A mathematical for periodic scheduling problems
SIAM Journal on Discrete Mathematics
A genetic algorithm approach to periodic railway synchronization
Computers and Operations Research
Discrete optimization in public rail transport
Mathematical Programming: Series A and B - Special issue: papers from ismp97, the 16th international symposium on mathematical programming, Lausanne EPFL
A Survey of Optimization Models for Train Routing and Scheduling
Transportation Science
Modeling and Solving the Train Timetabling Problem
Operations Research
The New Dutch Timetable: The OR Revolution
Interfaces
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
New heuristics to solve the “CSOP” railway timetabling problem
IEA/AIE'06 Proceedings of the 19th international conference on Advances in Applied Artificial Intelligence: industrial, Engineering and Other Applications of Applied Intelligent Systems
Non-cyclic train timetabling and comparability graphs
Operations Research Letters
Integral cycle bases for cyclic timetabling
Discrete Optimization
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In this paper we study the design and optimization of train timetabling adapted to a dynamic demand environment. This problem arises in rapid train services which are common in most important cities. We present three formulations for the problem, with the aim of minimizing passenger average waiting time. The most intuitive model would consider binary variables representing train departure times but it yields to non-linear objective function. Instead, we introduce flow variables, which allow a linear representation of the objective function. We provide incremental improvements on these formulations, which allows us to evaluate and compare the benefits and disadvantages of each modification. We present a branch-and-cut algorithm applicable to all formulations. Through extensive computational experiments on several instances derived from real data provided by the Madrid Metropolitan Railway, we show the advantages of designing a timetable adapted to the demand pattern, as opposed to a regular timetable. We also perform an extensive computational comparison of all linear formulations in terms of size, solution quality and running time.