Minimax regret p-center location on a network with demand uncertainty

Minimax regret p-center location on a network with demand uncertainty

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Article ID: iaor19991623
Country: United Kingdom
Volume: 5
Issue: 4
Start Page Number: 247
End Page Number: 254
Publication Date: Dec 1997
Journal: Location Science
Authors: ,
Keywords: -centre problem
Abstract:

We consider the weighted p-center problem on a transportation network with uncertain weights of nodes. Specifically, for each node, an interval estimate of its weight is known. The objective is to find the ‘minimax regret’ solution, i.e. to minimize the worst-case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place. We discuss properties of the problem and show that the problem can be solved by means of solving (n+1) regular weighted p-center problems. This leads to polynomial algorithms for the cases where the regular weighted p-center problem can be solved in polynomial time, e.g. for the case of a tree network, and for the case of a general network with p = 1.

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