Initial version

v0.1
Alinson S. Xavier 6 years ago
commit ab644377b6

2
.gitignore vendored

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.ipynb*
*.ipynb

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name = "ReverseManufacturing"
uuid = "a2afcdf7-cf04-4913-85f9-c0d81ddf2008"
authors = ["Alinson S Xavier <axavier@anl.gov>"]
version = "1.0.0"
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ReverseManufacturing.jl
=======================
**ReverseManufacturing.jl** is an optimization package for logistic decisions related to reverse manufacturing processes. For example, the package can be used to determine where to build recycling plants, what sizes should they have and which customers should be served by which plants. The package supports customized reverse manufacturing pipelines, with multiple types of plants, multiple types of product and multiple time periods.
Data Specification
==================
Each instance in ReverseManufacturing.jl is represented as a JSON file with two sections: `products` and `plants`. Below, we describe each section in more detail. For a concrete example, see the file `instances/samples/s2.json`.
Products
--------
The **products** section describes all products and subproducts in the simulation. The field `instance["products"]` is a dictionary mapping the name of the product to a dictionary which describes its characteristics. Each product description contains the following keys:
| Key | Description
|:------------------------------|:-----------------------------------
| `transportation cost` | The cost (in dollars per km) to transport this product
| `initial amounts` | A dictionary mapping the name of each location to its description. See below for more information. If this product is not initially available, this key may be omitted.
Each product may have some amount available at the beginning of the simulation. In this case, the key `initial amounts` maps to a dictionary with the following keys:
| Key | Description
|:------------------------------|:-----------------------------------
| `latitude` | The latitude of the location, in degrees.
| `longitude` | The longitude of the location, in degrees.
| `amount` | The amount (in kg) of the product initially available at the location.
Processing Plants
-----------------
The **plants** section describes the available types of reverse manufacturing plants, their potential locations and associated costs, as well as their inputs and outputs. The field `instance["plants"]` is a dictionary mapping the name of the plant to a dictionary with the following keys:
| Key | Description
|:------------------------------|:-----------------------------------
| `input` | The name of the product that this plant takes as input. Only one input is accepted per plant.
| `outputs` | A dictionary specifying how many kg of each product is produced for each kg of input. For example, if the plant outputs 0.5 kg of P2 and 0.25 kg of P3 for each kg of P1 provided, then this entry should be `{"P2": 0.5, "P3": 0.25}`. If the plant does not output anything, this key may be omitted.
| `locations` | A dictionary mapping the name of the location to a dictionary which describes the site characteristics. See below for a more detailed explanation.
Each type of plant is associated with a set of potential locations. Each location is represented by a dictionary with the following keys:
| Key | Description
|:------------------------------|:-----------------------------------
| `latitude` | The latitude of the location, in degrees.
| `longitude` | The longitude of the location, in degrees.
| `opening cost` | The cost (in dollars) to open the plant.
| `fixed operating cost` | The cost (in dollars) to keep the plant open, even if the plant doesn't process anything.
| `variable operating cost` | The cost (in dollars per kg) that the plant incurs to process each kg of input.
Authors
=======
* **Alinson S. Xavier,** Argonne National Laboratory <<axavier@anl.gov>>
* **Nwike Iloeje,** Argonne National Laboratory <<ciloeje@anl.gov>>

