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Algorithms for the Multi-Resource Generalized Assignment Problem

Author

Listed:
  • Bezalel Gavish

    (Owen Graduate School of Management, Vanderbilt University, Nashville, Tennessee 37203)

  • Hasan Pirkul

    (College of Business, The Ohio State University, Columbus, Ohio 43210)

Abstract

The multi-resource generalized assignment problem is encountered when a set of tasks have to be assigned to a set of agents in a way that permits assignment of multiple tasks to an agent subject to the availability of a set of multiple resources consumed by that agent. This problem differs from the generalized assignment problem in that an agent consumes not just one but a variety of resources in performing the tasks assigned to him. This paper develops effective solution procedures for the multi-resource generalized assignment problem. Various relaxations of the problem are studied and theoretical relations among these relaxations are pointed out. Rules for reducing problem size are discussed and are shown to be effective through computational experiments. Heuristic solution procedures and an efficient branch and bound procedure are developed. Results of computational experiments testing these procedures are reported.

Suggested Citation

  • Bezalel Gavish & Hasan Pirkul, 1991. "Algorithms for the Multi-Resource Generalized Assignment Problem," Management Science, INFORMS, vol. 37(6), pages 695-713, June.
    • Handle: RePEc:inm:ormnsc:v:37:y:1991:i:6:p:695-713
    DOI: 10.1287/mnsc.37.6.695
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    Citations

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    Cited by:

    1. Hong Zhang & Heng Li & C. M. Tam, 2006. "Heuristic scheduling of resource-constrained, multiple-mode and repetitive projects," Construction Management and Economics, Taylor & Francis Journals, vol. 24(2), pages 159-169.
    2. Robert M. Nauss, 2003. "Solving the Generalized Assignment Problem: An Optimizing and Heuristic Approach," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 249-266, August.
    3. Cemalettin Öztürk & F. Zeynep Sargut & M. Arslan Örnek & Deniz Türsel Eliiyi, 2017. "Optimisation and heuristic approaches for assigning inbound containers to outbound carriers," Maritime Policy & Management, Taylor & Francis Journals, vol. 44(7), pages 825-836, October.
    4. Franck Butelle & Laurent Alfandari & Camille Coti & Lucian Finta & Lucas Létocart & Gérard Plateau & Frédéric Roupin & Antoine Rozenknop & Roberto Wolfler Calvo, 2016. "Fast machine reassignment," Annals of Operations Research, Springer, vol. 242(1), pages 133-160, July.
    5. A Hertz & N Lahrichi, 2009. "A patient assignment algorithm for home care services," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(4), pages 481-495, April.
    6. Daniel Huttenlocher & Hannah Li & Liang Lyu & Asuman Ozdaglar & James Siderius, 2023. "Matching of Users and Creators in Two-Sided Markets with Departures," Papers 2401.00313, arXiv.org, revised Jan 2024.
    7. Mattfeld, D. C. & Kopfer, H., 2003. "Terminal operations management in vehicle transshipment," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(5), pages 435-452, June.
    8. Gavish, Bezalel, 1997. "Low earth orbit satellite based communication systems -- Research opportunities," European Journal of Operational Research, Elsevier, vol. 99(1), pages 166-179, May.
    9. LeBlanc, Larry J. & Shtub, Avraham & Anandalingam, G., 1999. "Formulating and solving production planning problems," European Journal of Operational Research, Elsevier, vol. 112(1), pages 54-80, January.
    10. Labelle, A. & Langevin, A. & Campbell, J. F., 2002. "Sector design for snow removal and disposal in urban areas," Socio-Economic Planning Sciences, Elsevier, vol. 36(3), pages 183-202, September.
    11. Crema, Alejandro, 1997. "A contraction algorithm for the multiparametric integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 101(1), pages 130-139, August.
    12. Monnerat, Filipe & Dias, Joana & Alves, Maria João, 2019. "Fleet management: A vehicle and driver assignment model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 64-75.
    13. Maria Cremers & Willem Klein Haneveld & Maarten Vlerk, 2009. "A two-stage model for a day-ahead paratransit planning problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(2), pages 323-341, May.
    14. Shtub, Avraham & Kogan, Konstantin, 1998. "Capacity planning by the dynamic multi-resource generalized assignment problem (DMRGAP)," European Journal of Operational Research, Elsevier, vol. 105(1), pages 91-99, February.

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