A mathematical for periodic scheduling problems
SIAM Journal on Discrete Mathematics
Computational Optimization and Applications
Modeling and Solving the Train Timetabling Problem
Operations Research
A Lagrangian heuristic algorithm for a real-world train timetabling problem
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
Cyclic railway timetabling: a stochastic optimization approach
ATMOS'04 Proceedings of the 4th international Dagstuhl, ATMOS conference on Algorithmic approaches for transportation modeling, optimization, and systems
Railway track allocation: models and methods
OR Spectrum
The periodicity and robustness in a single-track train scheduling problem
Applied Soft Computing
A Lagrangian Heuristic for Robustness, with an Application to Train Timetabling
Transportation Science
Railway Rolling Stock Planning: Robustness Against Large Disruptions
Transportation Science
Robustness for a single railway line: Analytical and simulation methods
Expert Systems with Applications: An International Journal
A pattern based, robust approach to cyclic master surgery scheduling
Journal of Scheduling
A demand-responsive decision support system for coal transportation
Decision Support Systems
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The train timetabling problem (TTP) consists of finding a train schedule on a railway network that satisfies some operational constraints and maximizes some profit function that accounts for the efficiency of the infrastructure usage. In practical cases, however, the maximization of the objective function is not enough, and one calls for a robust solution that is capable of absorbing, as much as possible, delays/disturbances on the network. In this paper we propose and computationally analyze four different methods to improve the robustness of a given TTP solution for the aperiodic (noncyclic) case. The approaches combine linear programming (LP) and ad hoc stochastic programming/robust optimization techniques. We computationally compare the effectiveness and practical applicability of the four techniques under investigation on real-world test cases from the Italian railway company Trenitalia. The outcome is that two of the proposed techniques are very fast and provide robust solutions of comparable quality with respect to the standard (but very time consuming) stochastic programming approach.