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A Heuristic for the Multisource Weber Problem with Service Level Constraints

Author

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  • Prahalad Venkateshan

    (Production and Quantitative Methods Area, Indian Institute of Management, Vastrapur, Ahmedabad 380015, India)

  • Kamlesh Mathur

    (Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, Ohio 44106)

Abstract

In this paper we develop a column-generation-based heuristic procedure to solve a generalized version of the multisource Weber problem where in addition to the transportation cost we also consider staffing level costs that arise due to consideration of service level constraints. Traditional solution procedures for the multisource Weber problem do not take into account the staffing costs. Our contribution is towards addressing this gap. We develop a lower bound for the problem using which we evaluate the performance of the heuristic procedure on problems of different sizes and cost parameters. Our computational experience indicates that problems with up to 100 customer regions can be solved using the heuristic within five minutes of computational time on average. The average gap is less than 5% for a majority of problem instances.

Suggested Citation

  • Prahalad Venkateshan & Kamlesh Mathur, 2015. "A Heuristic for the Multisource Weber Problem with Service Level Constraints," Transportation Science, INFORMS, vol. 49(3), pages 472-483, August.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:3:p:472-483
    DOI: 10.1287/trsc.2014.0547
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    References listed on IDEAS

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    1. Mark S. Daskin, 1983. "A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution," Transportation Science, INFORMS, vol. 17(1), pages 48-70, February.
    2. Venkateshan, Prahalad & Mathur, Kamlesh & Ballou, Ronald H., 2010. "Locating and staffing service centers under service level constraints," European Journal of Operational Research, Elsevier, vol. 201(1), pages 55-70, February.
    3. Rosing, K. E., 1992. "An optimal method for solving the (generalized) multi-Weber problem," European Journal of Operational Research, Elsevier, vol. 58(3), pages 414-426, May.
    4. Richard C. Larson, 1975. "Approximating the Performance of Urban Emergency Service Systems," Operations Research, INFORMS, vol. 23(5), pages 845-868, October.
    5. Berman, Oded & Mandowsky, Ronald R., 1986. "Location-allocation on congested networks," European Journal of Operational Research, Elsevier, vol. 26(2), pages 238-250, August.
    6. Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    7. J. P. Jarvis, 1985. "Approximating the Equilibrium Behavior of Multi-Server Loss Systems," Management Science, INFORMS, vol. 31(2), pages 235-239, February.
    8. Zuo-Jun Max Shen & Collette Coullard & Mark S. Daskin, 2003. "A Joint Location-Inventory Model," Transportation Science, INFORMS, vol. 37(1), pages 40-55, February.
    9. Zvi Drezner & Avram Mehrez & George O. Wesolowsky, 1991. "The Facility Location Problem with Limited Distances," Transportation Science, INFORMS, vol. 25(3), pages 183-187, August.
    10. Marianov, Vladimir & ReVelle, Charles, 1996. "The Queueing Maximal availability location problem: A model for the siting of emergency vehicles," European Journal of Operational Research, Elsevier, vol. 93(1), pages 110-120, August.
    11. Oded Berman & Richard C. Larson & Samuel S. Chiu, 1985. "Optimal Server Location on a Network Operating as an M / G /1 Queue," Operations Research, INFORMS, vol. 33(4), pages 746-771, August.
    12. Leyla Ozsen & Collette R. Coullard & Mark S. Daskin, 2008. "Capacitated warehouse location model with risk pooling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 295-312, June.
    13. Oded Berman & Richard C. Larson, 1985. "Optimal 2-Facility Network Districting in the Presence of Queuing," Transportation Science, INFORMS, vol. 19(3), pages 261-277, August.
    14. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
    15. Pey-Chun Chen & Pierre Hansen & Brigitte Jaumard & Hoang Tuy, 1998. "Solution of the Multisource Weber and Conditional Weber Problems by D.-C. Programming," Operations Research, INFORMS, vol. 46(4), pages 548-562, August.
    16. Ward Whitt, 2004. "A Diffusion Approximation for the G/GI/n/m Queue," Operations Research, INFORMS, vol. 52(6), pages 922-941, December.
    17. Jack Brimberg & Pierre Hansen & Nenad Mladenović & Eric D. Taillard, 2000. "Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem," Operations Research, INFORMS, vol. 48(3), pages 444-460, June.
    18. Giovanni Righini & Luca Zaniboni, 2007. "A branch-and-price algorithm for the multi-source Weber problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 2(2), pages 188-207.
    19. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    20. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    21. Robert F. Love, 1976. "Note--One-Dimensional Facility Location-Allocation using Dynamic Programming," Management Science, INFORMS, vol. 22(5), pages 614-617, January.
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