Journal of Intelligent Manufacturing

, Volume 25, Issue 6, pp 1455–1462 | Cite as

An integrated GA-DEA algorithm for determining the most effective maintenance policy for a k -out-of- n problem

  • M. Sheikhalishahi
  • V. Ebrahimipour
  • M. Hosseinabadi Farahani


This paper presents a novel hybrid GA-DEA algorithm in order to solve multi-objective \(k\)-out-of-\(n\) problem and determine preferred policy. The proposed algorithm maximizes overall system reliability and availability, while minimizing system cost and queue length, simultaneously. To meet these objectives, an adaptive hybrid GA-DEA algorithm is developed to identify the optimal solutions and improve computation efficiency. In order to improve computation efficiency genetic algorithm (GA) is used to simulate a series production line and find the Pareto-optimal solutions which are different values of \(k\) and \(n\) of \(k\)-out-of-\(n\) problem. Data envelopment analysis is used to find the best \(k\) and \(n\) from Genetic Algorithm’s Pareto solutions. An illustrative example is applied to show the flexibility and effectiveness of the proposed algorithm. The proposed algorithm of this study would help managers to identify the preferred policy considering and investigating various parameters and scenarios in logical time. Also considering different objectives result in Pareto-optimal solutions that would help decision makers to select the preferred solution based on their situation and preference.


Maintenance activities Genetic algorithm Data envelopment analysis Pareto optimal solution Maintenance policy 



The authors are grateful for the valuable comments and suggestion from the respected reviewers. Their valuable comments and suggestions have enhanced the strength and significance of our paper. The authors would like to acknowledge the financial support of University of Tehran for this research under grant number 27775/01/07.


