An Ordering Point Model with a Linear Backorder Ratio under the Uncertainty of Lead-Time Demand

Abstract

This paper deals with an economic ordering point model with a linear backorder ratio function which depends upon a backorder period. In the paper, demand during the lead time is assumed to be a random variable having a continuous distribution function. An average annual inventory cost (objective function), consisting of order cost, inventory holding cost, back-order cost and lost sales cost, is derived and then an iterative solution method for minimizing the objective function is presented. Finally, a numerical examination of how the reorder point and order quantity are related with the slope of the linear backorder ratio function is conducted.