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Perspectives on integer programming for time-dependent models

Author

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  • Natashia L. Boland

    (Georgia Institute of Technology)

  • Martin W. P. Savelsbergh

    (Georgia Institute of Technology)

Abstract

Integer programs for solving time-dependent models—models in which decisions have to be made about the times at which activities occur and/or resources are utilized—are pervasive in industry, but are notoriously difficult to solve. In the last few years, interest in the role of discretization in approaches to solve these problems has intensified. One novel paradigm, dynamic discretization discovery, has emerged with the potential to greatly enhance the practical tractability of time-dependent models using integer programming technology. We introduce dynamic discretization discovery, illustrate its use on the traveling salesman problem with time windows, highlight its core principles, and point to opportunities for further research. Relations to other approaches for tackling time-dependent models are also discussed.

Suggested Citation

  • Natashia L. Boland & Martin W. P. Savelsbergh, 2019. "Perspectives on integer programming for time-dependent models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 147-173, July.
    • Handle: RePEc:spr:topjnl:v:27:y:2019:i:2:d:10.1007_s11750-019-00514-4
    DOI: 10.1007/s11750-019-00514-4
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    7. Zhang, Yongxiang & Peng, Qiyuan & Lu, Gongyuan & Zhong, Qingwei & Yan, Xu & Zhou, Xuesong, 2022. "Integrated line planning and train timetabling through price-based cross-resolution feedback mechanism," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 240-277.
    8. Saint-Guillain, Michael & Paquay, Célia & Limbourg, Sabine, 2021. "Time-dependent stochastic vehicle routing problem with random requests: Application to online police patrol management in Brussels," European Journal of Operational Research, Elsevier, vol. 292(3), pages 869-885.
    9. Liu, Yiming & Roberto, Baldacci & Zhou, Jianwen & Yu, Yang & Zhang, Yu & Sun, Wei, 2023. "Efficient feasibility checks and an adaptive large neighborhood search algorithm for the time-dependent green vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 310(1), pages 133-155.
    10. Ammann, Pia & Kolisch, Rainer & Schiffer, Maximilian, 2023. "Driver routing and scheduling with synchronization constraints," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
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