Minmax regret location–allocation problem on a network under uncertainty

Minmax regret location–allocation problem on a network under uncertainty

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Article ID: iaor2009128
Country: Netherlands
Volume: 179
Issue: 3
Start Page Number: 1025
End Page Number: 1039
Publication Date: Jun 2007
Journal: European Journal of Operational Research
Authors:
Keywords: networks, optimization
Abstract:

We consider a robust location–allocation problem with uncertainty in demand coefficients. Specifically, for each demand point, only an interval estimate of its demand is known and we consider the problem of determining where to locate a new service when a given fraction of these demand points must be served by the utility. The optimal solution of this problem is determined by the ‘minimax regret’ location, i.e., the point that minimizes 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. For the case where the demand points are vertices of a network we show that the robust location–allocation problem can be solved in O(min{p, n − p}n3m) time, where n is the number of demand points, p (p < n) is the fixed number of demand points that must be served by the new service and m is the number of edges of the network.

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