Ranking Decomposition for the Discrete Ordered Median Problem

Marilène Cherkesly (), Claudio Contardo () and Matthieu Gruson ()
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Marilène Cherkesly: Département d’Analytique, Opérations et Technologies de l’Information, Université du Quèbec à Montréal, Montreal, Quebec H2X 3X2, Canada; and CIRRELT – Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3T 1J4, Canada; and GERAD – Group for Research in Decision Analysis, Montreal, Quebec H3T 1N8, Canada
Claudio Contardo: CIRRELT – Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3T 1J4, Canada; and GERAD – Group for Research in Decision Analysis, Montreal, Quebec H3T 1N8, Canada; and Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada
Matthieu Gruson: Département d’Analytique, Opérations et Technologies de l’Information, Université du Quèbec à Montréal, Montreal, Quebec H2X 3X2, Canada; and CIRRELT – Interuniversity Research Center on Enterprise Networks, Logistics and Transportation, Montreal, Quebec H3T 1J4, Canada; and GERAD – Group for Research in Decision Analysis, Montreal, Quebec H3T 1N8, Canada

INFORMS Journal on Computing, 2025, vol. 37, issue 2, 230-248

Abstract: Given a set N of size n , a nonnegative, integer-valued distance matrix D of dimensions n × n , an integer p ∈ N and an integer-valued weight vector λ ∈ Z n , the discrete ordered median problem ( DOMP ) consists of selecting a subset C of exactly p points from N (also referred to as the centers ) so as to: 1) assign each point in N to its closest center in C ; 2) rank the resulting distances (between every point and its center) from smallest to largest in a sorted vector that we denote d * ; 3) minimize the scalar product 〈 λ , d * 〉 . The DOMP generalizes several classical location problems such as the p -center, the p -median and the obnoxious median problem. We introduce an exact branch-and-bound algorithm to solve the DOMP . This branch-and-bound decouples the ranking attribute of the problem to form a series of simpler subproblems which are solved using innovative binary search methods. We consider several acceleration techniques such as warm-starts, primal heuristics, variable fixing, and symmetry breaking. We perform a thorough computational analysis and show that the proposed method is competitive against several MIP models from the scientific literature. We also comment on the limitations of our method and propose avenues of future research.

Keywords: discrete ordered median problem; ranking decomposition; p -center problem; p -median problem; branch-and-bound (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:37:y:2025:i:2:p:230-248

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