This paper presents a queueing model for a single-stage manufacturing system. The arrival process at the facility is the superposition of the unco-ordinated arrival processes of various items and is represented by a compound Poisson process. It is shown that the expected waiting time of an average unit depends on the expected batch size and the batch size variability, whereas the expected batch completion time depends only on the expected batch size. The optimal processessing rate is also derived as a function of the appropriate cost factors. A lot sizing model is developed which provides the optimal batch size as a function of inventory-related costs. Finally, it is demonstrated through simulation that the Poisson arrival approximation is less severe when the item mix is composed of a large number of items.