Pricing decisions in the closed-loop supply chain network, taking into account the queuing system in production centers

Abstract

In this paper, a multi-echelon closed-loop supply chain network is modeled considering pricing decisions and queuing system under uncertainty. The mathematical model's objective is to maximize the net present value (NPV) under uncertain parameters of potential demand and transportation costs. Therefore, the sensitivity of the actual demand on the pricing decisions of the final and returned products in the supply chain network. The main decisions of the mathematical model are to maximize the NPV related to the location of potential facilities, determine the amount of product inventory in the production center, reduce the length of the queue of production lines and determine the optimal amount of product transfer flow between facilities. Also, the most important decisions related to the related network are determining the optimal price of final products and returns in the supply chain network. Flexible Robust-Fuzzy optimization (FRFO) method is used to control the uncertainty parameters and the four algorithms G-HHO, PSO, ALO and GWO are used to solve the problem. The calculation results show that with the increase of uncertainty in the network, the value of NPV decreases and also with the increase of the number of production lines, due to the reduction of the queue length of the parts, the cost of waiting time decreases and the value of NPV increases. On the price of final and return products, the price in the forward and backward chain has increased and as a result, the NPV value has increased. By analyzing more tests, it was also observed that the G-HHO algorithm obtained the highest average NPV value in solving large numerical examples. While the PSO algorithm has reached the near-optimal solution in the shortest time. Also, there has been no significant difference between the averages of the comparison indices between the solution algorithms. Examination of the solution results between the solution methods shows that the maximum relative difference between the results is less than 5%, and the proposed G-HHO algorithm has the highest efficiency in solving large sample problems.