Many products deteriorate with time and have a maximum lifetime. An expiration date will be marked. And then the product will no longer be sold after the expiration date. Thereafter, the demand rate for the deteriorated item will near zero as its expiration date is due. Thus, to consider the demand rate incorporates with the expiration date is practical. Furthermore, as the storage capacity is limited, the retailer needs to rent a warehouse to store the excess quantities than can be stored. Consequently, to consider a two-warehouse inventory model is necessary. Nowadays, the supplier often provides a cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In addition, the cost is usually affected by the present value of time. For these reasons considered, a supplier-retailer-customer chain model here is established. The main task of this research is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. Numerical examples are performed for illustration and sensitivity analysis on the expiration date is conducted.

This study investigated non-instantaneous deteriorating items because not all products deteriorate immediately. In the high-tech product life cycle, the product demand increases linearly substantially in the growth stage and maintains a near-constant level in the maturity stage. This is a ramp-type demand rate. To satisfy the demand as shortages occur, partial backlogging is necessary. The advance-cash-credit payment scheme, comprising advance, cash, and credit payments, has gained popularity in business transactions to improve cash flow flexibility among supply chain participants. This study explored a partial backlogging inventory model with ramp-type demand for non-instantaneous deteriorating items under generalized payment. The proposed model also incorporated discounted cash flow analysis to account for the time value of the profit function. This study attempted to determine the optimal replenishment strategy to maximize the present value of the total profit. Finally, we conducted a sensitivity analysis to examine the efficacy of the proposed model and gain managerial insights. The optimal total profit rises with an increase in the permissible delay period and sale price but decreases with an increase in ordering and purchase costs. Then, the decision-maker can refer to the managerial insights to choose the appropriate parameter value for the operation.

Price is a pivotal determinant of market demand, as higher prices typically reduce sales while lower prices stimulate them. Thus, incorporating price-dependent demand into inventory models is both realistic and necessary. In practice, limited storage capacity often forces retailers to rent additional space, motivating the adoption of two-warehouse systems. Trade credit also plays a critical role in supply chain management: suppliers may offer cash discounts or deferred payments to encourage larger orders, while retailers extend credit to customers to boost sales. To reduce default risk, however, retailers usually provide only partial credit. Considering the time value of money, costs and profits are assessed using discounted cash-flow analysis to account for payment delays and inflation. This study develops an integrated supplier–retailer–customer chain model that (1) incorporates price-dependent demand, (2) includes a rented warehouse for limited storage, (3) considers partial trade credit, (4) links two-level trade credit terms to order quantity, and (5) evaluates financial performance on a present-value basis. The model aims to maximize total profit by determining optimal price, replenishment cycle, and order quantity. Numerical and sensitivity analyses confirm that extending supplier credit can lower prices and improve overall profitability, offering useful insights for strategic inventory management.