The Optimal Replenishment Policies under VMI System with Multi-retailer and Multi-period Random Demand

VMI is a process where the vendor creates orders for their customers based on demand information that they receive from the customers. This arrangement can promote a higher level of service and reduce cost by integrating the inventory and replenishment policies especially when the companies rely on third-party logistics providers to transport the products across the supply chain. For this purpose, a supply chain system of single supplier, single warehouse and multi-retailer is studied. At first, an integer programming model and network model of the problem for finding optimal replenishment policies with multi-period random demand is proposed. And then, a shortest path algorithm is designed to solve the network model. Finally, the computational results, comparing with the results of the integer programming model, demonstrate the effectiveness and availability of the network model and the shortest path algorithm.