Originally posted by: SaurabhA

Hi,

I am trying to solve standard transportation cost minimization problem using cplex java api.

The problem is we have multiple producers which supply some product (single product) and there is market (single market) which needs that product. That market has requirement of say r units of product. And say we have three producers P1, P2 and P3 and each can supply maximum of m1, m2 and m3 units of product X. The transportation cost per unit is t.

The objective function is to minimize the transportation cost x(i) * t for i = 1,2,3, where x(i) is no of units supplied from producer Pi.

Constraints are (for i =1,2,3):

1. x(i) cannot be negative. We cannot supply negative no. of units.

2. x(i) <= m(i) No. of units supplied cannot be more than the maximum units the producer has.

3. sum(x(i)) >= r The combined units supplied by all producers should meet the requirement of market which is r.

I implemented this and it gives me an answer when the producers P1, P2 and P3 combined together are able to fulfill the requirement r (3rd constraint). But when they are not able to fulfill 3rd constraint I don't get any answer.

My question is: Is it possible that CPLEX try to achieve 3rd constraint and if it is fulfilled it returns that answer. If it is not able to achieve 3rd constraint, it returns whatever best can be supplied by producer P1, P2 and P3 even though combined together they are less then requirement r?

Originally posted by: ol

Hello,

you can add a variable y > 0, add it in the objective as a weighted term to minimize, and modify 3 as sum(x(i)) + y  >= r 

Regards,

Olivier