The probabilistic 1-maximal covering problem on a network with discrete demand weights

The probabilistic 1-maximal covering problem on a network with discrete demand weights

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Article ID: iaor20097302
Country: United Kingdom
Volume: 59
Issue: 10
Start Page Number: 1398
End Page Number: 1405
Publication Date: Oct 2008
Journal: Journal of the Operational Research Society
Authors: ,
Abstract:

We discuss the probabilistic 1–maximal covering problem on a network with uncertain demand. A single facility is to be located on the network. The demand originating from a node is considered covered if the shortest distance from the node to the facility does not exceed a given service distance. It is assumed that demand weights are independent discrete random variables. The objective of the problem is to find a location for the facility so as to maximize the probability that the total covered demand is greater than or equal to a pre–selected threshold value. We show that the problem is NP–hard and that an optimal solution exists in a finite set of dominant points. We develop an exact algorithm and a normal approximation solution procedure. Computational experiment is performed to evaluate their performance.

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