聚合无容量网络设计问题的基本运输问题

Question

我正在和 Python Pulp 一起练习解决一些交通问题。

我已经能够用这段代码解决一个基本的啤酒运输问题：

import pulp as lp


model=lp.LpProblem('Modelo de localización',lp.LpMinimize)


fabricas=['A','B']
cap_fabricas={'A':1500,'B':1500}
tiendas=['1','2','3']
cap_tiendas={'1':1000,'2':1000,'3':1000}

rutas=[(i,j) for i in fabricas for j in tiendas]
dict_costes={'A':dict(zip(tiendas,[23,20,45])),'B':dict(zip(tiendas,[21,34,11]))}

x_ij=lp.LpVariable.dicts('rutas',(fabricas,tiendas),lowBound=0,cat=lp.LpInteger)
model+=lp.lpSum([x_ij[i][j]* dict_costes[i][j] for i in fabricas for j in tiendas]),'COSTES DE TRANSPORTE'
for i in fabricas:
    model+=lp.lpSum([x_ij[i][j] for j in tiendas])<=cap_fabricas[i]
for j in tiendas: 
    model+=lp.lpSum([x_ij[i][j] for i in fabricas])>=cap_tiendas[j]

model.solve(solver)


print('Solution status:',lp.LpStatus[model.status])
for v in model.variables():
    print('Quantity from:',v.name,' is',v.varValue(),'ud')
print('Cost is:',lp.value(model.objective),'€')

现在我必须解决 Uncapacitated Network Design Problem 但在 aggregate.

版本中

问题定义如基本的运输问题，只是一个货源，两个仓库。中间是1个中型仓库

视觉上的架构是这样的：

但我不知道如何在模型中添加它。我猜是源头数量之类的，应该等于中仓数量，等于天命仓。

知道如何将其添加到模型中吗？

Answer 1

运行:

import pulp as lp

# Model Data
nodes = [1, 2, 3, 4]
routes = [(1,2), (2,3), (3,4), (2,4), (1,4)]
fixed_costs = {(1,2):5, (2,3):25, (3,4):20, (2,4):15, (1,4):10}
var_costs = {(1,2):5, (2,3):5, (3,4):5, (2,4):5, (1,4):30}
demand = {1:0, 2:0, 3:1, 4:1}
source_capacity = {1:sum(demand.values()), 2:0, 3:0, 4:0}

# Declare Problem
model=lp.LpProblem('network opt',lp.LpMinimize)

# Are routes open?
rt_open = lp.LpVariable.dicts('rt_open',routes,lowBound=0,cat=lp.LpBinary)

# Flow along routes:
flow = lp.LpVariable.dicts('flow',routes,lowBound=0,cat=lp.LpInteger)

# units sourced at each node
source = lp.LpVariable.dicts('source',nodes,lowBound=0,cat=lp.LpInteger)

# Objective
model += lp.lpSum([fixed_costs[r]*rt_open[r] + var_costs[r]*flow[r] for r in routes])

# Constraints
for i in nodes:
    # Constrains on sourcing:
    model += source[i] <= source_capacity[i]

    # Constraint on flow: source + flow in = demand + flow out
    model += source[i] + lp.lpSum([flow[r] for r in routes if r[1] == i]) == \
                                demand[i] + lp.lpSum([flow[r] for r in routes if r[0] == i])

for r in routes:
    # Flow can only go along open routes
    model += flow[r] <= rt_open[r]*sum(demand.values())

# Solve problem & print results
model.solve()
print('Solution status:',lp.LpStatus[model.status])

for v in model.variables():
    print(v.name,': ',v.varValue)

print('Cost is:',lp.value(model.objective))

Returns:

flow_(1,_2) :  2.0
flow_(1,_4) :  0.0
flow_(2,_3) :  1.0
flow_(2,_4) :  1.0
flow_(3,_4) :  0.0
rt_open_(1,_2) :  1.0
rt_open_(1,_4) :  0.0
rt_open_(2,_3) :  1.0
rt_open_(2,_4) :  1.0
rt_open_(3,_4) :  0.0
source_1 :  2.0
source_2 :  0.0
source_3 :  0.0
source_4 :  0.0
Cost is: 65.0

聚合无容量网络设计问题的基本运输问题

Basic transportation problem to Aggregated Uncapacitated Network Design Problem

python

linear-programming

pulp