A stochastic production/inventory system with all-or-nothing demand and service measures

This paper considers a one-product production/inventory system with intermittent production and random demands with the stipulation that the demand of a customer is completely lost when current inventory is not sufficient for the whole demand. Customers asking for the product arrive according to a Poisson process and the demands of the customers are independent and identically distributed random variables. The production facility is controlled by a two-critical-numbers rule under which production is stopped when inventory becomes sufficiently high and thd productionis restarted when inventory has dropped sufficiently low. Production occurs at a constant rate. In accordance with common practice we consider as service measures the fraction of demand that is lost and the fraction of customers that are lost. the problem is to find the critical inventory level below which production must be restarted in order to achieve a specific service level. For the special cases of exponential and deterministic demands and exact analysis leads to computationally tractable results. For the general demand case we propose a simple approximation that requires only the first two moments of the demand distribution and is a weighted combination of the sulutions for the exponential and deterministic cases. This approximation shows an excellent performance wher the coefficient of variation of the demand is not too large. Numerical results are presented.