Optimizing a bi-objective inventory model for a two-echelon supply chain management using a tuned meta-heuristic algorithm

Since vendor-managed inventory strategy plays an important role to reduce total inventory costs, the focus of this paper is to develop an economic order quantity model presented for a two-echelon supply chain management including one vendor and one retailer. In this bi-objective model, the vendor delivers several products to the retailer while shortages are allowed. The aim of this paper is to determine order sizes and maximum backorder levels for each product to simultaneously minimize total inventory costs and a storage space. Moreover, two main constraints, namely budget and the number of orders, are considered to simulate real-world operating conditions for the proposed model. Since the presented model belongs to integer non-linear programming problems, a meta-heuristic algorithm, particle swarm optimization (PSO), is employed to optimize it. In addition, because the quality of solutions depends on the values of parameters of meta-heuristics, the parameters of PSO are tuned using the Taguchi method. Then, the proposed algorithm is compared to branch and bound method.