The p-median problem was first formulated as an integer-linear programming problem by ReVelle and Swain and further revised by Rosing et al. These two forms have withstood the test of time, as they have been used by virtually everyone since then. We prove that a property associated with geographical proximity makes it possible to eliminate many of the model variables through a substitution process. This new substitution technique has resulted in the elimination of up to 60% of the variables needed in either of these classic model formulations.