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{
"products": {
"P1": {
"transportation cost": 1.50,
"initial amounts": {
"C1": {
"latitude": 7.0,
"longitude": 7.0,
"amount": 934.56
},
"C2": {
"latitude": 7.0,
"longitude": 19.0,
"amount": 198.95
},
"C3": {
"latitude": 84.0,
"longitude": 76.0,
"amount": 212.97
},
"C4": {
"latitude": 21.0,
"longitude": 16.0,
"amount": 352.19
},
"C5": {
"latitude": 32.0,
"longitude": 92.0,
"amount": 510.33
},
"C6": {
"latitude": 14.0,
"longitude": 62.0,
"amount": 471.66
},
"C7": {
"latitude": 30.0,
"longitude": 83.0,
"amount": 785.21
},
"C8": {
"latitude": 35.0,
"longitude": 40.0,
"amount": 706.17
},
"C9": {
"latitude": 74.0,
"longitude": 52.0,
"amount": 30.08
},
"C10": {
"latitude": 22.0,
"longitude": 54.0,
"amount": 536.52
}
}
},
"P2": {
"transportation cost": 2.00
},
"P3": {
"transportation cost": 1.25
},
"P4": {
"transportation cost": 1.75
}
},
"plants": {
"F1": {
"input": "P1",
"outputs": {
"P2": 0.2,
"P3": 0.5
},
"locations": {
"L1": {
"latitude": 0.0,
"longitude": 0.0,
"capacity": 500,
"opening cost": 2000,
"fixed operating cost": 70.0,
"variable operating cost": 70.0
},
"L2": {
"latitude": 0.5,
"longitude": 0.5,
"opening cost": 1000,
"capacity": 750,
"opening cost": 1000,
"fixed operating cost": 50.0,
"variable operating cost": 50.0
}
}
},
"F2": {
"input": "P2",
"outputs": {
"P3": 0.05,
"P4": 0.80
},
"locations": {
"L3": {
"latitude": 25.0,
"longitude": 65.0,
"capacity": 1000,
"opening cost": 3000,
"fixed operating cost": 50.0,
"variable operating cost": 50.0
},
"L4": {
"latitude": 0.75,
"longitude": 0.20,
"processing cost": 250.0,
"opening cost": 3000,
"fixed operating cost": 50.0,
"variable operating cost": 50.0
}
}
},
"F3": {
"input": "P4",
"locations": {
"L5": {
"latitude": 100.0,
"longitude": 100.0,
"opening cost": 0.0,
"fixed operating cost": 0.0,
"variable operating cost": -15.0
}
}
},
"F4": {
"input": "P3",
"locations": {
"L6": {
"latitude": 50.0,
"longitude": 50.0,
"opening cost": 0.0,
"fixed operating cost": 0.0,
"variable operating cost": -15.0
}
}
}
}
}

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{
"products": {
"lead-acid batteries": {
"transportation cost": 0.0015,
"initial amounts": {
"Chicago": {
"latitude": 41.881944,
"longitude": -87.627778,
"amount": 175000.0
},
"Darien": {
"latitude": 41.745556,
"longitude": -87.981111,
"amount": 30000.0
},
"Westmont": {
"latitude": 41.794444,
"longitude": -87.976389,
"amount": 25000.0
},
"Milwaukee": {
"latitude": 43.05,
"longitude": -87.95,
"amount": 120000.0
}
}
},
"lead": {
"transportation cost": 0.0015
},
"lead ingots": {
"transportation cost": 0.0017
},
"plastic casings": {
"transportation cost": 0.0023
},
"plastic pellets": {
"transportation cost": 0.0020
}
},
"plants": {
"Disassembly Plant": {
"input": "lead-acid batteries",
"outputs": {
"lead": 0.60,
"plastic casings": 0.05
},
"locations": {
"Darien": {
"latitude": 41.745556,
"longitude": -87.981111,
"variable operating cost": 0.12,
"fixed operating cost": 1000,
"opening cost": 10000.0
},
"Lemont": {
"latitude": 41.668784,
"longitude": -87.988845,
"variable operating cost": 0.15,
"fixed operating cost": 1000,
"opening cost": 10000.0
},
"Greendale": {
"latitude": 42.9375,
"longitude": -87.996944,
"variable operating cost": 0.18,
"fixed operating cost": 1000,
"opening cost": 10000.0
}
}
},
"Plastic Recycling Plant": {
"input": "plastic casings",
"outputs": {
"plastic pellets": 0.9
},
"locations": {
"Milwaukee": {
"latitude": 43.05,
"longitude": -87.95,
"variable operating cost": 0.08,
"fixed operating cost": 1000,
"opening cost": 10000.0
},
"Chicago": {
"latitude": 41.881944,
"longitude": -87.627778,
"variable operating cost": 0.10,
"fixed operating cost": 1000,
"opening cost": 10000.0
}
}
},
"Lead Recycling Plant": {
"input": "lead",
"outputs": {
"lead ingots": 0.9
},
"locations": {
"Milwaukee": {
"latitude": 43.05,
"longitude": -87.95,
"variable operating cost": 0.20,
"fixed operating cost": 1000,
"opening cost": 10000.0
}
}
},
"Lead Sales Point": {
"input": "lead ingots",
"locations": {
"Chicago": {
"latitude": 41.881944,
"longitude": -87.627778,
"variable operating cost": -1.50,
"fixed operating cost": 1000,
"opening cost": 10000.0
},
"Milwaukee": {
"latitude": 43.05,
"longitude": -87.95,
"variable operating cost": -2.75,
"fixed operating cost": 0.0,
"opening cost": 0.0
}
}
},
"Plastic Sales Point": {
"input": "plastic pellets",
"locations": {
"Chicago": {
"latitude": 41.881944,
"longitude": -87.627778,
"variable operating cost": -0.50,
"fixed operating cost": 0.0,
"opening cost": 0.0
},
"Milwaukee": {
"latitude": 43.05,
"longitude": -87.95,
"variable operating cost": -0.62,
"fixed operating cost": 0.0,
"opening cost": 0.0
}
}
}
}
}

