Analysis and design of a Production–Inventory system using discrete-time queueing models

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 a discrete-time queueing model which can be used for evaluating the performance of a given PI system which processes customer orders with service times that are discrete random variables. This analysis can be embedded in an optimisation model which can be used for designing efficient inventory policies. In particular, we determine the optimal inventory level at the warehouse that minimises the long-term total expected cost per unit time of carrying inventory, backorder cost associated with serving orders in the backlog queue and order setup cost. In an alternate model, we impose a service level constraint in terms of probability of stockout at the warehouse. In these models, we assume that the customers do not balk from the system. In this paper, the orders arriving at warehouse are assumed to have a tractable probability distribution; 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.