr_it.global_obj)
        if obj_change < termination.min_improvement
            if mpi.root
                @info "Feasibility limit reached. Stopping."
            end
            return true
        end
    end
    return false
 end
--- a/src/solution/methods/ProgressiveHedging/read.jl
+++ b/src/solution/methods/ProgressiveHedging/read.jl
@@ -1,18 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 function read(
    paths::Vector{String},
    ::ProgressiveHedging,
 )::UnitCommitmentInstance
    comm = MPI.COMM_WORLD
    mpi = MpiInfo(comm)
    (length(paths) % mpi.nprocs == 0) || error(
        "Number of processes $(mpi.nprocs) is not a divisor of $(length(paths))",
    )
    bundled_scenarios = length(paths) ÷ mpi.nprocs
    sc_num_start = (mpi.rank - 1) * bundled_scenarios + 1
    sc_num_end = mpi.rank * bundled_scenarios
    return read(paths[sc_num_start:sc_num_end])
 end
--- a/src/solution/methods/ProgressiveHedging/solution.jl
+++ b/src/solution/methods/ProgressiveHedging/solution.jl
@@ -1,83 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using MPI, DataStructures
 const FIRST_STAGE_VARS = ["Is on", "Switch on", "Switch off"]
 function solution(model::JuMP.Model, method::ProgressiveHedging)::OrderedDict
    comm = MPI.COMM_WORLD
    mpi = MpiInfo(comm)
    sp_solution = UnitCommitment.solution(model)
    gather_solution = OrderedDict()
    for (solution_key, dict) in sp_solution
        if solution_key !== "Spinning reserve (MW)" &&
           solution_key ∉ FIRST_STAGE_VARS
            push!(gather_solution, solution_key => OrderedDict())
            for (gen_bus_key, values) in dict
                global T = length(values)
                receive_values =
                    MPI.UBuffer(Vector{Float64}(undef, T * mpi.nprocs), T)
                MPI.Gather!(float.(values), receive_values, comm)
                if mpi.root
                    push!(
                        gather_solution[solution_key],
                        gen_bus_key => receive_values.data,
                    )
                end
            end
        end
    end
    push!(gather_solution, "Spinning reserve (MW)" => OrderedDict())
    for (reserve_type, dict) in sp_solution["Spinning reserve (MW)"]
        push!(
            gather_solution["Spinning reserve (MW)"],
            reserve_type => OrderedDict(),
        )
        for (gen_key, values) in dict
            receive_values =
                MPI.UBuffer(Vector{Float64}(undef, T * mpi.nprocs), T)
            MPI.Gather!(float.(values), receive_values, comm)
            if mpi.root
                push!(
                    gather_solution["Spinning reserve (MW)"][reserve_type],
                    gen_key => receive_values.data,
                )
            end
        end
    end
    aggregate_solution = OrderedDict()
    if mpi.root
        for first_stage_var in FIRST_STAGE_VARS
            aggregate_solution[first_stage_var] = OrderedDict()
            for gen_key in keys(sp_solution[first_stage_var])
                aggregate_solution[first_stage_var][gen_key] =
                    sp_solution[first_stage_var][gen_key]
            end
        end
        for i in 1:mpi.nprocs
            push!(aggregate_solution, "s$i" => OrderedDict())
            for (solution_key, solution_dict) in gather_solution
                push!(aggregate_solution["s$i"], solution_key => OrderedDict())
                if solution_key !== "Spinning reserve (MW)"
                    for (gen_bus_key, values) in solution_dict
                        aggregate_solution["s$i"][solution_key][gen_bus_key] =
                            gather_solution[solution_key][gen_bus_key][(i-1)*T+1:i*T]
                    end
                else
                    for (reserve_name, reserve_dict) in solution_dict
                        push!(
                            aggregate_solution["s$i"][solution_key],
                            reserve_name => OrderedDict(),
                        )
                        for (gen_key, values) in reserve_dict
                            aggregate_solution["s$i"][solution_key][reserve_name][gen_key] =
                                gather_solution[solution_key][reserve_name][gen_key][(i-1)*T+1:i*T]
                        end
                    end
                end
            end
        end
    end
    return aggregate_solution
 end
--- a/src/solution/methods/ProgressiveHedging/structs.jl
+++ b/src/solution/methods/ProgressiveHedging/structs.jl
@@ -1,73 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using JuMP, MPI, TimerOutputs
 Base.@kwdef mutable struct PHTermination
    max_iterations::Int = 1000
    max_time::Float64 = 14400.0
    min_feasibility::Float64 = 1e-3
    min_improvement::Float64 = 1e-3
    min_iterations::Int = 2
 end
 Base.@kwdef mutable struct PHIterationInfo
    global_infeas::Float64
    global_obj::Float64
    global_residual::Float64
    iteration_number::Int
    iteration_time::Float64
    sp_vals::Array{Float64,1}
    sp_obj::Float64
    target::Array{Float64,1}
    total_elapsed_time::Float64
 end
 Base.@kwdef mutable struct ProgressiveHedging <: SolutionMethod
    initial_weights::Union{Vector{Float64},Nothing} = nothing
    initial_target::Union{Vector{Float64},Nothing} = nothing
    ρ::Float64 = 1.0
    λ::Float64 = 0.0
    print_interval::Int = 1
    termination::PHTermination = PHTermination()
    inner_method::SolutionMethod = XavQiuWanThi2019.Method()
 end
 struct SpResult
    obj::Float64
    vals::Array{Float64,1}
 end
 Base.@kwdef mutable struct PHSubProblem
    mip::JuMP.Model
    obj::AffExpr
    consensus_vars::Array{VariableRef,1}
    weights::Array{Float64,1}
 end
 Base.@kwdef struct PhSubProblemSolution
    obj::Float64
    vals::Array{Float64,1}
    residuals::Array{Float64,1}
 end
 Base.@kwdef mutable struct PHSubProblemParams
    ρ::Float64
    λ::Array{Float64,1}
    target::Array{Float64,1}
 end
 struct MpiInfo
    comm::Any
    rank::Int
    root::Bool
    nprocs::Int
    function MpiInfo(comm)
        rank = MPI.Comm_rank(comm) + 1
        is_root = (rank == 1)
        nprocs = MPI.Comm_size(comm)
        return new(comm, rank, is_root, nprocs)
    end
 end
--- a/src/solution/methods/TimeDecomposition/optimize.jl
+++ b/src/solution/methods/TimeDecomposition/optimize.jl
@@ -1,259 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 """
    optimize!(
        instance::UnitCommitmentInstance, 
        method::TimeDecomposition;
        optimizer,
        after_build = nothing,
        after_optimize = nothing,
    )::OrderedDict
 Solve the given unit commitment instance with time decomposition. 
 The model solves each sub-problem of a given time length specified by method.time_window,
 and proceeds to the next sub-problem by incrementing the time length of `method.time_increment`.
 Arguments
 ---------
 - `instance`:
    the UnitCommitment instance.
 - `method`:
    the `TimeDecomposition` method.
 - `optimizer`:
    the optimizer for solving the problem.
 - `after_build`:
    a user-defined function that allows modifying the model after building,
    must have 2 arguments `model` and `instance` in order.
 - `after_optimize`:
    a user-defined function that allows handling additional steps after optimizing,
    must have 3 arguments `solution`, `model` and `instance` in order.
