A Mathematical Model for Periodic Scheduling Problems

Serafini, Paolo; Ukovich, W.

doi:10.1137/0402049

Cited by 427 publications

(235 citation statements)

References 19 publications

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“…The periodic TTP's goal is to design a timetable that is operated cyclically after a (small) period of time; this is a typical requirement for passenger trains in order to come up with an easy-to-remember timetable. The first authors who developed a model for generating periodic timetables were Serafini and Ukovic [23], who introduced a mathematical model called Periodic Event Scheduling Problem (PESP). In PESP, a set of repetitive events is scheduled under periodic time-window constraints.…”

Section: Literature Reviewmentioning

confidence: 99%

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Fast Approaches to Improve the Robustness of a Railway Timetable

Fischetti

Salvagnin

Zanette

2009

Transportation Science

139

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Abstract. The Train Timetabling Problem (TTP) consists in finding a train schedule on a railway network that satisfies some operational constraints and maximizes some profit function which counts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the objective function is not enough and one calls for a robust solution that is capable of absorbing as much as possible delays/disturbances on the network. In this paper we propose and analyze computationally four different methods to improve the robustness of a given TTP solution for the aperiodic (non cyclic) case. The approaches combine Linear Programming (LP) and ad-hoc Stochastic Programming/Robust Optimization techniques. We compare computationally the effectiveness and practical applicability of the four techniques under investigation on real-world test cases from the Italian railway company (Trenitalia). The outcome is that two of the proposed techniques are very fast and provide robust solutions of comparable quality with respect to the standard (but very time consuming) Stochastic Programming approach.

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Section: Literature Reviewmentioning

confidence: 99%

“…A natural event-based model in the spirit of the Periodic Event Scheduling Problem (PESP) formulation used in the periodic (cyclic) case [23] can be sketched as follows:…”

Section: Literature Reviewmentioning

confidence: 99%

Fast Approaches to Improve the Robustness of a Railway Timetable

Fischetti

Salvagnin

Zanette

2009

Transportation Science

139

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“…Bertossi & Bonuccelli [1983 for the rather special case that the period of the ith operation is half the period of the (i + 1)th one. Serafini & Ukovich [1989] discuss nonpreemptive periodic scheduling subject to precedence constraints and show that this problem is NP-complete. Park & Yun [1985] give an ILP formulation of a nonpreemptive scheduling problem.…”

Section: Preemptive Periodic Schedulingmentioning

confidence: 99%

“…Many papers on periodic scheduling are concerned with specific applications, proposing solution strategies that are often strongly tailored to the application at hand, a notable exception being the paper by Serafini & Ukovich [1989], which presents a general mathematical model for periodic scheduling problems. However, their emphasis is on periodic scheduling subject to precedence constraints.…”

Section: Introductionmentioning

confidence: 99%

Periodic multiprocessor scheduling

Korst

Aarts

Lenstra

et al. 1991

PARLE '91 Parallel Architectures and Languages Europe

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“…An interesting application of Min FCB arises in periodic timetabling for transportation systems. In [5], the timetables of the Berlin underground are designed by considering a mathematical programming model based on the Periodic Event Scheduling Problem (PESP) [37] and the associated graph G in which nodes correspond to events. Since the number of integer variables in the model can be minimized by identifying an FCB of G and the Table 2 Computational results (CPU times in seconds or hh:mm:ss) for Euclidean random graphs.…”

Section: Instances From Real-life Applicationsmentioning

confidence: 99%

Edge-swapping algorithms for the minimum fundamental cycle basis problem

et al. 2008

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We consider the problem of finding a fundamental cycle basis with minimum total cost in an undirected graph. This problem is NP-hard and has several interesting applications. Since fundamental cycle bases correspond to spanning trees, we propose a local search algorithm, a tabu search and variable neighborhood search in which edge swaps are iteratively applied to a current spanning tree. We also present a mixed integer programming formulation of the problem whose linear relaxation yields tighter lower bounds than other known formulations. Computational results obtained with our algorithms are compared with those from the best available constructive heuristic on several types of graphs. 1

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A Mathematical Model for Periodic Scheduling Problems

Cited by 427 publications

References 19 publications

Fast Approaches to Improve the Robustness of a Railway Timetable

Fast Approaches to Improve the Robustness of a Railway Timetable

Periodic multiprocessor scheduling

Edge-swapping algorithms for the minimum fundamental cycle basis problem

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