Optimal replenishment, pricing and preservation technology investment policies for non-instantaneous deteriorating items under two-level trade credit policy

<p style='text-indent:20px;'>In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider an inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under two-level trade credit policy. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. The main objective is to determine the optimal replenishment, pricing and preservation technology investment strategies including whether or not invest in preservation technology and how much to invest in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. An algorithm is presented to derive the optimal solutions of the model. Numerous theorems and lemmas have been inserted to obtain the optimal solution. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.</p>

An EOQ inventory model for deteriorating items with controllable deterioration rate under stock-dependent demand rate and non-linear holding cost

<p style='text-indent:20px;'>The main purpose of this paper is to investigate the retailer's strategy in selecting the order-up-to level, the reorder point and the preservation technology investment for deteriorating items, aiming to maximize his total profit per unit time. We formulate the problem into a mathematical model that takes into account stock-dependent demand rate, stock-dependent holding cost. The terminal conditions are relaxed to allow that the reorder point can be one of the following two cases: (1) <inline-formula><tex-math id="M1">\begin{document}$ N\leq0 $\end{document}</tex-math></inline-formula>, i.e., the reorder point may be negative or zero. When the reorder point is negative, the shortage is allowed and partial backlogged. (2) <inline-formula><tex-math id="M2">\begin{document}$ N\geq0 $\end{document}</tex-math></inline-formula>, i.e., the reorder point may be without shortage or zero. We prove the existence and uniqueness of the optimal order-up-to level, the reorder point and the preservation technology investment under any given two of them for both the two cases. We then present an algorithm to search for decision variables such that the total profit per unit time is maximized. Finally, numerical examples, comparisons in performance and sensitivity analysis are carried out to examine the results obtained. On the basis of the above results, some useful managerial insights are revealed.</p>