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Inequality measures and equitable locations

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Abstract

While making location decisions, the distribution of distances (outcomes) among the service recipients (clients) is an important issue. In order to comply with the minimization of distances as well as with an equal consideration of the clients, mean-equity approaches are commonly used. They quantify the problem in a lucid form of two criteria: the mean outcome representing the overall efficiency and a scalar measure of inequality of outcomes to represent the equity (fairness) aspects. The mean-equity model is appealing to decision makers and allows a simple trade-off analysis. On the other hand, for typical dispersion indices used as inequality measures, the mean-equity approach may lead to inferior conclusions with respect to the distances minimization. Some inequality measures, however, can be combined with the mean itself into optimization criteria that remain in harmony with both inequality minimization and minimization of distances. In this paper we introduce general conditions for inequality measures sufficient to provide such an equitable consistency. We verify the conditions for the basic inequality measures thus showing how they can be used in location models not leading to inferior distributions of distances.

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Authors and Affiliations

  1. Institute of Control and Computation Engineering, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Włodzimierz Ogryczak

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  1. Włodzimierz Ogryczak
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Correspondence to Włodzimierz Ogryczak.

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The research was supported by the Ministry of Science and Information Society Technologies under grant 3T11C 005 27 “Models and Algorithms for Efficient and Fair Resource Allocation in Complex Systems”.

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Ogryczak, W. Inequality measures and equitable locations. Ann Oper Res 167, 61–86 (2009). https://doi.org/10.1007/s10479-007-0234-9

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