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Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach. (English) Zbl 0941.90045

Summary: Models developed to analyze facility location decisions have typically optimized one or more objectives, subject to physical, structural, and policy constraints, in a static or deterministic setting. Because of the large capital outlays that are involved, however, facility location decisions are frequently long-term in nature. Consequently, there may be considerable uncertainty regarding the way in which relevant parameters in the location decision will change over time. In this paper, we propose two approaches for analyzing these types of dynamic location problems, focussing on situations where the total number of facilities to be located is uncertain. We term this type of location problem NOFUN (Number Of Facilities UNcertain). We analyze the NOFUN problem using two well-established decision criteria: the minimization of expected opportunity loss (E0L), and the minimization of maximum regret. In general, these criteria assume that there are a finite number of decision options and a finite number of possible states of nature. The minisum E0L criterion assumes that one can assign probabilities for the occurrence of the various states of nature and, therefore, find the initial set of facility locations that minimize the sum of expected losses across all future states. The minimax regret criteria finds the pattern of initial facility locations whose maximum loss is minimized over all possible future states.

MSC:

90B80 Discrete location and assignment
90B50 Management decision making, including multiple objectives
Full Text: DOI

References:

[1] Anderson, D. R.; Sweeney, D. J.; Williams, T. A., An Introduction of Management Science: Quantitative Approaches to Decision Making (1994), West Publishing Co: West Publishing Co St. Paul, MN
[2] Balinski, M. L., Integer programming: Methods, uses, computation, Management Science, 12, 253-313 (1965) · Zbl 0129.12004
[3] Ballou, R. H., Dynamic warehouse location analysis, Journal of Marketing Research, 7, 271-276 (1968)
[4] Bean, J. C.; Higle, J. L.; Smith, R. L., Capacity expansion under stochastic demands, Operations Research, 40, S210-S216 (1992) · Zbl 0764.90021
[5] Berman, O., Locating a facility on a congested network with random lengths, Networks, 15, 275-294 (1985) · Zbl 0579.90021
[6] Berman, O.; Chiu, S. S.; Larson, R. C.; Odoni, A. R.; Batta, R., Location of mobile units in a stochastic environment, (Mirchandani, P. B.; Francis, R. L., Discrete Location Analysis (1990), Wiley: Wiley New York) · Zbl 0738.90043
[7] Berman, O.; Le Blanc, B., Location-relocation of mobile facilities on a stochastic network, Transportation Science, 18, 315-330 (1984)
[8] Berman, O.; Odoni, A. R., Locating mobile servers on a network with Markovean properties, Networks, 12, 73-86 (1982) · Zbl 0478.90016
[9] Bianchi, C.; Church, R., A hybrid FLEET model for emergency medical service system design, Social Sciences in Medicine, 26, 163-171 (1988)
[10] Brandeau, M. L.; Chiu, S. S., An overview of representative problems in location research, Management Science, 35, 645-674 (1989) · Zbl 0669.90040
[11] Campbell, J. F., Locating transportation terminals to serve an expanding demand, Transportation Research B, 24, 173-192 (1990)
[12] Chruch, R.; ReVelle, C., The maximal covering location problem, Papers of the Regional Science Association, 32, 101-118 (1974)
[13] Current, J.; Min, H.; Schilling, D., Multiobjective analysis of facility location decisions, European Journal of Operational Research, 49, 295-307 (1990) · Zbl 0717.90042
[14] Daskin, M. S., A maximum expected covering location model: Formulation, properties and heuristic solution, Transportation Science, 17, 48-70 (1983)
[15] Daskin, M. S.; Hogan, K.; ReVelle, C., Integration of multiple, excess, backup, and expected covering models, Environment and Planning B, 15, 15-35 (1988)
[16] Daskin, M. S.; Hopp, W. J.; Medina, B., Forecast horizons and dynamic facility location planning, Annals of Operations Research, 40, 125-152 (1992) · Zbl 0787.90038
[17] Drezner, Z., Dynamic facility location: The progressive p-median problem, Location Science, 3, 1-7 (1995) · Zbl 0917.90224
[18] Drezner, Z.; Wesolowsky, G. O., Facility location when demand is time dependent, Naval Research Logistics, 38, 763-777 (1991) · Zbl 0748.90036
[19] Erlenkotter, D., A comparative study of approaches to dynamic location problems, European Journal of Operational Research, 6, 133-143 (1981) · Zbl 0451.90038
