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We demonstrate that the fraction of sales lost for the (r, q) system underconsideration can be conveniently bounded in a manner suitable for quick,back-of-the-envelope estimates. We assume that customer demand arises from aPoisson process with one unit demanded at a time, that all demand occurringduring a stockout is lost, and that lead time is constant. In addition, weallow the situation where multiple replenishment orders may be simultaneouslyoutstanding. We show that the difference between the upper and lower bounds onthe the fraction of sales lost appears likely to be no more than 6:5% (0:065),and is typically significantly better than that. In particular, the boundsappear to be very useful when the reorder point is relatively high or when themean lead time demand is significantly different from the reorder point. Inaddition, we relate the common performance measures for the system, and soenable bounding the total operating costs.

Bounds on performance measures for the (r, q) lost sales system with Poisson demand and constant lead time