This study addresses a parallel machine production and transportation operations’ scheduling problem with a tight time window associated with the transfer and delivery process. The orders located at the parallel machines need to be delivered to customers by train. Each order must be processed within a limited completion time in order for the product to be matched with the optimal trip to its destination within the delivery period. A mathematical analysis method is used to reveal the impact of tight time windows on the scheduling of production and transportation operations. The order transfer redundancy time and order transfer waiting time are employed to reflect the impact scheduling of production on the transfer process. The order delivery redundancy time and order delivery waiting time are used to describe delivery operations. The goal is to maximize the coordination level of order transfer and delivery, which are reflected in the order transfer time and the order delivery time, respectively. Additionally, a simulated annealing algorithm using the column generation technique was developed to solve this problem. The results show that the use of the system coordination model in this method obviously improves the number of successful transfers and deliveries.
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.
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