linearization of a conditioal constraint

thank you so much for your assistance. I didn't work though

when you say it didnt work, what exactly do you mean? You get infeasible solution? Or the result is contrary to expectation?

There is a correction I need to make. The first constraint should look like this: r2-r1 >= (30*b1-29) because as per the requirement in the problem the binary variable should be active (1) when r2 > r1, and since they are integers the difference should be atleast 1. Was it this that caused it to not work?

it didn't so much affect the result. May be because i was inaccurate when answering your question. r1,r2 are parameters whose values are predefined. A2 and A1 are variables whose values should be calculated. b1 and b2 are binary variables that i introduced to manage the constraints.

if r1, and r2 are constants, you wouldnt need the binary variables, you can already construct the constraint saing A2 -A1 >= e, or A2 - A1 <= 0, based on what the values of r1 and r2 at the time you generate the lp model to solve. Maybe I am still not understanding your problem.

in more details: r is the rank where r(u)<r(v) implies that the rank of u is smaller than the rank of v. 1 is the smallest rank and 30 is the highest rank. i want to force A(u) to be smaller than A(v) in the case that r(u)<r(v)