Optimal production run length for deteriorating production system with two-state continuous-time Markovian processes under allowable shortages

The paper studies optimal production run length for a deteriorating production system in which the shortages are allowed and the deterioration processes are characterized by a two-state continuous-time Markov chain. We show that there exists a unique optimal production run length to minimize the expected total relevant cost. In addition, bounds for the optimal production run length are provided to develop the solution procedure. Finally, a numerical example is given to illustrate the results and sensitivity analysis is also performed.