PERISHABLE INVENTORY MODEL WITH FINITE RATE OF REPLENISHMENT HAVING GENERALIZED PARETO DECAY

Abstract

In this paper an EPQ model for deteriorating items is developed and analyzed an inventory model for deteriorating items with the assumptions that the lifetime of the community is random and follows a Generalized Pareto distribution, having constant demand rate with shortages. The total cycle length in this model is divided into our non-over lapping intervals depending on the decrease of stock. Assuming that shortages are allowed and fully back backlogged, the differential equations governing the instantaneous state of inventory are developed and solved for I(t). The loss due to deterioration, the total backlogged demand, the ordering quantity is also derived with suitable cost consideration. The total profit per unit time is developed and optimized with respect to the time at which production is to be started, time at which shortages occur, the time at which production is to be restated. The optimal ordering quantity, Q is also obtained for given values of the parameters. A numerical illustration is presented. This model also includes some of the earlier models as particular cases for specific values of the parameters. KEYWORDS: Random Replenishment; Generalized Pareto Decay; Constant Demand; Shortages.