Studies on inventory model for deteriorating items with Weibull replenishment and generalised Pareto decay having time dependent demand

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 analysed 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 generalised Pareto distribution and demand is a function of time. Using the differential equations the instantaneous state of inventory is derived. With suitable cost considerations the total cost function is obtained. By minimising 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 significance 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.