Railway Timetabling Using Lagrangian Relaxation
Transportation Science
Sorting Permutations by Reversals Through Branch-and-Price
INFORMS Journal on Computing
Modeling and Solving the Train Timetabling Problem
Operations Research
Computers and Industrial Engineering
Exact formulations and algorithm for the train timetabling problem with dynamic demand
Computers and Operations Research
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We consider the customary formulation of non-cyclic train timetabling, calling for a maximum-profit collection of compatible paths in a suitable graph. The associated ILP models look for a maximum-weight clique in a (n exponentially-large) compatibility graph. By taking a close look at the structure of this graph, we analyze the existing ILP models, propose some new stronger ones, all having the essential property that both the separation and the column generation can be carried out efficiently, and report the computational results on highly-congested instances.