## A Binary Quadratic Programming Approach to the Vehicle Positioning Problem

Please always quote using this URN: urn:nbn:de:0297-zib-11242

- The Vehicle Positioning Problem (VPP) consists of the assignment of vehicles (buses, trams or trains) of a public transport or railway company to parking positions in a depot and to timetabled trips. Such companies have many different types of vehicles, and each trip can be performed only by vehicles of some of these types. These assignments are non-trivial due to the topology of depots. The parking positions are organized in tracks, which work as one- or two-sided stacks or queues. If a required type of vehicle is not available in the front of any track, shunting movements must be performed in order to change vehicles' positions, which is undesirable and should be avoided. In this text we present integer linear and non-linear programming formulations for some versions of the problem and compare them from a theoretical and a computational point of view.

Author: | Ralf BorndörferORCiD, Carlos Cardonha |
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Document Type: | ZIB-Report |

Tag: | integer programming; nonlinear programming; quadratic programming; vehicle positioning |

MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C20 Quadratic programming | |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming | |

Contributing Corporation: | CNPq (Sponsor) |

Date of first Publication: | 2009/04/06 |

Series (Serial Number): | ZIB-Report (09-12) |

ISSN: | 1438-0064 |

ZIB-Reportnumber: | 09-12 |

Published in: | A rev. vers. appeared in: H.-G. Bock, X. P. Hoang, R. Rannacher, and J. P. Schlöder (eds.), Modeling, Simulation and Optimization of Complex Processes, Proceedings of the Fourth International Conference on High Performance Scientific Computing, March 2 – 6, 2009, Hanoi, Vietnam, pages 41 – 52. Springer Verlag, 2012 |