Journal of Mathematics and Statistics

Establishing an Adaptive Production-Procurement System with Markov Chain Approach Associated with 3C Theory

Chun-Ta Lin

DOI : 10.3844/jmssp.2011.187.197

Journal of Mathematics and Statistics

Volume 7, Issue 3

Pages 187-197


Problem statement: In this study, we classify the imperfect situations that the unreliability of production and the defective products might be incurred from production process into eight independently recurrent categories. Approach: With the property of recurrence of Markov chain, the limiting probability of each imperfect production category can be calculated through the transition probabilities matrix generated from these imperfect production categories. Results: The 3C Theory has been applied based on a certain group of products to integrate the relationship between order model and resource requirement plans. Therefore, an adaptive (s, Q) production system with Markov Chain Approach associated with (R, s, S) procurement system based on 3C Theory has been proposed to smooth supply disruptions incurred from imperfect production. Conclusion/Recommendations: We have demonstrated that the candidate solutions identified by the proposed method are not only superior to traditional EPQ model solutions, but also result in significantly smaller cost flow variability.


© 2011 Chun-Ta Lin. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.