An if-then-else logic to construct constraint

Question

I was hoping to get some help in modelling the following logic, I know that it would use some kind of Big M formulation but I am not sure how. Thank you in advance!

$\Omega$ is a set whose values are all binary, $\Omega(n,k)$ is one of the value.

If $\Omega(n,k)=1$, then $p(k,n)\ge 0$, else $p(k,n)=0$.

This question is similar to the following: Modelling an if-then-else logic in MIP

What type of variable is $p$? – RobPratt Dec 19 '22 at 04:00 — RobPratt, Dec 19 '22 at 04:00

score 2 · Accepted Answer · edited Dec 19 '22 at 13:25

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Assuming that $\Omega$ is a set of variables, as opposed to parameters, you can just write $0 \le p(k,n) \le M_{k,n} \cdot \Omega(n, k)$ where $M_{k,n}$ is a known upper bound for $p(k,n).$

edited Dec 19 '22 at 13:25

SecretAgentMan

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answered Dec 19 '22 at 04:24

prubin

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Thanks for your solution, the method is concise and easy to understand ! – WaMIMO Dec 19 '22 at 11:19

Sutanu Majumdar · Answer 2 · 2022-12-19T14:34:37.487

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I missed the part where $p$ is continuous and just have to be non-negative. Then same as above answer
$p(n,k) \le M\Omega(k,n)$
$p(n,k) \ge 0$
$M$ is upper bound of $p(n,k)$

edited Dec 19 '22 at 14:34

answered Dec 19 '22 at 13:55

Sutanu Majumdar

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An if-then-else logic to construct constraint

2 Answers2