 Examples
 --------
 ```julia
 using UnitCommitment, JuMP, Cbc, HiGHS
 import UnitCommitment: 
    TimeDecomposition,
    ConventionalLMP,
    XavQiuWanThi2019,
    Formulation
 # specifying the after_build and after_optimize functions
 function after_build(model, instance)
    @constraint(
        model,
        model[:is_on]["g3", 1] + model[:is_on]["g4", 1] <= 1,
    )
 end
 lmps = []
 function after_optimize(solution, model, instance)
    lmp = UnitCommitment.compute_lmp(
        model,
        ConventionalLMP(),
        optimizer = HiGHS.Optimizer,
    )
    return push!(lmps, lmp)
 end
 # assume the instance is given as a 120h problem
 instance = UnitCommitment.read("instance.json")
 solution = UnitCommitment.optimize!(
    instance,
    TimeDecomposition(
        time_window = 36,  # solve 36h problems
        time_increment = 24,  # advance by 24h each time
        inner_method = XavQiuWanThi2019.Method(),
        formulation = Formulation(),
    ),
    optimizer = Cbc.Optimizer,
    after_build = after_build,
    after_optimize = after_optimize,
 )
 """
 function optimize!(
    instance::UnitCommitmentInstance,
    method::TimeDecomposition;
    optimizer,
    after_build = nothing,
    after_optimize = nothing,
 )::OrderedDict
    # get instance total length
    T = instance.time
    solution = OrderedDict()
    if length(instance.scenarios) > 1
        for sc in instance.scenarios
            solution[sc.name] = OrderedDict()
        end
    end
    # for each iteration, time increment by method.time_increment
    for t_start in 1:method.time_increment:T
        t_end = t_start + method.time_window - 1
        # if t_end exceed total T
        t_end = t_end > T ? T : t_end
        # slice the model 
        @info "Solving the sub-problem of time $t_start to $t_end..."
        sub_instance = UnitCommitment.slice(instance, t_start:t_end)
        # build and optimize the model 
        sub_model = UnitCommitment.build_model(
            instance = sub_instance,
            optimizer = optimizer,
            formulation = method.formulation,
        )
        if after_build !== nothing
            @info "Calling after build..."
            after_build(sub_model, sub_instance)
        end
        UnitCommitment.optimize!(sub_model, method.inner_method)
        # get the result of each time period
        sub_solution = UnitCommitment.solution(sub_model)
        if after_optimize !== nothing
            @info "Calling after optimize..."
            after_optimize(sub_solution, sub_model, sub_instance)
        end
        # merge solution 
        if length(instance.scenarios) == 1
            _update_solution!(solution, sub_solution, method.time_increment)
        else
            for sc in instance.scenarios
                _update_solution!(
                    solution[sc.name],
                    sub_solution[sc.name],
                    method.time_increment,
                )
            end
        end
        # set the initial status for the next sub-problem
        _set_initial_status!(instance, solution, method.time_increment)
    end
    return solution
 end
 """
    _set_initial_status!(
        instance::UnitCommitmentInstance,
        solution::OrderedDict,
        time_increment::Int,
    )
 Set the thermal units' initial power levels and statuses based on the last bunch of time slots 
 specified by time_increment in the solution dictionary.
 """
 function _set_initial_status!(
    instance::UnitCommitmentInstance,
    solution::OrderedDict,
    time_increment::Int,
 )
    for sc in instance.scenarios
        for thermal_unit in sc.thermal_units
            if length(instance.scenarios) == 1
                prod = solution["Thermal production (MW)"][thermal_unit.name]
                is_on = solution["Is on"][thermal_unit.name]
            else
                prod =
                    solution[sc.name]["Thermal production (MW)"][thermal_unit.name]
                is_on = solution[sc.name]["Is on"][thermal_unit.name]
            end
            thermal_unit.initial_power = prod[end]
            thermal_unit.initial_status = _determine_initial_status(
                thermal_unit.initial_status,
                is_on[end-time_increment+1:end],
            )
        end
    end
 end
 """
    _determine_initial_status(
        prev_initial_status::Union{Float64,Int},
        status_sequence::Vector{Float64},
    )::Union{Float64,Int}
 Determines a thermal unit's initial status based on its previous initial status, and
 the on/off statuses in the last operation.
 """
 function _determine_initial_status(
    prev_initial_status::Union{Float64,Int},
    status_sequence::Vector{Float64},
 )::Union{Float64,Int}
    # initialize the two flags
    on_status = prev_initial_status
    off_status = prev_initial_status
    # read through the status sequence
    # at each time if the unit is on, reset off_status, increment on_status
    # if the on_status < 0, set it to 1.0
    # at each time if the unit is off, reset on_status, decrement off_status
    # if the off_status > 0, set it to -1.0
    for status in status_sequence
        if status == 1.0
            on_status = on_status < 0.0 ? 1.0 : on_status + 1.0
            off_status = 0.0
        else
            on_status = 0.0
            off_status = off_status > 0.0 ? -1.0 : off_status - 1.0
        end
    end
    # only one of them has non-zero value
    return on_status + off_status
 end
 """
    _update_solution!(
        solution::OrderedDict,
        sub_solution::OrderedDict,
        time_increment::Int,
    )
 Updates the solution (of each scenario) by concatenating the first bunch of 
 time slots of the newly generated sub-solution to the end of the final solution dictionary.
 This function traverses through the dictionary keys, finds the vector and finally
 does the concatenation. For now, the function is hardcoded to traverse at most 3 layers
 of depth until it finds a vector object.
 """
 function _update_solution!(
    solution::OrderedDict,
    sub_solution::OrderedDict,
    time_increment::Int,
 )
    # the solution has at most 3 layers
    for (l1_k, l1_v) in sub_solution
        for (l2_k, l2_v) in l1_v
            if l2_v isa Array
                # slice the sub_solution
                values_of_interest = l2_v[1:time_increment]
                sub_solution[l1_k][l2_k] = values_of_interest
                # append to the solution
                if !isempty(solution)
                    append!(solution[l1_k][l2_k], values_of_interest)
                end
            elseif l2_v isa OrderedDict
                for (l3_k, l3_v) in l2_v
                    # slice the sub_solution
                    values_of_interest = l3_v[1:time_increment]
                    sub_solution[l1_k][l2_k][l3_k] = values_of_interest
                    # append to the solution
                    if !isempty(solution)
                        append!(solution[l1_k][l2_k][l3_k], values_of_interest)
                    end
                end
            end
        end
    end
    # if solution is never initialized, deep copy the sliced sub_solution
    if isempty(solution)
        merge!(solution, sub_solution)
    end
 end
--- a/src/solution/methods/TimeDecomposition/structs.jl
+++ b/src/solution/methods/TimeDecomposition/structs.jl
@@ -1,35 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 import ..SolutionMethod
 import ..Formulation
 """
    mutable struct TimeDecomposition <: SolutionMethod
        time_window::Int
        time_increment::Int
        inner_method::SolutionMethod = XavQiuWanThi2019.Method()
        formulation::Formulation = Formulation()
    end
 Time decomposition method to solve a problem with moving time window.
 Fields
 ------
 - `time_window`:
    the time window of each sub-problem during the entire optimization procedure.
 - `time_increment`: 
    the time incremented to the next sub-problem.
 - `inner_method`: 
    method to solve each sub-problem.
 - `formulation`:
    problem formulation.
 """
 Base.@kwdef mutable struct TimeDecomposition <: SolutionMethod
    time_window::Int
    time_increment::Int
    inner_method::SolutionMethod = XavQiuWanThi2019.Method()
    formulation::Formulation = Formulation()
 end
--- a/src/solution/solution.jl
+++ b/src/solution/solution.jl
@@ -103,30 +103,6 @@ function solution(model::JuMP.Model)::OrderedDict
                ] for pu in sc.profiled_units
            )
        end
        if !isempty(sc.storage_units)
            sol[sc.name]["Storage level (MWh)"] =
                timeseries(model[:storage_level], sc.storage_units, sc = sc)
            sol[sc.name]["Is charging"] =
                timeseries(model[:is_charging], sc.storage_units, sc = sc)
            sol[sc.name]["Storage charging rates (MW)"] =
                timeseries(model[:charge_rate], sc.storage_units, sc = sc)
            sol[sc.name]["Storage charging cost (\$)"] = OrderedDict(
                su.name => [
                    value(model[:charge_rate][sc.name, su.name, t]) *
                    su.charge_cost[t] for t in 1:instance.time
                ] for su in sc.storage_units
            )
            sol[sc.name]["Is discharging"] =
                timeseries(model[:is_discharging], sc.storage_units, sc = sc)
            sol[sc.name]["Storage discharging rates (MW)"] =
                timeseries(model[:discharge_rate], sc.storage_units, sc = sc)
            sol[sc.name]["Storage discharging cost (\$)"] = OrderedDict(
                su.name => [
                    value(model[:discharge_rate][sc.name, su.name, t]) *
                    su.discharge_cost[t] for t in 1:instance.time
                ] for su in sc.storage_units
            )
        end
        sol[sc.name]["Spinning reserve (MW)"] = OrderedDict(
            r.name => OrderedDict(
                g.name => [
--- a/src/transform/initcond.jl
+++ b/src/transform/initcond.jl
@@ -5,31 +5,13 @@
 using JuMP
 """
-    generate_initial_conditions!(instance, optimizer)
+    generate_initial_conditions!(sc, optimizer)
-Generates feasible initial conditions for the given instance, by constructing
+Generates feasible initial conditions for the given scenario, by constructing
 and solving a single-period mixed-integer optimization problem, using the given
-optimizer. The instance is modified in-place.
