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Scaling and Rounding Periodic Event Scheduling Instances to Different Period Times

In: Operations Research Proceedings 2023

Author

Listed:
  • Enrico Bortoletto

    (Zuse Institute Berlin)

  • Niels Lindner

    (Zuse Institute Berlin)

Abstract

The Periodic Event Scheduling Problem (PESP) is a notoriously hard combinatorial optimization problem, essential for the design of periodic timetables in public transportation. The coefficients of the integer variables in the standard mixed integer linear programming formulations of PESP are the period time, e.g., 60 for a horizon of one hour with a resolution of one minute. In many application scenarios, lines with different frequencies have to be scheduled, leading to period times with many divisors. It then seems natural to consider derived instances, where the period time is a divisor of the original one, thereby smaller, and bounds are scaled and rounded accordingly. To this end, we identify two rounding schemes: wide and tight. We then discuss the approximation performance of both strategies, in theory and practice.

Suggested Citation

  • Enrico Bortoletto & Niels Lindner, 2025. "Scaling and Rounding Periodic Event Scheduling Instances to Different Period Times," Lecture Notes in Operations Research, in: Guido Voigt & Malte Fliedner & Knut Haase & Wolfgang Brüggemann & Kai Hoberg & Joern Meissner (ed.), Operations Research Proceedings 2023, chapter 0, pages 397-402, Springer.
    • Handle: RePEc:spr:lnopch:978-3-031-58405-3_51
    DOI: 10.1007/978-3-031-58405-3_51
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