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In this paper, we concern ourselves with a production-inventory (PI) system consisting of a manufacturing plant and one warehouse which faces a stream of demands from customers. We present discrete-time queueing models which can be used for evaluating the performance of a given production-inventory system which processes customer orders with service times that are discrete random variables. This analysis can be embedded in an optimization model which can be used for designing efficient inventory policies. In particular we determine the optimal base-stock level at the warehouse that minimizes the long term total expected cost per unit time of carrying inventory, backorder cost associated with serving orders in the backlog queue. In an alternate model, we impose stock out as a service level constraint in terms of probability of stock out at the warehouse. In these models we assume that customers do not balk from the system. In this paper, the customers orders arriving at warehouse are assumed to Poisson process; the service process at the manufacturing plant has the distribution of a discrete random variable. Several examples are presented to validate the model and to illustrate its various features.