A Stock Dependent Economic Order Quantity Model for Perishable Items Under Inflationary Conditions

Abstract

Problem statement: In most of the earlier inventory models, effect of inflation has been ignored, which is playing pilot role in present environment. In this article, we have proposed an economic order quantity model for deteriorating items having stock dependent demand (whose demand varies with the stock) under the effect of inflation. Approach: Firstly, problem is framed in the form of linear differential equation model and then this model has been solved with general solution technique of linear differential equations. Using the solution the expression for total cost of inventory has been obtained. Results: Using total cost equation an optimal order quantity is obtained and convexity of various costs is also studied. This model helps retailer to decide his economic order quantity for deteriorating items having stock dependent demand. The consideration of effect of inflation makes this model more relevant for present business environment. Conclusion: The convexity of various costs proves the validity of this model. The effect of inflation with two different rates is also studied in tables below considering both constant as well as stock dependent demand. The graph of these tables shows that the optimal inventory cost increases with increase in number of cycles it increases rapidly in starting but becomes stable for large number of cycles. The proposed model can be extended in several ways. For instance, we may generalize the model to allow for shortages, quantity discounts, time value of money, finite replenishment rate, permissible delay in payments and others.