The application of Game Theory in Selective maintenance problems

Document Type : Research Paper


1 Lecturer /Alzahra University

2 Faculty of Engineering, Alzahra University, Tehran, Iran


Selective maintenance is of crucial importance in the multi-state systems because of the necessity of running consecutive missions with a limited break. This paper presents a novel approach based on Game Theory for the problem of selective maintenance in the case of multi-state systems under the influence of stochastic dependency. Because of the priority of customer’s opinion in today’s world, the Stackelberg model is used in order to show the interaction between the customer and workshop. In this model, first, the customer, as the leader, introduce the suggested contract containing the level of system reliability for maximizing desirability. Consequently, the workshop, as the follower, determines costs based on details of the proposed contract. Numerical examples are studied the model performance, and the sensitivity analysis of results about the key parameters of the model is probed.


Main Subjects

1. Myerson, R. (1991). Game Theory: Analysis of Conflict. Harvard Univ. Press, Cambridge.
2. Rice, W., Cassady, C., and Nachlas, J. (1998). Optimal maintenance plans under limited maintenance time. Paper presented at the Proceedings of the seventh industrial engineering research conference.
3. Meng, M. H., and Zuo, M. (1999). Selective maintenance optimization for multi-state systems. Paper presented at the Electrical and Computer Engineering, 1999 IEEE Canadian Conference on.
4. Cassady, C. R., Pohl, E. A., and Murdock, W. P. (2001). “Selective Maintenance Modeling For Industrial Systems”, Journal of Quality in Maintenance Engineering, Vol. 7, No. 2, PP. 104–117.
5. Cassady, C. R., Murdock, W. P., and Pohl, E. A. (2001). “Selective Maintenance for Support Equipment Involving Multiple Maintenance Actions”, European Journal of Operational Research, Vol. 129, No. 2, PP. 252-258.
6. Schneider, K., and Cassady, C. R. (2004). Fleet Performance Under Selective Maintenance. Reliability and Maintainability, 2004 Annual Symposium-RAMS, IEEE, 571-576.
7. Rajagopalan, R., and Cassady, C.R. (2006). “An Improved Selective Maintenance Solution Approach”, Journal of Quality In Maintenance Engineering, Vol. 12, No. 2, PP. 172–185.
8. Maillart, L. M.  et al. (2009). “Selective Maintenance Decision-Making Over Extended Planning Horizons”, IEEE Trans Reliability, Vol. 58, No. 3, PP. 462–469.
9. Lust, T., Roux, O., and Riane, F. (2009). “Exact and Heuristic Methods for the Selective Maintenance Problem”, European Journal of Operational Research, Vol. 3, No. 197, PP. 1166-1177.
10. Khan, M. F., and Ali, I. (2012). “Allocation Problem of Repairable and Replaceable Components for a System Reliability Using Selective Maintenance”, International Journal of Scientific and Engineering Research, Vol. 3, No. 5, PP. 1-4.
11. Maaroufi, G., Chelbi, A., and Rezg, N. (2012). A Selective Maintenance Policy for Multi-Component Systems with Stochastic and Economic Dependence, 9th International Conference on Modeling, Optimization - MOSIM’12.
12. Liu, Y., Huang, H. Z., and Zuo, M. J. (2009). “Optimal Selective Maintenance for Multi-State Systems Under Imperfect Maintenance”, Reliability and Maintainability Symposium. RAMS 2009. Annual, IEEE, 321-326.
13. Chen, Chujie., Liu, Yu., and Huang, Hong-Zhong. (2012). “Optimal Load Distribution for Multi-State Systems Under Selective Maintenance Strategy”, (ICQR2MSE), International Conference on, IEEE, 436-442.
14. Dao, C. D., Zuo, M. J., and Pandey, M. (2014). “Selective Maintenance for Multi-State Series–Parallel Systems Under Economic Dependence”, Reliability Engineering and System Safety, Vol. 121, PP. 240-249.
15. Maaroufi, G., Chelbi, A., and Rezg, N. (2013). “Optimal Selective Renewal Policy for Systems Subject to Propagated Failures with Global Effect and Failure Isolation Phenomena”, Reliability Engineering, 114, 61–70.
16. Dao, Cuong D., Zuo, and Ming J. (2015). “Selective Maintenance for Multi-State Systems Considering the Benefi Ts of Repairing Multiple Components Simultaneously”, In Engineering Asset Management-Systems, 413-425.
17. Quddoos, Abdul., Ali, Irfan., Khalid, Masood, M. (2015). “Bi-Objective Fuzzy Selective Maintenance Allocation Problem”, American Journal of Mathematical and Management Sciences, Vol. 34, No. 4, PP. 289-308.
18. Farhadi, F., and Amin Nasseri, M. R. (2016). “Prediction of Rotating Machineries Failure by Intelligent Systems”, Journal of Industrial Engineering, Vol. 50, No. 3, PP. 461-470.
19. Farughi, H., and Goudarzi, Z. (2016). Selective Maintenance Under Stochastic Dependence and Propagated Failure with Global Effect for All Components System, 12th International Conference on Industrial Engineering, Tehran, Http://Civilica.Com/Paper-IIEC12
20. Murthy, D., and Asgharizadeh, E. (1999). “Optimal Decision Making in a Maintenance Service Operation”, European Journal of Operational Research, Vol. 2, No. 116, PP. 259-273.
21. Ashgarizadeh, E., and Murthy, D. D. (2000). “Service Contracts: A Stochastic Model”, Mathematical and Computer Modelling, Vol. 31, No. 10 and 12, PP. 11-20.
22. Jackson, C., and Pascual, R. (2008). “Optimal Maintenance Service Constract Negotiation with Aging Equipment”, European Journal of Operation Research, Vol. 2, No. 189, PP. 387-398.
23. Min, C. et al. (2013). “Game-Theory-Based Generation Maintenance Scheduling in Electricity Markets”, Energy, Vol. 55, PP. 310-318.
24. Esmaeili, M., Gamchi, N. S., and Asgharizadeh, E. (2014). “Three-Level Warranty Service Contract Among Manufacturer, Agent and Customer: A Game-Theoretical Approach”, European Journal of Operational Research, Vol. 1, No. 239, PP. 177-186.
25. Jin, T., Tian, Z., and Xie, M. (2015). “A Game-Theoretical Approach for Optimizing Maintenance, Spares and Service Capacity in Performance Contracting”, International Journal of Production Economics, Vol. 161, PP. 31-43.
26. Hamidi, M., Liao, H., and Szidarovszky, F. (2016). “Non-Cooperative and Cooperative Game-Theoretic Models for Usage-Based Lease Contracts”, European Journal of Operational Research, Vol. 1, No. 255, PP. 163-174.
27. Taleizadeh, A., and Sarokhani, A. (2017). “Cooperative Advertising and Pricing in a Competitive Market with Customers, Excitations Effects”, Journal of Industrial Engineering, Vol. 3, No. 51, PP. 351-361.
28. Srinivasan, D. et al. (2017). “Game-Theory Based Dynamic Pricing Strategies for Demand Side Management in Smart Grids”, Energy, Vol. 126, PP. 132-143.