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Locating Discretionary Service Facilities Based on Probabilistic Customer Flows

Author

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  • Oded Berman

    (University of Toronto, Division of Management and Economics at Scarborough and the Facility of Management, Toronto, Ontario, M5S 1V4, Canada)

  • Dmitry Krass

    (University of Toronto, Faculty of Management, Toronto, Ontario M5S 1V4, Canada)

  • Chen Wei Xu

    (University of Toronto, Faculty of Management, Toronto, Ontario M5S 1V4, Canada)

Abstract

In this paper, we consider the problem of locating discretionary facilities on a network. In contrast to previous work in the area, we no longer assume that information on customers' flows along all paths of the network is known (in practice such information is rarely available). Assuming that the fraction of customers that travel from any node to any adjacent node in the network is available, the problem of locating the facilities so as to maximize the fraction of customers that pass by a facility before reaching their destination is formulated as a nonlinear Integer Program. It is shown that by employing the theory of constrained Markov Decision Processes this problem can be reformulated as a linear Mixed Integer Program. The paper presents some preliminary computational results for this formulation as well as results for a greedy heuristic algorithm.

Suggested Citation

  • Oded Berman & Dmitry Krass & Chen Wei Xu, 1995. "Locating Discretionary Service Facilities Based on Probabilistic Customer Flows," Transportation Science, INFORMS, vol. 29(3), pages 276-290, August.
    • Handle: RePEc:inm:ortrsc:v:29:y:1995:i:3:p:276-290
    DOI: 10.1287/trsc.29.3.276
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    Citations

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    Cited by:

    1. John Hodgson, M. & Rosing, K. E. & Leontien, A. & Storrier, G., 1996. "Applying the flow-capturing location-allocation model to an authentic network: Edmonton, Canada," European Journal of Operational Research, Elsevier, vol. 90(3), pages 427-443, May.
    2. Daniel J. Rosenkrantz & Giri K. Tayi & S. S. Ravi, 2000. "Algorithms for Path-Based Placement of Inspection Stations on Networks," INFORMS Journal on Computing, INFORMS, vol. 12(2), pages 136-149, May.
    3. Walid Klibi & Francis Lasalle & Alain Martel & Soumia Ichoua, 2010. "The Stochastic Multiperiod Location Transportation Problem," Transportation Science, INFORMS, vol. 44(2), pages 221-237, May.
    4. Wu, Tai-Hsi & Lin, Jen-Nan, 2003. "Solving the competitive discretionary service facility location problem," European Journal of Operational Research, Elsevier, vol. 144(2), pages 366-378, January.
    5. Bar-Gera, Hillel & Mirchandani, Pitu B. & Wu, Fan, 2006. "Evaluating the assumption of independent turning probabilities," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 903-916, December.
    6. Lucio Bianco & Giuseppe Confessore & Pierfrancesco Reverberi, 2001. "A Network Based Model for Traffic Sensor Location with Implications on O/D Matrix Estimates," Transportation Science, INFORMS, vol. 35(1), pages 50-60, February.
    7. Faping Wang & Rui Chen & Lixin Miao & Peng Yang & Bin Ye, 2019. "Location Optimization of Electric Vehicle Mobile Charging Stations Considering Multi-Period Stochastic User Equilibrium," Sustainability, MDPI, vol. 11(20), pages 1-19, October.
    8. Ho-Yin Mak & Ying Rong & Zuo-Jun Max Shen, 2013. "Infrastructure Planning for Electric Vehicles with Battery Swapping," Management Science, INFORMS, vol. 59(7), pages 1557-1575, July.
    9. Lucio Bianco & Giuseppe Confessore & Monica Gentili, 2006. "Combinatorial aspects of the sensor location problem," Annals of Operations Research, Springer, vol. 144(1), pages 201-234, April.
    10. Yang, Hai & Zhou, Jing, 1998. "Optimal traffic counting locations for origin-destination matrix estimation," Transportation Research Part B: Methodological, Elsevier, vol. 32(2), pages 109-126, February.

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