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Solving the selective multi-category parallel-servicing problem

Author

Listed:
  • Range, Troels Martin

    (Department of Business and Economics)

  • Lusby, Richard Martin

    (Department of Engineering Management)

  • Larsen, Jesper

    (Department of Engineering Management)

Abstract

In this paper we present a new scheduling problem and describe a shortest path based heuristic as well as a dynamic programming based exact optimization algorithm to solve it. The Selective Multi-Category Parallel-Servicing Problem (SMCPSP) arises when a set of jobs has to be scheduled on a server (machine) with limited capacity. Each job requests service in a prespecified time window and belongs to a certain category. Jobs may be serviced partially, incurring a penalty; however, only jobs of the same category can be processed simultaneously. One must identify the best subset of jobs to process in each time interval of a given planning horizon while respecting the server capacity and scheduling requirements. We compare the proposed solution methods with a MILP formulation and show that the dynamic programming approach is faster when the number of categories is large, whereas the MILP can be solved faster when the number of categories is small.

Suggested Citation

  • Range, Troels Martin & Lusby, Richard Martin & Larsen, Jesper, 2013. "Solving the selective multi-category parallel-servicing problem," Discussion Papers on Economics 5/2013, University of Southern Denmark, Department of Economics.
    • Handle: RePEc:hhs:sdueko:2013_005
    as

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    File URL: https://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2013/dpbe5_2013.pdf
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    References listed on IDEAS

    as
    1. Martin Desrochers & Jacques Desrosiers & Marius Solomon, 1992. "A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows," Operations Research, INFORMS, vol. 40(2), pages 342-354, April.
    2. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    3. Zhi-Long Chen & Warren B. Powell, 1999. "Solving Parallel Machine Scheduling Problems by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 11(1), pages 78-94, February.
    4. Range, Troels Martin & Lusby, Richard Martin & Larsen, Jesper, 2013. "A column generation approach for solving the patient admission scheduling problem," Discussion Papers on Economics 1/2013, University of Southern Denmark, Department of Economics.
    5. Stefan Irnich & Guy Desaulniers, 2005. "Shortest Path Problems with Resource Constraints," Springer Books, in: Guy Desaulniers & Jacques Desrosiers & Marius M. Solomon (ed.), Column Generation, chapter 0, pages 33-65, Springer.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Machine scheduling; dynamic programming; node-disjoint shortest-path problem; preprocessing;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

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