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

Abstract

<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>