Studies on Some Inventory Model for Deteriorating Items with Weibull Replinishment and Generalised Pareto Decay Having Demands as Function of on Hand Inventory

Abstract

Inventory models play an important role in determining the optimal ordering and pricing policies. Much work has been reported in literature regarding inventory models with finite or infinite replenishment. But in many practical situations the replenishment is governed by random factors like procurement, transportation, environmental condition, availability of raw material etc., Hence, it is needed to develop inventory models with random replenishment. In this paper, an EPQ model for deteriorating items is developed and analyzed with the assumption that the replenishment is random and follows a Weibull distribution. It is further assumed that the life time of a commodity is random and follows a generalized Pareto distribution and demand is a function of on hand inventory. Using the differential equations, the instantaneous state of inventory is derived. With suitable cost considerations, the total cost function is obtained. By minimizing the total cost function, the optimal ordering policies are derived. Through numerical illustrations, the sensitivity analysis is carried. The sensitivity analysis of the model reveals that the random replenishment has significant influence on the ordering and pricing policies of the model. This model also includes some of the earlier models as particular cases for specific values of the parameters.

Keywords

• Random replenishment
• Generalized Pareto decay
• Stock on hand
• EPQ model
• Weibull distribution