How to handle two ways of shipping for supply network problem
回答済みI am trying to create a model in which for each arc there are two carrier options to deliver with different costs associated with the carrier options. I created dictionaries for the demand from customers and the supply of the products, demand for express delivery option as well as a multidict for the arcs and the different costs which looks like this:
arcs,cost0,cost1=gp.multidict({
('s0','c0s0'):[28.536319,0.323409],
('s1','c0s1'):[0.786101,0.258617],
('s4','c0s4'):[2.0,0.418180],
('s0','c1s0'):[42.701323,1.256058],
('s1','c1s1'):[1.7,0.651774],
('s4','c1s4'):[2.108387,0.406466],
('s0','c2s0'):[44.812141,2.332005],
('s1','c2s1'):[0.788449,1.665496],
('s0','c3s0'):[73.373559,1.294359],
('s1','c3s1'):[80,4.572656],
('s4','c3s4'):[80,12.418360],
('s0','c6s0'):[37.286300,1.312147],
('s1','c6s1'):[1.116815,1.365350],
('s4','c6s4'):[1.697969,0.45]
})
In which si represents the supply of the product and cisi represents the customer
the Objective function is to minimize sum(Cijk+Xijk) in which cijk is the cost of shipping product i to customer j through delivery option k and X is the flow of product to ship that way.
I created variables for the two delivery options this way
carrier1flow=model.addVars(arcs, obj=cost1, name='carrier1')
carrier0flow=model.addVars(arcs, obj=cost0, name='carrier0')
and supply and demand constraints this way:
##### supply constraints
segments=supply_dict.keys()
supply_flow= model.addConstrs((gp.quicksum(carrier1flow.select(segment)+carrier0flow.select(segment))<=supply_dict[segment]
for segment in segments), name='segment')
# #####demand constraints
customers=demand_dict.keys()
demand_flow= model.addConstrs((gp.quicksum(carrier1flow.select('*',customer)+carrier0flow.select('*',customer))==demand_dict[customer]########de demand is not getting through!!!!!!!!!
for customer in customers), name='customer')
Besides, there are other constraints associated with the different carriers. carrier 0 has to fulfill a certain portion of the demand and carrier 1 flows have to be greater than a minimum weight those look like this
express_flow=model.addConstrs((gp.quicksum(carrier0flow.select('*',customer))>=express_demand[customer]
for customer in customers), name='customer')
carrier_flow=model.addConstrs((gp.quicksum(carrier1flow.select('*',customer))>=minweight####carrier minimum
for customer in customers), name='customer')
If I include only the first three constraints I get a solution but in the solution, only one carrier is chosen to fulfill the demand of one customer and I want the demand to be split amongst carriers due to the express demand. Moreover, when I add the minimum flow, the model becomes unfeasible and I wonder if that is because I have the variables set wrong. I would appreciate any help, it is my first time using gurobi
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Gurobi Staff
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Ok so I was able to solve the first portion. I changed my multidict to the following:
arcs,cost=gp.multidict({
('s0','c0s0','r0'):[28.536319],
('s0','c0s0','r1'):[0.323409],
('s1','c0s1','r0'):[0.786101],
('s1','c0s1','r1'):[0.258617],
('s4','c0s4','r0'):[2.0],
('s4','c0s4','r1'):[0.418180],####carrier 0 cost assumed no data
('s0','c1s0','r0'):[42.701323],
('s0','c1s0','r1'):[1.256058],
('s1','c1s1','r0'):[1.7],
('s1','c1s1','r1'):[0.651774],####carrier 0 cost assumed no data
('s4','c1s4','r0'):[2.108387],
('s4','c1s4','r1'):[0.406466],
('s0','c2s0','r0'):[44.812141],
('s0','c2s0','r1'):[2.332005],
('s1','c2s1','r0'):[0.788449],
('s1','c2s1','r1'):[1.665496],
('s0','c3s0','r0'):[73.373559],
('s0','c3s0','r1'):[1.294359],
('s1','c3s1','r0'):[80],
('s1','c3s1','r1'):[4.572656],####carrier 0 cost assumed no data
('s4','c3s4','r0'):[80],
('s4','c3s4','r1'):[12.418360],####carrier 0 cost assumed no data
('s0','c6s0','r0'):[37.286300],
('s0','c6s0','r1'):[1.312147],
('s1','c6s1','r0'):[1.116815],
('s1','c6s1','r1'):[1.365350],
('s4','c6s4','r0'):[1.697969],
('s4','c6s4','r1'):[0.45]####carrier 1 cost assumed no data
})and the constraints to the following
##### supply constraints
segments=supply_dict.keys()
supply_flow= model.addConstrs((gp.quicksum(flow.select(segment))<=supply_dict[segment]
for segment in segments), name='segment')
# #####demand constraints
customers=demand_dict.keys()
demand_flow= model.addConstrs((gp.quicksum(flow.select('*',customer,'*'))==demand_dict[customer]
for customer in customers), name='customer')
# ######## Carrier constraints
express_flow=model.addConstrs((gp.quicksum(flow.select('*',customer,'r0'))>=express_demand[customer]
for customer in customers), name='express')And that works just like I wanted!
However, this last constraint is giving me an infeasible solution and I am not sure whycarrier_flow=model.addConstrs((gp.quicksum(flow.select('*',customer,'r1'))>=minweight####carrier minimum
for customer in customers), name='minimum')0 -
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Hi Nestor,
The Knowledge Base article How do I determine why my model is infeasible? might come in handy.
Best regards,
Jaromił0 -
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