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# Copyright (C) 2020 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
module ReverseManufacturing
include("dotdict.jl")
include("instance.jl")
include("model.jl")
end

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# Copyright (C) 2019 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
struct DotDict
inner::Dict
end
DotDict() = DotDict(Dict())
function Base.setproperty!(d::DotDict, key::Symbol, value)
setindex!(getfield(d, :inner), value, key)
end
function Base.getproperty(d::DotDict, key::Symbol)
(key == :inner ? getfield(d, :inner) : d.inner[key])
end
function Base.getindex(d::DotDict, key::Int64)
d.inner[Symbol(key)]
end
function Base.getindex(d::DotDict, key::Symbol)
d.inner[key]
end
function Base.keys(d::DotDict)
keys(d.inner)
end
function Base.values(d::DotDict)
values(d.inner)
end
function Base.iterate(d::DotDict)
iterate(values(d.inner))
end
function Base.iterate(d::DotDict, v::Int64)
iterate(values(d.inner), v)
end
function Base.length(d::DotDict)
length(values(d.inner))
end
function Base.show(io::IO, d::DotDict)
print(io, "DotDict with $(length(keys(d.inner))) entries:\n")
count = 0
for k in keys(d.inner)
count += 1
if count > 10
print(io, " ...\n")
break
end
print(io, " :$(k) => $(d.inner[k])\n")
end
end
function recursive_to_dot_dict(el)
if typeof(el) == Dict{String, Any}
return DotDict(Dict(Symbol(k) => recursive_to_dot_dict(el[k]) for k in keys(el)))
else
return el
end
end
export recursive_to_dot_dict

