A Lagrangian heuristic algorithm for a real-world train timetabling problem
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Optimal Real-Time Traffic Control in Metro Stations
Operations Research
Fast Approaches to Improve the Robustness of a Railway Timetable
Transportation Science
A Lagrangian heuristic algorithm for a real-world train timetabling problem
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Modeling Network Transition Constraints with Hypergraphs
Transportation Science
Modeling Network Transition Constraints with Hypergraphs
Transportation Science
Railway track allocation: models and methods
OR Spectrum
A Lagrangian Heuristic for Robustness, with an Application to Train Timetabling
Transportation Science
Non-cyclic train timetabling and comparability graphs
Operations Research Letters
Statistical modelling of delays in a rail freight transportation network
Proceedings of the Winter Simulation Conference
SIMARAIL: simulation based optimization software for scheduling railway network
Proceedings of the Winter Simulation Conference
Computers and Industrial Engineering
Exact formulations and algorithm for the train timetabling problem with dynamic demand
Computers and Operations Research
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The train timetabling problem aims at determining a periodic timetable for a set of trains that does not violate track capacities and satisfies some operational constraints. In particular, we concentrate on the problem of a single, one-way track linking two major stations, with a number of intermediate stations in between. Each train connects two given stations along the track (possibly different from the two major stations) and may have to stop for a minimum time in some of the intermediate stations. Trains can overtake each other only in correspondence of an intermediate station, and a minimum time interval between two consecutive departures and arrivals of trains in each station is specified.In this paper, we propose a graph theoretic formulation for the problem using a directed multigraph in which nodes correspond to departures/arrivals at a certain station at a given time instant. This formulation is used to derive an integer linear programming model that is relaxed in a Lagrangian way. A novel feature of our model is that the variables in the relaxed constraints are associated only with nodes (as opposed to arcs) of the aforementioned graph. This allows a considerable speed-up in the solution of the relaxation. The relaxation is embedded within a heuristic algorithm which makes extensive use of the dual information associated with the Lagrangian multipliers. We report extensive computational results on real-world instances provided from Ferrovie dello Stato SpA, the Italian railway company, and from Ansaldo Segnalamento Ferroviario SpA.