Solving a New Bi-Objective Multi-Echelon Supply Chain Problem with a Jackson Open-Network Issue Under Uncertainty

Abstract

In today’s world, changes in the economic and industrial sectors are taking place more quickly than in the past. Based on today’s competitive market, considering the needs and desires of the customer is very important. Thus, designing the supply chain network to minimize the costs and improve the system efficiency, the service facility, and attention to the timely service delivery to the customer should be considered. Also, deployment costs to determine the number and position of facilities are regarded as another strategic issue. Therefore, to become closer to the real-world application, by considering the Jackson network model (queuing theory), the present study aims to design a closed-loop supply chain (CLSC) network to reduce the waiting time in the queue. Two objectives, namely minimizing the cost and waiting time incurred in queues formed in producers and distributors, are investigated. Queuing mathematical expressions are used both in dealing with objectives and constraints. To develop a model, which is close to real by considering uncertainty, the parameters, including demand rate and shipping cost of products, were considered as a trapezoidal fuzzy number. Also, we crisp this fuzzy uncertainty using both Jimenez and chance-constrained programming approaches. Due to the suggested model’s complexity and nonlinearity, we linearized the mathematical model as much as possible, then two meta-heuristic algorithms, namely multi-objective particle swarm optimization (MOPSO) and non-dominated sorted genetic algorithm (NSGA-II), are used to solve the model. First, the structural parameters of these algorithms are tuned by the Taguchi method. Then, numerous numerical test problems ranging from small to large scales are used to compare these algorithms considering Pareto front measuring indexes and various hypothesis tests.