Implement transportation emissions

docs/src/problem.md

@@ -39,6 +39,7 @@ The mathematical model employed by RELOG is based on three main components:
 | $C$      | Set of collection and distribution centers                                                                                                          |
 | $P$      | Set of manufacturing and recycling plants                                                                                                           |
 | $M$      | Set of products and materials                                                                                                                       |
+| $G$      | Set of greenhouse gases                                                                                                                             |
 | $M^+_u$  | Set of output products of plant/center $u$.                                                                                                         |
 | $M^-_u$  | Set of input products of plant/center $u$.                                                                                                          |
 | $T$      | Set of time periods in the planning horizon. We assume $T=\{1,\ldots,t^{max}\}.$                                                                    |
@@ -49,13 +50,14 @@ The mathematical model employed by RELOG is based on three main components:
 ## Constants
 
 | Symbol                      | Description                                                                                                                                                                                                      | Unit           |
-| :-------------------------- | :--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | :---------- |
+| :-------------------------- | :--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | :------------- |
 | $K^{\text{dist}}_{uv}$      | Distance between plants/centers $u$ and $v$                                                                                                                                                                      | km             |
 | $K^\text{cap}_{p}$          | Capacity of plant $p$, if the plant is open                                                                                                                                                                      | tonne          |
 | $K^\text{disp-limit}_{mt}$  | Maximum amount of material $m$ that can be disposed of (globally) at time $t$                                                                                                                                    | tonne          |
 | $K^\text{disp-limit}_{mut}$ | Maximum amount of material $m$ that can be disposed of at plant/center $u$ at time $t$                                                                                                                           | tonne          |
 | $K^\text{mix}_{pmt}$        | If plant $p$ receives one tonne of input material at time $t$, then $K^\text{mix}_{pmt}$ is the amount of product $m$ in this mix. Must be between zero and one, and the sum of these amounts must equal to one. | tonne          |
 | $K^\text{output}_{pmt}$     | Amount of material $m$ produced by plant $p$ at time $t$ for each tonne of input material processed                                                                                                              | tonne          |
+| $K^\text{tr-em}_{gmt}$      | Amount of greenhouse gas $g$ released by transporting 1 tonne of material $m$ over one km at time $t$                                                                                                            | tonne/km-tonne |
 | $R^\text{tr}_{mt}$          | Cost to send material $m$ at time $t$                                                                                                                                                                            | \$/km-tonne    |
 | $R^\text{collect}_{cmt}$    | Cost of collecting material $m$ at center $c$ at time $t$                                                                                                                                                        | \$/tonne       |
