Fuzzy Sets and Systems
Optimal pacing of trains in freight railroads: model formulation and solution
Operations Research
Modelling the number and location of sidings on a single line railway
Computers and Operations Research
Theory and Practice of Uncertain Programming
Theory and Practice of Uncertain Programming
Heuristic Techniques for Single Line Train Scheduling
Journal of Heuristics
Railway Timetabling Using Lagrangian Relaxation
Transportation Science
A survey of credibility theory
Fuzzy Optimization and Decision Making
Fuzzy fixed charge solid transportation problem and algorithm
Applied Soft Computing
Uncertainty Theory
Expected value of fuzzy variable and fuzzy expected value models
IEEE Transactions on Fuzzy Systems
Entropy of Credibility Distributions for Fuzzy Variables
IEEE Transactions on Fuzzy Systems
Railway freight transportation planning with mixed uncertainty of randomness and fuzziness
Applied Soft Computing
Entropy maximization model for the trip distribution problem with fuzzy and random parameters
Journal of Computational and Applied Mathematics
Fractional Liu process with application to finance
Mathematical and Computer Modelling: An International Journal
Engineering Applications of Artificial Intelligence
Fuzzy numbers from raw discrete data using linear regression
Information Sciences: an International Journal
Engineering Applications of Artificial Intelligence
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The aim of the train timetable problem is to determine arrival and departure times at each station so that no collisions will happen between different trains and the resources can be utilized effectively. Due to uncertainty of real systems, train timetables have to be made under an uncertain environment under most circumstances. This paper mainly investigates a passenger train timetable problem with fuzzy passenger demand on a singleline railway in which two objectives, i.e., fuzzy total passengers' time and total delay time, are considered. As a result, an expected value goal-programming model is constructed for the problem. A branch-and-bound algorithm based on the fuzzy simulation is designed in order to obtain an optimal solution. Finally, some numerical experiments are given to show applications of the model and the algorithm.