Analysis of a production–inventory model with Erlangian demand arrival process

We study a production–inventory system having a machine, a storage facility. The demand for the product is governed by an Erlangian demand arrival process, where demand sizes are independent and identically distributed random variables. A two-critical number policy (m, M) is used to control a machine's setups and shutdowns, namely, a machine is shut down whenever the inventory level reaches M, and resumes operating only when the inventory level falls below the critical number m (a function of M). We obtain the steady state distribution of the inventory process and some performance measures of the process.