How can I control decision variables?

I use MILP and have two decision variables u(i),v(i). u and v are non-negative variables which cannot both be non-zero simultaneously. more detailed, if u have some value, then v is zero value. The opposite is also true. How can I do that?

Answer 1

[Alan Weiss]

I assume that u and v are integers, because otherwise the problem is ill-posed.

In that case, to say that both variables cannot simultaneously be zero (for nonnegative variables) is equivalent to

u + v >= 1

This is a linear inequality that you can easily put in intlinprog syntax.

For the other part (when one variable is nonzero the other must be zero), I suppose that there is an upper bound M to your variables. In that case, these inequalities enforces that constraint:

(M+1)*u <= v % enforces u = 0 when v >= 1

(M+1)*v <= u % enforces v = 0 when u >= 1

Alan Weiss

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