Optimal Ordering Policy for Delayed Deteriorating Items under the Effects of Stock-Dependent Demand Rate, Price Discounting, and Trade Credit Policy

Abstract

Classical inventory models are developed under the restrictive assumptions of time-varying demand combined with a fixed unit selling price throughout the inventory cycle. These assumptions rarely hold in practical settings. Specifically, the quantity of items displayed or available in stock affects how much customers buy. Higher inventory levels may signal product popularity or availability, thereby stimulating demand. Products with limited shelf life or seasonal characteristics often prompt promotional or bulk sales to reduce wastage. Moreover, once deterioration begins, retailers frequently adopt price discount strategies to accelerate sales and reduce holding costs. These strategies also attract additional customers and mitigate losses arising from spoilage.  Motivated by these practical considerations, this study develops an inventory model for delayed deteriorating items that simultaneously incorporates stock-dependent demand, price discounting, and trade credit policy. The demand rate is stock-dependent before deterioration and constant afterward; price discounts are applied only after deterioration begins. The proposed model determines the optimal cycle length and order quantity that maximize the average total profit of the inventory system. Rigorous analytical results are derived. The necessary and sufficient conditions for the existence and uniqueness of the optimal solution are established. Numerical examples are provided to demonstrate the applicability of the model. A comparative analysis with an existing benchmark model shows that the proposed approach yields a higher average total profit per unit time.  Finally, a sensitivity analysis is conducted to examine the effects of key parameters on the optimal decision variables. Relevant managerial insights for profit maximization are also discussed.