Asymptotic analysis for a production–inventory control model with renewal arrivals and exponential demands

Abstract

We consider a production–inventory problem in which the production rate can be dynamically adjusted to cope with random fluctuations in demand. Customers arrive according to a renewal process, and the customer's demand is assumed to be exponentially distributed. Excess demand is backlogged. The production is controlled by a two-critical-number rule that prescribes which one of the two possible production rates must be used. Tractable expressions are given for several services measures including the fraction of demand backlogged. The analysis is based on the results for hitting probabilities in random walks, where the jump distribution has an exponential right or left tail.