Scaling and Rounding Periodic Event Scheduling Instances to Different Period Times

Enrico Bortoletto () and Niels Lindner ()
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Enrico Bortoletto: Zuse Institute Berlin
Niels Lindner: Zuse Institute Berlin

Chapter Chapter 51 in Operations Research Proceedings 2023, 2025, pp 397-402 from Springer

Abstract: 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.

Keywords: Timetabling; Mixed-integer programming; Public transport (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-58405-3_51

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