CREW-OPT: Crew Scheduling by Column Generation (Extended abstract)

Martin Desrochers; François Soumis

doi:10.1007/978-3-642-85966-3_8

Computer-Aided Transit Scheduling pp 83-90 | Cite as

CREW-OPT: Crew Scheduling by Column Generation (Extended abstract)

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Martin Desrochers
François Soumis

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Part of the Lecture Note in Economics Mathematical Systems book series (LNE, volume 308)

Abstract

Three main types of algorithms to solve the urban transit crew scheduling problem have been I developed and used in practice: the Runcutting, the HASTUS and the Set Covering methods. In this J paper, we will restrict ourself to the solution of the Set Covering method using a column generation approach.

The urban transit crew scheduling problem arises in mass transit corporations who have to create minimal cost bus driver schedule respecting both the collective agreement and the bus schedule. This problem is often modeled as a set covering problem where each column represents a driver’s workday and each row represents a task i.e. a given bus trip. In previous solution methods, a subset of the feasible workdays was created and a heuristic solution using only these workdays was found by solving the resulting set covering problem. We propose a column generation approach to solve the transit crew scheduling problem. The column generation approach decomposes the problem in two parts. The set covering problem chooses a schedule from already known feasible workdays. The subproblem is modeled as a shortest path problem with resource constraints and proposes new feasible workdays to improve the actual solution of the set covering problem. The approach was tested successfully on real-life problems.

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References

[1]
Desrochers, M.: A New Algorithm for the Shortest Path Problem with Resource Constraints. Report #421A, Centre de Recherche sur les Transports, Université de Montréal; Montréal, 1986Google Scholar
[2]
Desrochers, M.: La fabrication d’horaires de travail pour les conducteurs d’autobus par une méthode de généeration de colonnes. Ph.D thesis, Report #470, Centre de Recherche sur les Transports, Université de Montréal; Montreal 1986Google Scholar
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Hartley, T.: A Glossary of Terms in Bus and Crew Scheduling. Computer Scheduling of Public Transport. A. Wren, ed.; North-Holland, Amsterdam 1981Google Scholar
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Marsten, R.E. (1981): The Design of the XMP Linear Programming Library. ACM Transaction on Mathematical Software 7 (1981), 481–497CrossRefGoogle Scholar
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Ryan, D.M.; Forster, B.A.: An Integer Programming Approach to Scheduling. Computer Scheduling of Public Transport. A. Wren, ed.; North-Holland, Amsterdam, 1981, 269–280.Google Scholar

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Authors and Affiliations

Martin Desrochers
- 1
François Soumis
- 2

1.GERAD, Ecole des H.E.C.Université de MontréalMontréalCanada
2.GERAD, Ecole PolytechniqueUniversité de MontréalMontréalCanada

CREW-OPT: Crew Scheduling by Column Generation (Extended abstract)

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