A Fast Approximate Method for the Large-scale One-source P-median Problem

Abstract

The p-median problem (PMP) involves determining <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$p$</tex> locations among a set of candidates on which for building <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$q$</tex> facilitates to best serve the customers scattered around. In real industrial applications, the scales of the problems may be large, with hundreds of candidate locations and thousands of demanding customers, such that solving directly the PMP using a mixed-integer programming (MIP) solvers may consume a lot of CPU time. In this paper, we presented a fast clustering-based method with continuous optimization model for the large-scale one-source PMP, where a two-stage strategy is applied to obtain the globally optimized solutions. Computational experiments were conducted on two groups of synthesized datasets to test the performances of the proposed method. The experimental results showed that optimal results could be obtained with much higher efficiencies, even hundreds of times faster than that of the traditional way.