Modelling Cross-Docking in a Three-Level Supply Chain with Stochastic Service and Queuing System: MOWFA Algorithm

Abstract

In today’s competitive world, it is essential to provide a new method through which maximum efficiency can be created in the production and supply cycle. In many production environments, sending goods directly from the producer to the consumer brings many problems. Therefore, an efficient transport system should be established between producers and consumers. Such a system is designed in the field of supply chain management knowledge. Supply chain management is the evolutionary result of warehousing management and is one of the important infrastructural foundations of business implementation, in many of which the main effort is to shorten the time between the customer’s order and the actual delivery of the goods. In this research, the supply chain consists of three levels. Suppliers are placed on the first level, cross-docks on the second level, and factories on the third level. In this system, a number of suppliers send different raw materials to several different cross-docks. Each channel is assigned to a cross-dock for a specific product. The main goal of this article is to focus on optimizing the planning of incoming and outgoing trucks with the aim of minimizing the total operation time within the supply chain. The arrival rate of goods from suppliers to the cross-dock is stochastic with a general probability distribution. On the other hand, the time required to prepare and send the goods is random with a general probability distribution. The service time in each cross-dock depends on the number of its doors. Therefore, each cross-dock can be modeled as a G/G/m queueing system where m represents the number of doors. The mathematical model of the research has been developed based on these assumptions. Since the problem is NP-hard, the time to solve it increases drastically with the increase in the dimensions of the problem. Therefore, three metaheuristics, including multi-objective water flow, non-dominated sorting genetic, and a multi-objective simulated annealing algorithm have been used to find near-optimal solutions to the problem. After adjusting the parameters of the algorithms using the Taguchi method, the results obtained from the algorithms were analyzed with a statistical test and the performance of the algorithms was evaluated. The results vividly demonstrate that non-dominated sorting genetics is the best of all.