A generalized model of equality measures in network location problems

Authors:
M. C. López-de-los-Mozos;Juan A. Mesa;Justo Puerto
Affiliations:
Departamento de Matemática Aplicada I. Universidad de Sevilla, Spain and Departamento de Matemática Aplicada II. Universidad de Sevilla, Spain;Departamento de Matemática Aplicada I. Universidad de Sevilla, Spain and Departamento de Matemática Aplicada II. Universidad de Sevilla, Spain;Departamento de Estadística e Investigación Operativa. Universidad de Sevilla, Spain
Venue:
Computers and Operations Research
Year:
2008

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Abstract

In this paper, the concept of the ordered weighted averaging operator is applied to define a model which unifies and generalizes several inequality measures. For a location x, the value of the new objective function is the ordered weighted average of the absolute deviations from the average distance from the facilities to the location x. Several kinds of networks are studied: cyclic, tree and path networks and, for each of them, the properties of the objective function are analyzed in order to identify a finite dominating set for optimal locations. Polynomial-time algorithms are proposed for these problems, and the corresponding complexity is discussed.