I want to build a Goal Programming Model that uses Satisfaction Functions Here for more information
I now want to build functions that work like this
My variables depend on an additional index j. delta represents the deviation from goal i at alternative j and the alphas represent certain thresholds defined for each scenario.
What is the easiest/simplest way to achieve this? I want to avoid using binary variables because I already tried it and the calculation of the variables did not work and additionally it does not protect against division by 0 if alpha_one and alpha_two happen to be equal.
If there is an easier way to achieve this please let me know :)
@Koli , the paper you linked to is behind a paywall that we cannot access.
@mohansx for answering.
I simplified my case so that I only have one alpha and two binary variables beta1 and beta2. beta1 = 1 if delta <= alpha and beta2 = 1 if delta > alpha. I managed this with two constraints: