A Binary Quadratic Programming Approach to the Vehicle Positioning Problem

The Vehicle Positioning Problem (VPP) is a classical combinato-rial optimization problem that has a natural formulation as an integer quadratic 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 the integer linear models com-putationally. The strengthening technique that raises the lower bound might also be useful for other combinatorial optimization problems.