A continuous review, (Q, r) inventory model for a deteriorating item with random demand and positive lead time

Abstract

In this paper, a single-product, single-location inventory system is considered. A fraction of the stock is lost every time unit, i.e., inventory experiences continuous decay. Demand is uncertain and replenishments require a positive lead time. Shortages are allowed and backorders-lost sales mixtures are considered. Inventory is reviewed continuously and a (Q, r) policy is applied. The problem is to find the order quantity and the reorder point that minimize the long-run expected total cost per time unit. It is known, in literature, that approaching this problem is a very difficult task. Moreover, very little research has been performed in this regard, although improvement of continuous review policy in an inventory system is a vital issue in ERP solutions, in particular for Industry 4.0. The cost model is developed by making some simplifying hypotheses and assuming that the dynamics of inventory level (i.e., stock on hand minus backorders) is captured through an Itō diffusion. An iterative method is proposed to minimize the cost function. Numerical experiments are performed to investigate the efficiency of the proposed model. Comparisons with an estimate of the optimal policy and with a former heuristic model are given. Results show that the model developed in this work should provide a very good approximation of the optimal policy over a reasonably wide range of parameter values. A sensitivity analysis is finally carried out in order to draw some managerial insights.