An Inventory Model for Deteriorating Items with Quadratic Demand and Partial Backlogging

Abstract

Aims: The scope of the model lies in its applicability in the management inventories of time-quadratic demand. It is also seen that large pile of goods displayed in a supermarket will motivate the customer to buy more. So the presence of inventory has a motivational effect on the people around it. Also there may be occasional shortages in inventory due to many reasons. Therefore, we develop an EOQ model for the inventory of a deteriorating item, taking demand rate and allowing shortages in inventory. Study Design: This paper presents an inventory model for deteriorating items with quadratic demand. In the model, shortages are allowed and partially backordered. The backlogging rate is a variable and dependent on the waiting time for the next replenishment. A numerical example is taken to illustrate the model and the sensitivity analysis is also studied.  Methodology: Our purpose is to devise a mathematical model on inventory management taking all these factors into consideration.  Results: Convexity condition of the cost function is established to ensure the existence of unique point of minimum.  Conclusion: The proposed model can be extended in several ways. For instance, we may extend the demand function to stochastic fluctuating demand patterns or stock-dependent demand rate. Finally, we could extend the model to incorporate some more realistic features such as quantity discounts, permissible delay in payments, time value of money and inflation etc.