Solving a new bi-objective multi-echelon supply chain problem with a Jackson open-network issue under uncertainty

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