Abstract
In many rural areas, the public bus service is demand-oriented: By far the biggest group of customers are pupils who are transported to their schools within certain strict time limits. Usually, all schools start around the same time, which causes a morning peak in the number of deployed buses. However, schools are allowed to change their starting times within some interval. The question is, how to simultanenously rectify the starting times for all schools and bus trips in a certain county so that the number of scheduled buses is minimal. This problem can be formulated as a vehicle routing problem with coupled time windows (VRP-CTW), which is an extension of the vehicle routing problem with time windows (VRP-TW), where additional coupling constraints on the time windows are introduced. We give a mixed-integer programming formulation for VRP-CTW, and present solutions and lower bounds for randomly generated and real-world instances.
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References
Bar-Yehuda R., Rawitz D. (2001), Efficient algorithms for integer programs with two variables per constraint. Algorithmica 29(4), 595–609.
Bowerman R.L., Hall G.B., Calamai P.H. (1995), A multi-objective optimisation approach to school bus routing problems. Transp. Research A 28(5), 107–123.
Braca J., Bramel J., Posner B., Simchi-Levi D. (1997), A Computerized Approach to the New York City School Bus Routing Problem. IIE Transactions 29, 693–702.
Corberan A., Fernandez E., Laguna M., Marti R. (2000), Heuristic Solutions to the Problem of Routing School Buses with Multiple Objectives. Technical Report TR08-2000, Dep. of Statistics and OR, University of Valencia, Spain.
Cordeau J.-F., Desaulniers G., Desrosiers J., Solomon M., Soumis F. (2002), VRP with Time Windows. In: Toth P., Vigo D. (Eds.), The Vehicle Routing Problem. SIAM Monogr. on Disc. Math, and Applications. SIAM, Philadelphia.
Savelsbergh M. (1986), Local search for routing problems with time windows. Annals of Operations Research 4, 285–305.
Stöveken P. (2000), Wirtschaftlicherer Schulverkehr: ÖPNV-Optimierung mit erfolgsabhängiger Honorierung. Der Nahverkehr 3, 65–68. (In German).
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© 2005 Springer-Verlag Berlin Heidelberg
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Fügenschuh, A., Martin, A., Stöveken, P. (2005). Integrated Optimization of School Starting Times and Public Bus Services. In: Fleuren, H., den Hertog, D., Kort, P. (eds) Operations Research Proceedings 2004. Operations Research Proceedings, vol 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27679-3_19
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DOI: https://doi.org/10.1007/3-540-27679-3_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24274-1
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