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.
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Visiting researcher at the Center for Industrial Location of the Vrije Universiteit Brussel during this research.
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Carrizosa, E., Plastria, F. On minquantile and maxcovering optimisation. Mathematical Programming 71, 101–112 (1995). https://doi.org/10.1007/BF01592247
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DOI: https://doi.org/10.1007/BF01592247