+optimizer. The scenario is modified in-place.
 """
 function generate_initial_conditions!(
    instance::UnitCommitmentInstance,
    optimizer,
 )::Nothing
    # Process first scenario
    _generate_initial_conditions!(instance.scenarios[1], optimizer)
    # Copy initial conditions to remaining scenarios
    for (si, sc) in enumerate(instance.scenarios)
        si > 1 || continue
        for (gi, g) in sc.thermal_units
            g_ref = instance.scenarios[1].thermal_units[gi]
            g.initial_power = g_ref.initial_power
            g.initial_status = g_ref.initial_status
        end
    end
 end
 function _generate_initial_conditions!(
    sc::UnitCommitmentScenario,
    optimizer,
 )::Nothing
--- a/src/transform/randomize/XavQiuAhm2021.jl
+++ b/src/transform/randomize/XavQiuAhm2021.jl
@@ -137,11 +137,6 @@ function _randomize_costs(
        α = rand(rng, distribution)
        pu.cost *= α
    end
    for su in sc.storage_units
        α = rand(rng, distribution)
        su.charge_cost *= α
        su.discharge_cost *= α
    end
    return
 end
--- a/src/transform/slice.jl
+++ b/src/transform/slice.jl
@@ -56,21 +56,6 @@ function slice(
            ps.demand = ps.demand[range]
            ps.revenue = ps.revenue[range]
        end
        for su in sc.storage_units
            su.min_level = su.min_level[range]
            su.max_level = su.max_level[range]
            su.simultaneous_charge_and_discharge =
                su.simultaneous_charge_and_discharge[range]
            su.charge_cost = su.charge_cost[range]
            su.discharge_cost = su.discharge_cost[range]
            su.charge_efficiency = su.charge_efficiency[range]
            su.discharge_efficiency = su.discharge_efficiency[range]
            su.loss_factor = su.loss_factor[range]
            su.min_charge_rate = su.min_charge_rate[range]
            su.max_charge_rate = su.max_charge_rate[range]
            su.min_discharge_rate = su.min_discharge_rate[range]
            su.max_discharge_rate = su.max_discharge_rate[range]
        end
    end
    return modified
 end
--- a/src/validation/validate.jl
+++ b/src/validation/validate.jl
@@ -334,195 +334,6 @@ function _validate_units(instance::UnitCommitmentInstance, solution; tol = 0.01)
                end
            end
        end
        for su in sc.storage_units
            storage_level = solution[sc.name]["Storage level (MWh)"][su.name]
            charge_rate =
                solution[sc.name]["Storage charging rates (MW)"][su.name]
            discharge_rate =
                solution[sc.name]["Storage discharging rates (MW)"][su.name]
            actual_charge_cost =
                solution[sc.name]["Storage charging cost (\$)"][su.name]
            actual_discharge_cost =
                solution[sc.name]["Storage discharging cost (\$)"][su.name]
            is_charging = bin(solution[sc.name]["Is charging"][su.name])
            is_discharging = bin(solution[sc.name]["Is discharging"][su.name])
            # time in hours
            time_step = sc.time_step / 60
            for t in 1:instance.time
                # Unit must store at least its minimum level 
                if storage_level[t] < su.min_level[t] - tol
                    @error @sprintf(
                        "Storage unit %s stores below its minimum level at time %d (%.2f < %.2f)",
                        su.name,
                        t,
                        storage_level[t],
                        su.min_level[t]
                    )
                    err_count += 1
                end
                # Unit must store at most its maximum level 
                if storage_level[t] > su.max_level[t] + tol
                    @error @sprintf(
                        "Storage unit %s stores above its maximum level at time %d (%.2f > %.2f)",
                        su.name,
                        t,
                        storage_level[t],
                        su.max_level[t]
                    )
                    err_count += 1
                end
                if t == instance.time
                    # Unit must store at least its minimum level at last time period
                    if storage_level[t] < su.min_ending_level - tol
                        @error @sprintf(
                            "Storage unit %s stores below its minimum ending level (%.2f < %.2f)",
                            su.name,
                            storage_level[t],
                            su.min_ending_level
                        )
                        err_count += 1
                    end
                    # Unit must store at most its maximum level at last time period
                    if storage_level[t] > su.max_ending_level + tol
                        @error @sprintf(
                            "Storage unit %s stores above its maximum ending level (%.2f > %.2f)",
                            su.name,
                            storage_level[t],
                            su.max_ending_level
                        )
                        err_count += 1
                    end
                end
                # Unit must follow the energy transition constraint 
                prev_level = t == 1 ? su.initial_level : storage_level[t-1]
                current_level =
                    (1 - su.loss_factor[t]) * prev_level +
                    time_step * (
                        charge_rate[t] * su.charge_efficiency[t] -
                        discharge_rate[t] / su.discharge_efficiency[t]
                    )
                if abs(storage_level[t] - current_level) > tol
                    @error @sprintf(
                        "Storage unit %s has unexpected level at time %d (%.2f should be %.2f)",
                        unit.name,
                        t,
                        storage_level[t],
                        current_level
                    )
                    err_count += 1
                end
                # Unit cannot simultaneous charge and discharge if it is not allowed
                if !su.simultaneous_charge_and_discharge[t] &&
                   is_charging[t] &&
                   is_discharging[t]
                    @error @sprintf(
                        "Storage unit %s is charging and discharging simultaneous at time %d",
                        su.name,
                        t
                    )
                    err_count += 1
                end
                # Unit must charge at least its minimum rate 
                if is_charging[t] &&
                   (charge_rate[t] < su.min_charge_rate[t] - tol)
                    @error @sprintf(
                        "Storage unit %s charges below its minimum limit at time %d (%.2f < %.2f)",
                        unit.name,
                        t,
                        charge_rate[t],
                        su.min_charge_rate[t]
                    )
                    err_count += 1
                end
                # Unit must charge at most its maximum rate 
                if is_charging[t] &&
                   (charge_rate[t] > su.max_charge_rate[t] + tol)
                    @error @sprintf(
                        "Storage unit %s charges above its maximum limit at time %d (%.2f > %.2f)",
                        unit.name,
                        t,
                        charge_rate[t],
                        su.max_charge_rate[t]
