Dear Julia Nguyen,

I suggest you to see links on topic.

https://www.lindo.com/index.php/products/lingo-and-optimization-modeling

https://www.routledge.com/Optimization-Modelling-A-Practical-Approach/Sarker-Newton/p/book/9781420043105

https://www.win.tue.nl/~wscor/OW/LPcodes.html

Best regards

You can define that family of constraints using the same logic to convert SAT into ILP:

x[i] [j] [k] == 1 => x[j] [i] [k] == 0

Writing it as a logical expression:

x[i] [j] [k] => ~ x[j] [i] [k]

~ x[i] [j] [k] v ~x[j] [i] [k] (by p==>q = ~p v q)

Writing it as an algebric linear expression:

(1-x[i] [j] [k])+(1-x[j] [i] [k]) >= 1 (check SAT problem)

x[i] [j] [k] +x[j] [i] [k]