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Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty

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  • Merve Bodur

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada)

  • James R. Luedtke

    (Department of Industrial and Systems Engineering, University of Wisconsin, Madison, Wisconsin 53706)

Abstract

We study server scheduling in multiclass service systems under uncertainty in the customer arrival volumes. Common practice in such systems is to first identify staffing levels and then determine schedules for the servers that cover these levels. We propose a new stochastic integer programming (SIP) model that integrates these two decisions, which can yield lower scheduling costs by exploiting the presence of alternative server configurations that yield similar quality of service. We find that a branch-and-cut algorithm based on Benders decomposition may fail due to the weakness of the relaxation bound. We propose a novel application of mixed-integer rounding to improve the Benders cuts used in this algorithm, a technique that is applicable to any SIP with integer first-stage decision variables. Numerical examples illustrate the computational efficiency of the proposed approach and the potential benefit of solving the integrated model compared to considering the staffing and scheduling problems separately.

Suggested Citation

  • Merve Bodur & James R. Luedtke, 2017. "Mixed-Integer Rounding Enhanced Benders Decomposition for Multiclass Service-System Staffing and Scheduling with Arrival Rate Uncertainty," Management Science, INFORMS, vol. 63(7), pages 2073-2091, July.
    • Handle: RePEc:inm:ormnsc:v:63:y:2017:i:7:p:2073-2091
    DOI: 10.1287/mnsc.2016.2455
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