                    )
                    err_count += 1
                end
                # Unit must have zero charge when it is not charging
                if !is_charging[t] && (charge_rate[t] > tol)
                    @error @sprintf(
                        "Storage unit %s charges power at time %d while not charging (%.2f > 0)",
                        unit.name,
                        t,
                        charge_rate[t]
                    )
                    err_count += 1
                end
                # Unit must discharge at least its minimum rate 
                if is_discharging[t] &&
                   (discharge_rate[t] < su.min_discharge_rate[t] - tol)
                    @error @sprintf(
                        "Storage unit %s discharges below its minimum limit at time %d (%.2f < %.2f)",
                        unit.name,
                        t,
                        discharge_rate[t],
                        su.min_discharge_rate[t]
                    )
                    err_count += 1
                end
                # Unit must discharge at most its maximum rate 
                if is_discharging[t] &&
                   (discharge_rate[t] > su.max_discharge_rate[t] + tol)
                    @error @sprintf(
                        "Storage unit %s discharges above its maximum limit at time %d (%.2f > %.2f)",
                        unit.name,
                        t,
                        discharge_rate[t],
                        su.max_discharge_rate[t]
                    )
                    err_count += 1
                end
                # Unit must have zero discharge when it is not charging
                if !is_discharging[t] && (discharge_rate[t] > tol)
                    @error @sprintf(
                        "Storage unit %s discharges power at time %d while not discharging (%.2f > 0)",
                        unit.name,
                        t,
                        discharge_rate[t]
                    )
                    err_count += 1
                end
                # Compute storage costs 
                charge_cost = su.charge_cost[t] * charge_rate[t]
                discharge_cost = su.discharge_cost[t] * discharge_rate[t]
                # Compare costs
                if abs(actual_charge_cost[t] - charge_cost) > tol
                    @error @sprintf(
                        "Storage unit %s has unexpected charge cost at time %d (%.2f should be %.2f)",
                        unit.name,
                        t,
                        actual_charge_cost[t],
                        charge_cost
                    )
                    err_count += 1
                end
                if abs(actual_discharge_cost[t] - discharge_cost) > tol
                    @error @sprintf(
                        "Storage unit %s has unexpected discharge cost at time %d (%.2f should be %.2f)",
                        unit.name,
                        t,
                        actual_discharge_cost[t],
                        discharge_cost
                    )
                    err_count += 1
                end
            end
        end
    end
    return err_count
 end
@@ -535,8 +346,6 @@ function _validate_reserve_and_demand(instance, solution, tol = 0.01)
            fixed_load = sum(b.load[t] for b in sc.buses)
            ps_load = 0
            production = 0
            storage_charge = 0
            storage_discharge = 0
            if length(sc.price_sensitive_loads) > 0
                ps_load = sum(
                    solution[sc.name]["Price-sensitive loads (MW)"][ps.name][t]
@@ -555,38 +364,23 @@ function _validate_reserve_and_demand(instance, solution, tol = 0.01)
                    for pu in sc.profiled_units
                )
            end
            if length(sc.storage_units) > 0
                storage_charge += sum(
                    solution[sc.name]["Storage charging rates (MW)"][su.name][t]
                    for su in sc.storage_units
                )
                storage_discharge += sum(
                    solution[sc.name]["Storage discharging rates (MW)"][su.name][t]
                    for su in sc.storage_units
                )
            end
            if "Load curtail (MW)" in keys(solution)
                load_curtail = sum(
                    solution[sc.name]["Load curtail (MW)"][b.name][t] for
                    b in sc.buses
                )
            end
-            balance =
+            balance = fixed_load - load_curtail - production + ps_load
                fixed_load - load_curtail - production +
                ps_load +
                storage_charge - storage_discharge
            # Verify that production equals demand
            if abs(balance) > tol
                @error @sprintf(
-                    "Non-zero power balance at time %d (%.2f + %.2f - %.2f - %.2f + %.2f - %.2f != 0)",
+                    "Non-zero power balance at time %d (%.2f + %.2f - %.2f - %.2f != 0)",
                    t,
                    fixed_load,
                    ps_load,
                    load_curtail,
                    production,
                    storage_charge,
                    storage_discharge,
                )
                err_count += 1
            end
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -13,8 +13,6 @@ JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
 JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 JuliaFormatter = "98e50ef6-434e-11e9-1051-2b60c6c9e899"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MIPLearn = "2b1277c3-b477-4c49-a15e-7ba350325c68"
 MPI = "da04e1cc-30fd-572f-bb4f-1f8673147195"
 MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
--- a/test/fixtures/case14-storage.json.gz
+++ b/test/fixtures/case14-storage.json.gz
--- a/test/fixtures/case14.json.gz.h5
+++ b/test/fixtures/case14.json.gz.h5
--- a/test/fixtures/market_da_scenario.json.gz
+++ b/test/fixtures/market_da_scenario.json.gz
--- a/test/fixtures/market_da_simple.json.gz
+++ b/test/fixtures/market_da_simple.json.gz
--- a/test/fixtures/market_rt1_simple.json.gz
+++ b/test/fixtures/market_rt1_simple.json.gz
--- a/test/fixtures/market_rt2_simple.json.gz
+++ b/test/fixtures/market_rt2_simple.json.gz
--- a/test/fixtures/market_rt3_simple.json.gz
+++ b/test/fixtures/market_rt3_simple.json.gz
--- a/test/fixtures/market_rt4_simple.json.gz
+++ b/test/fixtures/market_rt4_simple.json.gz
--- a/test/src/UnitCommitmentT.jl
+++ b/test/src/UnitCommitmentT.jl
@@ -1,7 +1,6 @@
 module UnitCommitmentT
 using JuliaFormatter
 using MIPLearn
 using UnitCommitment
 using Test
@@ -13,18 +12,12 @@ include("model/formulations_test.jl")
 include("solution/methods/XavQiuWanThi19/filter_test.jl")
 include("solution/methods/XavQiuWanThi19/find_test.jl")
 include("solution/methods/XavQiuWanThi19/sensitivity_test.jl")
 include("solution/methods/ProgressiveHedging/usage_test.jl")
 include("solution/methods/TimeDecomposition/initial_status_test.jl")
 include("solution/methods/TimeDecomposition/optimize_test.jl")
 include("solution/methods/TimeDecomposition/update_solution_test.jl")
 include("solution/methods/MIPLearn/usage_test.jl")
 include("transform/initcond_test.jl")
 include("transform/slice_test.jl")
 include("transform/randomize/XavQiuAhm2021_test.jl")
 include("validation/repair_test.jl")
 include("lmp/conventional_test.jl")
