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Multivalued Decision Diagrams for Sequencing Problems

Author

Listed:
  • Andre A. Cire

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

  • Willem-Jan van Hoeve

    (Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213)

Abstract

Sequencing problems are among the most prominent problems studied in operations research, with primary application in, e.g., scheduling and routing. We propose a novel approach to solving generic sequencing problems using multivalued decision diagrams (MDDs). Because an MDD representation may grow exponentially large, we apply MDDs of limited size as a discrete relaxation to the problem. We show that MDDs can be used to represent a wide range of sequencing problems with various side constraints and objective functions, and we demonstrate how MDDs can be added to existing constraint-based scheduling systems. Our computational results indicate that the additional inference obtained by our MDDs can speed up a state-of-the art solver by several orders of magnitude, for a range of different problem classes.

Suggested Citation

  • Andre A. Cire & Willem-Jan van Hoeve, 2013. "Multivalued Decision Diagrams for Sequencing Problems," Operations Research, INFORMS, vol. 61(6), pages 1411-1428, December.
    • Handle: RePEc:inm:oropre:v:61:y:2013:i:6:p:1411-1428
    DOI: 10.1287/opre.2013.1221
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    References listed on IDEAS

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    1. Michel Gendreau & Alain Hertz & Gilbert Laporte & Mihnea Stan, 1998. "A Generalized Insertion Heuristic for the Traveling Salesman Problem with Time Windows," Operations Research, INFORMS, vol. 46(3), pages 330-335, June.
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    Citations

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    Cited by:

    1. David Bergman & Andre A. Cire & Willem-Jan van Hoeve & J. N. Hooker, 2016. "Discrete Optimization with Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 47-66, February.
    2. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    3. Bahman Naderi & Vahid Roshanaei & Mehmet A. Begen & Dionne M. Aleman & David R. Urbach, 2021. "Increased Surgical Capacity without Additional Resources: Generalized Operating Room Planning and Scheduling," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2608-2635, August.
    4. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2020. "An MDD-Based Lagrangian Approach to the Multicommodity Pickup-and-Delivery TSP," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 263-278, April.
    5. Kinable, Joris & Cire, Andre A. & van Hoeve, Willem-Jan, 2017. "Hybrid optimization methods for time-dependent sequencing problems," European Journal of Operational Research, Elsevier, vol. 259(3), pages 887-897.
    6. Daniel Kowalczyk & Roel Leus, 2018. "A Branch-and-Price Algorithm for Parallel Machine Scheduling Using ZDDs and Generic Branching," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 768-782, November.
    7. Amin Hosseininasab & Willem-Jan van Hoeve, 2021. "Exact Multiple Sequence Alignment by Synchronized Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 721-738, May.
    8. Khachai, Daniil & Sadykov, Ruslan & Battaia, Olga & Khachay, Michael, 2023. "Precedence constrained generalized traveling salesman problem: Polyhedral study, formulations, and branch-and-cut algorithm," European Journal of Operational Research, Elsevier, vol. 309(2), pages 488-505.
    9. David Bergman & Andre A. Cire, 2018. "Discrete Nonlinear Optimization by State-Space Decompositions," Management Science, INFORMS, vol. 64(10), pages 4700-4720, October.
    10. Margarita P. Castro & Andre A. Cire & J. Christopher Beck, 2022. "Decision Diagrams for Discrete Optimization: A Survey of Recent Advances," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2271-2295, July.
    11. Johannes Maschler & Günther R. Raidl, 2021. "Multivalued decision diagrams for prize-collecting job sequencing with one common and multiple secondary resources," Annals of Operations Research, Springer, vol. 302(2), pages 507-531, July.
    12. Christian Tjandraatmadja & Willem-Jan van Hoeve, 2019. "Target Cuts from Relaxed Decision Diagrams," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 285-301, April.
    13. Salii, Yaroslav, 2019. "Revisiting dynamic programming for precedence-constrained traveling salesman problem and its time-dependent generalization," European Journal of Operational Research, Elsevier, vol. 272(1), pages 32-42.
    14. de Weerdt, Mathijs & Baart, Robert & He, Lei, 2021. "Single-machine scheduling with release times, deadlines, setup times, and rejection," European Journal of Operational Research, Elsevier, vol. 291(2), pages 629-639.
    15. Selvaprabu Nadarajah & Andre A. Cire, 2020. "Network-Based Approximate Linear Programming for Discrete Optimization," Operations Research, INFORMS, vol. 68(6), pages 1767-1786, November.

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