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# Copyright (C) 2020 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
using Printf, JSON
import Base.getindex, Base.time
"""
mutable struct ReverseManufacturingInstance
Representation of an instance of the Facility Location for Reverse Manufacturing problem.
"""
mutable struct ReverseManufacturingInstance
json::Dict
products::Dict
plants::Dict
end
function Base.show(io::IO, instance::ReverseManufacturingInstance)
n_plants = length(instance["plants"])
n_products = length(instance["products"])
print(io, "ReverseManufacturingInstance with ")
print(io, "$n_plants plants, ")
print(io, "$n_products products")
end
"""
load(name::String)::ReverseManufacturingInstance
Loads an instance from the benchmark set.
Example
=======
julia> ReverseManufacturing.load("samples/s1.json")
"""
function load(name::String) :: ReverseManufacturingInstance
basedir = dirname(@__FILE__)
return ReverseManufacturing.readfile("$basedir/../instances/$name.json")
end
"""
readfile(path::String)::ReverseManufacturingInstance
Loads an instance from the given JSON file.
Example
=======
julia> ReverseManufacturing.load("/home/user/instance.json")
"""
function readfile(path::String)::ReverseManufacturingInstance
json = JSON.parsefile(path)
products = Dict(key => json["products"][key]
for key in keys(json["products"]))
plants = Dict(key => json["plants"][key]
for key in keys(json["plants"]))
for product_name in keys(products)
product = products[product_name]
product["name"] = product_name
product["input plants"] = []
product["output plants"] = []
end
for plant_name in keys(plants)
plant = plants[plant_name]
plant["name"] = plant_name
# Input product
input_product = products[plant["input"]]
plant["input product"] = input_product
push!(input_product["input plants"], plant)
# Output products
if haskey(plant, "outputs")
for product_name in keys(plant["outputs"])
product = products[product_name]
push!(product["output plants"], plant)
end
end
end
return ReverseManufacturingInstance(json, products, plants)
end
export ReverseManufacturingInstance