  1. Azadeh, A., Sheikhalishahi, M., & Asadzadeh, S. M. (2011). A flexible neural network-fuzzy data envelopment analysis app roach for location optimization of solar plants with uncertainty and complexity. Renewable Energy, 36, 3394–3401.CrossRefGoogle Scholar
  2. Allella, F., Chiodo, E., & Lauria, D. (2005). Optimal reliability allocation under uncertain condition, with application to hybrid electric vehicle design. International Journal of Quality and Reliability Management, 22(6), 626–641.CrossRefGoogle Scholar
  3. Banker, R. D., Charnes, R. F., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078–1092.CrossRefGoogle Scholar
  4. Bates, A. D., O’Dea, M. H., & Gellert, M. (1996). Energy coupling in Escherichia coli DNA gyrase: The relationship between nucleotide binding, strand passage, and DNA supercoiling. Biochemistry, 35, 1408–1416.CrossRefGoogle Scholar
  5. Bessent, A., & Bessent, W. (1980). Determining the comparative efficiency of schools through data envelopment analysis. Educational Administration Quarterly, 1, 57–75.CrossRefGoogle Scholar
  6. Booker, A. J., Meckesheimer, M., & Torng, T. (2004). Reliability based design optimization using design explorer. Optimization and Engineering, 5, 179–205.CrossRefGoogle Scholar
  7. Charnes, A., Cooper, W., & Rhodes, E. (1978a). Measuring the efficiency of decision-making units. European Journal of Operational Research, 2, 429–444.CrossRefGoogle Scholar
  8. Charnes, A., Cooper, W., & Rhodes, E. (1978b). Measuring the efficiency of decision-making units. European Journal of Operational Research, 2, 429–444.CrossRefGoogle Scholar
  9. Coit, D. W., & Smith, A. (1995). Optimization approaches to the redundancy allocation to the redundancy allocation problem for series-parallel systems. In: Proceedings of the fourth industrial engineering research conference (pp. 342–349). Nashville, TN, May.Google Scholar
  10. Dai, Y. S., & Wang, X. L. (2006). Optimal resource allocation on grid systems for maximizing service reliability using a genetic algorithm. Reliability Engineering and System Safety, 91, 1071–1082.CrossRefGoogle Scholar
  11. Ding, Y., & Lisnianskia, A. (2008). Fuzzy universal generating functions for multi-state system reliability assessment. Fuzzy Sets and Systems, 159, 307–324.CrossRefGoogle Scholar
  12. Ebrahimipour, V., & Sheikhalishahi, M. (2010). Application of multi-objective particle swarm optimization to solve a fuzzy multi-objective reliability redundancy allocation problem. 2011 IEEE International Systems Conference (pp. 326–333). Quebec, Canada: Montreal.Google Scholar
  13. Ebrahimipour, V., Sheikhalishahi, M., Maleki Shoja, B., & Goldansaz, M. (2010). A universal generating function approach for redundancy optimization for hot-standby Multi-State Series-Parallel k-out-of-n Systems (pp. 235–239). Pisa: Fourth UKSim European Symposium on Computer Modeling and Simulation.Google Scholar
  14. Eschenauer, H., Koski, J., & Osyczka, A. (1990). Multicriteria design optimization: Procedures and optimization, Berlin, Heidelberg, New York: Springer-Verlag.Google Scholar
  15. Fare, R., Grosskopf, S., & Tyteca, D. (1996). An activity analysis model of the environment performance of firms: Application to fossil-fuel-fired electric utilities. Ecological Economics, 18, 161–175.Google Scholar
  16. Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society, 120, 253–281.CrossRefGoogle Scholar
  17. Ganley, J., & Cubbin, J. (1992). Public sector efficiency measurement: Applications of data envelopment analysis. North-Holland: Elsevier.Google Scholar
  18. Gupta, R. K., Bhunia, A. K., & Roy, D. (2009). A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components. Computational and Applied Mathematics, 232, 275–284.CrossRefGoogle Scholar
  19. Kumar, R., Izui, K., Yoshimura, M., & Nishiwaki, S. (2009). Optimal multilevel redundancy allocation in series and series-parallel systems. Computers and Industrial Engineering, 57, 169–180.CrossRefGoogle Scholar
  20. Lai, Y. J., & Hwang, C. L. (1992). Fuzzy mathematical programming. Berlin, Heidelberg, USA, Newyork: Springer.CrossRefGoogle Scholar
  21. Levitin, G. (2005). Universal generating function in reliability analysis and optimization, Springer Series in Reliability Engineering.Google Scholar
  22. Levitin, G., & Amari, S. (2010). Approximation algorithm for evaluating time-to-failure distribution of k-out-of-n system with shared standby elements. Reliability Engineering and System Safety, 95, 396–401.CrossRefGoogle Scholar
  23. Li, C. Y., Chen, X., Yi, X. S., & Tao, J. Y. (2010). Heterogeneous redundancy optimization for multi-state series-parallel systems subject to common cause failures. Reliability Engineering and System Safety, 95, 202–207.CrossRefGoogle Scholar
