Fast Edge-Orientation Heuristics for Job-Shop Scheduling Problems with Applications to Train Scheduling

A train scheduling problem in a single-track railway can be modeled as a job-shop scheduling problem. We use a mixed graph model for such a job-shop problem 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 constructive heuristics have been developed using different priorities based on the release times of the jobs, the job due-dates and the job completion times. Experiments on a computer were used for evaluating the quality and efficiency of the heuristic algorithms developed for appropriate job-shop problems. The release times, due-dates and completion times of the jobs have been used as input parameters (priorities) to see the effect of them on the quality of the schedules with different objective functions. The efficiency of the developed heuristics was tested on a set of 118 randomly generated instances of small and large sizes with up to 2000 operations.