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A Lagrangean Relaxation Algorithm for the Two Duty Period Scheduling Problem

Author

Listed:
  • Fred Shepardson

    (Stanford University)

  • Roy E. Marsten

    (University of Arizona)

Abstract

The two duty period scheduling problem is an integer programming problem with 0-1 constraint coefficients. It is recognized that the problem can be reformulated as a one duty period problem with side constraints. Since the one duty period problem can be solved as a minimal cost network flow problem, we dualize with respect to the side constraints, forming a Lagrangean relaxation which is easily solved. Subgradient optimization is used to maximize the Lagrangean. Computational results are reported for several large problems.

Suggested Citation

  • Fred Shepardson & Roy E. Marsten, 1980. "A Lagrangean Relaxation Algorithm for the Two Duty Period Scheduling Problem," Management Science, INFORMS, vol. 26(3), pages 274-281, March.
    • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:3:p:274-281
    DOI: 10.1287/mnsc.26.3.274
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    Citations

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    Cited by:

    1. El-Darzi, Elia & Mitra, Gautam, 1995. "Graph theoretic relaxations of set covering and set partitioning problems," European Journal of Operational Research, Elsevier, vol. 87(1), pages 109-121, November.
    2. Meltem Denizel, 2003. "Minimization of the Number of Tool Magazine Setups on Automated Machines: A Lagrangean Decomposition Approach," Operations Research, INFORMS, vol. 51(2), pages 309-320, April.
    3. Dilip Chhajed & Timothy J. Lowe, 1998. "Solving a selected class of location problems by exploiting problem structure: A decomposition approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(8), pages 791-815, December.
    4. Calvete, Herminia I., 2003. "Network simplex algorithm for the general equal flow problem," European Journal of Operational Research, Elsevier, vol. 150(3), pages 585-600, November.
    5. Larsson, Torbjörn & Patriksson, Michael, 1999. "Side constrained traffic equilibrium models-- analysis, computation and applications," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 233-264, May.
    6. Monique Guignard, 2007. "En hommage à Joseph-Louis Lagrange et à Pierre Huard," Annals of Operations Research, Springer, vol. 149(1), pages 103-116, February.

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