GUROBI案例实战(一)——Supply Network Design(网络流模型)

GUROBI官方给出的案例，但本篇实现方式与其有些不一样，并且对一些函数给出了解释：ymodeling-examples/supply_network_design/supply_network_design_1.ipynb at master · Gurobi/modeling-examples (github.com)

一、问题描述

给定两个工厂、四个中转站、六个客户:

二、建模

1.集合

工厂集合：

中转站集合：

客户点集合：

2.参数

工厂的最大生产能力 ：

中转站的最大吞吐量：

客户的资源需求：

从节点s到节点t的单位资源的运输成本：

3.决策变量

从节点s到节点t运输的资源数量：

4.目标函数

最小化总的运输成本: 

5.约束条件

工厂的产量约束：

中转站的吞吐量约束：

中转站的流量平衡约束：

客户点的需求约束：

三、代码实现

import gurobipy as gp
from gurobipy import *
# 参数
supply = dict({
    "F1": 150000,
    "F2": 200000
})

through = dict({
    "D1": 70000,
    "D2": 50000,
    "D3": 100000,
    "D4": 40000
})

demand = dict({
    "C1": 50000,
    "C2": 10000,
    "C3": 40000,
    "C4": 35000,
    "C5": 60000,
    "C6": 20000
})

arcs, cost = gp.multidict({
    ("F1","D1"): 0.5,
    ("F1","D2"):0.5,
    ("F1","D3"): 1.0,
    ("F1","D4"):0.2,
    ("F1","C1"):1.0,
    ("F1","C3"):1.5,
    ("F1","C4"):2.0,
    ("F1","C6"):1.0,
    ("F2","D2"):0.3,
    ("F2","D3"):0.5,
    ("F2","D4"):0.2,
    ("F2","C1"):2.0,
    ("D1","C2"):1.5,
    ("D1","C3"):0.5,
    ("D1","C5"):1.5,
    ("D1","C6"):1.0,
    ("D2","C1"):1.0,
    ("D2","C2"):0.5,
    ("D2","C3"):0.5,
    ("D2","C4"):1.0,
    ("D2","C5"):0.5,
    ("D3","C2"):1.5,
    ("D3","C3"):2.0,
    ("D3","C5"):0.5,
    ("D3","C6"):1.5,
    ("D4","C3"):0.2,
    ("D4","C4"):1.5,
    ("D4","C5"):0.5,
    ("D4","C6"):1.5
})
print(arcs)
# model
model = gp.Model()
# decision var
flow = model.addVars(arcs, vtype = GRB.CONTINUOUS, name = "flow")  # flow为tupledict
print(flow)
# constraints
# factory production
factory = supply.keys()
model.addConstrs((flow.sum(f, "*") <= supply[f] for f in factory), name = "factory constraints")
# depot constraints
depot = through.keys()
model.addConstrs((flow.sum("*", d) <= through[d] for d in depot), name = "depot constraint 1")
model.addConstrs((flow.sum("*", d) == flow.sum(d, "*") for d in depot), name = "depot constraint 2")
# customer constraints
customers = demand.keys()
model.addConstrs((flow.sum("*", c) == demand[c] for c in customers), name = "customers constraints")
# objective
obj = flow.prod(cost)
model.setObjective(obj, GRB.MINIMIZE)

# optimize
model.write("test.lp")
model.update()
model.optimize()

提示：上述代码实现中用到的multidict（）、sum（）、prod（）等在另一篇帖子里有详细介绍

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