A tri-level location-allocation model for forward/reverse supply chain

Abstract The design of supply chain network usually directly influences the performance of location-allocation of facilities, especially for the main parties. This paper firstly addresses the tri-level location-allocation design problem which considers the forward and reverse network, simultaneously. The proposed problem is formulated on the static Stackelberg game between the Distribution Centers (DCs), Customer Zones (CZs) and Recover Centers (RCs) in the framework. The literature reports that most of previous works have utilized the various exact approaches which are not efficient and are so complex. In this study, three old and successful methods consist of Variable Neighborhood Search (VNS), Tabu Search (TS) and Particle Swarm Optimization (PSO), as well as two recent nature-inspired algorithms; Keshtel Algorithm (KA) and Water Wave Optimization (WWO) are utilized. Besides, according the nature of the problem, this study proposes a simple nested approach named as tri-level metaheuristic for the first time in order to solve the large scale problems. The performances of the algorithms are probed by using Taguchi experimental method to set the proper values for the parameters. Eventually, the efficiency of the algorithms is compared by different criteria and validated through a real case study. The obtained results show that tri-level metaheuristics are effective approaches to solve the underlying tri-level models in large scale network.