Extensive facility location problems on networks with equity measures

Authors:
Justo Puerto;Federica Ricca;Andrea Scozzari
Affiliations:
Universidad de Sevilla, Dep. Estadistica e Investigación Operativa, Spain;Universití di Roma "La Sapienza", Dip. Statistica, Probabilití e Statistiche Applicate, Italy;Universití di Roma "La Sapienza", Dip. Matematica per le Decisioni Economiche, Finanziarie ed Assicurative, Italy
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

This paper deals with the problem of locating path-shaped facilities of unrestricted length on networks. We consider as objective functions measures conceptually related to the variability of the distribution of the distances from the demand points to a facility. We study the following problems: locating a path which minimizes the range, that is, the difference between the maximum and the minimum distance from the vertices of the network to a facility, and locating a path which minimizes a convex combination of the maximum and the minimum distance from the vertices of the network to a facility, also known in decision theory as the Hurwicz criterion. We show that these problems are NP-hard on general networks. For the discrete versions of these problems on trees, we provide a linear time algorithm for each objective function, and we show how our analysis can be extended also to the continuous case.