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

Document Type : Research Paper


1 Industrial Engineering Department, Yazd University, Yazd, Iran

2 Industrial Engineering Department, Sharif university of Technology, P.O. Box 11155-9414, Tehran, Iran


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.


Main Subjects

[1] Fallahnezhad M.S., Niaki S.T.A., Eshragh-Jahromi A. (2007), A one-stage two-machines replacement
strategy based on the Bayesian inference method; Journal of Industrial and Systems Engineering 1; 235-
[2] Fallahnezhad M.S., Niaki S.T.A. (2010), A multi-stage two-machines replacement strategy using mixture
models, Bayesian inference and stochastic dynamic programming; Communications in Statistics-Theory
and Methods 40; 702-725.
[3] Fallahnezhad M.S., Niaki S.T.A. (2011), A new machine replacement policy based on number of
defective items and Markov chains; Iranian Journal of Operations Research 2; 17-28.
[4] Grosfeld-Nir A. (2007), Control limits for two-state partially observable Markov decision processes;
European Journal of Operational Research 182; 300–304.
[5] Iravani S., Duenyas I. (2002), Integrated Maintenance and Production Control of a Deteriorating
Production System; IIE Transactions 34; 423-435.
[6] Niaki S.T.A., Fallahnezhad M.S. (2007), A decision making framework in production processes using
Bayesian inference and stochastic dynamic programming; Journal of Applied Science 7; 3618-3627
[7] Singh, M., Song J.-S., Yano C., Moreno-Beltran A. (2004), Production and repair decisions with timeconsuming repair and a deadline; Working Paper.