Assignment and scheduling trucks in cross-docking system with energy consumption consideration and trucks queuing

Abstract

Cross-docking, as one of the efficient strategies of distribution systems can reduce the inventory costs and accelerate the delivery of products to customers. One of the important truck scheduling problems in multi-door cross-docks is a multi-period planning horizon, which is rarely taken into consideration. In addition, a way to assign the cross-dock transportation equipment, such as forklifts to doors and trucks as well as the energy consumption optimization of the equipment has not yet been addressed. Furthermore, due to a number of constraints in transportation equipment of the cross-docks, the formation of a waiting queue for outbound trucks for assigning to outbound doors is one of the most important issues that have been rarely investigated. Accordingly, in this research, a bi-objective optimization model is presented for the problem of scheduling, the sequence of trucks, and the assignment of trucks and forklifts to the doors in a multi-door cross-dock with flexible doors. In addition, in order to make a better plan for inbound and outbound trucks, the time window constraints are used. Moreover, an M/M/1 queuing system is provided to minimize the waiting times for trucks in the queue for the assignment to doors. The first objective function of the proposed model seeks to minimize the costs of holding products in a cross-dock, delaying trucks in delivering shipments to customers, and waiting for trucks in the queue. The aim of the second objective function is to minimize the energy consumption of forklift in a cross-dock. In order to solve the problem, two multi-objective meta-heuristic algorithms, including a multi objective imperialist competitive algorithm (MOICA) and a multi objective grey wolf optimizer (MOGWO) are presented. Finally, to illustrate the accuracy of the model and algorithms presented, various numerical examples are solved and the results are discussed.