nested condition on endogenous variable

Problems with modeling
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nested condition on endogenous variable

Post by Zib » 2 months ago

Hello all,

I am trying to model this problem:
x is a positive and nonzero parameter, y is a continuous and nonnegative variable, and z is a binary variable. I'd like to model this nested condition:
1- if y=0 then z=0
2- if y>0, then if x<=y then z=0, but if x>y then z=1.

I tried to use a big M method like this: x<= y+bigm*z but since z is nonzero when y=0 I get infeasibility.

I appreciate any help or idea on modeling this problem.


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