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Fair task allocation problem

Author

Listed:
  • Christian Billing

    (University of Augsburg)

  • Florian Jaehn

    (Helmut Schmidt University - University of the Federal Armed Forces Hamburg)

  • Thomas Wensing

    (INFORM GmbH)

Abstract

In fields like transport or materials sourcing, it is common industrial practice nowadays to contract several partners for the fulfilment of similar sets of tasks. A typical approach is to include quotes to the contracts that specify which portion of the total volume should be given to each partner. In this study, which is inspired by a real-world problem, we examine the question of operationally distributing jobs to a set of partners in order to meet the contracted quotes in different dimensions as closely as possible. We propose the term fair task allocation problem and analyze its complexity. While the problem is NP-hard in the strong sense for the general case, we show that it is solvable in pseudopolynomial time for a given number of partners and dimensions. Besides an exact solution approach based on dynamic programming, we present an efficient Tabu Search procedure. The Tabu Search is applied to real world as well as to self-generated instances. To verify its quality, the results are compared to the solutions of a commercial MIP-solver.

Suggested Citation

  • Christian Billing & Florian Jaehn & Thomas Wensing, 2020. "Fair task allocation problem," Annals of Operations Research, Springer, vol. 284(1), pages 131-146, January.
    • Handle: RePEc:spr:annopr:v:284:y:2020:i:1:d:10.1007_s10479-018-3052-3
    DOI: 10.1007/s10479-018-3052-3
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    References listed on IDEAS

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    1. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    2. Xin Chen & Malgorzata Sterna & Xin Han & Jacek Blazewicz, 2016. "Scheduling on parallel identical machines with late work criterion: Offline and online cases," Journal of Scheduling, Springer, vol. 19(6), pages 729-736, December.
    3. Martello, Silvano & Toth, Paolo, 1995. "A note on exact algorithms for the bottleneck generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 83(3), pages 711-712, June.
    4. Sterna, Malgorzata, 2011. "A survey of scheduling problems with late work criteria," Omega, Elsevier, vol. 39(2), pages 120-129, April.
    5. Mazzola, J. B. & Neebe, A. W., 1988. "Bottleneck generalized assignment problems," Engineering Costs and Production Economics, Elsevier, vol. 14(1), pages 61-65, May.
    6. Wieslaw Kubiak & George Steiner & Julian Scott Yeomans, 1997. "Optimal level schedules for mixed-model, multi-level just-in-time assembly systems," Annals of Operations Research, Springer, vol. 69(0), pages 241-259, January.
    7. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    8. Martello, Silvano & Toth, Paolo, 1995. "The bottleneck generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 83(3), pages 621-638, June.
    9. Cattrysse, Dirk G. & Van Wassenhove, Luk N., 1992. "A survey of algorithms for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 60(3), pages 260-272, August.
    10. Pentico, David W., 2007. "Assignment problems: A golden anniversary survey," European Journal of Operational Research, Elsevier, vol. 176(2), pages 774-793, January.
    11. Jaehn, Florian, 2016. "Sustainable Operations," European Journal of Operational Research, Elsevier, vol. 253(2), pages 243-264.
    12. Wieslaw Kubiak, 2009. "Proportional Optimization and Fairness," International Series in Operations Research and Management Science, Springer, number 978-0-387-87719-8, December.
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