Abstract
This paper considers an optimal (r, Q) policy for a single-product single-machine production/inventory problem with a compound Poisson demand process and backloggings allowed, Under the assumption that during each production period the cumulative amount of production is greater than that of demands in expected term, the associated inventory process is found to be an ergodic Markov chain with infinite states. Thereupon, the steady-stat:e probability distribution is derived. Further, the total cost in the production/inventory system is expressed in terms of the long-run expected average cost, C(r, Q), which is verified as the convex function of r , given Q fixed. A solution procedure is illustrated with a numerical example having random demand sizes taking values one or two.
