Hallo to everyone,

I appreciate any help. I am really stuck and becoming frustrated.

I wanted to implement a vendor selection problem.

The objective is to minimze the associated transportation cost for each supplier (1. term) and the amount of suppliers (2nd term) to avoid high overhead costs

obj_fun… SUM( (i,j),x(i,j)*q(j)*p(i,j))+Sum( (i), y(i)) =e= z;

where the decision variables are x(i,j) which is the fractional transport volume (between 0 and 1) for supplier i on lane j

and y(i) which is a binary variable indicating if supplier i is selected.

The constraints:

demand(j)… Sum( (i), x(i,j)) =e= 1;

capacity(i,j)… x(i,j)*q(j) =l= c(i,j);

inscope1(i,j)… x(i,j) =g= 0;

inscope2(i,j)… x(i,j) =l= 1;

The problem is to set an upper bound a for the number of selected carriers.

maxcarrier… Sum( (i), y(i)) =l= a;

selectedcarrier(i)… Sum( (j), x(i,j)) =l= y(i);

The first constraint sets an upper limit a. The constraint selectedcarrier(i) sets the decision variable y(i) to 1 if carrier i ships something on at least one of the lanes.

The problem must be the last constraint because the solver gives a solution without it. If the constraint is included it gives an “integer infeasible” message. Is the problem that I have decision variables on each side of the inequation?

Does anyone have an idea how to solve this?

## Would be great!

Cheers,

Nadine

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