Abstract. Markov models of the queuing-inventory systems with variable order size are investigated. Two classes of models, with instantaneous and non-zero service times of customers are considered. The model with non-zero service time assumes that impatient customers can form a queue of either finite or infinite length. Exact and approximate methods are developed to calculate the characteristics of the systems under given lead policies.

Keywords: queuing-inventory systems, lead policy, variable order size.