Joint Pricing and Inventory Control for Non-instantaneous Deteriorating Items When Trade Credit is Linked to Order Quantity

Abstract

This research investigated the problem of joint inventory control and pricing for non-instantaneous deteriorating products; while, the quantity dependent trade credit is allowed. It was observed here that the buyer order amount is equal or more than the amount specified by the seller. The Shortage was not permitted in the system. It was aimed in present study to find a procedure for achieving the optimal selling price and replenish cycle and to be able to maximize the system's profit. To do so, first, the system's total profit function was derived. Then, the uniqueness of the optimal replenishment cycle for a given price was proved. Next, the concavity of the total profit function concerning the price was revealed, depending on the trade credit policy. Thereafter, an algorithm was provided to fulfill the optimal solution and eventually a dual-purpose numerical analysis was carried out both to show the model performance and to evaluate the sensitivity of the main parameters.

Keywords

• pricing
• inventory control
• quantity dependent trade credit
• non-instantaneous deteriorating items