A mathematical inventory model for a single-vendor multi-retailer supply chain based on the Vendor Management Inventory Policy

In supply chain management, the vendor managed inventory plays a vital role in production systems to decrease the total costs by reducing the bullwhip effect. The vendor managed inventory (VMI) policy reduces the decision-making levels by which prediction error of demand is reduced. This policy significantly reduces demand variations in inventory management. This paper develops an inventory model based on the vendor-managed policy in which there are single-vendor and multiple retailers. In addition to inventory decisions, the proposed model optimizes an upper limit for inventory levels based on a penalty. To close real-world conditions, we consider integer values for order quantities per cycle for retailers. Moreover, the number of vendor’s orders has an upper limit. The purpose of the developed mathematical model is to find an optimal value for replenishment frequencies of retailers, order quantities, and upper limits on the inventory level of retailers. Since the proposed model is an integer non-linear programming problem (INLP), we employ a metaheuristic optimization approach called the imperialist competitive algorithm. To verify the proposed methodology and algorithm, we compare the obtained solutions with an exact method. In different scenarios, the mathematical model is solved, and the results showed that vendors follow the normal situation in which there is no overstock penalty in such a way that vendors experience backorder inventory problems. The main contribution of this paper was to include the upper limits on the inventory levels in VMI mathematical models along with a verified meta-heuristic algorithm.