Two-warehouse inventory model for deteriorating items with price-sensitive demand and partially backlogged shortages under inflationary conditions

In today’s competition inherited business world, managing inventory of goods is a major challenge in all the sectors of economy. The demand of an item plays a significant role while managing the stock of goods, as it may depend on several factors viz., inflation, selling price, advertisement, etc. Among these, selling price of an item is a decisive factor for the organization; because in this competitive world of business one is constantly on the lookout for the ways to beat the competition. It is a well-known accepted fact that keeping a reasonable price helps in attracting more customers, which in turn increases the aggregate demand. Thus in order to improve efficiency of business performance organization needs to stock a higher inventory, which needs an additional storage space. Moreover, in today’s unstable global economy there is consequent decline in the real value of money, because the general level of prices of goods and services is rising (i.e., inflation). And since inventories represent a considerable investment for every organization, it is inevitable to consider the effects of inflation and time value of money while determining the optimal inventory policy. With this motivation, this paper is aimed at developing a two-warehouse inventory model for deteriorating items where the demand rate is a decreasing function of the selling price under inflationary conditions. In addition, shortages are allowed and partially backlogged, and the backlogging rate has been considered as an exponentially decreasing function of the waiting time. The model jointly optimizes the initial inventory and the price for the product, so as to maximize the total average profit. Finally, the model is analysed and validated with the help of numerical examples, and a comprehensive sensitivity analysis has been performed which provides some important managerial implications.