Production policies under deteriorating process conditions

This paper examines a single-stage production system that manufactures multiple products under deteriorating equipment conditions. The machine condition worsens with production, and improves with maintenance. The condition of the process can be in any one of several discrete states, and transitions from state to state follow a semi-Markov process. In many production environments, the quality or yield of output depends heavily on the condition of the production process. The problem considers the trade-offs between manufacturing products that have a higher profit, a longer processing time, and therefore, a higher deterioration probability versus products that have a smaller profit, shorter processing time with a lower process deterioration probability. The firm needs to determine the optimal production choice in each state in a way that maximizes the long-run expected average reward per unit time. The paper makes three sets of contributions. First, it introduces the concept of critical ratios for the firm’s manufacturing decision at each state regarding whether to switch from one product to another. Second, through the use of critical ratios, the main result shows that the optimal production choice for each state can be determined independently of the actions taken in other states, despite the complex interconnections between the production decisions and state transitions. Third, the paper provides generalizations that illustrate the depth, scope and richness of the proposed solution technique by extending the model in the number of machine states, to settings where maintenance is performed in intermediate states, and to settings where transition probabilities are influenced by both mean and variance of processing times.