This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.
The paper makes four contributions: (1) It introduces three critical ratios for the firm’s choices. The first enables the firm to decide whether to manufacture or perform maintenance, the second reveals the best product to manufacture, and the third determines the best maintenance action. The economic interpre- tations of these critical ratios provide managerial insights. (2) The paper shows how the critical ratios can be combined in order to determine the optimal policy, simultaneously accounting for the trade-offs involving production profits, maintenance costs, and the impact on the process condition. We show how these results generalize to problem settings with an arbitrary number of machine states. (3) The paper demonstrates the impact of market demand conditions on the optimal policy. And (4) it develops a set of sufficient conditions that lead to monotone optimal policies. These conditions generalize those reported in earlier studies.