Train Scheduling Problem with Consideration of Praying Constraint as an Application of Job Shop Scheduling Problem

The present paper extends the idea of job shop scheduling problem with resting constraints to the train scheduling problem with the Muslim praying considerations. For this purpose, after proposing the new mathematical model, a heuristic algorithm based on the Electromagnetism-Like algorithm (EM) which is well adjusted to scheduling problems is employed to solve the large-size practical cases. The effectiveness of the proposed algorithm is then validated by comparing with optimum solution using small-size instances and simulated annealing algorithm, and Particle swarm Optimization (PSO) using medium and large-size instances. At the end, a practical case from Iranian railway network is studied and the results are reported. The results indicate that in the case of considering the Muslim praying constraint, the ratios of total tardiness of trains, and the total praying times are 14.5%, and 3.5%, respectively, while in the case of relaxing this constraint; the first ratio reduces to 12.3%. This result demonstrates that the proposed algorithm is able to schedule the praying times so that in many cases the trains with different directions meet each other during the praying times.