Finite dominating set for the p-facility cent-dian network location problem

Finite dominating set for the p-facility cent-dian network location problem

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Article ID: iaor2000715
Country: Greece
Volume: 11
Issue: 1
Start Page Number: 27
End Page Number: 40
Publication Date: Dec 1997
Journal: Studies In Locational Analysis
Authors: , ,
Keywords: networks
Abstract:

A dominating set for a location problem is a set of points that contains an optimal solution for all instances of the problem. The p-facility location problems on a network appear when the possible selections for locating the facilities are the sets of p points of the network. Hooker, Garfinkel and Chen consider a theoretical result to extend the dominating set for the 1-facility problems to the corresponding p-facility problems, and apply this result to propose a finite dominating set for the p-facility cent-dian problem on a network. The optimal solutions of the cent-dian problems are those minimizing a linear combination of the center and median objective functions. Since it is known that the set of vertices and local centers is a dominating set for the single facility cent-dian problem, they claim that it is also a dominating set for the p-facility cent-dian problem. We show a counterexample for p = 2 and give an alternative finite dominating set for the p-facility cent-dian. We also provide a solution method that avoids the exhaustive search in all the sets of p points of this dominating set.

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