Optimal Charging Scheduling and Management with Bus-Driver-Trip Assignment considering Mealtime Windows for an Electric Bus Line

Abstract

Compared to a charging scheduling and management problem characterized by predetermined trip assignment, this study takes bus and driver scheduling into account, and mealtime windows must be guaranteed as one of the major labor regulations. A discretized mixed-integer linear programming (MIPL) model is developed based on a single electric bus route. We aim to obtain fast and high-quality global solutions for this problem, and the model can be easily executed by bus operators by directly invoking an available optimization solver such as IBM ILOG CPLEX. We test our model on a real round-trip bus route. Numerical experiments show that CPLEX takes approximately 6 sec to obtain an optimal solution. The model can not only reasonably arrange daily trips for each electric bus and driver but also effectively determine the optimal charging schedule and management for an electric bus line. Besides, we analyze the sensitivity of the key parameters in the model. With the increase in the drivers’ maximum workload, the drivers’ average idle time decreases by approximately 11.25%. The objective value decreases by approximately 38.71% and 40.04% with increases in the battery capacity and fleet size, respectively, and the objective value increases by approximately 30.06% with the decrease in the initial battery driving range. In addition, we compare the effectiveness of our time discretization modeling method in solving the same case study to that from other similar studies, and the validity of our method can be verified by the calculation time. We also compare the computational efficiency of CPLEX in solving the same case study problem with and without implementing valid inequalities, and the computational efficiency of the valid inequality method is greatly improved. Finally, through the testing of a multiline network, the potential application of the model to a large-scale traffic network is verified.