 include("lmp/aelmp_test.jl")
 include("market/market_test.jl")
 basedir = dirname(@__FILE__)
@@ -44,19 +37,12 @@ function runtests()
        solution_methods_XavQiuWanThi19_filter_test()
        solution_methods_XavQiuWanThi19_find_test()
        solution_methods_XavQiuWanThi19_sensitivity_test()
        solution_methods_ProgressiveHedging_usage_test()
        solution_methods_TimeDecomposition_initial_status_test()
        solution_methods_TimeDecomposition_optimize_test()
        solution_methods_TimeDecomposition_update_solution_test()
        solution_methods_MIPLearn_usage_test()
        transform_initcond_test()
        transform_slice_test()
        transform_randomize_XavQiuAhm2021_test()
        validation_repair_test()
        lmp_conventional_test()
        lmp_aelmp_test()
        simple_market_test()
        stochastic_market_test()
    end
    return
 end
--- a/test/src/instance/read_test.jl
+++ b/test/src/instance/read_test.jl
@@ -21,11 +21,11 @@ function instance_read_test()
        @test length(sc.contingencies) == 19
        @test length(sc.price_sensitive_loads) == 1
        @test instance.time == 4
        @test sc.time_step == 60
        @test sc.lines[5].name == "l5"
        @test sc.lines[5].source.name == "b2"
        @test sc.lines[5].target.name == "b5"
        @test sc.lines[5].reactance ≈ 0.17388
        @test sc.lines[5].susceptance ≈ 10.037550333
        @test sc.lines[5].normal_flow_limit == [1e8 for t in 1:4]
        @test sc.lines[5].emergency_flow_limit == [1e8 for t in 1:4]
@@ -35,6 +35,7 @@ function instance_read_test()
        @test sc.lines[1].name == "l1"
        @test sc.lines[1].source.name == "b1"
        @test sc.lines[1].target.name == "b2"
        @test sc.lines[1].reactance ≈ 0.059170
        @test sc.lines[1].susceptance ≈ 29.496860773945
        @test sc.lines[1].normal_flow_limit == [300.0 for t in 1:4]
        @test sc.lines[1].emergency_flow_limit == [400.0 for t in 1:4]
@@ -137,20 +138,20 @@ function instance_read_test()
        sc = instance.scenarios[1]
        @test length(sc.profiled_units) == 2
-        pu1 = sc.profiled_units[1]
+        first_pu = sc.profiled_units[1]
-        @test pu1.name == "g7"
+        @test first_pu.name == "g7"
-        @test pu1.bus.name == "b4"
+        @test first_pu.bus.name == "b4"
-        @test pu1.cost == [100.0 for t in 1:4]
+        @test first_pu.cost == [100.0 for t in 1:4]
-        @test pu1.min_power == [60.0 for t in 1:4]
+        @test first_pu.min_power == [60.0 for t in 1:4]
-        @test pu1.max_power == [100.0 for t in 1:4]
+        @test first_pu.max_power == [100.0 for t in 1:4]
        @test sc.profiled_units_by_name["g7"].name == "g7"
-        pu2 = sc.profiled_units[2]
+        second_pu = sc.profiled_units[2]
-        @test pu2.name == "g8"
+        @test second_pu.name == "g8"
-        @test pu2.bus.name == "b5"
+        @test second_pu.bus.name == "b5"
-        @test pu2.cost == [50.0 for t in 1:4]
+        @test second_pu.cost == [50.0 for t in 1:4]
-        @test pu2.min_power == [0.0 for t in 1:4]
+        @test second_pu.min_power == [0.0 for t in 1:4]
-        @test pu2.max_power == [120.0 for t in 1:4]
+        @test second_pu.max_power == [120.0 for t in 1:4]
        @test sc.profiled_units_by_name["g8"].name == "g8"
    end
@@ -164,64 +165,4 @@ function instance_read_test()
        @test sc.thermal_units[6].commitment_status ==
              [false, nothing, true, nothing]
    end
    @testset "read_benchmark storage" begin
        instance = UnitCommitment.read(fixture("case14-storage.json.gz"))
        sc = instance.scenarios[1]
        @test length(sc.storage_units) == 4
        su1 = sc.storage_units[1]
        @test su1.name == "su1"
        @test su1.bus.name == "b2"
        @test su1.min_level == [0.0 for t in 1:4]
        @test su1.max_level == [100.0 for t in 1:4]
        @test su1.simultaneous_charge_and_discharge == [true for t in 1:4]
        @test su1.charge_cost == [2.0 for t in 1:4]
        @test su1.discharge_cost == [2.5 for t in 1:4]
        @test su1.charge_efficiency == [1.0 for t in 1:4]
        @test su1.discharge_efficiency == [1.0 for t in 1:4]
        @test su1.loss_factor == [0.0 for t in 1:4]
        @test su1.min_charge_rate == [0.0 for t in 1:4]
        @test su1.max_charge_rate == [10.0 for t in 1:4]
        @test su1.min_discharge_rate == [0.0 for t in 1:4]
        @test su1.max_discharge_rate == [8.0 for t in 1:4]
        @test su1.initial_level == 0.0
        @test su1.min_ending_level == 0.0
        @test su1.max_ending_level == 100.0
        @test sc.storage_units_by_name["su1"].name == "su1"
        su2 = sc.storage_units[2]
        @test su2.name == "su2"
        @test su2.bus.name == "b2"
        @test su2.min_level == [10.0 for t in 1:4]
        @test su2.simultaneous_charge_and_discharge == [false for t in 1:4]
        @test su2.charge_cost == [3.0 for t in 1:4]
        @test su2.discharge_cost == [3.5 for t in 1:4]
        @test su2.charge_efficiency == [0.8 for t in 1:4]
        @test su2.discharge_efficiency == [0.85 for t in 1:4]
        @test su2.loss_factor == [0.01 for t in 1:4]
        @test su2.min_charge_rate == [5.0 for t in 1:4]
        @test su2.min_discharge_rate == [2.0 for t in 1:4]
        @test su2.initial_level == 70.0
        @test su2.min_ending_level == 80.0
        @test su2.max_ending_level == 85.0
        @test sc.storage_units_by_name["su2"].name == "su2"
        su3 = sc.storage_units[3]
        @test su3.bus.name == "b9"
        @test su3.min_level == [10.0, 11.0, 12.0, 13.0]
        @test su3.max_level == [100.0, 110.0, 120.0, 130.0]
        @test su3.charge_cost == [2.0, 2.1, 2.2, 2.3]
        @test su3.discharge_cost == [1.0, 1.1, 1.2, 1.3]
        @test su3.charge_efficiency == [0.8, 0.81, 0.82, 0.82]
        @test su3.discharge_efficiency == [0.85, 0.86, 0.87, 0.88]
        @test su3.min_charge_rate == [5.0, 5.1, 5.2, 5.3]
        @test su3.max_charge_rate == [10.0, 10.1, 10.2, 10.3]
        @test su3.min_discharge_rate == [4.0, 4.1, 4.2, 4.3]
        @test su3.max_discharge_rate == [8.0, 8.1, 8.2, 8.3]
        su4 = sc.storage_units[4]
        @test su4.simultaneous_charge_and_discharge ==
              [false, false, true, true]
    end
 end
--- a/test/src/lmp/aelmp_test.jl
+++ b/test/src/lmp/aelmp_test.jl
@@ -12,10 +12,7 @@ function lmp_aelmp_test()
        instance = UnitCommitment.read(path)
        model = UnitCommitment.build_model(
            instance = instance,
-            optimizer = optimizer_with_attributes(
+            optimizer = Cbc.Optimizer,
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
            variable_names = true,
        )
        JuMP.set_silent(model)
@@ -25,10 +22,7 @@ function lmp_aelmp_test()
        aelmp_1 = UnitCommitment.compute_lmp(
            model,
            AELMP(),
-            optimizer = optimizer_with_attributes(
+            optimizer = HiGHS.Optimizer,
                HiGHS.Optimizer,
                "log_to_console" => false,
            ),
        )
        @test aelmp_1["s1", "B1", 1] ≈ 231.7 atol = 0.1
@@ -39,10 +33,7 @@ function lmp_aelmp_test()
                allow_offline_participation = false,
                consider_startup_costs = true,
            ),
-            optimizer = optimizer_with_attributes(
+            optimizer = HiGHS.Optimizer,
                HiGHS.Optimizer,
                "log_to_console" => false,
            ),
        )