[20] Frank, H., Optimum locations on a graph with probabilistic demands, Operations Research, 14, 409-421 (1966) · Zbl 0142.17704
[21] Galvão, R. D., The use of Lagrangean Relaxation in the solution of uncapacitated facility location problems, Location Science, 1, 57-70 (1993) · Zbl 0923.90102
[22] Garey, M. R.; Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness (1979), Freeman: Freeman San Francisco, CA · Zbl 0411.68039
[23] Hakimi, S. L., Optimal distributions of switching centers in a communication network and some related graph theoretic problems, Operations Research, 13, 462-475 (1965) · Zbl 0135.20501
[24] Jucker, J. V.; Carlson, R. C., The simple plant location problem under uncertainty, Operations Research, 24, 1045-1055 (1976) · Zbl 0343.90054
[25] Kariv, O.; Hakimi, L., An algorithmic approach to network location problems. Part 2. The p-median, SIAM Journal of Applied Mathematics, 37, 539-560 (1979) · Zbl 0432.90075
[26] Louveaux, F. V., Discrete stochastic location models, Annals of Operations Research, 6, 23-34 (1986)
[27] Manne, A. S., Capacity expansion and probabilistic growth, Econometrica, 29, 632-649 (1961) · Zbl 0103.13203
[28] (Manne, A. S., Investments for Capacity Expansion: Size, Location, and Time Phasing (1967), MIT Press: MIT Press Cambridge, MA)
[29] Marianov, V.; ReVelle, C., A probabilistic fire-protecting siting model with joint vehicle reliability requirements, The Journal of the RSAI, 71, 217-241 (1992)
[30] Mirchandani, P., The p-median problem and generalizations, (Mirchandani, P. B.; Francis, R. L., Discrete Location Theory (1990), Wiley: Wiley New York), 55-117 · Zbl 0731.90050
[31] (Mirchandani, P. B.; Francis, R. L., Discrete Location Theory (1990), Wiley: Wiley New York) · Zbl 0718.00021
[32] Mirchandani, P. B.; Odoni, A. R., Locations of medians on stochastic networks, Transportation Science, 13, 85-97 (1979)
[33] Osleep, J.; Ratick, S., A dynamic location-allocation model for evaluating the spatial impacts of just-in-time planning, Geographical Analysis, 22, 50-69 (1990)
[34] Ratick, S.; Osleep, J.; Kuby, M.; Lee, K., Interperiod network storage location-allocation (INSLA) Models, (Rushton, G.; Ghosh, A., Spatial Analysis and Location Allocation Models (1987), Van Nostrand: Van Nostrand New York), 269-301
[35] ReVelle, C., Review, extension and prediction in emergency service siting models, European Journal of Operational Research, 40, 58-69 (1989) · Zbl 0667.90033
[36] Revelle, C.; Hogan, K., The maximum availability location problem, Transportation Science, 23, 192-200 (1989) · Zbl 0681.90036
[37] ReVelle, C.; Hogan, K., The maximum reliability location problem and α-reliability p-center problem: Derivatives of the probabilistic location set covering problem, Annals of Operations Research, 18, 155-174 (1989) · Zbl 0707.90063
[38] ReVelle, C.; Bergman, D.; Schilling, D.; Cohon, J.; Church, R., Facility location: A review of context free and EMS models, Health Services Research, 129-146 (1977), Summer
[39] ReVelle, C.; Toregas, C.; Falkson, L., Applications of the location set covering problem, Geographical Analysis, 8, 65-76 (1976)
[40] ReVelle, C.; Swain, R. W., Central facilities location, Geographical Analysis, 2, 30-42 (1970)
[41] Roodman, G. M.; Schwartz, L. B., Optimal and heuristic facility phase-out strategies, AIIE Transactions, 7, 177-184 (1975)
[42] Schilling, D. A., Dynamic location modeling for public-sector facilities: A multicriteria approach, Decision Science, 11, 714-724 (1980)
[43] Schilling, D. A., Strategic facility planning: The analysis of options, Decision Science, 13, 1-14 (1982)
[44] Serra, D.; Ratick, S.; ReVelle, C., The maximum capture problem with uncertainty, Environment & Planning B, 23 (1996), (forthcoming)
[45] Toregas, C.; ReVelle, C., Optimal location under time or distance constraints, Papers of the Regional Science Association, 28, 133-143 (1972)
[46] Van Roy, T. J.; Erlenkotter, D., A dual-based procedure for dynamic facility location, Management Science, 28, 1091-1103 (1982) · Zbl 0495.90033
[47] Weaver, J. R.; Church, R. L., Computational procedures for location problems on stochastic networks, Transportation Science, 17, 168-180 (1983)
[48] Wesolowsky, G. O., Dynamic facility location, Management Science, 7, 1241-1248 (1973)
[49] Wesolowsky, G. O.; Truscott, W. G., The multiperiod location-allocation problem with relocation of facilities, Management Science, 22, 57-65 (1975) · Zbl 0309.90066
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