A vendor managed inventory supply chain with deteriorating raw materials and products

Fast deteriorating raw materials such as raw milk, fruit and vegetables are commonly used to produce slowly deteriorating finished products such as milk powders, cheeses, and pastas. This paper studies a Vendor Managed Inventory (VMI) type supply chain where the manufacturing vendor decides how to manage the system‐wide inventories of its fast deteriorating raw material and its slowly deteriorating product. The decision variables are a common replenishment cycle of the product and the replenishment frequency of the raw material. We assume the deteriorating rates are known constants and every retailer's demand is deterministic. We develop an integrated model to calculate the total inventory and deterioration cost for such a system. We prove the convexity of the cost functions, and based on this a golden search algorithm is developed to find the optimal solution of the model. Our numerical results show that the deteriorating rate of the product may increase the total cost by more than 40% compared to the zero‐deteriorating rate, while the deteriorating raw material has less impact on the total cost (commonly less than 5% in our numerical examples). This indicates that more attention should be paid to the product than the raw material. Further, an increase in the number of retailers can make the replenishment frequency of the raw material increase significantly but the common replenishment cycle of the product decreases a little. This indicates that adding a new retailer would not be felt strongly by the other retailers but would be felt by the supplier of the raw material.