Originally posted by: Zoubeir

I have the following constraint: (xij is a binary variable and qi is an integer variable)

if then 

else if  then qi > 0

How can I write it in an optimization problem?

The answer is indicator or logical constraints. How to add these constraints depends on the API you are using. What API do you use?

Note however that strict inequality is not supported in linear programming. So you will not be able to say "qi>0" but only "qi>=epsilon". This is not always a problem since sometimes it is sufficient to only have "x[ij]=0 implies q[i]=0" since a non-zero q[i] improves the objective function and the solver will thus choose that automatically if possible.

Originally posted by: Zoubeir

I am using CPLEX with Python. 

In Python use Cplex.indicator_constraints.add().