Theory of linear and integer programming
Theory of linear and integer programming
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
Simultaneous Vehicle and Crew Scheduling in Urban Mass Transit Systems
Transportation Science
A Variable Trip Time Model for Cyclic Railway Timetabling
Transportation Science
Disjoint congruence classes and a timetabling application
Discrete Applied Mathematics
Computing delay resistant railway timetables
Computers and Operations Research
Engineering the modulo network simplex heuristic for the periodic timetabling problem
SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Integral cycle bases for cyclic timetabling
Discrete Optimization
Solving periodic event scheduling problems with SAT
IEA/AIE'12 Proceedings of the 25th international conference on Industrial Engineering and Other Applications of Applied Intelligent Systems: advanced research in applied artificial intelligence
Improving the modulo simplex algorithm for large-scale periodic timetabling
Computers and Operations Research
Service-Oriented Line Planning and Timetabling for Passenger Trains
Transportation Science
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In the planning process of railway companies, we propose to integrate important decisions of network planning, line planning, and vehicle scheduling into the task of periodic timetabling. From such an integration, we expect to achieve an additional potential for optimization. Models for periodic timetabling are commonly based on the Periodic Event Scheduling Problem (PESP). We show that, for our purpose of this integration, the PESP has to be extended by only two features, namely a linear objective function and a symmetry requirement. These extensions of the PESP do not really impose new types of constraints. Indeed, practitioners have already required them even when only planning timetables autonomously without interaction with other planning steps. Even more important, we only suggest extensions that can be formulated by mixed integer linear programs. Moreover, in a selfcontained presentation we summarize the traditional PESP modeling capabilities for railway timetabling. For the first time, also special practical requirements are considered that we proove not being expressible in terms of the PESP.