On the newsboy model with a cutoff transaction size

In this paper we analyse the effect of a cutoff transaction size on the average inventory cost in a simple newsboy setting. It is assumed that customers with an order larger than a prespecified cutoff transaction size are satisfied in an alternative way, against additional cost. For compound Poisson demand with discrete order sizes, we show how to determine the average cost and an optimal cutoff transaction size. Because the computational effort to calculate the exact cost is quite large, we also consider an approximate model. By approximating the distribution of the total demand during a period by the normal distribution one can determine an expression for the average cost function that solely depends on the cutoff transaction size. A significant advantage of this approximation is that we can solve problems of any size. The quality of using the normal approximation is evaluated through a number of numerical experiments, which show that the approximate results are satisfactory.