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

提示：上述代码实现中用到的。等在另一篇帖子里有详细介绍。

qq_44533176

1119人浏览 · 2024-03-20 14:09:02

qq_44533176 · 2024-03-20 14:09:02 发布

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:

Factory	Supply（最大生产量）
F1	150,000
F2	200,000

Depot	Throughput（吞吐量：中转站不生产、不消耗资源，只是传递资源）
D1	70,000
D2	50,000
D3	100,000
D4	40,000

Customers	Demands（需要的资源）
C1	50,000
C2	10,000
C3	40,000
C4	35,000
C5	60,000
C6	20,000

二、建模

1.集合

工厂集合： $f \in F =\left \{ F1,F2 \right \}$

中转站集合： $d\in D = \left \{ D1, D2, D3, D4\right \}$

客户点集合： $c \in C=\left \{ C1, C2, C3, C4, C5, C6 \right \}$

2.参数

工厂 $f$ 的最大生产能力： $supply_{f}\in R^{+}$

中转站 $d$ 的最大吞吐量： $through_{d}\in R^{+}$

客户 $c$ 的资源需求： $demand_{c}\in R^{+}$

从节点s到节点t的单位资源的运输成本： $cost(s,t) \in R^{+}$

3.决策变量

从节点s到节点t运输的资源数量： $flow_{s,t}$

4.目标函数

最小化总的运输成本: $min z = \sum cost_{s,t}*flow_{s,t}$

5.约束条件

工厂的产量约束： $\sum_{t} flow_{f,t} <= supply_{f}$

中转站的吞吐量约束： $\sum_{f} flow_{f, d}<=through_{d}$

中转站的流量平衡约束： $\sum_{f} flow_{f,d} == \sum_{c}flow_{d,c}$

客户点的需求约束： $\sum_{s}flow_{s,c} == demand_{c}$

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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