Modelling and Decision-making on Deteriorating Production Systems using Stochastic Dynamic Programming Approach


Department of Industrial Engineering, Yazd University, Yazd, Iran


This study aimed at presenting a method for formulating optimal production, repair and replacement policies. The system was based on the production rate of defective parts and machine repairs and then was set up to optimize maintenance activities and related costs. The machine is either repaired or replaced. The machine is changed completely in the replacement process, but the production rate of defective parts decreases in the repair process. The repair time and number of repairs will affect this process. The aim of this study is to find decision variables that minimize the final cost of repair, replacement, maintenance and prevention of failures in a given time horizon. As a case study, the variables were evaluated at Arak Pishgam Company to achieve optimal conditions. The proposed model was developed based on the semi-Markov decision process (SMDP). In addition, stochastic dynamic programming model was used to achieve optimal conditions.


  1. Rostamian, H., Total Productive Maintenance (TPM) , Termeh Publications. (2008).
  2. Hajshirmohammadi, Ali., Total Productive Maintenance (TPM), Arkan Publications. (2000).
  3. Sepanlou, K.,Behzad, M. "Principles and fundamentals of vibration in maintenance and fault detection of rotating machines", National Iranian Petrochemical Company, (2007).
  4. Fallahnezhad M. S., "A finite horizon dynamic programming model for production and repair decisions", Communications in Statistics-Theory and Methods, Vol. 43 , (2014), 3302-3313.
  5. Hajshirmohammadi, A. Total Productive Maintenance (TPM), Published by Industrial Management Institute. (2009).
  6. Fallahnezhad M.S., Niaki S.T.A. "A new machine replacement policy based on number of defective items and Markov chains", Iranian Journal of Operations Research, Vol. 2; (2011), 17-28.
  7. Makouei, H., "Compliance of the logistics system using the customer value determination method (case study of the automobile maker)" , Journal of  Management Knowledge , Vol. 78, (2005),91-114.
  8. Lai, M. T., and Chen, Y. C." Optimal periodic replacement policy for a two-unit system with failure rate interaction", International Journal of Advanced Manufacturing Technology, Vol. 29, (2006), 367-371.
  9. Wu, S. and Clements-Croome, D., "A novel repair model for imperfect maintenance", IMA Journal of Management Mathematics, Vol. 17, (2006), 235-243.
  10. Fallahnezhad M.S., Niaki S.T.A. "A multi-stage two-machines replacement strategy using mixture models, Bayesian inference and stochastic dynamic programming",Communications in Statistics-Theory and Methods, Vol. 40, No. 4 (2011), 702-725.
  11. Fallahnejad, M. S., Pourgharib Shahi, M. "Design of an optimal maintenance policy for machine replacement problem using a sequential sampling plan", International Conference on Industrial Engineering (IIEC), Vol. 13, (2017).
  12. Fallahnezhad M.S., Niaki S.T.A.,Eshragh-Jahromi A. "A one-stage two-machines replacement strategy based on the Bayesian inference method", Journal of Industrial and Systems Engineering , Vol. 1, (2007), 235- 250.
  13. Niaki, S.T.A., Fallahnezhad, M.S. "A decision making framework in production processes using Bayesian inference and stochastic dynamic programming". Journal of Applied Science, Vol. 7, (2007),  3618-3627
  14. Boukas, E. K., Haurie, A. "Manufacturing flow control and preventive maintenance: a stochastic control approach", IEEE Transactions on Automatic Control , Vol. 35, No. 9, (1990). 1024-1031.
  15. Ivy, J.S. , Nembhard, H.B." A modeling approach to maintenance decisions using statistical quality control and optimization", Quality and Reliability Engineering International, Vol. 21, (2005), 355-366.
  16. Kenne, J. P., Gharbi ,"Production planning problem in manufacturing systems with general failure and repair time distributions", Production Planning & Control, Vol. 11, No. 6 (2000), 581-588.