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Reformulating linear programs with transportation constraints—With applications to workforce scheduling

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  • Tolga Çezik
  • Oktay Günlük

Abstract

We study linear programming models that contain transportation constraints in their formulation. Typically, these models have a multistage nature and the transportation constraints together with the associated flow variables are used to achieve consistency between consecutive stages. We describe how to reformulate these models by projecting out the flow variables. The reformulation can be more desirable since it has fewer variables and can be solved faster. We apply these ideas to reformulate two well‐known workforce staffing and scheduling problems: the shift scheduling problem and the tour scheduling problem. We also present computational results. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:2:p:275-296
    DOI: 10.1002/nav.10115
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    References listed on IDEAS

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    1. 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.
    2. Fred Glover, 1967. "Maximum matching in a convex bipartite graph," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(3), pages 313-316.
    3. Gary M. Thompson, 1995. "Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem," Management Science, INFORMS, vol. 41(4), pages 595-607, April.
    4. 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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    1. Idris Addou & François Soumis, 2007. "Bechtold-Jacobs generalized model for shift scheduling with extraordinary overlap," Annals of Operations Research, Springer, vol. 155(1), pages 177-205, November.
    2. Youngbum Hur & Jonathan F. Bard & Markus Frey & Ferdinand Kiermaier, 2019. "An investigation of shift and break flexibility with real-time break assignments using a rolling horizon approach," Flexible Services and Manufacturing Journal, Springer, vol. 31(1), pages 174-211, March.

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