 | $R^\text{disp}_{umt}$       | Cost to dispose of material at plant/center $u$ at time $t$                                                                                                                                                      | \$/tonne       |
@@ -70,13 +72,14 @@ The mathematical model employed by RELOG is based on three main components:
 ## Decision variables
 
 | Symbol                       | JuMP name                                    | Description                                                                                             | Unit   |
-| :--------------------------- | :------------------------------- | :------------------------------------------------------------------------------- | :----- |
+| :--------------------------- | :------------------------------------------- | :------------------------------------------------------------------------------------------------------ | :----- |
 | $x_{pt}$                     | `x[p.name, t]`                               | One if plant $p$ is operational at time $t$                                                             | binary |
 | $y_{uvmt}$                   | `y[u.name, v.name, m.name, t]`               | Amount of product $m$ sent from plant/center $u$ to plant/center $v$ at time $t$                        | tonne  |
 | $z^{\text{collected}}_{cmt}$ | `z_collected[c.name, m.name, t]`             | Amount of material $m$ collected by center $c$ at time $t$                                              | tonne  |
 | $z^{\text{disp}}_{umt}$      | `z_disp[u.name, m.name, t]`                  | Amount of product $m$ disposed of at plant/center $u$ at time $t$                                       | tonne  |
 | $z^{\text{input}}_{ut}$      | `z_input[u.name, t]`                         | Total plant/center input at time $t$                                                                    | tonne  |
 | $z^{\text{prod}}_{umt}$      | `z_prod[u.name, m.name, t]`                  | Amount of product $m$ produced by plant/center $u$ at time $t$                                          | tonne  |
+| $z^{\text{tr-em}}_{guvmt}$   | `z_tr_em[g.name, u.name, v.name, m.name, t]` | Amount of greenhouse gas $g$ released at time $t$ due to transportation of material $m$ from $u$ to $v$ | tonne  |
 
 ## Objective function
 
@@ -265,3 +268,12 @@ The goals is to minimize a linear objective function with the following terms:
 & \forall m \in M, t \in T
 \end{align*}
 ```
+
+- Computation of transportation emissions (`eq_tr_em[g.name, u.name, v.name, m.name, t`)
+
+```math
+\begin{align*}
+& z^{\text{tr-em}}_{guvmt} = K^{\text{dist}}_{uv} K^\text{tr-em}_{gmt} y_{uvmt}
+& \forall g \in G, (u, v, m) \in E, t \in T
+\end{align*}
+```

src/instance/parse.jl

@@ -20,10 +20,11 @@ function parse(json)::Instance
         error("Invalid distance metric: $distance_metric_str")
     end
 
-    timeseries(::Nothing; null_val=nothing) = repeat([null_val], time_horizon)
+    timeseries(::Nothing; null_val = nothing) = repeat([null_val], time_horizon)
-    timeseries(x::Number; null_val=nothing) = repeat([x], time_horizon)
+    timeseries(x::Number; null_val = nothing) = repeat([x], time_horizon)
-    timeseries(x::Array; null_val=nothing) = [xi === nothing ? null_val : xi for xi in x]
+    timeseries(x::Array; null_val = nothing) = [xi === nothing ? null_val : xi for xi in x]
-    timeseries(d::OrderedDict; null_val=nothing) = OrderedDict(k => timeseries(v; null_val) for (k, v) in d)
+    timeseries(d::OrderedDict; null_val = nothing) =
+        OrderedDict(k => timeseries(v; null_val) for (k, v) in d)
 
     # Read products
     products = Product[]
@@ -32,7 +33,7 @@ function parse(json)::Instance
         tr_cost = timeseries(pdict["transportation cost (\$/km/tonne)"])
         tr_energy = timeseries(pdict["transportation energy (J/km/tonne)"])
         tr_emissions = timeseries(pdict["transportation emissions (tonne/km/tonne)"])
-        disposal_limit = timeseries(pdict["disposal limit (tonne)"], null_val=Inf)
+        disposal_limit = timeseries(pdict["disposal limit (tonne)"], null_val = Inf)
         prod = Product(; name, tr_cost, tr_energy, tr_emissions, disposal_limit)
         push!(products, prod)
         products_by_name[name] = prod
@@ -52,10 +53,8 @@ function parse(json)::Instance
         end
         outputs = [products_by_name[p] for p in cdict["outputs"]]
         operating_cost = timeseries(cdict["operating cost (\$)"])