        @test aelmp_2["s1", "B1", 1] ≈ 274.3 atol = 0.1
    end
--- a/test/src/lmp/conventional_test.jl
+++ b/test/src/lmp/conventional_test.jl
@@ -3,12 +3,13 @@
 # Released under the modified BSD license. See COPYING.md for more details.
 using UnitCommitment, Cbc, HiGHS, JuMP
 import UnitCommitment: ConventionalLMP
 function solve_conventional_testcase(path::String)
    instance = UnitCommitment.read(path)
    model = UnitCommitment.build_model(
        instance = instance,
-        optimizer = optimizer_with_attributes(Cbc.Optimizer, "logLevel" => 0),
+        optimizer = Cbc.Optimizer,
        variable_names = true,
    )
    JuMP.set_silent(model)
@@ -16,10 +17,7 @@ function solve_conventional_testcase(path::String)
    lmp = UnitCommitment.compute_lmp(
        model,
        ConventionalLMP(),
-        optimizer = optimizer_with_attributes(
+        optimizer = HiGHS.Optimizer,
            HiGHS.Optimizer,
            "log_to_console" => false,
        ),
    )
    return lmp
 end
--- a/test/src/market/market_test.jl
+++ b/test/src/market/market_test.jl
@@ -1,151 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using UnitCommitment, Cbc, HiGHS, JuMP
 import UnitCommitment: MarketSettings
 function simple_market_test()
    @testset "da-to-rt simple market" begin
        da_path = fixture("market_da_simple.json.gz")
        rt_paths = [
            fixture("market_rt1_simple.json.gz"),
            fixture("market_rt2_simple.json.gz"),
            fixture("market_rt3_simple.json.gz"),
            fixture("market_rt4_simple.json.gz"),
        ]
        # solve market with default setting
        solution = UnitCommitment.solve_market(
            da_path,
            rt_paths,
            MarketSettings(), # keep everything default
            optimizer = optimizer_with_attributes(
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
            lp_optimizer = optimizer_with_attributes(
                HiGHS.Optimizer,
                "log_to_console" => false,
            ),
        )
        # the commitment status must agree with DA market
        da_solution = solution["Day-ahead market"]
        @test da_solution["Is on"]["GenY"] == [0.0, 1.0]
        @test da_solution["Locational marginal price"][("s1", "B1", 1)] == 50.0
        @test da_solution["Locational marginal price"][("s1", "B1", 2)] == 56.0
        rt_solution = solution["Real-time markets"]
        @test length(rt_solution) == 4
        @test rt_solution[rt_paths[1]]["Is on"]["GenY"] == [0.0, 0.0]
        @test rt_solution[rt_paths[2]]["Is on"]["GenY"] == [0.0, 1.0]
        @test rt_solution[rt_paths[3]]["Is on"]["GenY"] == [1.0, 1.0]
        @test rt_solution[rt_paths[4]]["Is on"]["GenY"] == [1.0]
        @test length(rt_solution[rt_paths[1]]["Locational marginal price"]) == 2
        @test length(rt_solution[rt_paths[2]]["Locational marginal price"]) == 2
        @test length(rt_solution[rt_paths[3]]["Locational marginal price"]) == 2
        @test length(rt_solution[rt_paths[4]]["Locational marginal price"]) == 1
        # solve market with no lmp method
        solution_no_lmp = UnitCommitment.solve_market(
            da_path,
            rt_paths,
            MarketSettings(lmp_method = nothing), # no lmp
            optimizer = optimizer_with_attributes(
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
        )
        # the commitment status must agree with DA market
        da_solution = solution_no_lmp["Day-ahead market"]
        @test haskey(da_solution, "Locational marginal price") == false
        rt_solution = solution_no_lmp["Real-time markets"]
        @test haskey(rt_solution, "Locational marginal price") == false
    end
 end
 function stochastic_market_test()
    @testset "da-to-rt stochastic market" begin
        da_path = [
            fixture("market_da_simple.json.gz"),
            fixture("market_da_scenario.json.gz"),
        ]
        rt_paths = [
            fixture("market_rt1_simple.json.gz"),
            fixture("market_rt2_simple.json.gz"),
            fixture("market_rt3_simple.json.gz"),
            fixture("market_rt4_simple.json.gz"),
        ]
        # after build and after optimize 
        function after_build(model, instance)
            @constraint(model, model[:is_on]["GenY", 1] == 1,)
        end
        lmps_da = []
        lmps_rt = []
        function after_optimize_da(solution, model, instance)
            lmp = UnitCommitment.compute_lmp(
                model,
                ConventionalLMP(),
                optimizer = optimizer_with_attributes(
                    HiGHS.Optimizer,
                    "log_to_console" => false,
                ),
            )
            return push!(lmps_da, lmp)
        end
        function after_optimize_rt(solution, model, instance)
            lmp = UnitCommitment.compute_lmp(
                model,
                ConventionalLMP(),
                optimizer = optimizer_with_attributes(
                    HiGHS.Optimizer,
                    "log_to_console" => false,
                ),
            )
            return push!(lmps_rt, lmp)
        end
        # solve the stochastic market with callbacks
        solution = UnitCommitment.solve_market(
            da_path,
            rt_paths,
            MarketSettings(), # keep everything default
            optimizer = optimizer_with_attributes(
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
            lp_optimizer = optimizer_with_attributes(
                HiGHS.Optimizer,
                "log_to_console" => false,
            ),
            after_build_da = after_build,
            after_optimize_da = after_optimize_da,
            after_optimize_rt = after_optimize_rt,
        )
        # the commitment status must agree with DA market
        da_solution_sp = solution["Day-ahead market"]["market_da_simple"]
        da_solution_sc = solution["Day-ahead market"]["market_da_scenario"]
        @test da_solution_sc["Is on"]["GenY"] == [1.0, 1.0]
        @test da_solution_sp["Locational marginal price"][(
            "market_da_simple",
            "B1",
            1,
        )] == 25.0
        @test da_solution_sc["Locational marginal price"][(
            "market_da_scenario",
            "B1",
            2,
        )] == 0.0
        rt_solution = solution["Real-time markets"]
        @test rt_solution[rt_paths[1]]["Is on"]["GenY"] == [1.0, 1.0]
        @test rt_solution[rt_paths[2]]["Is on"]["GenY"] == [1.0, 1.0]
        @test rt_solution[rt_paths[3]]["Is on"]["GenY"] == [1.0, 1.0]
        @test rt_solution[rt_paths[4]]["Is on"]["GenY"] == [1.0]
        @test length(lmps_rt) == 4
    end
 end
--- a/test/src/solution/methods/MIPLearn/usage_test.jl
+++ b/test/src/solution/methods/MIPLearn/usage_test.jl
@@ -1,20 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using HiGHS
 function solution_methods_MIPLearn_usage_test()
    dirname = mktempdir()
    cp(fixture("case14.json.gz"), "$dirname/case14.json.gz")
    train_data = ["$dirname/case14.json.gz"]
    method = UnitCommitment.MIPLearnMethod(optimizer = HiGHS.Optimizer)
    UnitCommitment.collect!(train_data, method)
    UnitCommitment.fit!(train_data, method)
    UnitCommitment.optimize!(train_data[1], method)
    instance = UnitCommitment.read(train_data[1])
    UnitCommitment.optimize!(instance, method)
    return
 end
--- a/test/src/solution/methods/ProgressiveHedging/ph.jl
+++ b/test/src/solution/methods/ProgressiveHedging/ph.jl
@@ -1,40 +0,0 @@
 using HiGHS
 using MPI
 using JuMP
 using UnitCommitment
 UnitCommitment._setup_logger(level = Base.CoreLogging.Error)
 function fixture(path::String)::String
    basedir = dirname(@__FILE__)
    return "$basedir/../../../../fixtures/$path"
 end
 # Initialize MPI
 MPI.Init()
 # Configure progressive hedging method
 ph = UnitCommitment.ProgressiveHedging()
 # Read problem instance
 instance = UnitCommitment.read(
    [fixture("case14.json.gz"), fixture("case14.json.gz")],
    ph,
 )
 # Build JuMP model
 model = UnitCommitment.build_model(
    instance = instance,
    optimizer = optimizer_with_attributes(
        HiGHS.Optimizer,
        MOI.Silent() => true,
    ),
 )
 # Run the decentralized optimization algorithm
 UnitCommitment.optimize!(model, ph)
 # Fetch the solution
 solution = UnitCommitment.solution(model, ph)
 # Close MPI
 MPI.Finalize()
