Job-shop Problems with Objectives Appropriate for Train Scheduling in a Single-track Railway

A train scheduling problem in a single-track railway is studied using a mixed graph model for a job-shop with appropriate criteria. There are several performance evaluations for a train schedule. Optimizing a train schedule subtends minimizing total tardiness of the trains, minimizing the sum of train transit times, minimizing the makespan for a train schedule, etc. Since the corresponding job-shop problems with the above three criteria are NP-hard, several heuristic algorithms have been developed using different priorities based on release times of jobs, job due-dates and job completion times. Simulation on a computer was used for evaluating the quality and efficiency of the heuristic algorithms developed for the appropriate job-shop problems. Release times, due-dates and completion times of the jobs have been used as input parameters (priorities) in the computer simulation to see effect of them on a quality of schedules with different objective functions. The efficiency of the developed heuristics was demonstrated via simulation on a set of randomly generated instances of small and medium sizes. Computational results showed that one heuristic algorithm outperformed other algorithms tested for two of three objective functions under consideration.