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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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    Cited by:

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    6. 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.
    7. 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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    10. 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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