Optimizing ordered median functions with applications to single facility location

Victor Blanco (), Justo Puerto () and Safae El Haj Ben Ali
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Victor Blanco: Universidad de Granada
Justo Puerto: Universidad de Sevilla, IMUS
Safae El Haj Ben Ali: Universidad de Sevilla, IMUS

A chapter in Operations Research Proceedings 2011, 2012, pp 329-334 from Springer

Abstract: Abstract This paper considers the problem of minimizing the ordered median function of finitely many rational functions over compact semi-algebraic sets. Ordered median of rational functions are not, in general, neither rational functions nor the supremum of rational functions.We prove that the problem can be transformed into a new problem embedded in a higher dimension space where it admits a convenient representation. This reformulation admits a hierarchy of SDP relaxations that approximates, up to any degree of accuracy, the optimal value of those problems. We apply this general framework to a broad family of continuous location problems solving some difficult problems.

Keywords: Rational Function; Demand Point; Ordered Weight Average; Median Function; Convenient Representation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-642-29210-1_53

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DOI: 10.1007/978-3-642-29210-1_53

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