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A Binary Quadratic Programming Approach to the Vehicle Positioning Problem

In: Modeling, Simulation and Optimization of Complex Processes

Author

Listed:
  • Ralf Borndörfer

    (Zuse Institute Berlin)

  • Carlos Cardonha

    (Zuse Institute Berlin)

Abstract

The Vehicle Positioning Problem (VPP) is a classical combinatorial optimization problem that has a natural formulation as a Mixed Integer Quadratically Constrained Program. This MIQCP is closely related to the Quadratic Assignment Problem and, as far as we know, has not received any attention yet. We show in this article that such a formulation has interesting theoretical properties. Its QP relaxation produces, in particular, the first known nontrivial lower bound on the number of shuntings. In our experiments, it also outperformed alternative integer linear models computationally. The strengthening technique that raises the lower bound might also be useful for other combinatorial optimization problems.

Suggested Citation

  • Ralf Borndörfer & Carlos Cardonha, 2012. "A Binary Quadratic Programming Approach to the Vehicle Positioning Problem," Springer Books, in: Hans Georg Bock & Xuan Phu Hoang & Rolf Rannacher & Johannes P. Schlöder (ed.), Modeling, Simulation and Optimization of Complex Processes, edition 127, pages 41-51, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25707-0_4
    DOI: 10.1007/978-3-642-25707-0_4
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