-        prod_dict(key, null_val) = OrderedDict(
+        prod_dict(key, null_val) =
-            p => timeseries(cdict[key][p.name]; null_val)
+            OrderedDict(p => timeseries(cdict[key][p.name]; null_val) for p in outputs)
-            for p in outputs
-        )
         fixed_output = prod_dict("fixed output (tonne)", 0.0)
         var_output = prod_dict("variable output (tonne/tonne)", 0.0)
         collection_cost = prod_dict("collection cost (\$/tonne)", 0.0)

src/model/build.jl

@@ -118,6 +118,12 @@ function build_model(instance::Instance; optimizer, variable_names::Bool = false
         z_collected[c.name, m.name, t] = @variable(model, lower_bound = 0)
     end
 
+    # Transportation emissions by greenhouse gas
+    z_tr_em = _init(model, :z_tr_em)
+    for (p1, p2, m) in E, t in T, g in keys(m.tr_emissions)
+        z_tr_em[g, p1.name, p2.name, m.name, t] = @variable(model, lower_bound = 0)
+    end
+
 
     # Objective function
     # -------------------------------------------------------------------------
@@ -310,6 +316,16 @@ function build_model(instance::Instance; optimizer, variable_names::Bool = false
         )
     end
 
+    # Transportation emissions
+    eq_tr_em = _init(model, :eq_tr_em)
+    for (p1, p2, m) in E, t in T, g in keys(m.tr_emissions)
+        eq_tr_em[g, p1.name, p2.name, m.name, t] = @constraint(
+            model,
+            z_tr_em[g, p1.name, p2.name, m.name, t] ==
+            distances[p1, p2, m] * m.tr_emissions[g][t] * y[p1.name, p2.name, m.name, t]
+        )
+    end
+
     if variable_names
         _set_names!(model)
     end

src/reports/transportation.jl

@@ -52,5 +52,48 @@ function transportation_report(model)::DataFrame
     return df
 end
 
+function transportation_emissions_report(model)::DataFrame
+    df = DataFrame()
+    df."source" = String[]
+    df."destination" = String[]
+    df."product" = String[]
+    df."emission" = String[]
+    df."year" = Int[]
+    df."amount sent (tonne)" = Float64[]
+    df."distance (km)" = Float64[]
+    df."emission factor (tonne/km/tonne)" = Float64[]
+    df."emission amount (tonne)" = Float64[]
+
+    E = model.ext[:E]
+    distances = model.ext[:distances]
+    T = 1:model.ext[:instance].time_horizon
+
+    for (p1, p2, m) in E, t in T, g in keys(m.tr_emissions)
+        amount = value(model[:y][p1.name, p2.name, m.name, t])
+        amount > 1e-3 || continue
+        distance = distances[p1, p2, m]
+        emission_factor = m.tr_emissions[g][t]
+        emissions = value(model[:z_tr_em][g, p1.name, p2.name, m.name, t])
+        push!(
+            df,
+            Dict(
+                "source" => p1.name,
+                "destination" => p2.name,
+                "product" => m.name,
+                "emission" => g,
+                "year" => t,
+                "amount sent (tonne)" => _round(amount),
+                "distance (km)" => _round(distance),
+                "emission factor (tonne/km/tonne)" => _round(emission_factor),
+                "emission amount (tonne)" => _round(emissions),
+            ),
+        )
+    end
+    return df
+end
+
 write_transportation_report(solution, filename) =
     CSV.write(filename, transportation_report(solution))
+
+write_transportation_emissions_report(solution, filename) =
+    CSV.write(filename, transportation_emissions_report(solution))

test/fixtures/boat_example.jl

@@ -68,7 +68,8 @@ function run_boat_example()
     prod = dict(
         "transportation cost (\$/km/tonne)" => 0.30,
         "transportation energy (J/km/tonne)" => 7_500,
-        "transportation emissions (tonne/km/tonne)" => dict("CO2" => 2.68),
+        "transportation emissions (tonne/km/tonne)" =>
+            dict("CO2" => 2.68, "NH4" => 1.02),
         "disposal limit (tonne)" => nothing,
     )
 
@@ -176,6 +177,10 @@ function run_boat_example()
     RELOG.write_centers_report(model, fixture("boat_example/centers.csv"))
     RELOG.write_center_outputs_report(model, fixture("boat_example/center_outputs.csv"))
     RELOG.write_transportation_report(model, fixture("boat_example/transportation.csv"))
+    RELOG.write_transportation_emissions_report(
+        model,
+        fixture("boat_example/tr_emissions.csv"),
+    )
 
     return
 end

test/fixtures/boat_example.json

@@ -11,7 +11,8 @@
