On minquantile and maxcovering optimisation |
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Authors: | E Carrizosa F Plastria |
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Institution: | (1) Departamento de Estadistica e I.O., Universidad de Sevilla, 41012 Sevilla, Spain;(2) Center for Industrial Location, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium |
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Abstract: | In this paper we introduce the parametric minquantile problem, a weighted generalisation ofkth maximum minimisation. It is shown that, under suitable quasiconvexity assumptions, its resolution can be reduced to solving a polynomial number of minmax problems.It is also shown how this simultaneously solves (parametric) maximal covering problems. It follows that bicriteria problems, where the aim is to both maximize the covering and minimize the cover-level, are reducible to a discrete problem, on which any multiple criteria method may be applied.Corresponding author.Visiting researcher at the Center for Industrial Location of the Vrije Universiteit Brussel during this research. |
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Keywords: | Minmax Maximal covering problems Multi criteria decision-making |
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