--- a/test/src/solution/methods/ProgressiveHedging/usage_test.jl
+++ b/test/src/solution/methods/ProgressiveHedging/usage_test.jl
@@ -1,16 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using MPI
 function solution_methods_ProgressiveHedging_usage_test()
    basedir = dirname(@__FILE__)
    @testset "ProgressiveHedging" begin
        mpiexec() do exe
            return run(
                `$exe -n 2 $(Base.julia_cmd()) --project=test $basedir/ph.jl`,
            )
        end
    end
 end
--- a/test/src/solution/methods/TimeDecomposition/initial_status_test.jl
+++ b/test/src/solution/methods/TimeDecomposition/initial_status_test.jl
@@ -1,159 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using UnitCommitment, DataStructures
 function solution_methods_TimeDecomposition_initial_status_test()
    @testset "determine_initial_status" begin
        hot_start = 100
        cold_start = -100
        # all on throughout
        stat_seq = ones(36)
        # hot start
        new_stat = UnitCommitment._determine_initial_status(hot_start, stat_seq)
        @test new_stat == 136
        # cold start
        new_stat =
            UnitCommitment._determine_initial_status(cold_start, stat_seq)
        @test new_stat == 36
        # off in the last 12 periods
        stat_seq = ones(36)
        stat_seq[25:end] .= 0
        # hot start
        new_stat = UnitCommitment._determine_initial_status(hot_start, stat_seq)
        @test new_stat == -12
        # cold start
        new_stat =
            UnitCommitment._determine_initial_status(cold_start, stat_seq)
        @test new_stat == -12
        # off in one period
        stat_seq = ones(36)
        stat_seq[10] = 0
        # hot start
        new_stat = UnitCommitment._determine_initial_status(hot_start, stat_seq)
        @test new_stat == 26
        # cold start
        new_stat =
            UnitCommitment._determine_initial_status(cold_start, stat_seq)
        @test new_stat == 26
        # off in several of the first 24 periods
        stat_seq = ones(36)
        stat_seq[[10, 11, 20]] .= 0
        # hot start
        new_stat = UnitCommitment._determine_initial_status(hot_start, stat_seq)
        @test new_stat == 16
        # cold start
        new_stat =
            UnitCommitment._determine_initial_status(cold_start, stat_seq)
        @test new_stat == 16
        # all off throughout
        stat_seq = zeros(36)
        # hot start
        new_stat = UnitCommitment._determine_initial_status(hot_start, stat_seq)
        @test new_stat == -36
        # cold start
        new_stat =
            UnitCommitment._determine_initial_status(cold_start, stat_seq)
        @test new_stat == -136
        # on in the last 12 periods
        stat_seq = zeros(36)
        stat_seq[25:end] .= 1
        # hot start
        new_stat = UnitCommitment._determine_initial_status(hot_start, stat_seq)
        @test new_stat == 12
        # cold start
        new_stat =
            UnitCommitment._determine_initial_status(cold_start, stat_seq)
        @test new_stat == 12
    end
    @testset "set_initial_status" begin
        # read one scenario
        instance = UnitCommitment.read(fixture("case14.json.gz"))
        psuedo_solution = OrderedDict(
            "Thermal production (MW)" => OrderedDict(
                "g1" => [0.0, 112.0, 114.0, 116.0],
                "g2" => [0.0, 102.0, 0.0, 0.0],
                "g3" => [0.0, 0.0, 0.0, 0.0],
                "g4" => [0.0, 34.0, 66.0, 99.0],
                "g5" => [0.0, 34.0, 66.0, 99.0],
                "g6" => [0.0, 100.0, 100.0, 100.0],
            ),
            "Is on" => OrderedDict(
                "g1" => [0.0, 1.0, 1.0, 1.0],
                "g2" => [0.0, 1.0, 0.0, 0.0],
                "g3" => [0.0, 0.0, 0.0, 0.0],
                "g4" => [0.0, 1.0, 1.0, 1.0],
                "g5" => [0.0, 1.0, 1.0, 1.0],
                "g6" => [0.0, 1.0, 1.0, 1.0],
            ),
        )
        UnitCommitment._set_initial_status!(instance, psuedo_solution, 3)
        thermal_units = instance.scenarios[1].thermal_units
        @test thermal_units[1].initial_power == 116.0
        @test thermal_units[1].initial_status == 3.0
        @test thermal_units[2].initial_power == 0.0
        @test thermal_units[2].initial_status == -2.0
        @test thermal_units[3].initial_power == 0.0
        @test thermal_units[3].initial_status == -9.0
        # read multiple scenarios
        instance = UnitCommitment.read([
            fixture("case14.json.gz"),
            fixture("case14-profiled.json.gz"),
        ])
        psuedo_solution = OrderedDict(
            "case14" => OrderedDict(
                "Thermal production (MW)" => OrderedDict(
                    "g1" => [0.0, 112.0, 114.0, 116.0],
                    "g2" => [0.0, 102.0, 0.0, 0.0],
                    "g3" => [0.0, 0.0, 0.0, 0.0],
                    "g4" => [0.0, 34.0, 66.0, 99.0],
                    "g5" => [0.0, 34.0, 66.0, 99.0],
                    "g6" => [0.0, 100.0, 100.0, 100.0],
                ),
                "Is on" => OrderedDict(
                    "g1" => [0.0, 1.0, 1.0, 1.0],
                    "g2" => [0.0, 1.0, 0.0, 0.0],
                    "g3" => [0.0, 0.0, 0.0, 0.0],
                    "g4" => [0.0, 1.0, 1.0, 1.0],
                    "g5" => [0.0, 1.0, 1.0, 1.0],
                    "g6" => [0.0, 1.0, 1.0, 1.0],
                ),
            ),
            "case14-profiled" => OrderedDict(
                "Thermal production (MW)" => OrderedDict(
                    "g1" => [0.0, 113.0, 116.0, 115.0],
                    "g2" => [0.0, 0.0, 0.0, 0.0],
                    "g3" => [0.0, 0.0, 0.0, 20.0],
                    "g4" => [0.0, 34.0, 66.0, 98.0],
                    "g5" => [0.0, 34.0, 66.0, 97.0],
                    "g6" => [0.0, 100.0, 100.0, 100.0],
                ),
                "Is on" => OrderedDict(
                    "g1" => [0.0, 1.0, 1.0, 1.0],
                    "g2" => [0.0, 0.0, 0.0, 0.0],
                    "g3" => [0.0, 0.0, 0.0, 1.0],
                    "g4" => [0.0, 1.0, 1.0, 1.0],
                    "g5" => [0.0, 1.0, 1.0, 1.0],
                    "g6" => [0.0, 1.0, 1.0, 1.0],
                ),
            ),
        )
        UnitCommitment._set_initial_status!(instance, psuedo_solution, 3)
        thermal_units_sc2 = instance.scenarios[2].thermal_units
        @test thermal_units_sc2[1].initial_power == 115.0
        @test thermal_units_sc2[1].initial_status == 3.0
        @test thermal_units_sc2[2].initial_power == 0.0
        @test thermal_units_sc2[2].initial_status == -11.0
        @test thermal_units_sc2[3].initial_power == 20.0
        @test thermal_units_sc2[3].initial_status == 1.0
    end
 end
--- a/test/src/solution/methods/TimeDecomposition/optimize_test.jl
+++ b/test/src/solution/methods/TimeDecomposition/optimize_test.jl
@@ -1,88 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using UnitCommitment, DataStructures, Cbc, HiGHS
 import UnitCommitment: TimeDecomposition, ConventionalLMP
 function solution_methods_TimeDecomposition_optimize_test()
    @testset "optimize_time_decomposition" begin
        # read one scenario
        instance = UnitCommitment.read(fixture("case14.json.gz"))
        solution = UnitCommitment.optimize!(
            instance,
            TimeDecomposition(time_window = 3, time_increment = 2),
            optimizer = optimizer_with_attributes(
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
        )
        @test length(solution["Thermal production (MW)"]["g1"]) == 4
        @test length(solution["Is on"]["g2"]) == 4
        @test length(solution["Spinning reserve (MW)"]["r1"]["g2"]) == 4
        # read one scenario with after_build and after_optimize
        function after_build(model, instance)
            @constraint(
                model,
                model[:is_on]["g3", 1] + model[:is_on]["g4", 1] <= 1,
            )
        end
        lmps = []
        function after_optimize(solution, model, instance)
            lmp = UnitCommitment.compute_lmp(
                model,
                ConventionalLMP(),
                optimizer = optimizer_with_attributes(
                    HiGHS.Optimizer,
                    "log_to_console" => false,
                ),
            )
            return push!(lmps, lmp)
        end
