Optimal replenishment policy for an integrated inventory system with defective items and allowable shortage under trade credit

This study proposes a single-supplier, single-retailer integrated inventory model that accounts for defective items that arrive in a retailer's order under a full-lot inspection policy. All defective items are returned to the supplier in next delivery. After receipt of the returned items, the supplier will classify them into two types: items that still have some worth and waste items. For those items that still have some worth, the supplier will offer customers a discount in order to minimize losses arising from these defective items. The supplier needs to pay a disposal fee for those items classified as waste items. Shortages are allowed and are fully backlogged. To encourage sales the supplier offers trade credit to the retailer. A two-echelon inventory model is established, and the decision variables include: replenishment cycle time, the time taken to run out of stock and the number of lots delivered from the supplier to the retailer. An algorithm is developed to determine the optimal supply chain strategy and numerical examples are provided to show the solution procedure. Also, a sensitivity analysis is conducted on the main parameters of the model.