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External factors such as improper handling, extreme weather and insect attacks affect product quality. It is most obvious in fruit products which have a high deterioration rate. Moreover, decaying fruits will increase the deteriorating of other good ones. The purpose of this study is to derive the optimal pricing and replenishment decisions for agricultural products considering the effect of external factors that induce deterioration.

In this paper, the study investigates ways to reduce the product deterioration rate by separating the near defective items from the other good products and accelerating the quick sales of the near defective items at a discounted price. The objective is to maximize the total profit by optimizing the selling price and the replenishment cycles. Two scenarios are investigated. In the first scenario, the retailer offers a selling price discount for near defective products to stimulate customer demand. In the second scenario, the retailer does not offer such discounts.

An algorithm to solve the model is derived. Further, numerical examples are developed to compare the total profit for the two scenarios. Theoretical derivations and graphical results show the concavity of the profit function. Finally, the sensitivity analysis shows that the total profit of the discount model is higher.

This study contributes to a new pricing and inventory decision model. The research provides insights to retailers on making optimal pricing and replenishment decisions for non-instantaneous deterioration items, as well as reducing the external factors that influence higher deterioration rate through separating good products from the near defective ones which are sold at a discount to induce the sale.

This paper aims to simultaneously consider an inventory model with price and advertisement dependent demand, non-instantaneous deterioration rate with preservation technology investment, partially backlogged shortages and trade credit.

This model considered a non-instantaneous deterioration, which starts after a certain storage period with a constant rate. The proposed model focused on two things. The first one is to reduce the deterioration rate by preservation technology investment, and the second one is using an appropriate trade credit period to maximize the total profit. The classical optimization technique is used to solve the problem.

The authors found that trade credit, advertising cost, preservation technology affect the total cost and selling price is one of the most important decision variables affecting the model.

This study provides a reference for a manufacturer and a retailer on making inventory decisions under different pricing, advertisement expense, preservation technology investment and credit strategies. Four cases are presented to illustrate the inventory model. Sensitivity analyses are performed to gain managerial insights for decision-making.

The study simultaneously considers a non-instantaneous deterioration inventory model, trade-credit, and preservation technology and advertisement policy. From our literature search, no researcher has undergone this type of study.

This paper aims to consider a sustainable inventory model with price dependent demand, non-instantaneous deterioration rate, discount facility, partially backlogged shortages and advance and delay in payments for a two-warehouse system.

This model considered a non-instantaneous deterioration, which starts after a certain period with a constant rate. The deterioration rate in the rented warehouse is more compared to own warehouse. The proposed model focused on two things. The first one is to the benefits of the advance payments strategy and delayed payment for the retailer and supplier, where the two-warehouse system is available and the second one is using an appropriate discount facility on no of the installment to maximize the total profit. The classical optimization technique is used to solve the problem.

The combination of trade-credits and advance payments is initiated to provide more benefits to the retailer. The findings prove that advance payments, which are received from the retailer to the supplier are beneficial for the supplier, who can influence the demand increase because of higher lower selling prices. Decreasing the selling price is used as a catalyst to increase demand. It also extends the discount concept of Khan et al. (2019, 2019b).

This model is limited by the fact that it does not consider variable deterioration. Therefore, the proposed inventory model could be extended by considering variable deterioration, as well as fully backlogged shortages and time-dependent demand function.

The study simultaneously considers a non-instantaneous deterioration inventory model, advance-payment, trade-credit for a sustainable two-warehouse inventory system. From the literature search to the best of knowledge no researcher has undergone this sort of study.