A note on a production control model for a facility with limited storage capacity in a random environment

This note presents an extension of our earlier paper on a production–inventory system with limited storage capacity in a multi-state random environment [i.e., E. Mohebbi, A production–inventory model with randomly changing environmental conditions, Eur. J Res. 174 (2006) 539–552]. More specifically, it assumes that the production rate as well as the occurrence rate and batch sizes of a compound Poisson demand stream are influenced by the state of a continuous-time homogeneous Markov chain representing the random environment. We present an adaptation of the system-point method of level crossings which yields the limiting distribution of inventory level (stock-on-hand) for a two-parameter production control policy when stockouts are lost.