HI everyone, so I have to model a problem but when I run the procedure, it tells me:

Warning: CPLEX: Q matrix is not positive semi-definite.

Warning: Model status 13: Error no solution, Solver status 9: Error: Setup failure (see message window).

I have no idea where my mistakes are, that's why I come to ask for your help.

so here is my problem :

I have 4 variables, X(j,i) and Q(i,l) are non negative and Y(i) and E(i) are binary variables

My function to minimize is : sum( (j,i), csb(j,i)*X(j,i) ) + sum( (i,l), cbd(i,l)*Q(i,l) ) + sum( i, ce(i)*E(i) ) + sum( i, co(i)*Y(i) )

My constraints are:

sum(i, X(j,i)*Y(i)) <= capmp(j)

sum(l, Q(i,l)) <= capb(i) + 50*E(i)

sum(i, Q(i,l)) >= ed(l)

8.333*(sum(j, X(j|j="Afyon",i))+sum(j, X(j|j="Konya",i))) + 9.091*sum(j, X(j| j="Import",i)) = sum(l, Q(i,l))

sum(i, Y(i|i="Istanbul")) =1

sum(i, Y(i|i="Ankara")) =1

sum(i, Y(i|i="Izmir")) + sum(i, Y(i|i="Sakarya")) + sum(i, Y(i|i="Adana")) =1

sum(i, E(i|i="Izmir")) + sum(i, E(i|i="Sakarya")) + sum(i, E(i|i="Adana")) + sum(i, E(i|i="Sakarya")) + sum(i, E(i|i="Adana")) =1

From my point of view, I think the problem should be either in the first 4 constraints or in the objective function but I’m not sure..

Thanks you in advance! 😁

**Best answer by Farid**

Dear Mmoureau,

Good to see that you have already found the problem. However, I write an answer in case somebody else faces a similar problem.