An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: An extension of Philipʹs model

The scope of the model lies in its applicability in the management of inventories of deteriorating items. It has been empirically observed that failure and life expectancy of many items can be expressed in terms of Weibull distribution. This empirical observation has prompted researchers to represent the time to deterioration of a product by a Weibull distribution. It is also seen that the demand of a consumer product usually varies with time and hence, the demand rate should be taken as time-dependent. Also there may be occasional shortages in inventory due to many reasons. Our purpose is to devise a mathematical model on inventory management taking all these factors into consideration. We, therefore, develop an economic order quantity model for the inventory of a deteriorating item, taking a time-variable demand rate and allowing shortages in inventory. This paper presents an inventory model for deteriorating items with instantaneous supply, linearly increasing demand and shortages in inventory. A three-parameter Weibull distribution is used to represent the distribution of the time to deterioration. The theory for finding the optimal solution of the problem is developed. Two numerical examples are then taken to illustrate the solution procedure.