A queueing system with inventory and mixed exponentially distributed lead times.

We consider M/M/1/∞ systems with inventory in which completing each service in the queueing system requires an on-hand inventory. Continuous review (r, Q) policy is considered for the inventory system, and lead times are assumed to be mixed exponentially distributed. During stockout, arriving demands get rejected from the queue and become lost (lost sale situation). We derive stationary distribution of product form of joint queue length and on-hand inventory. The resulting distribution is employed to compute performance measures which can be used to derive the optimal policy. Optimal order size for predetermined reorder policy is initially determined and finally, optimal reorder point and corresponding optimal order size are simultaneously computed for several numerical examples. [ABSTRACT FROM AUTHOR]