       "transportation cost ($/km/tonne)": 0.3,
       "transportation energy (J/km/tonne)": 7500,
       "transportation emissions (tonne/km/tonne)": {
-        "CO2": 2.68
+        "CO2": 2.68,
+        "NH4": 1.02
       },
       "disposal limit (tonne)": null
     },
@@ -19,7 +20,8 @@
       "transportation cost ($/km/tonne)": 0.3,
       "transportation energy (J/km/tonne)": 7500,
       "transportation emissions (tonne/km/tonne)": {
-        "CO2": 2.68
+        "CO2": 2.68,
+        "NH4": 1.02
       },
       "disposal limit (tonne)": null
     },
@@ -27,7 +29,8 @@
       "transportation cost ($/km/tonne)": 0.3,
       "transportation energy (J/km/tonne)": 7500,
       "transportation emissions (tonne/km/tonne)": {
-        "CO2": 2.68
+        "CO2": 2.68,
+        "NH4": 1.02
       },
       "disposal limit (tonne)": null
     },
@@ -35,7 +38,8 @@
       "transportation cost ($/km/tonne)": 0.3,
       "transportation energy (J/km/tonne)": 7500,
       "transportation emissions (tonne/km/tonne)": {
-        "CO2": 2.68
+        "CO2": 2.68,
+        "NH4": 1.02
       },
       "disposal limit (tonne)": null
     }

test/fixtures/boat_example/tr_emissions.csv

@@ -0,0 +1,81 @@
+source,destination,product,emission,year,amount sent (tonne),distance (km),emission factor (tonne/km/tonne),emission amount (tonne)
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,CO2,1,0.15789,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,NH4,1,0.15789,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,CO2,2,0.57341,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,NH4,2,0.57341,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,CO2,3,0.79428,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,NH4,3,0.79428,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,CO2,4,0.84522,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,NH4,4,0.84522,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,CO2,5,0.86354,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Nail,NH4,5,0.86354,0.0,1.02,0.0
+NailFactory (Chicago),BoatFactory (Dallas),Nail,CO2,1,1.0,1293.093,2.68,3465.48924
+NailFactory (Chicago),BoatFactory (Dallas),Nail,NH4,1,1.0,1293.093,1.02,1318.95486
+NailFactory (Chicago),BoatFactory (Dallas),Nail,CO2,2,1.0,1293.093,2.68,3465.48924
+NailFactory (Chicago),BoatFactory (Dallas),Nail,NH4,2,1.0,1293.093,1.02,1318.95486
+NailFactory (Chicago),BoatFactory (Dallas),Nail,CO2,3,1.0,1293.093,2.68,3465.48924
+NailFactory (Chicago),BoatFactory (Dallas),Nail,NH4,3,1.0,1293.093,1.02,1318.95486
+NailFactory (Chicago),BoatFactory (Dallas),Nail,CO2,4,1.0,1293.093,2.68,3465.48924
+NailFactory (Chicago),BoatFactory (Dallas),Nail,NH4,4,1.0,1293.093,1.02,1318.95486
+NailFactory (Chicago),BoatFactory (Dallas),Nail,CO2,5,1.0,1293.093,2.68,3465.48924
+NailFactory (Chicago),BoatFactory (Dallas),Nail,NH4,5,1.0,1293.093,1.02,1318.95486
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,CO2,1,1.0,1423.57,2.68,3815.1676
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,NH4,1,1.0,1423.57,1.02,1452.0414
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,CO2,2,1.0,1423.57,2.68,3815.1676
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,NH4,2,1.0,1423.57,1.02,1452.0414
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,CO2,3,1.0,1423.57,2.68,3815.1676
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,NH4,3,1.0,1423.57,1.02,1452.0414
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,CO2,4,1.0,1423.57,2.68,3815.1676
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,NH4,4,1.0,1423.57,1.02,1452.0414
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,CO2,5,1.0,1423.57,2.68,3815.1676
+NailFactory (Phoenix),BoatFactory (Dallas),Nail,NH4,5,1.0,1423.57,1.02,1452.0414
+NailFactory (Dallas),BoatFactory (Dallas),Nail,CO2,1,1.0,0.0,2.68,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,NH4,1,1.0,0.0,1.02,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,CO2,2,1.0,0.0,2.68,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,NH4,2,1.0,0.0,1.02,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,CO2,3,1.0,0.0,2.68,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,NH4,3,1.0,0.0,1.02,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,CO2,4,1.0,0.0,2.68,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,NH4,4,1.0,0.0,1.02,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,CO2,5,1.0,0.0,2.68,0.0
