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Profit Maximizing Distributed Service System Design with Congestion and Elastic Demand

Author

Listed:
  • Robert Aboolian

    (College of Business Administration, California State University San Marcos, San Marcos, California 92096)

  • Oded Berman

    (Rotman School of Management, University of Toronto, Toronto, Ontario, Canada M5S 3E6)

  • Dmitry Krass

    (Rotman School of Management, University of Toronto, Toronto, Ontario, Canada M5S 3E6)

Abstract

In this paper we develop a service network design model that explicitly takes into account the elasticity of customer demand with respect to travel distance and congestion delays. The model incorporates a feedback loop between customer demand and congestion at the facilities. The problem is to determine the number of facilities, their locations, their service capacity, and the assignment of customers to facilities so as to maximize the overall profit of the system. Two versions of the problem are presented. In one, each facility is modeled as an M / M /1 queuing system where the service rate is a decision variable; in the other one, the facility is modeled as an M / M / k queuing model where the service rate is given, but the number k is a decision variable. An exact algorithm and heuristics are developed and tested via computational experiments. Although our model is of the “directed choice” type where the assignment of customers to facilities is controlled by the decision maker, computational results show that in the vast majority of cases the customers are assigned to the utility-maximizing facility, indicating that there is no conflict between the customers' and decision makers' goals. A case study of locating preventive medicine clinics in Toronto, Ontario, illustrates the model.

Suggested Citation

  • Robert Aboolian & Oded Berman & Dmitry Krass, 2012. "Profit Maximizing Distributed Service System Design with Congestion and Elastic Demand," Transportation Science, INFORMS, vol. 46(2), pages 247-261, May.
    • Handle: RePEc:inm:ortrsc:v:46:y:2012:i:2:p:247-261
    DOI: 10.1287/trsc.1110.0392
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    References listed on IDEAS

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    8. O Berman & Z Drezner, 2007. "The multiple server location problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(1), pages 91-99, January.
    9. Vedat Verter & Sophie Lapierre, 2002. "Location of Preventive Health Care Facilities," Annals of Operations Research, Springer, vol. 110(1), pages 123-132, February.
    10. Zhang, Yue & Berman, Oded & Verter, Vedat, 2009. "Incorporating congestion in preventive healthcare facility network design," European Journal of Operational Research, Elsevier, vol. 198(3), pages 922-935, November.
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    Citations

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    Cited by:

    1. Sachin Jayaswal & Navneet Vidyarthi, 2017. "Facility location under service level constraints for heterogeneous customers," Annals of Operations Research, Springer, vol. 253(1), pages 275-305, June.
    2. repec:iim:iimawp:13011 is not listed on IDEAS
    3. Jalili Marand, Ata & Hoseinpour, Pooya, 2024. "A congested facility location problem with strategic customers," European Journal of Operational Research, Elsevier, vol. 318(2), pages 442-456.
    4. Jayaswal, Sachin, 2014. "Emergency Medical Service System Design under Service Level Constraints for Heterogeneous Patients," IIMA Working Papers WP2014-11-04, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Hoseinpour, Pooya & Jalili Marand, Ata, 2022. "Designing a service system with price- and distance-sensitive demand: A case study in mining industry," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1355-1371.
    6. Hoseinpour, Pooya & Ahmadi-Javid, Amir, 2016. "A profit-maximization location-capacity model for designing a service system with risk of service interruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 113-134.
    7. Ouyang, Yanfeng & Wang, Zhaodong & Yang, Hai, 2015. "Facility location design under continuous traffic equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 18-33.
    8. Fischetti, Matteo & Ljubić, Ivana & Sinnl, Markus, 2016. "Benders decomposition without separability: A computational study for capacitated facility location problems," European Journal of Operational Research, Elsevier, vol. 253(3), pages 557-569.
    9. An, Shi & Cui, Na & Bai, Yun & Xie, Weijun & Chen, Mingliu & Ouyang, Yanfeng, 2015. "Reliable emergency service facility location under facility disruption, en-route congestion and in-facility queuing," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 82(C), pages 199-216.
    10. Parajuli, Anubhuti & Kuzgunkaya, Onur & Vidyarthi, Navneet, 2021. "The impact of congestion on protection decisions in supply networks under disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 145(C).
    11. Robert Aboolian & Oded Berman & Vedat Verter, 2016. "Maximal Accessibility Network Design in the Public Sector," Transportation Science, INFORMS, vol. 50(1), pages 336-347, February.
    12. Robert Aboolian & Tingting Cui & Zuo-Jun Max Shen, 2013. "An Efficient Approach for Solving Reliable Facility Location Models," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 720-729, November.
    13. Cornelia Schön & Pratibha Saini, 2018. "Market-Oriented Service Network Design When Demand is Sensitive to Congestion," Transportation Science, INFORMS, vol. 52(5), pages 1253-1275, October.
    14. Hossein Abouee-Mehrizi & Oded Berman & M. Reza Baharnemati, 2014. "Designing Production-Inventory-Transportation Systems with Capacitated Cross-Docks," Transportation Science, INFORMS, vol. 48(1), pages 121-135, February.
    15. Wang, Zhaodong & Xie, Siyang & Ouyang, Yanfeng, 2022. "Planning reliable service facility location against disruption risks and last-mile congestion in a continuous space," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 123-140.
    16. Zetina, Carlos Armando & Contreras, Ivan & Cordeau, Jean-François, 2019. "Profit-oriented fixed-charge network design with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 1-19.
    17. Esma Akgun & Sibel A. Alumur & F. Safa Erenay, 2023. "Determining optimal COVID-19 testing center locations and capacities," Health Care Management Science, Springer, vol. 26(4), pages 748-769, December.
    18. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.
    19. Teodora Dan & Andrea Lodi & Patrice Marcotte, 2020. "Joint location and pricing within a user-optimized environment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 61-84, March.
    20. König, Eva & Schön, Cornelia, 2021. "Railway delay management with passenger rerouting considering train capacity constraints," European Journal of Operational Research, Elsevier, vol. 288(2), pages 450-465.

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