An extended covering model for flexible discrete and equity location problems
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To model flexible objectives for discrete location problems, ordered median functions can be applied. These functions multiply a weight to the cost of fulfilling the demand of a customer which depends on the position of that cost relative to the costs of fulfilling the demand of the other customers. In this paper a reformulated and more compact version of a covering model for the discrete ordered median problem (DOMP) is considered. It is shown that by using this reformulation better solution times can be obtained. This is especially true for some objectives that are often employed in location theory. In addition, the covering model is extended so that ordered median functions with negative weights are feasible as well. This type of modeling weights has not been treated in the literature on the DOMP before. We show that several discrete location problems with equity objectives are particular cases of this model. As a result, a mixed-integer linear model for this type of problems is obtained for the first time.
KeywordsEquity Flexible model Discrete location Integer programming
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- Domínguez-Marín P (2003) The discrete ordered median problem: models and solution methods. Kluwer, PhD ThesisGoogle Scholar
- Eiselt H, Laporte G (1995) Objectives in location. In: Drezner Z(eds) Facility location: a survey of applications and methods. Springer, New York, pp 151–180Google Scholar
- Kalcsics J (2006) Unified approaches to territory design and facility location. Shaker, AachenGoogle Scholar
- Nickel S (2001) Discrete ordered weber problems. In: Operations research proceedings 2000. Springer, Heidelberg, pp 71–76Google Scholar
- Nickel S, Puerto J (2005) Facility location: a unified approach. Springer, BerlinGoogle Scholar
- Puerto J, Fernández F (1995) The symmetrical single facility location problem. Technical Report, Prepublicación de la Facultaf de Mathemáticas, Universidad de SevillaGoogle Scholar
- Slater P (1978) Structure of the k-centra in a tree. In: Proceedings of the 9th Southwest conference on combinatorics, Graph Theory and Computing, pp 663–670Google Scholar