How to model Non-Linear constraint for-

Question

I need non-linear programming constraint for following condition:

If($x_{ik}=1 \, AND \, x_{jk}=1$)then

{ $y_i+p_n \leq y_j$

OR

$y_j+p_m \leq y_i$ }

where $x_{ik}$, $x_{jk}$ are binary decision variables. And $y_{i}$, $y_{j}$ are integer decision variables.

Kindly help. Thank you.

Answer 1

Introduce binary variables $z^1_{ij}$ and $z^2_{ij}$ and linear constraints: \begin{align} x_{ik}+x_{jk}-1&\le z^1_{ij}+z^2_{ij}\\ y_i+p_n-y_j &\le M^1_{ij}(1-z^1_{ij})\\ y_j+p_m-y_i&\le M^2_{ij}(1-z^2_{ij}) \end{align}