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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References
Berman O (1994). The p maximal cover—p partial center problem on networks. Eur J Opl Res 72: 432–442.
Berman O and Wang J (2004). Probabilistic location problems with discrete demand weights. Networks 44: 47–57.
Berman O and Wang J (2007). The 1-median and 1-animedian problems with continuous probabilistic demand weights. INFOR, forthcoming..
Berman O, Wang J, Drezner Z and Wesolowsky GO (2003a). A probabilistic minimax location problem on the plane. Ann Opns Res 122: 59–70.
Berman O, Wang J, Drezner Z and Wesolowsky GO (2003b). The minimax and maximin location problems on a network with uniform distributed weights. IIE Trans 35: 1017–1025.
Charnes A and Cooper WW (1963). Deterministic equivalents for optimizing and satisfying under chance constraints. Opns Res 11: 18–39.
Church RL and Meadows ME (1978). Location modeling utilizing maximum service distance criteria. Geographic Anal 11: 358–373.
Church RL and ReVelle C (1974). The maximal covering location problem. Papers Region Sci Assoc 32: 101–118.
Frank H (1966). Optimum locations on a graph with probabilistic demands. Opns Res 14: 409–421.
Frank H (1967). Optimum locations on a graph with correlated normal demands. Opns Res 15: 552–556.
Garey MR and Johnson D (1979). Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman: New York.
Handler GY (1990). p-Center problems. In: Mirchandani P.B. and Francis R.L. (eds). Discrete Facility Location 1990. Wiley: New York, pp. 305–346.
Revelle C and Willimas JC (2002). Reserve design and facility siting. In: Drezner Z. and Hamacher H.W. (eds). Facility Location: Applications and Theory 2002. Springer-Verlag: Berlin, pp. 307–328.
Simon HA (1957). Models of Man. Wiley: New York pp 243–273.
Acknowledgements
We would like to thank the two anonymous referees for their comments and suggestions. Oded Berman was supported by grants from NSERC. Jiamin Wang was supported by a grant from the Research Committee at the C. W. Post Campus of Long Island University.
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Berman, O., Wang, J. The probabilistic 1-maximal covering problem on a network with discrete demand weights. J Oper Res Soc 59, 1398–1405 (2008). https://doi.org/10.1057/palgrave.jors.2602466
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DOI: https://doi.org/10.1057/palgrave.jors.2602466