A comparative study of formulations and solution methods for the discrete ordered p-median problem. (February 2017)

• Record Type: Journal Article
• Authors: Labbé, Martine; Ponce, Diego; Puerto, Justo
• Is Part Of: Computers & operations research. Volume 78(2017)
• Page Start: 230
• Page End: 242
• Publication Date: 2017-02
• Subjects: Discrete multifacility location -- MIP formulations -- Ordered median problem; Operations research -- Periodicals; Electronic digital computers -- Periodicals; 004.05
• DOI: 10.1016/j.cor.2016.06.004
• Languages: English
• ISSNs: 0305-0548

Abstract

Abstract: This paper presents several new formulations for the Discrete Ordered Median Problem (DOMP) based on its similarity with some scheduling problems. Some of the new formulations present a considerably smaller number of constraints to define the problem with respect to some previously known formulations. Furthermore, the lower bounds provided by their linear relaxations improve the ones obtained with previous formulations in the literature even when strengthening is not applied. We also present a polyhedral study of the assignment polytope of our tightest formulation showing its proximity to the convex hull of the integer solutions of the problem. Several resolution approaches, among which we mention a branch and cut algorithm, are compared. Extensive computational results on two families of instances, namely randomly generated and from Beasley's OR-library, show the power of our methods for solving DOMP. Abstract : Highlights: New formulations for Discrete Ordered Median Problem. Polyhedral analysis of new formulations. Comparison of formulations. Extensive computational results.