+NailFactory (Dallas),BoatFactory (Dallas),Nail,NH4,5,1.0,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,CO2,1,3.0,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,NH4,1,3.0,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,CO2,2,10.89474,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,NH4,2,10.89474,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,CO2,3,15.09141,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,NH4,3,15.09141,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,CO2,4,16.05912,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,NH4,4,16.05912,0.0,1.02,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,CO2,5,16.40733,0.0,2.68,0.0
+RecyclingPlant (Dallas),BoatFactory (Dallas),Wood,NH4,5,16.40733,0.0,1.02,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,CO2,1,57.0,0.0,2.68,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,NH4,1,57.0,0.0,1.02,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,CO2,2,57.0,0.0,2.68,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,NH4,2,57.0,0.0,1.02,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,CO2,3,57.0,0.0,2.68,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,NH4,3,57.0,0.0,1.02,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,CO2,4,57.0,0.0,2.68,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,NH4,4,57.0,0.0,1.02,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,CO2,5,57.0,0.0,2.68,0.0
+Forest (Dallas),BoatFactory (Dallas),Wood,NH4,5,57.0,0.0,1.02,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,CO2,1,63.15789,0.0,2.68,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,NH4,1,63.15789,0.0,1.02,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,CO2,2,71.46814,0.0,2.68,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,NH4,2,71.46814,0.0,1.02,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,CO2,3,75.8857,0.0,2.68,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,NH4,3,75.8857,0.0,1.02,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,CO2,4,76.90434,0.0,2.68,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,NH4,4,76.90434,0.0,1.02,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,CO2,5,77.27087,0.0,2.68,0.0
+BoatFactory (Dallas),Retail (Dallas),NewBoat,NH4,5,77.27087,0.0,1.02,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,CO2,1,6.31579,0.0,2.68,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,NH4,1,6.31579,0.0,1.02,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,CO2,2,22.93629,0.0,2.68,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,NH4,2,22.93629,0.0,1.02,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,CO2,3,31.7714,0.0,2.68,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,NH4,3,31.7714,0.0,1.02,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,CO2,4,33.80867,0.0,2.68,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,NH4,4,33.80867,0.0,1.02,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,CO2,5,34.54174,0.0,2.68,0.0
+Retail (Dallas),RecyclingPlant (Dallas),UsedBoat,NH4,5,34.54174,0.0,1.02,0.0

test/src/model/build_test.jl

@@ -9,6 +9,7 @@ function model_build_test()
     y = model[:y]
     z_disp = model[:z_disp]
     z_input = model[:z_input]
+    z_tr_em = model[:z_tr_em]
     x = model[:x]
     obj = objective_function(model)
     # print(model)
@@ -44,6 +45,12 @@ function model_build_test()
         300 # fixed operating cost
     )
 
+    # Variables: Transportation emissions
+    @test haskey(z_tr_em, ("CO2", "L1", "C3", "P4", 1))
+    @test haskey(z_tr_em, ("CH4", "L1", "C3", "P4", 1))
+    @test haskey(z_tr_em, ("CO2", "C2", "L1", "P1", 1))
+    @test haskey(z_tr_em, ("CH4", "C2", "L1", "P1", 1))
+
     # Plants: Definition of total plant input
     @test repr(model[:eq_z_input]["L1", 1]) ==
           "eq_z_input[L1,1] : -y[C2,L1,P1,1] - y[C1,L1,P2,1] + z_input[L1,1] = 0"
@@ -118,4 +125,8 @@ function model_build_test()
     @test repr(model[:eq_disposal_limit]["P3", 1]) ==
           "eq_disposal_limit[P3,1] : z_disp[L1,P3,1] + z_disp[C1,P3,1] ≤ 5"
     @test ("P4", 1) ∉ keys(model[:eq_disposal_limit])
+
+    # Products: Transportation emissions
+    @test repr(model[:eq_tr_em]["CH4", "L1", "C3", "P4", 1]) ==
+          "eq_tr_em[CH4,L1,C3,P4,1] : -0.333354 y[L1,C3,P4,1] + z_tr_em[CH4,L1,C3,P4,1] = 0"
 end