Scheduling jobs with fixed start and end times
Discrete Applied Mathematics
Integer and combinatorial optimization
Integer and combinatorial optimization
Using Integer Programming to Solve the Train-Platforming Problem
Transportation Science
A combinatorial algorithm for weighted stable sets in bipartite graphs
Discrete Applied Mathematics - Special issue: 2nd cologne/twente workshop on graphs and combinatorial optimization (CTW 2003)
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In this paper we study a general formulation of the train platforming problem, which contains as special cases all the versions previously considered in the literature as well as a case study from Rete Ferroviaria Italiana, the Italian Infrastructure Manager. In particular, motivated by our case study, we consider a general quadratic objective function, and propose a new way to linearize it by using a small number of new variables along with a set of constraints that can be separated efficiently by solving an appropriate linear program. The resulting integer linear programming formulation has a continuous relaxation that leads to strong bounds on the optimal value. For the instances in our case study, the solution approach based on this relaxation produces solutions that are much better than those produced by a simple heuristic method currently in use, and that often turn out to be (nearly) optimal.