In this article, we shall construct a lost sales inventory model with Poisson demand. Lost sales are linear increasing function of waiting time in the stockout period. Then, the optimal planning and shortage periods are determined such that the expected profit per unit time is maximized.There are two special cases are also discussed.One is the whole period is stockout, and the other is the whole period is non-stockout. And we also find the optimal supply cycle and optimal order quantity of goods such that expected profit per unit time is maximized.
International Journal of Service Science, Management and Engineering 1(1), p.17-20