A Global Optimizing Policy for Decaying Items with Ramp-Type Demand Rate under Two-Level Trade Credit Financing Taking Account of Preservation Technology

An inventory system for deteriorating items, with ramp-type demand rate, under two-level trade credit policy taking account of preservation technology is considered. The objective of this study is to develop a deteriorating inventory policy when the supplier provides to the retailer a permissible delay in payments, and during this credit period, the retailer accumulates the revenue and earns interest on that revenue; also the retailer invests on the preservation technology to reduce the rate of product deterioration. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples draw attention to the obtained results, and the sensitivity analysis of the optimal solution with respect to leading parameters of the system is carried out. 1. Introduction In broad spectrum, deterioration is defined as the damage, spoilage, dryness, vaporization, and so forth, that result in the decrease of usefulness of the original one. In the past few decades, inventory problems for deteriorating items have been widely studied. The first attempt to derive optimal policies for deteriorating items was made by Ghare and Schrader [1], who derived a revised form of the economic order quantity (EOQ) model assuming exponential decay. This model was extended to consider the Weibull distribution deterioration by Covert and Philip [2]. Raafat [3] presented a complete survey of the available inventory literature for deteriorating inventory models. Goyal and Giri [4] also provided a detailed review of deteriorating inventory literatures. Teng et al. [5] developed an inventory model for deteriorating items with time varying demand and partial backlogging. Recently, C. Singh and S. R. Singh [6] presented an inventory model considering the Weibull distribution deterioration. Investing in preservation technology (PT) for reducing deterioration rate has received little attention in the past years. The consideration of PT is important due to rapid social changes and the fact that P can reduce the deterioration rate significantly. Moreover, sales, inventories, and order quantities are very sensitive to the rate of deterioration, especially for fast deteriorating products. The higher rate of deterioration would result in a higher total annual relevant cost and a lower demand rate [7, 8]. Ouyang et al. [9] found that if the retailer can reduce effectively the deteriorating rate of item by improving the storage facility, the total