Supply chain model for a deteriorating product with time‐varying demand and production rate

The paper develops a two‐echelon supply chain model with a single‐buyer and a single‐vendor. The buyer sells a seasonal product over a short selling period and its inventory is subject to deterioration at a constant rate over time. The vendor's production rate is dependent on the buyer's demand rate, which is a linear function of time. Also, the vendor's production process is not perfectly reliable; it may shift from an in‐control state to an out‐of‐control state at any time during a production run and produce some defective (non‐conforming) items. Assuming that the vendor follows a lot‐for‐lot policy for replenishment made to the buyer, the average total cost of the supply chain is derived and an algorithm for finding the optimal solution is developed. The numerical study shows that the supply chain coordination policy is more beneficial than those policies obtained separately from the buyer's and the vendor's perspectives.