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Ensuring feasibility in location problems with stochastic demands and congestion

Author

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  • Opher Baron
  • Oded Berman
  • Seokjin Kim
  • Dmitry Krass

Abstract

A location problem with stochastic demand and congestion where mobile servers respond to service calls originating from nodes is considered. The problem is of the set-covering type: only servers within the coverage radius of the demand-generating node may respond to a call. The service level constraint requires that at least one server must be available to respond to an arriving call, with some prespecified probability. The objective is to minimize the total number of servers. It is shown that earlier models quite often overestimate servers' availability and thus may lead to infeasible solutions (i.e., solutions that fail to satisfy the service level constraint). System stability conditions and lower bounds on system availability are developed by analyzing the underlying partially accessible queueing system. These lead to the development of two new models for which feasibility is guaranteed. Simulation-based computational experiments show that the proposed models achieve feasibility without significantly increasing the total number of servers.[Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplemental resource: Appendix of Tables of Computational Results for Section 7.]

Suggested Citation

  • Opher Baron & Oded Berman & Seokjin Kim & Dmitry Krass, 2009. "Ensuring feasibility in location problems with stochastic demands and congestion," IISE Transactions, Taylor & Francis Journals, vol. 41(5), pages 467-481.
    • Handle: RePEc:taf:uiiexx:v:41:y:2009:i:5:p:467-481
    DOI: 10.1080/07408170802382758
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    Cited by:

    1. Zhang, Sizhe & Cardin, Michel-Alexandre, 2017. "Flexibility and real options analysis in emergency medical services systems using decision rules and multi-stage stochastic programming," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 107(C), pages 120-140.
    2. Miguel A. Lejeune & Francois Margot, 2018. "Aeromedical Battlefield Evacuation Under Endogenous Uncertainty in Casualty Delivery Times," Management Science, INFORMS, vol. 64(12), pages 5481-5496, December.
    3. 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.

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