Abstract
The integrated multi-depot vehicle and crew scheduling problem simultaneously builds vehicle blocks and crew duties. We present an integer mathematical formulation that combines a multi-commodity flow model with a mixed set partitioning/covering model. We propose solution approaches that start by solving the linear programming relaxation of the model. Whenever the resulting linear programming solution is not integer, three branching alternative strategies can be applied: a branch-and-bound algorithm and two branch-and-price schemes. The branch-and-bound algorithm performs branching over the set of feasible crew duties generated while solving the linear relaxation. In the first branch-and-price scheme the linear programming relaxation is solved approximately, while in the second one it is solved exactly. Computational experience is reported over two different types of problems: randomly generated data publicly available for benchmarking in the Internet and data from a bus company operating in Lisbon.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Borndörfer R, Löbel A, Weider S (2008) A bundle method for integrated multi-depot vehicle and duty scheduling in public transit. In: Hickman M, Mirchandani P, Voß S (eds) Computer-aided systems in public transport. Lecture notes in economics and mathematical systems, vol 600. Springer, Berlin, pp 3–24
Gaffi A, Nonato M (1999) An integrated approach to ex-urban crew and vehicle scheduling. In: Wilson NHM (ed) Computer-aided transit scheduling. Lecture notes in economics and mathematical systems, vol 471. Springer, Berlin, pp 103–128
Gintner V, Steinzen I, Suhl L (2005) A variable fixing heuristic for the multiple-depot integrated vehicle and crew scheduling. In: Jaszkiewicz A, Kaczmarek M, Zak J, Kubiak M (eds) Advanced OR and AI methods in transportation. Publishing House of Poznan University of Technology, Poznan, pp 547–552
Gintner V, Kliewer N, Suhl L (2008) A crew scheduling approach for public transit enhanced with aspects from vehicle scheduling. In: Hickman M, Mirchandani P, Voß S (eds) Computer-aided systems in public transport. Lecture notes in economics and mathematical systems, vol 600. Springer, Berlin, pp 25–42
Haase K, Friberg C (1999) An exact branch and cut algorithm for the vehicle and crew scheduling. In: Wilson NHM (ed) Computer-aided transit scheduling. Lecture notes in economics and mathematical systems, vol 471. Springer, Berlin, pp 63–80
Haase K, Desaulniers G, Desrosiers J (2001) Simultaneous vehicle and crew scheduling in urban mass transit systems. Transp Sci 35(3):286–303
Huisman D, Freling R, Wagelmans APM (2005) Multiple-depot integrated vehicle and crew scheduling. Transp Sci 39:491–502
Mesquita M, Paixão J (1992) Multiple depot vehicle scheduling problem: a new heuristic based on quasi-assignment algorithms. In: Desrochers M, Rousseau JM (eds) Computer-aided transit scheduling. Lecture notes in economics and mathematical systems, vol 386. Springer, Berlin, pp 167–180
Mesquita M, Paias A (2008) Set partitioning/covering-based approaches for the integrated vehicle and crew scheduling problem. Comput Oper Res 35(5):1562–1575. (Available online 20 October 2006)
Valouxis C, Housos E (2002) Combined bus and driver scheduling. Comput Oper Res 29:243–259
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mesquita, M., Paias, A. & Respício, A. Branching approaches for integrated vehicle and crew scheduling. Public Transp 1, 21–37 (2009). https://doi.org/10.1007/s12469-008-0005-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12469-008-0005-2