This paper examines the robustness of lead time demand models for the continuous review (r, Q) inventory policy. A number of classic distributions, (e.g. normal, lognormal, gamma, Poisson and negative binomial) as well as distribution selection rules are examined under a wide variety of demand conditions. First, the models are compared to each other by assuming a known demand process and evaluating the errors associated with using a different model. Then, the models are examined using a large sample of simulated demand conditions. Approximation results of inventory performance measures–ready rate, expected number of backorders and on‐hand inventory levels are reported. Results indicate that distribution selection rules have great potential for modeling the lead time demand.