@ -0,0 +1,210 @@
# Copyright (C) 2019 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
using JuMP, LinearAlgebra, Geodesy
mutable struct ReverseManufacturingModel
mip::JuMP.Model
vars::DotDict
arcs
decision_nodes
process_nodes
end
mutable struct Node
product_name::String
plant_name::String
location_name::String
balance::Float64
incoming_arcs::Array
outgoing_arcs::Array
cost::Float64
end
function Node(product_name::String,
plant_name::String,
location_name::String;
balance::Float64 = 0.0,
incoming_arcs::Array = [],
outgoing_arcs::Array = [],
cost::Float64 = 0.0,
) :: Node
return Node(product_name,
plant_name,
location_name,
balance,
incoming_arcs,
outgoing_arcs,
cost)
end
function Base.show(io::IO, node::Node)
print(io, "Node($(node.product_name), $(node.plant_name), $(node.location_name)")
if node.balance != 0.0
print(io, ", $(node.balance)")
end
print(io, ")")
end
mutable struct Arc
source::Node
dest::Node
costs::Dict
values::Dict
end
function Base.show(io::IO, arc::Arc)
print(io, "Arc($(arc.source), $(arc.dest))")
end
function build_model(instance::ReverseManufacturingInstance,
optimizer,
) :: ReverseManufacturingModel
mip = isa(optimizer, JuMP.OptimizerFactory) ? Model(optimizer) : direct_model(optimizer)
decision_nodes, process_nodes, arcs = create_nodes_and_arcs(instance)
vars = DotDict()
vars.flow = Dict(a => @variable(mip, lower_bound=0) for a in arcs)
vars.node = Dict(n => @variable(mip, binary=true) for n in values(process_nodes))
create_decision_node_constraints!(mip, decision_nodes, vars)
create_process_node_constraints!(mip, process_nodes, vars)
flow_costs = sum(a.costs[c] * vars.flow[a] for a in arcs for c in keys(a.costs))
node_costs = sum(n.cost * vars.node[n] for n in values(process_nodes))
@objective(mip, Min, flow_costs + node_costs)
return return ReverseManufacturingModel(mip,
vars,
arcs,
decision_nodes,
process_nodes)
end
function create_decision_node_constraints!(mip, nodes, vars)
for (id, n) in nodes
@constraint(mip,
sum(vars.flow[a] for a in n.incoming_arcs) + n.balance ==
sum(vars.flow[a] for a in n.outgoing_arcs))
end
end
function create_process_node_constraints!(mip, nodes, vars)
for (id, n) in nodes
# Output amount is implied by input amount
input_sum = sum(vars.flow[a] for a in n.incoming_arcs)
for a in n.outgoing_arcs
@constraint(mip, vars.flow[a] == a.values["weight"] * input_sum)
end
# If plant is closed, input must be zero
@constraint(mip, input_sum <= 1e6 * vars.node[n])
end
end
function create_nodes_and_arcs(instance)
arcs = Arc[]
decision_nodes = Dict()
process_nodes = Dict()
# Create all nodes
for (product_name, product) in instance.products
# Decision nodes for initial amounts
if haskey(product, "initial amounts")
for location_name in keys(product["initial amounts"])
amount = product["initial amounts"][location_name]["amount"]
n = Node(product_name, "Origin", location_name, balance=amount)
decision_nodes[n.product_name, n.plant_name, n.location_name] = n
end
end
# Process nodes for each plant
for plant in product["input plants"]
for (location_name, location) in plant["locations"]
cost = location["opening cost"] + location["fixed operating cost"]
n = Node(product_name, plant["name"], location_name, cost=cost)
process_nodes[n.product_name, n.plant_name, n.location_name] = n
end
end
# Decision nodes for each plant
for plant in product["output plants"]
for location_name in keys(plant["locations"])
n = Node(product_name, plant["name"], location_name)
decision_nodes[n.product_name, n.plant_name, n.location_name] = n
end
end
end
# Create arcs
for (product_name, product) in instance.products
# Transportation arcs from initial location to plants
if haskey(product, "initial amounts")
for source_location_name in keys(product["initial amounts"])
source_location = product["initial amounts"][source_location_name]
for dest_plant in product["input plants"]
for dest_location_name in keys(dest_plant["locations"])
dest_location = dest_plant["locations"][dest_location_name]
source = decision_nodes[product_name, "Origin", source_location_name]
dest = process_nodes[product_name, dest_plant["name"], dest_location_name]
distance = calculate_distance(source_location["latitude"],
source_location["longitude"],
dest_location["latitude"],
dest_location["longitude"])
costs = Dict("transportation" => product["transportation cost"] * distance,
"variable" => dest_location["variable operating cost"])
values = Dict("distance" => distance)
a = Arc(source, dest, costs, values)
push!(arcs, a)
push!(source.outgoing_arcs, a)
push!(dest.incoming_arcs, a)
end
end
end
end
for source_plant in product["output plants"]
for source_location_name in keys(source_plant["locations"])
source_location = source_plant["locations"][source_location_name]
# Process-arcs within a plant
source = process_nodes[source_plant["input"], source_plant["name"], source_location_name]
dest = decision_nodes[product_name, source_plant["name"], source_location_name]
costs = Dict()
values = Dict("weight" => source_plant["outputs"][product_name])
a = Arc(source, dest, costs, values)
push!(arcs, a)
push!(source.outgoing_arcs, a)
push!(dest.incoming_arcs, a)
# Transportation-arcs from one plant to another
for dest_plant in product["input plants"]
for dest_location_name in keys(dest_plant["locations"])
dest_location = dest_plant["locations"][dest_location_name]
source = decision_nodes[product_name, source_plant["name"], source_location_name]
dest = process_nodes[product_name, dest_plant["name"], dest_location_name]
distance = calculate_distance(source_location["latitude"],
source_location["longitude"],
dest_location["latitude"],
dest_location["longitude"])
costs = Dict("transportation" => product["transportation cost"] * distance,
"variable" => dest_location["variable operating cost"])
values = Dict("distance" => distance)
a = Arc(source, dest, costs, values)
push!(arcs, a)
push!(source.outgoing_arcs, a)
push!(dest.incoming_arcs, a)
end
end
end
end
end
return decision_nodes, process_nodes, arcs
end
function calculate_distance(source_lat, source_lon, dest_lat, dest_lon)::Float64
x = LLA(source_lat, source_lon, 0.0)
y = LLA(dest_lat, dest_lon, 0.0)
return round(distance(x, y) / 1000.0, digits=2)
end
export FlowArc

@ -0,0 +1,18 @@
# Copyright (C) 2020 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
using ReverseManufacturing
@testset "Instance" begin
instance = ReverseManufacturing.load("samples/s1")
plants, products = instance.plants, instance.products
@test length(products) == 4
@test sort(collect(keys(plants))) == ["F1", "F2", "F3", "F4"]
@test plants["F1"]["input product"] == products["P1"]
@test sort(collect(keys(products))) == ["P1", "P2", "P3", "P4"]
@test products["P1"]["input plants"] == [plants["F1"]]
@test products["P1"]["transportation cost"] == 1.5
@test products["P1"]["initial amounts"]["C1"]["latitude"] == 7.0
end