  24. Li, W., & Zuo, M. J. (2008). Reliability evaluation of multi-state weighted k-out-of- n systems. Reliability Engineering and System Safety, 93, 160–167.CrossRefGoogle Scholar
  25. Li, Z., Liao, H., & Coit, D. W. (2009). A two-stage approach for multi-objective decision making with applications to system reliability optimization. Reliability Engineering and System Safety, 94, 1585–1592.CrossRefGoogle Scholar
  26. Lin, T. W., & Wang, C. H. (2012). A hybrid genetic algorithm to minimize the periodic preventive maintenance cost in a series-parallel system. Journal of Intelligent Manufacturing, 23(4), 1225–1236.CrossRefGoogle Scholar
  27. Long, Q., Xie, M., Ng, S. H., & Levitin, G. (2008). Reliability analysis and optimization of weighted voting systems with continuous states input. European Journal of Operational Research, 191(1), 240–252.CrossRefGoogle Scholar
  28. Luxhoj, J. T., & Shyur, H. J. (1997). Comparison of proportional hazards models and neural networks for reliability estimation. Journal of Intelligent Manufacturing, 8(3), 227–234.CrossRefGoogle Scholar
  29. Marseguerra, M., & Zio, E. (2000). Optimizing maintenance and repair policies via a combination of genetic algorithms and Monte Carlo simulation. Reliability Engineering and System Safety, 68, 69–83.CrossRefGoogle Scholar
  30. Munoz, A., Martorell, S., & Serradell, V. (1997). Genetic algorithm in optimizing surveillance and maintenance of components. Reliability Engineering and System Safety, 57, 107–120.CrossRefGoogle Scholar
  31. Oh, H., Shibutani, T., & Pecht, M. (2012). Precursor monitoring approach for reliability assessment of cooling fans. Journal of Intelligent Manufacturing, 23(2), 173–178. Google Scholar
  32. Olsen, O., & Petersen, N. (1995). Chance constrained efficiency evaluation. Management Science, 41, 442–457.CrossRefGoogle Scholar
  33. Patel, J., & Choi, S. K. (2012). An enhanced classification approach for reliability estimation of structural systems. Journal of Intelligent Manufacturing,. doi: 10.1007/s10845-012-0702-1.Google Scholar
  34. Prabhu Gaonkar, R. S., Xie, M., Ng, K. M., & Habibullah, M. S. (2011). Subjective operational reliability assessment of maritime transportation system. Expert Systems with Applications, 38(11), 13835–13846.Google Scholar
  35. Ramirez-Marquez, J. E., & Coit, D. W. (2004). A heuristic for solving the redundancy allocation problem for multi-state series-parallel systems. Reliability Engineering and System Safety, 83, 341–349.CrossRefGoogle Scholar
  36. Ramirez-Marqueza, J. E., & Coit, D. W. (2007). Optimization of system reliability in the presence of common cause failures. Reliability Engineering and System Safety, 92, 1421–1434.CrossRefGoogle Scholar
  37. Srinivas, N., & Deb, K. (1994). Muiltiobjective optimization using nondominated sorting in genetic algorithms. Journal Evolutionary Computation, 2(3), 221–248.Google Scholar
  38. Tian, Z., & Zuo, M. J. (2006). Redundancy allocation for multi-state systems using physical programming and genetic algorithms. Reliability Engineering and System Safety, 91, 1049–1056.CrossRefGoogle Scholar
  39. Vidyarthi, D. P., & Tripathi, A. K. (2001). Maximizing reliability of distributed computing system with task allocation using simple genetic algorithm. Systems Architecture, 47, 549–554.CrossRefGoogle Scholar
  40. Wang, K. S., Chang, W. H., Tsai, Y. T., Hsu, F. S. (1996). Using genetic algorithm planning preventive replacement of components in a system. In: Proceedings of the 13th National conference of the Chinese society of mechanical engineers, pp. 271–278.Google Scholar
  41. Wang, S., & Watada, J. (2009). Modelling redundancy allocation for a fuzzy random parallel_series System. Computational and Applied Mathematics, 232, 539–557.Google Scholar
  42. Yeh, Q.-J. (1996). Application of data envelopment analysis in conjunction with financial ratios for bank performance evaluation. The Journal of the Operational Research Society, 47(8), 980–988.CrossRefGoogle Scholar
  43. Yun, W. Y., Song, Y. M., & Kim, H. G. (2007). Multiple multi-level redundancy allocation in series systems. Reliability Engineering and System Safety, 92, 308–313.CrossRefGoogle Scholar
  44. Zhang, T., Xiea, M., & Horigome, M. (2006). Availability and reliability of k-out-of-(M+N): G warm standby systems. Reliability Engineering and System Safety, 91, 381–387.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • M. Sheikhalishahi
    • 1
  • V. Ebrahimipour
    • 2
    • 1
  • M. Hosseinabadi Farahani
    • 1
  1. 1.Department of Industrial Engineering, University college of EngineeringUniversity of TehranTehranIran
  2. 2.Mathematics and Industrial Engineering DepartmentEcole Polytechnique de MontrealMontrealCanada

Personalised recommendations