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Combining integer programming and the randomization method to schedule employees

  • Ingolfsson, Armann
  • Campello, Fernanda
  • Wu, Xudong
  • Cabral, Edgar
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    We describe a method to find low cost shift schedules with a time-varying service level that is always above a specified minimum. Most previous approaches used a two-step procedure: (1) determine staffing requirements and (2) find a minimum cost schedule that provides the required staffing in every period. Approximations in the first step sometimes cause the two-step approach to find infeasible or suboptimal solutions. Our method iterates between a schedule evaluator and a schedule generator. The schedule evaluator calculates transient service levels using the randomization method and identifies infeasible intervals, where the service level is lower than desired. The schedule generator solves a series of integer programs to produce improved schedules, by adding constraints for every infeasible interval, in an attempt to eliminate infeasibility without eliminating the optimal solution. We present computational results for several test problems and discuss factors that make our approach more likely to outperform previous approaches.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00301-4
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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 202 (2010)
    Issue (Month): 1 (April)
    Pages: 153-163

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    Handle: RePEc:eee:ejores:v:202:y:2010:i:1:p:153-163
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Turgut Aykin, 1996. "Optimal Shift Scheduling with Multiple Break Windows," Management Science, INFORMS, vol. 42(4), pages 591-602, April.
    2. 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.
    3. Mehmet Tolga Cezik & Pierre L'Ecuyer, 2008. "Staffing Multiskill Call Centers via Linear Programming and Simulation," Management Science, INFORMS, vol. 54(2), pages 310-323, February.
    4. Júlíus Atlason & Marina A. Epelman & Shane G. Henderson, 2008. "Optimizing Call Center Staffing Using Simulation and Analytic Center Cutting-Plane Methods," Management Science, INFORMS, vol. 54(2), pages 295-309, February.
    5. Ingolfsson, Armann & Amanul Haque, Md. & Umnikov, Alex, 2002. "Accounting for time-varying queueing effects in workforce scheduling," European Journal of Operational Research, Elsevier, vol. 139(3), pages 585-597, June.
    6. Júlíus Atlason & Marina Epelman & Shane Henderson, 2004. "Call Center Staffing with Simulation and Cutting Plane Methods," Annals of Operations Research, Springer, vol. 127(1), pages 333-358, March.
    7. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    8. Otis B. Jennings & Avishai Mandelbaum & William A. Massey & Ward Whitt, 1996. "Server Staffing to Meet Time-Varying Demand," Management Science, INFORMS, vol. 42(10), pages 1383-1394, October.
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