A Multi-Stage Single-Machine Replacement Strategy Using Stochastic Dynamic Programming

In this paper, the single machine replacement problem is being modeled into the frameworks of stochastic dynamic programming and control threshold policy, where some properties of the optimal values of the control thresholds are derived. Using these properties and by minimizing a cost function, the optimal values of two control thresholds for the time between productions of two successive nonconforming products is determined. If this time exceeds the first threshold, the production continues. If it is less than the second one, inspection, repair, or replacement occur. However, if it falls within the control thresholds, then the process of sampling continues. At the end, the application of the proposed methodology is demonstrated using a numerical illustration.