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The equivalence of general set‐covering and implicit integer programming formulations for shift scheduling

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  • Stephen E. Bechtold
  • Larry W. Jacobs

Abstract

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set‐covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate. © 1996 John Wiley & Sons, Inc.

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  • Stephen E. Bechtold & Larry W. Jacobs, 1996. "The equivalence of general set‐covering and implicit integer programming formulations for shift scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(2), pages 233-249, March.
    • Handle: RePEc:wly:navres:v:43:y:1996:i:2:p:233-249
    DOI: 10.1002/(SICI)1520-6750(199603)43:23.0.CO;2-B
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    References listed on IDEAS

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    1. William G. Nulty & H. Donald Ratliff, 1991. "Interactive optimization methodology for fleet scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 669-677, October.
    2. Matteo Fischetti & Silvano Martello & Paolo Toth, 1987. "The Fixed Job Schedule Problem with Spread-Time Constraints," Operations Research, INFORMS, vol. 35(6), pages 849-858, December.
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    4. George B. Dantzig, 1954. "Letter to the Editor---A Comment on Edie's “Traffic Delays at Toll Booths”," Operations Research, INFORMS, vol. 2(3), pages 339-341, August.
    5. Beasley, J. E., 1987. "An algorithm for set covering problem," European Journal of Operational Research, Elsevier, vol. 31(1), pages 85-93, July.
    6. 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.
    7. Willie B. Henderson & William L. Berry, 1976. "Heuristic Methods for Telephone Operator Shift Scheduling: An Experimental Analysis," Management Science, INFORMS, vol. 22(12), pages 1372-1380, August.
    8. Baker, Edward & Fisher, Michael, 1981. "Computational results for very large air crew scheduling problems," Omega, Elsevier, vol. 9(6), pages 613-618.
    9. 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. 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.

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