Joint Optimization of Preservation Technology, Hybrid Payment Policies, and Prepayment Discounts for Non-Instantaneously Deteriorating Items with Shortages

Retailers of non-instantaneously deteriorating items must jointly set inventory, preservation technology, and payment decisions. Preservation technology reduces deterioration, but excessive investment increases operational costs, making the determination of an optimal preservation level essential for maximizing profit. Although preservation technology, hybrid payment schemes, and prepayment discounts have been studied individually, their joint treatment alongside partially backlogged shortages remains largely unexplored. To address this gap, this study develops an inventory model that simultaneously incorporates preservation technology investment, a hybrid payment structure, advance payment combined with trade credit, optionally supplemented by a prepayment discount, and partially backlogged shortages for non-instantaneously deteriorating items. A classical optimization approach is employed, yielding quasi-closed-form solutions for the shortage and replenishment timing across four trade credit scenarios, while the profit-maximizing preservation investment level is identified through sensitivity analysis. Numerical examples and sensitivity analysis show that increasing the number of prepayment installments lowers the discount rate offered by the supplier; because this forgone discount outweighs the benefit of retaining capital longer, the retailer’s profit falls. Profit responds most strongly to purchasing cost, the advance payment period, and lead time. These results give retailers a practical basis for balancing preservation investment, payment structure, and shortage policy to maximize profitability. In the sensitivity analysis, profit varies by more than 45% over the tested range of the purchasing cost and by up to 21% depending on the number of prepayment installments negotiated with the supplier. That gives retailers a concrete ranked basis for prioritizing which contract terms to negotiate first.