python - PYOMO 优化以满足供给 < 需求

Question

我有一些基于成本的供应链管理代码，其中供应尝试满足需求，但这仅在供应大于需求时才有效。有什么方法可以优化它以两种方式工作(即当 supply > demand 和 supply < demand 时)？

from pyomo.core import *
model = AbstractModel()
model.warehouses = Set()
model.stores = Set()
model.supply = Param(model.warehouses)
model.demand = Param(model.stores)
model.costs = Param(model.warehouses, model.stores)
model.amounts = Var(model.warehouses, model.stores, 
within=NonNegativeReals)

def costRule(model):
   return sum(
      model.costs[n,i]
      for n in model.warehouses
      for i in model.stores
)

model.cost=Objective(rule=costRule)

def minDemandRule(model, store):
    return sum(model.amounts[i, store] for i in model.warehouses) >= 
model.demand[store]

model.demandConstraint = Constraint(model.stores, rule=minDemandRule)

def maxSupplyRule(model, warehouse):
    return sum(model.amounts[warehouse, j] for j in model.stores) <= 
model.supply[warehouse]

model.supplyConstraint = Constraint(model.warehouses, rule=maxSupplyRule)

我的输入:

set warehouses := hyd ban coh;
set stores := cbe mdu cnr whc whe;
param: supply :=
hyd   10
ban   10
coh   10;
param: demand :=
cbe    5
mdu    5
cnr    5
whc    5
whe    5;
param costs:
      cbe mdu cnr whc whe:=
hyd    1   3    2   2    1
ban    4   5    1   1    3
coh    2   3    3   2    1;

这里supply = 30和demand = 25 。它有效，我得到的输出是变量:

amounts[ban,cbe]:
    Value: 5
amounts[ban,whc]:
    Value: 5
amounts[coh,whe]:
    Value: 5
amounts[hyd,cnr]:
    Value: 5
amounts[hyd,mdu]:
  Value: 5

但是当供给小于需求时它就不起作用了。这里supply = 30和demand = 40 :

param: supply :=
hyd   10
ban   10
coh   10;
param: demand :=
cbe    5
mdu    5
cnr    5
whc    5
whe    20;
param costs:
      cbe mdu cnr whc whe:=
hyd    1   3    2   2    1
ban    4   5    1   1    3
coh    2   3    3   2    1;

我需要如下所示的所需输出:变量:

amounts[ban,cbe]:
  Value: 5
amounts[ban,whc]:
  Value: 5
amounts[coh,whe]:
  Value: 10
amounts[hyd,cnr]:
  Value: 5
amounts[hyd,mdu]:
  Value: 5

 whe_demand =10

Answer 1

由于 model.demandConstraint 约束，当需求大于供给时，您的模型似乎不可行。发货数量无法满足需求，否则将违反另一个约束 model.supplyConstraint。

如果您想惩罚需求满足不足的情况，那么您可以为相关约束定义松弛变量，并将这些项添加到目标中。

这本书对您来说可能是一个很好的资源:https://www.wiley.com/en-us/Model+Building+in+Mathematical+Programming%2C+5th+Edition-p-9781118443330