Branching strategies to improve regularity of crew schedules in ex-urban public transit
- 95 Downloads
We discuss timetables in ex-urban bus traffic that consist of many trips serviced every day together with some exceptions that do not repeat daily. Traditional optimization methods for vehicle and crew scheduling in such cases usually produce schedules that contain irregularities which are not desirable especially from the point of view of the bus drivers. We propose a solution method which improves regularity while partially integrating the vehicle and crew scheduling problems. The approach includes two phases: first we solve the LP relaxation of a set covering formulation, using column generation together with Lagrangean relaxation techniques. In a second phase, we generate integer solutions using a new combination of local branching and various versions of follow-on branching. Numerical tests with artificial and real instances show that regularity can be improved significantly with no or just a minor increase of costs.
KeywordsColumn Generation Crew Schedule Vehicle Schedule Regular Chain Regular Pair
- Borndoerfer R, Loebel A, Weider S (2004) A bundle method for integrated multi-depot vehicle and duty scheduling in public transit. Technical report ZR-04-14, ZIB, Zuse Institute Berlin, Berlin, GermanyGoogle Scholar
- Dallaire A, Fleurent C, Rousseau J-M (2004) Dynamic constraint generation in crewopt, a column generation approach for transit crew scheduling. Technical report, GIRO Inc., Montreal, CanadaGoogle Scholar
- GIRO (2007) Hastus transit scheduling and operations. Available at http://www.giro.ca/en/products/hastus/index.htm, July 2007.
- Guo Y, Suhl L, Thiel MP (2005) Solving the airline crew recovery problem by a genetic algorithm with local improvement. Oper Res Int J 5Google Scholar
- Huisman D (2005) Random data instances for multiple-depot vehicle and crew scheduling. Available at http://www.few.eur.nl/few/people/huisman/instances.htm, April
- Huisman D (2004) Integrated and dynamic vehicle and crew scheduling. Ph.D thesis, Tinbergen Institute, Erasmus University RotterdamGoogle Scholar
- Ryan DM, Foster B (1981) An integer programming approach to scheduling. In: Wren A (ed), Computer scheduling of public transport: urban passenger vehicle and crew scheduling. North-Holland, Amsterdam, pp 269–280Google Scholar
- Steinzen I (2007) Topics in integrated vehicle and crew scheduling in public transit. Ph.D thesis, DSOR Lab, University of PaderbornGoogle Scholar
- Steinzen I, Gintner V, Suhl L (2007) Local Branching und Branching-Strategien fuer Umlauf- und Dienstplanung im Regionalverkehr mit unregelmaessigen Fahrplaenen. In: Guenther H-O, Mattfeld D, Suhl L(eds) Management logistischer Netzwerke: Entscheidungsunterstuetzung, Informationssysteme und OR-Tools. Physica-Verlag, Heidelberg, pp 407–424CrossRefGoogle Scholar
- Tajima A, Misono S (1997) Airline crew-scheduling with many irregular flights. In: Leong H, Imai H, Jain S (eds) Lecture notes in computer science: proceedings of the 8th international symposium on algorithms and computation—ISAAC97. Springer, Heidelberg, pp 2–11Google Scholar
- Vance PH, Atamtuerk A, Barnhart C, Gelman F, Johnson E, Krishna A, Mahidhara D, Rebello R (1997) A heuristic branch-and-price approach for the airline crew pairing problem. Technical report LEC-97-06, Georgia Institute of Technology, Atlanta, USAGoogle Scholar
- Vanderbeck F (1994) Decomposition and column generation for integer programs. Ph.D thesis, Universite Catholique de LouvainGoogle Scholar