@ -0,0 +1,74 @@
# Copyright (C) 2020 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
using ReverseManufacturing, Cbc, JuMP, Printf
@testset "Model" begin
instance = ReverseManufacturing.load("samples/s1")
model = ReverseManufacturing.build_model(instance, with_optimizer(Cbc.Optimizer))
# Verify nodes
@test ("P1", "Origin", "C1") in keys(model.decision_nodes)
@test ("P1", "Origin", "C3") in keys(model.decision_nodes)
@test ("P1", "Origin", "C8") in keys(model.decision_nodes)
@test ("P2", "F1", "L1") in keys(model.decision_nodes)
@test ("P2", "F1", "L2") in keys(model.decision_nodes)
@test ("P3", "F1", "L1") in keys(model.decision_nodes)
@test ("P3", "F1", "L2") in keys(model.decision_nodes)
@test ("P3", "F2", "L3") in keys(model.decision_nodes)
@test ("P3", "F2", "L4") in keys(model.decision_nodes)
@test ("P4", "F2", "L3") in keys(model.decision_nodes)
@test ("P4", "F2", "L4") in keys(model.decision_nodes)
@test ("P1", "F1", "L1") in keys(model.process_nodes)
@test ("P1", "F1", "L2") in keys(model.process_nodes)
@test ("P2", "F2", "L3") in keys(model.process_nodes)
@test ("P2", "F2", "L4") in keys(model.process_nodes)
@test ("P3", "F4", "L6") in keys(model.process_nodes)
@test ("P4", "F3", "L5") in keys(model.process_nodes)
# Verify some arcs
p1_orig_c1 = model.decision_nodes["P1", "Origin", "C1"]
p1_f1_l1 = model.process_nodes["P1", "F1", "L1"]
@test length(p1_orig_c1.outgoing_arcs) == 2
@test length(p1_f1_l1.incoming_arcs) == 10
arc = p1_orig_c1.outgoing_arcs[1]
@test arc.dest.location_name == "L1"
@test arc.values["distance"] == 1095.62
@test round(arc.costs["transportation"], digits=2) == 1643.43
@test arc.costs["variable"] == 70.0
p2_f1_l1 = model.decision_nodes["P2", "F1", "L1"]
p2_f2_l3 = model.process_nodes["P2", "F2", "L3"]
@test length(p2_f1_l1.incoming_arcs) == 1
@test length(p2_f1_l1.outgoing_arcs) == 2
arc = p2_f1_l1.incoming_arcs[1]
@test arc.values["weight"] == 0.2
@test isempty(arc.costs)
# @show model.mip
# JuMP.optimize!(model.mip)
# values = Dict(a => JuMP.value(model.vars.flow[a]) for a in model.arcs)
# @printf("source,dest,amount\n")
# for (arc, value) in values
# if value > 1e-6
# @printf("%s-%s-%s,%s-%s-%s,%.2f\n",
# arc.source.plant_name,
# arc.source.location_name,
# arc.source.product_name,
# arc.dest.plant_name,
# arc.dest.location_name,
# arc.dest.product_name,
# value)
# end
# end
# for a in model.arcs
# @printf("%20s\t%20s\t%8.2f\n",
# "$(a.source.product_name) $(a.source.plant_name) $(a.source.location_name)",
# "$(a.dest.product_name) $(a.dest.plant_name) $(a.dest.location_name)",
# a.weight)
# end
end

@ -0,0 +1,9 @@
# Copyright (C) 2020 Argonne National Laboratory
# Written by Alinson Santos Xavier <axavier@anl.gov>
using Test
@testset "ReverseManufacturing" begin
include("instance_test.jl")
include("model_test.jl")
end
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