A mathematical for periodic scheduling problems
SIAM Journal on Discrete Mathematics
Optimal pacing of trains in freight railroads: model formulation and solution
Operations Research
A procedure to adjust transit trip departure times through minimizing the maximum headway
Computers and Operations Research
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
Railway Timetabling Using Lagrangian Relaxation
Transportation Science
Modeling and Solving the Train Timetabling Problem
Operations Research
A Variable Trip Time Model for Cyclic Railway Timetabling
Transportation Science
Distributed search in railway scheduling problems
Engineering Applications of Artificial Intelligence
Scheduling trains as a blocking parallel-machine job shop scheduling problem
Computers and Operations Research
The First Optimized Railway Timetable in Practice
Transportation Science
Solving Real-Life Railroad Blocking Problems
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
Modeling Network Transition Constraints with Hypergraphs
Transportation Science
A Tactical Planning Model for Railroad Transportation of Dangerous Goods
Transportation Science
Railway track allocation: models and methods
OR Spectrum
Mathematical and Computer Modelling: An International Journal
Non-cyclic train timetabling and comparability graphs
Operations Research Letters
Modelling disruptions and resolving conflicts optimally in a railway schedule
Computers and Industrial Engineering
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In this paper we extend the work of Bergmann (1975) to investigate the capacity of a single track, unidirectional rail line that adheres to a cyclic timetable. A set of intermediate stations lies between an origin and destination with one siding at each station. Two types of trains-express and local-are dispatched from the origin in alternating fashion. The local stops at every intermediate station and the express stops at no intermediate stations. A mixed integer linear program is developed in order to minimize the length of the dispatching cycle and minimize the total stopping (dwell) time of the local train at all stations combined. Constraints include a minimum dwell time for the local train at each station, a maximum total dwell time for the local train, and headway considerations on the main line and in stations. Hundreds of randomly generated problem instances with up to 70 stations are considered and solved to optimality in a reasonable amount of time using IBM ILOG CPLEX.