Solving a school bus scheduling problem with integer programming
In many rural areas in Germany pupils on the way to school are a large if not the largest group of customers in public transport. If all schools start more or less at the same time then the bus companies need a high number of vehicles to serve the customer peak in the morning rush hours. In this article, we present an integer programming model for the integrated coordination of the school starting times and the public bus services. We discuss preprocessing techniques, model reformulations, and cutting planes that can be incorporated into a branch-and-cut algorithm. Computational results show that in our test counties a much lower number of buses would be sufficient if the schools start at different times.
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- Desaulniers, Guy & Lavigne, June & Soumis, Francois, 1998. "Multi-depot vehicle scheduling problems with time windows and waiting costs," European Journal of Operational Research, Elsevier, vol. 111(3), pages 479-494, December.
- Bowerman, Robert & Hall, Brent & Calamai, Paul, 1995. "A multi-objective optimization approach to urban school bus routing: Formulation and solution method," Transportation Research Part A: Policy and Practice, Elsevier, vol. 29(2), pages 107-123, March.
- Francesco Maffioli & Anna Sciomachen, 1997. "A mixed-integer model for solving ordering problems with side constraints," Annals of Operations Research, Springer, vol. 69(0), pages 277-297, January.
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