Abstract
Given a set of clients and a set of potential sites for facilities, the p-median problem consists of opening a set of p sites and assigning each client to the closest open facility to it. It can be viewed as a variation of the uncapacitated facility location problem. We propose a new formulation of this problem by a mixed integer linear problem. We show that this formulation, while it has the same value by LP-relaxation, can be much more efficient than two previous formulations. The computational experiment performed on two sets of benchmark instances has showed that the efficiency of the standard branch-and-cut algorithm has been significantly improved. Finally, we explore the structure of the new formulation in order to derive reduction rules and to accelerate the LP-relaxation resolution.
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References
Avella P, Sassano A (2001) On the p-median polytope. Math Program 89:395–411
Avella P, Sassano A, Vasil’ev I (2007) Computational study of large-scale p-median problems. Math Program 109(1):89–114
Beasley JE (1990) OR-Library: distributing test problems by electronic mail. J Oper Res Soc 41:1069–1072. http://mscmga.ms.ic.ac.uk/info.html
Beltran C, Tadonki C, Vial J-Ph (2006) Solving the p-median problem with a semi-Lagrangian relaxation. Comput Optim Appl 35(2):239–260
Briant O, Naddef D (2004) The optimal diversity management problem. Oper Res 52(4):515–526
Church RL (2003) COBRA: a new formulation of the classic p-median location problem. Ann Oper Res 122:103–120
Cornuejols G, Nemhauser G, Wolsey LA (1980) A canonical representation of simple plant location problems and its applications. SIMAX 1(3):261–272
Cornuejols G, Nemhauser G, Wolsey LA (1990) The uncapacitated facility location problem. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley, New York
Fung G, Mangasarian OL (2001) Semi-supervised support vector machines for unlabeled data classification. Optim Methods Softw 15:29–44
Reese J (2006) Solution methods for the p-median problem: an annotated bibliography. Networks 48(3):125–142
Resende MGC, Werneck RF (2004) A hybrid heuristic for the p-median problem. J Heuristics 10(1):59–88
ReVelle CS, Swain R (1970) Central facilities location. Geogr Anal 2:30–42
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Elloumi, S. A tighter formulation of the p-median problem. J Comb Optim 19, 69–83 (2010). https://doi.org/10.1007/s10878-008-9162-0
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DOI: https://doi.org/10.1007/s10878-008-9162-0