        instance = UnitCommitment.read(fixture("case14-profiled.json.gz"))
        solution = UnitCommitment.optimize!(
            instance,
            TimeDecomposition(time_window = 3, time_increment = 2),
            optimizer = optimizer_with_attributes(
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
            after_build = after_build,
            after_optimize = after_optimize,
        )
        @test length(lmps) == 2
        @test lmps[1]["s1", "b1", 1] == 50.0
        @test lmps[2]["s1", "b10", 2] ≈ 38.04 atol = 0.1
        @test solution["Is on"]["g3"][1] == 1.0
        @test solution["Is on"]["g4"][1] == 0.0
        # read multiple scenarios
        instance = UnitCommitment.read([
            fixture("case14.json.gz"),
            fixture("case14-profiled.json.gz"),
        ])
        solution = UnitCommitment.optimize!(
            instance,
            TimeDecomposition(time_window = 3, time_increment = 2),
            optimizer = optimizer_with_attributes(
                Cbc.Optimizer,
                "logLevel" => 0,
            ),
        )
        @test length(solution["case14"]["Thermal production (MW)"]["g3"]) == 4
        @test length(solution["case14"]["Is on"]["g4"]) == 4
        @test length(
            solution["case14-profiled"]["Thermal production (MW)"]["g5"],
        ) == 4
        @test length(solution["case14-profiled"]["Is on"]["g6"]) == 4
        @test length(
            solution["case14-profiled"]["Profiled production (MW)"]["g7"],
        ) == 4
        @test length(
            solution["case14-profiled"]["Spinning reserve (MW)"]["r1"]["g3"],
        ) == 4
    end
 end
--- a/test/src/solution/methods/TimeDecomposition/update_solution_test.jl
+++ b/test/src/solution/methods/TimeDecomposition/update_solution_test.jl
@@ -1,55 +0,0 @@
 # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
 using UnitCommitment, DataStructures
 function solution_methods_TimeDecomposition_update_solution_test()
    @testset "update_solution" begin
        psuedo_solution = OrderedDict()
        time_increment = 4
        psuedo_sub_solution = OrderedDict(
            "Thermal production (MW)" => OrderedDict(
                "g1" => [100.0, 200.0, 300.0, 400.0, 500.0, 600.0],
            ),
            "Is on" => OrderedDict("g1" => [1.0, 0.0, 1.0, 1.0, 0.0, 1.0]),
            "Profiled production (MW)" => OrderedDict(
                "g1" => [199.0, 299.0, 399.0, 499.0, 599.0, 699.0],
            ),
            "Spinning reserve (MW)" => OrderedDict(
                "r1" => OrderedDict(
                    "g1" => [31.0, 32.0, 33.0, 34.0, 35.0, 36.0],
                ),
            ),
        )
        # first update should directly copy the first 4 entries of sub solution
        UnitCommitment._update_solution!(
            psuedo_solution,
            psuedo_sub_solution,
            time_increment,
        )
        @test psuedo_solution["Thermal production (MW)"]["g1"] ==
              [100.0, 200.0, 300.0, 400.0]
        @test psuedo_solution["Is on"]["g1"] == [1.0, 0.0, 1.0, 1.0]
        @test psuedo_solution["Profiled production (MW)"]["g1"] ==
              [199.0, 299.0, 399.0, 499.0]
        @test psuedo_solution["Spinning reserve (MW)"]["r1"]["g1"] ==
              [31.0, 32.0, 33.0, 34.0]
        # second update should append the first 4 entries of sub solution
        UnitCommitment._update_solution!(
            psuedo_solution,
            psuedo_sub_solution,
            time_increment,
        )
        @test psuedo_solution["Thermal production (MW)"]["g1"] ==
              [100.0, 200.0, 300.0, 400.0, 100.0, 200.0, 300.0, 400.0]
        @test psuedo_solution["Is on"]["g1"] ==
              [1.0, 0.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0]
        @test psuedo_solution["Profiled production (MW)"]["g1"] ==
              [199.0, 299.0, 399.0, 499.0, 199.0, 299.0, 399.0, 499.0]
        @test psuedo_solution["Spinning reserve (MW)"]["r1"]["g1"] ==
              [31.0, 32.0, 33.0, 34.0, 31.0, 32.0, 33.0, 34.0]
    end
 end
--- a/test/src/transform/initcond_test.jl
+++ b/test/src/transform/initcond_test.jl
@@ -2,32 +2,27 @@
 # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
 # Released under the modified BSD license. See COPYING.md for more details.
-using UnitCommitment, HiGHS, JuMP
+using UnitCommitment, Cbc, JuMP
 function transform_initcond_test()
    @testset "generate_initial_conditions!" begin
        # Load instance
        instance = UnitCommitment.read(fixture("case118-initcond.json.gz"))
-        optimizer =
+        optimizer = optimizer_with_attributes(Cbc.Optimizer, "logLevel" => 0)
-            optimizer_with_attributes(HiGHS.Optimizer, MOI.Silent() => true)
+        sc = instance.scenarios[1]
        # All units should have unknown initial conditions
-        for sc in instance.scenarios
+        for g in sc.thermal_units
-            for g in sc.thermal_units
+            @test g.initial_power === nothing
-                @test g.initial_power === nothing
+            @test g.initial_status === nothing
                @test g.initial_status === nothing
            end
        end
        # Generate initial conditions
-        UnitCommitment.generate_initial_conditions!(instance, optimizer)
+        UnitCommitment.generate_initial_conditions!(sc, optimizer)
        # All units should now have known initial conditions
-        for sc in instance.scenarios
+        for g in sc.thermal_units
-            for g in sc.thermal_units
+            @test g.initial_power !== nothing
-                @test g.initial_power !== nothing
+            @test g.initial_status !== nothing
                @test g.initial_status !== nothing
            end
        end
        # TODO: Check that initial conditions are feasible
--- a/test/src/transform/randomize/XavQiuAhm2021_test.jl
+++ b/test/src/transform/randomize/XavQiuAhm2021_test.jl
@@ -102,28 +102,5 @@ function transform_randomize_XavQiuAhm2021_test()
            test_approx(pu1.cost[1], 98.039)
            test_approx(pu2.cost[1], 48.385)
        end
        @testset "storage unit cost" begin
            sc = UnitCommitment.read(
                fixture("case14-storage.json.gz"),
            ).scenarios[1]
            # Check original costs
            su1 = sc.storage_units[1]
            su3 = sc.storage_units[3]
            test_approx(su1.charge_cost[4], 2.0)
            test_approx(su1.discharge_cost[1], 2.5)
            test_approx(su3.charge_cost[2], 2.1)
            test_approx(su3.discharge_cost[3], 1.2)
            randomize!(
                sc,
                XavQiuAhm2021.Randomization(randomize_load_profile = false),
                rng = MersenneTwister(42),
            )
            # Check randomized costs
            test_approx(su1.charge_cost[4], 1.961)
            test_approx(su1.discharge_cost[1], 2.451)
            test_approx(su3.charge_cost[2], 2.196)
            test_approx(su3.discharge_cost[3], 1.255)
        end
    end
 end
--- a/test/src/transform/slice_test.jl
+++ b/test/src/transform/slice_test.jl
@@ -65,34 +65,4 @@ function transform_slice_test()
            variable_names = true,
        )
    end
    @testset "slice storage units" begin
        instance = UnitCommitment.read(fixture("case14-storage.json.gz"))
        modified = UnitCommitment.slice(instance, 2:4)
        sc = modified.scenarios[1]
        # Should update all time-dependent fields
        for su in sc.storage_units
            @test length(su.min_level) == 3
            @test length(su.max_level) == 3
            @test length(su.simultaneous_charge_and_discharge) == 3
            @test length(su.charge_cost) == 3
            @test length(su.discharge_cost) == 3
            @test length(su.charge_efficiency) == 3
            @test length(su.discharge_efficiency) == 3
            @test length(su.loss_factor) == 3
            @test length(su.min_charge_rate) == 3
            @test length(su.max_charge_rate) == 3
            @test length(su.min_discharge_rate) == 3
            @test length(su.max_discharge_rate) == 3
        end
        # Should be able to build model without errors
        optimizer = optimizer_with_attributes(Cbc.Optimizer, "logLevel" => 0)
        model = UnitCommitment.build_model(
            instance = modified,
            optimizer = optimizer,
            variable_names = true,
        )
    end
 end