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A cutting plane approach for the multi-machine precedence-constrained scheduling problem

Author

Listed:
  • Prahalad Venkateshan

    (Indian Institute of Management)

  • Joseph Szmerekovsky

    (North Dakota State University)

  • George Vairaktarakis

    (Case Western Reserve University)

Abstract

A cutting-plane approach is developed for the problem of optimally scheduling jobs with arbitrary precedence constraints on unrelated parallel machines to minimize weighted completion time. While the single machine version of this problem has attracted much research efforts, enabling solving problems with up to 100 jobs, not much has been done on the multiple machines case. A novel mixed-integer programming model is presented for the problem with multiple machines. For this model, many classes of valid inequalities that cut off fractional linear programming solutions are developed. This leads to an increase of the linear programming lower bound from 89.3 to 94.6% of the corresponding optimal solution, and a substantial reduction in the computational time of an optimal branch-and-bound algorithm for this problem. This enables us to report optimal solutions for problem instances with up to 25 jobs and 5 machines, which is more than twice the size of problems for which optimal solutions have been reported in the literature thus far. For a special case of the problem—that of minimizing makespan—application of our model helps solve 18 of 27 previously unsolved problem instances to optimality.

Suggested Citation

  • Prahalad Venkateshan & Joseph Szmerekovsky & George Vairaktarakis, 2020. "A cutting plane approach for the multi-machine precedence-constrained scheduling problem," Annals of Operations Research, Springer, vol. 285(1), pages 247-271, February.
    • Handle: RePEc:spr:annopr:v:285:y:2020:i:1:d:10.1007_s10479-019-03212-3
    DOI: 10.1007/s10479-019-03212-3
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    References listed on IDEAS

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    1. DYER, Martin E. & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 878, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Herrmann, Jeffrey & Proth, Jean-Marie & Sauer, Nathalie, 1997. "Heuristics for unrelated machine scheduling with precedence constraints," European Journal of Operational Research, Elsevier, vol. 102(3), pages 528-537, November.
    3. E. DYER, Martin & WOLSEY, Laurence A., 1990. "Formulating the single machine sequencing problem with release dates as a mixed integer program," LIDAM Reprints CORE 917, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Mokotoff, E. & Chretienne, P., 2002. "A cutting plane algorithm for the unrelated parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 141(3), pages 515-525, September.
    5. Mokotoff, Ethel, 2004. "An exact algorithm for the identical parallel machine scheduling problem," European Journal of Operational Research, Elsevier, vol. 152(3), pages 758-769, February.
    6. 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.
    7. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    8. Maurice Queyranne & Yaoguang Wang, 1991. "Single-Machine Scheduling Polyhedra with Precedence Constraints," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 1-20, February.
    9. Fanjul-Peyro, Luis & Perea, Federico & Ruiz, Rubén, 2017. "Models and matheuristics for the unrelated parallel machine scheduling problem with additional resources," European Journal of Operational Research, Elsevier, vol. 260(2), pages 482-493.
    10. Olaguibel, Ramon Alvarez-Valdes & Goerlich, JoseManuel Tamarit, 1993. "The project scheduling polyhedron: Dimension, facets and lifting theorems," European Journal of Operational Research, Elsevier, vol. 67(2), pages 204-220, June.
    11. Kolisch, Rainer & Sprecher, Arno, 1997. "PSPLIB - A project scheduling problem library : OR Software - ORSEP Operations Research Software Exchange Program," European Journal of Operational Research, Elsevier, vol. 96(1), pages 205-216, January.
    12. C. N. Potts, 1985. "A Lagrangean Based Branch and Bound Algorithm for Single Machine Sequencing with Precedence Constraints to Minimize Total Weighted Completion Time," Management Science, INFORMS, vol. 31(10), pages 1300-1311, October.
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