Bi-objective Optimization of Train Scheduling and Locomotive Assignment

The train scheduling is one of the most important problems in transportation planning. This problem aims to generate a feasible train timetable subject to operational constraints. Furthermore, optimal utilization of locomotives should be considered in rail transportation planning. In this paper, a new mathematical model is proposed for train scheduling and locomotive assignment. In this model, the train scheduling problem is modeled using the job shop scheduling problem with the total length of schedule or makespan minimization as the objective function. Then, locomotive minimization is added to the model as the second objective. The obtained bi-objective model is analyzed by benefiting Pareto frontier method. Numerical examples are illustrated to prove the model efficiency.