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An integer programming model for the weekly tour scheduling problem

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  • Tolga Çezik
  • Oktay Günlük
  • Hanan Luss

Abstract

We study a workforce planning and scheduling problem in which weekly tours of agents must be designed. Our motivation for this study comes from a call center application where agents serve customers in response to incoming phone calls. Similar to many other applications in the services industry, the demand for service in call centers varies significantly within a day and among days of the week. In our model, a weekly tour of an agent consists of five daily shifts and two days off, where daily shifts within a tour may be different from each other. The starting times of any two consecutive shifts, however, may not differ by more than a specified bound. Furthermore, a tour must also satisfy constraints regarding the days off, for example, it may be required that one of the days off is on a weekend day. The objective is to determine a collection of weekly tours that satisfy the demand for agents' services, while minimizing the total labor cost of the workforce. We describe an integer programming model where a weekly tour is obtained by combining seven daily shift scheduling models and days‐off constraints in a network flow framework. The model is flexible and can accommodate different daily models with varying levels of detail. It readily handles different days‐off rules and constraints regarding start time differentials in consecutive days. Computational results are also presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 607–624, 2001.

Suggested Citation

  • Tolga Çezik & Oktay Günlük & Hanan Luss, 2001. "An integer programming model for the weekly tour scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(7), pages 607-624, October.
    • Handle: RePEc:wly:navres:v:48:y:2001:i:7:p:607-624
    DOI: 10.1002/nav.1037
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    References listed on IDEAS

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    1. Fred F. Easton & Donald F. Rossin, 1991. "Sufficient Working Subsets for the Tour Scheduling Problem," Management Science, INFORMS, vol. 37(11), pages 1441-1451, November.
    2. Turgut Aykin, 1996. "Optimal Shift Scheduling with Multiple Break Windows," Management Science, INFORMS, vol. 42(4), pages 591-602, April.
    3. Michael J. Brusco & Larry W. Jacobs, 1993. "A simulated annealing approach to the cyclic staff‐scheduling problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(1), pages 69-84, February.
    4. M. Segal, 1974. "The Operator-Scheduling Problem: A Network-Flow Approach," Operations Research, INFORMS, vol. 22(4), pages 808-823, August.
    5. Bechtold, Stephen E. & Brusco, Michael J., 1994. "Working set generation methods for labor tour scheduling," European Journal of Operational Research, Elsevier, vol. 74(3), pages 540-551, May.
    6. Michael J. Brusco & Larry W. Jacobs, 1998. "Personnel Tour Scheduling When Starting-Time Restrictions Are Present," Management Science, INFORMS, vol. 44(4), pages 534-547, April.
    7. Phil Quinn & Bruce Andrews & Henry Parsons, 1991. "Allocating Telecommunications Resources at L. L. Bean, Inc," Interfaces, INFORMS, vol. 21(1), pages 75-91, February.
    8. James G. Morris & Michael J. Showalter, 1983. "Simple Approaches to Shift, Days-Off and Tour Scheduling Problems," Management Science, INFORMS, vol. 29(8), pages 942-950, August.
    9. Anthony J. Brigandi & Dennis R. Dargon & Michael J. Sheehan & Thomas Spencer, 1994. "AT&T's Call Processing Simulator (CAPS) Operational Design for Inbound Call Centers," Interfaces, INFORMS, vol. 24(1), pages 6-28, February.
    10. Bruce Andrews & Henry Parsons, 1993. "Establishing Telephone-Agent Staffing Levels through Economic Optimization," Interfaces, INFORMS, vol. 23(2), pages 14-20, April.
    11. Gary M. Thompson, 1995. "Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem," Management Science, INFORMS, vol. 41(4), pages 595-607, April.
    12. Stephen E. Bechtold & Larry W. Jacobs, 1990. "Implicit Modeling of Flexible Break Assignments in Optimal Shift Scheduling," Management Science, INFORMS, vol. 36(11), pages 1339-1351, November.
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    Cited by:

    1. Jens O. Brunner & Jonathan F. Bard & Jan M. Köhler, 2013. "Bounded flexibility in days‐on and days‐off scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 678-701, December.
    2. Hua Ni & Hernán Abeledo, 2007. "A branch-and-price approach for large-scale employee tour scheduling problems," Annals of Operations Research, Springer, vol. 155(1), pages 167-176, November.
    3. Ferdinand Kiermaier & Markus Frey & Jonathan F. Bard, 2020. "The flexible break assignment problem for large tour scheduling problems with an application to airport ground handlers," Journal of Scheduling, Springer, vol. 23(2), pages 177-209, April.
    4. Hans Corsten & Ferdinand Becker & Hagen Salewski, 2020. "Integrating truck and workforce scheduling in a cross-dock: analysis of different workforce coordination policies," Journal of Business Economics, Springer, vol. 90(2), pages 207-237, March.
    5. Liu, Han & Hua, Cheng & Lei, Chao, 2021. "Planning for time-varying volunteer firefighter systems under probabilistic service disruptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    6. María I. Restrepo & Bernard Gendron & Louis-Martin Rousseau, 2016. "Branch-and-Price for Personalized Multiactivity Tour Scheduling," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 334-350, May.
    7. Tolga Çezik & Oktay Günlük, 2004. "Reformulating linear programs with transportation constraints—With applications to workforce scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 275-296, March.
    8. Douglas S. Altner & Anthony C. Rojas & Leslie D. Servi, 2018. "A two-stage stochastic program for multi-shift, multi-analyst, workforce optimization with multiple on-call options," Journal of Scheduling, Springer, vol. 21(5), pages 517-531, October.
    9. Oyku Ahipasaoglu & Nesim Erkip & Oya Ekin Karasan, 2019. "The venue management problem: setting staffing levels, shifts and shift schedules at concession stands," Journal of Scheduling, Springer, vol. 22(1), pages 69-83, February.

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