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A Noncompact Formulation for Job-Shop Scheduling Problems in Traffic Management

Author

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  • Leonardo Lamorgese

    (Optrail S.R.L., 00154 Rome, Italy)

  • Carlo Mannino

    (SINTEF Digital, 0373 Oslo, Norway; University of Oslo, 0315 Oslo, Norway)

Abstract

A central problem in traffic management is that of scheduling the movements of vehicles so as to minimize the cost of the schedule. It arises in important applications such as train timetabling, rescheduling, delay and disruption management, airplane surface routing, runway scheduling, air-traffic control, and more. This problem can be modeled as a job-shop scheduling problem. We introduce a new mixed-integer linear program (MILP) formulation for job-shop scheduling, which is an alternative to classical approaches, namely, big- M and time-indexed formulations. It does not make use of artificially large coefficients, and its constraints correspond to basic graph structures, such as paths, cycles, and trees. The new formulation can be obtained by strengthening and lifting the constraints of a classical Benders’ reformulation. Tests on a large set of real-life instances from train rescheduling show that the new approach performs on average better than our previous approaches based on big- M formulations and particularly better on a class of instances with nonconvex costs very common in the practice.

Suggested Citation

  • Leonardo Lamorgese & Carlo Mannino, 2019. "A Noncompact Formulation for Job-Shop Scheduling Problems in Traffic Management," Operations Research, INFORMS, vol. 67(6), pages 1586-1609, November.
    • Handle: RePEc:inm:oropre:v:67:y:2019:i:6:p:1586-1609
    DOI: 10.1287/opre.2018.1837
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    1. Michael Schachtebeck & Anita Schöbel, 2010. "To Wait or Not to Wait---And Who Goes First? Delay Management with Priority Decisions," Transportation Science, INFORMS, vol. 44(3), pages 307-321, August.
    2. 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).
    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. MARCHAND, Hugues & WOLSEY, Laurence A., 1999. "The 0-1 Knapsack problem with a single continuous variable," LIDAM Reprints CORE 1390, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Leonardo Lamorgese & Carlo Mannino & Mauro Piacentini, 2016. "Optimal Train Dispatching by Benders’-Like Reformulation," Transportation Science, INFORMS, vol. 50(3), pages 910-925, August.
    6. Egon Balas, 1969. "Machine Sequencing Via Disjunctive Graphs: An Implicit Enumeration Algorithm," Operations Research, INFORMS, vol. 17(6), pages 941-957, December.
    7. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    8. Gianni Codato & Matteo Fischetti, 2006. "Combinatorial Benders' Cuts for Mixed-Integer Linear Programming," Operations Research, INFORMS, vol. 54(4), pages 756-766, August.
    9. Lamorgese, Leonardo & Mannino, Carlo & Natvig, Erik, 2017. "An exact micro–macro approach to cyclic and non-cyclic train timetabling," Omega, Elsevier, vol. 72(C), pages 59-70.
    10. Mascis, Alessandro & Pacciarelli, Dario, 2002. "Job-shop scheduling with blocking and no-wait constraints," European Journal of Operational Research, Elsevier, vol. 143(3), pages 498-517, December.
    11. Leonardo Lamorgese & Carlo Mannino, 2015. "An Exact Decomposition Approach for the Real-Time Train Dispatching Problem," Operations Research, INFORMS, vol. 63(1), pages 48-64, February.
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    Cited by:

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    2. Jiateng Yin & Lixing Yang & Andrea D’Ariano & Tao Tang & Ziyou Gao, 2022. "Integrated Backup Rolling Stock Allocation and Timetable Rescheduling with Uncertain Time-Variant Passenger Demand Under Disruptive Events," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3234-3258, November.
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    5. Oddvar Kloster & Bjørnar Luteberget & Carlo Mannino & Giorgio Sartor, 2023. "An Optimization-Based Decision Support Tool for Incremental Train Timetabling," SN Operations Research Forum, Springer, vol. 4(3), pages 1-20, September.
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    7. Leutwiler, Florin & Corman, Francesco, 2022. "A logic-based Benders decomposition for microscopic railway timetable planning," European Journal of Operational Research, Elsevier, vol. 303(2), pages 525-540.
    8. Huang, Yeran & Mannino, Carlo & Yang, Lixing & Tang, Tao, 2020. "Coupling time-indexed and big-M formulations for real-time train scheduling during metro service disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 38-61.
    9. Yin, Jiateng & Pu, Fan & Yang, Lixing & D’Ariano, Andrea & Wang, Zhouhong, 2023. "Integrated optimization of rolling stock allocation and train timetables for urban rail transit networks: A benders decomposition approach," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).

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