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The demand-dependent optimization of regular train timetables. (English) Zbl 1152.90435
Liberti, Leo (ed.) et al., Workshop on graphs and combinatorial optimization. Papers from the workshop, Como, Italy, May 31, 2004. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 17, 99-104 (2004).
Summary: Regular timetables, in which the trains arrive and depart at constant intervals, have been adopted in various European countries, because of the simpler and fairer service they allow. The design of such a timetable has recently received a certain attention in the literature. This paper extends the commonly adopted model to take into account the reciprocal influence between the quality of a timetable and the transport demand captured by the railway with respect to alternative means of transport. The resulting mixed-integer nonlinear model remains nonconvex even after relaxing the integrality constraints. We solve it by a branch-and-bound algorithm based on Outer Approximation and a heuristic algorithm exploiting the decomposition and reciprocal update of two submodels. Preliminary computational results concern a regional network in North-western Italy.
For the entire collection see [Zbl 1109.05009].

MSC:
90B35 Deterministic scheduling theory in operations research
90C11 Mixed integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C59 Approximation methods and heuristics in mathematical programming
Software:
PESPLib
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