CODEWITHSUNDEEP
pythonpython-3.xpyomopython-packaging
Vigneshwar A
Vigneshwar A

Reputation: 31

PYOMO optimization to meet supply < demand

I have some code for supply chain management on based on cost where supply tries meets the demand but this only works when the supply is greater than the demand. Is there any way I can optimize it to work in both ways (i.e. when supply > demand and supply < demand)?

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)

My input:

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;

Here supply = 30 and demand = 25. It works and the output I get is Variable:

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

But it doesn't work when the supply is less than the demand. Here supply = 30 and 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;

I require the desired output as below: Variable:

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

Upvotes: 1

Views: 822

Answers (1)

Qi Chen
Qi Chen

Reputation: 1718

It looks like your model is infeasible when demand is greater than supply, because of the constraint model.demandConstraint. The shipment quantities cannot fulfill demand because otherwise the other constraint model.supplyConstraint would be violated.

If you want to penalize lack of demand satisfaction, then you could define slack variables for the relevant constraint and add those terms to the objective.

This book could be a good resource for you: https://www.wiley.com/en-us/Model+Building+in+Mathematical+Programming%2C+5th+Edition-p-9781118443330

Upvotes: 3

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