  The p-median problem concerns the location of facilities so that the sum of
distances between the demand points and their nearest facility is minimized. We
study a variant of this classic location problem where minimum distance
constraints exist both between the facilities and between the facilities and
the demand points. This specific type of problem can be used to model
situations where the facilities to be located are semi-obnoxious. But despite
its relevance to real life scenarios, it has received little attention within
the vast literature on location problems. We present twelve ILP models for this
problem, coupling three formulations of the p-median problem with four
formulations of the distance constraints. We utilize Gurobi Optimizer v9.0.3 in
order to compare these ILP models on a large dataset of problems. Experimental
results demonstrate that the classic p-median model proposed by ReVelle \&
Swain and the model proposed by Rosing et al. are the best performers.
