Optimal ordering policies of an inventory model for deteriorating items with demand inversely proportional to the on-hand inventory

In this paper, we develop and analyse an inventory model for deteriorating items with the assumption that the lifetime of the commodity is random and follows an exponential distribution and the demand is inversely proportional to the stock on-hand, having variable cycle lengths declining in arithmetic progression. It is further assumed that the shortages are allowed and fully backlogged. Using the differential equations, the instantaneous level of inventory is derived. With suitable cost consideration, the total cost function is obtained. By minimising the total cost, the optimal cycle length and ordering quantities are derived. The sensitivity of the model with respect to the parameters and costs is also performed. This model is extended to the case of without shortages. This model is useful in practical situations arising at places such as textile markets, fruit and vegetable markets.