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Resource-Constrained Assignment Scheduling

Author

Listed:
  • Joseph B. Mazzola

    (Duke University, Durham, North Carolina)

  • Alan W. Neebe

    (The University of North Carolina, Chapel Hill, North Carolina)

Abstract

Many resource-constrained assignment scheduling problems can be modeled as 0-1 assignment problems with side constraints (APSC). Unlike the well-known assignment problem of linear programming, APSC is NP-complete. In this paper we define a branch-and-bound algorithm for solving APSC to optimality. The algorithm employs a depth-first, polychotomous branching strategy in conjunction with a bounding procedure that utilizes subgradient optimization. We also define a heuristic procedure for obtaining approximate solutions to APSC. The heuristic uses subgradient optimization to guide the search for a good solution as well as to provide a bound on solution quality. We present computational experience with both procedures, applied to over 400 test problems. The algorithm is demonstrated to be effective across three different classes of resource-constrained assignment scheduling problems. The heuristic generates solutions for these problems that are, on average, within 0.8% of optimality.

Suggested Citation

  • Joseph B. Mazzola & Alan W. Neebe, 1986. "Resource-Constrained Assignment Scheduling," Operations Research, INFORMS, vol. 34(4), pages 560-572, August.
    • Handle: RePEc:inm:oropre:v:34:y:1986:i:4:p:560-572
    DOI: 10.1287/opre.34.4.560
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    Citations

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    Cited by:

    1. Gaétan Caron & Pierri Hansen & Brigitte Jaumard, 1999. "The Assignment Problem with Seniority and Job Priority Constraints," Operations Research, INFORMS, vol. 47(3), pages 449-453, June.
    2. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    3. Chase Rainwater & Joseph Geunes & H. Edwin Romeijn, 2014. "Resource-Constrained Assignment Problems with Shared Resource Consumption and Flexible Demand," INFORMS Journal on Computing, INFORMS, vol. 26(2), pages 290-302, May.
    4. Punnen, Abraham P. & Aneja, Y. P., 1995. "Minmax combinatorial optimization," European Journal of Operational Research, Elsevier, vol. 81(3), pages 634-643, March.
    5. M. Gaudioso & L. Moccia & M. F. Monaco, 2010. "Repulsive Assignment Problem," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 255-273, February.
    6. Prabuddha De & Jay B. Ghosh & Charles E. Wells, 1992. "On the solution of a stochastic bottleneck assignment problem and its variations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 389-397, April.
    7. Hesham K. Alfares, 2022. "Plant shutdown maintenance workforce team assignment and job scheduling," Journal of Scheduling, Springer, vol. 25(3), pages 321-338, June.
    8. Mazzola, Joseph B. & Neebe, Alan W., 1999. "Lagrangian-relaxation-based solution procedures for a multiproduct capacitated facility location problem with choice of facility type," European Journal of Operational Research, Elsevier, vol. 115(2), pages 285-299, June.
    9. Przybylski, Anthony & Gandibleux, Xavier & Ehrgott, Matthias, 2008. "Two phase algorithms for the bi-objective assignment problem," European Journal of Operational Research, Elsevier, vol. 185(2), pages 509-533, March.
    10. Yang Wang & Wei Yang & Abraham P. Punnen & Jingbo Tian & Aihua Yin & Zhipeng Lü, 2021. "The Rank-One Quadratic Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 979-996, July.
    11. Richard Freling & H. Edwin Romeijn & Dolores Romero Morales & Albert P.M. Wagelmans, 1999. "A Branch and Price Algorithm for the Multi-Period Single-Sourcing Problem," Tinbergen Institute Discussion Papers 99-092/4, Tinbergen Institute.
    12. Joseph B. Mazzola & Steven P. Wilcox, 2001. "Heuristics for the multi‐resource generalized assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(6), pages 468-483, September.
    13. Lieshout, P.M.D. & Volgenant, A., 2007. "A branch-and-bound algorithm for the singly constrained assignment problem," European Journal of Operational Research, Elsevier, vol. 176(1), pages 151-164, January.
    14. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.

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