Robust optimization in an agricultural closed-loop supply chain network design with a price and freshness-dependent demand: hybrid rat with particle swarm optimization algorithm

This study seeks to develop a closed-loop network for managing the pistachio Supply Chain (SC) under uncertainty. Then, a Mixed-Integer Linear Programming model is suggested to achieve optimal costs of the SC such transportation, production costs and CO₂ emissions tax. It is assumed that the demand for the product depends on the freshness and price of the product and, to deal with uncertainty, a robust optimization approach is used. Furthermore, GAMS software as an exact solution method and four meta-heuristics algorithms including Whale Optimization Algorithm, Particle Swarm Optimization, Rat Swarm Optimizer and a new hybrid algorithm are used as the solution approach. The accuracy of the planned model is examined using a case study and to more measurement, a sensitivity analysis is performed. Finally, the computational time of the mentioned algorithms and their obtained results are compared. The numerical analysis showed that the hybrid algorithm, although having more computational time, is superior to others, which the results had a difference between 0.9 and 2.7% with the exact method. Therefore, it is showed that the hybrid approach is a valid approach to solve large-scale problems. Our findings are helpful for pistachio-producing countries.