Unreliable production–inventory model with a two-phase Erlang demand arrival process

A production–inventory system is studied in which an unreliable machine is susceptible to failure following which it must be repaired to make it operative again. The demand for the product is governed by a two-phase Erlang process and 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, the machine is shut down whenever the inventory level reaches M, and is resumed to operate only when the inventory level falls below the critical number m (m ≤ M). We obtain the steady-state distribution of the inventory process and some performance measures of the process.