Originally posted by: sandeepsinghchauhan

I have a equation

A >= M => S ==D;

A <= M => S == E;

How can i write this constraint without implication (=>) just in terms of inequalities ?

Please help

Is D the same as E? If not this yields a contradiction in case A == M (in that case S must be equal to D and E simultaneously). If D is the same as E then you can just fix S=D (or E) and be done.

Why do you want to avoid the implication?

Originally posted by: sandeepsinghchauhan

No D is not same as E they both have different their own equations.

I don't want to use implication because i want to keep my whole model in inequalities form.

Originally posted by: sandeepsinghchauhan

In opl examples

Is there any example which shows this conditional constraints ?

Then you have to think what should happen in case A==M. With your constraints this option is excluded.

What is the point in keeping your whole model in inequalities? This will just make things harder for the solver then they need to be. It seems like a bad idea, both performance-wise and with respect to numerical robustness.

In order to formulate this without implication you need to create something called a big-M constraint. You can find more informations about these constraints on the Internet. I don't want to give too many details since I think it is a bad idea in your case :-)