Bi-Criteria Optimization Technique in Stochastic System Maintenance Allocation Problem

Irfan Ali, S. Suhaib Hasan

Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh, India.

DOI: 10.4236/ajor.2013.31002                

Abstract

In this paper, the problem of optimum allocation of repairable and replaceable components in a system is formulated as a Bi-objective stochastic non linear programming problem. The system maintenance time and cost are random variable and has gamma and normal distribution respectively. A Bi-criteria optimization technique, weighted Tchebycheff is used to obtain the optimum allocation for a system. A numerical example is also presented to illustrate the computational details.

Keywords

Selective Maintenance; Weighted Tchebycheff Technique; Multi-Criteria Optimization; Stochastic Programming; Chance Constrained; Modified E-Model; System Reliability

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	I. Ali, M. F. Khan, Y. S. Raghav and A. Bari, “Allocating Repairable and Replaceable Components for a System Availability Using Selective Maintenance with Probabilistic Constraints,” American Journal of Operations Research, Vol. 1, No. 3, 2011, pp. 147-154. doi:10.4236/ajor.2011.13016
[2]	W. F. Rice, C. R. Cassady and J. A. Nachlas, “Optimal Maintenance Plans under Limited Maintenance Time,” Proceedings of the 7th Industrial Engineering Research Conference, Banff, 9-10 May 1998.
[3]	C. R. Cassady, E. A. Pohl and J. Song, “Managing Availability Improvement Efforts with Importance Measures and Optimization,” IMA Journal of Management Mathematics, Vol. 15, No. 2, 2004, pp. 161-174. doi:10.1093/imaman/15.2.161
[4]	R. Rajagopalan and C. R. Cassady, “An Improved Selective Maintenance Approach,” Journal of Quality in Maintenance Engineering, Vol. 12, No. 2, 2006, pp. 172-185. doi:10.1108/13552510610667183
[5]	K. Schneider, L. M. Maillart, C. R. Cassady and C. Rainwater, “Selective Maintenance Decision-Making over Extended Planning Horizons,” IEEE Transactions on Reliability, Vol. 58, No. 3, 2009, pp. 462-469. doi:10.1109/TR.2009.2026689
[6]	I. M. Iyoob, C. R. Cassady and E. A. Pohl., “Establishing Maintenance Resource Levels Using Selective Maintenance,” The Engineering Economist, Vol. 51, No. 2, 2006, pp. 99-114. doi:10.1080/00137910600695627
[7]	I. Ali, Y. S. Raghav and A. Bari, “Allocating Repairable and Replaceable Components for a System Availability Using Selective Maintenance: An Integer Solution,” Safety and Reliability Society, Vol. 31, No. 2, 2011, pp. 9-18.
[8]	I. Ali, Y. S. Raghav and A. Bari, “Integer Goal Programming Approach for Finding a Compromise Allocation of Repairable Components,” International Journal of Engineering Science and Technology, Vol. 3, No. 6, 2011, pp. 184-195.
[9]	I. Ali, Y. S. Raghav and A. Bari, “Compromise Allocation in Multivariate Stratified Surveys with Stochastic Quadratic Cost Function,” Journal of Statistical Computation and Simulation, 2011. doi:10.1080/00949655.2011.643890
[10]	I. Ali, M. F. Khan, Y. S. Raghav and A. Bari, “Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components,” Communications in Statistics—Simulation and Computation, 2012. http://www.tandfonline.com/doi/abs/10.1080/03610918.2012
[11]	M. F. Khan and I. Ali, “Allocation Problem of Repairable and Replaceable Components for a System Reliability using Selective Maintenance: An Integer Solution,” International Journal of Scientific and Engineering Research, Vol. 3, No. 5, 2012, pp. 1-4.
[12]	S. S. Rao, “Optimization Theory and Applications,” Wiley Eastern Limited, New Delhi, 1979.
[13]	V. J. Bowman Jr., “On the Relationship of the Tchebycheff Norm and the Efficient Frontier of Multiple-Criteria Objectives,” In: H. Thiriez and S. Zionts, Eds., “Multiple Criteria Decision Making,” Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 1976, pp. 76-85.
[14]	K. M. Miettinen, “Non Linear Multiobjective Optimization,” Kluwer Academic Publishers, Boston, 1999.
[15]	A. P. Wierzbicki, “On the Completeness and Constructiveness of Parametric Characterizations to Vector Optimization Problem,” Operations-Research-Spektrum, Vol. 8, No. 2, 1986, pp. 73-87. doi:10.1007/BF01719738
[16]	M. T. Khasawneh, S. R. Bowling, S. Kaewkuekool and B. R. Cho, “A Cost-Effective Strength-Stress Reliability Modeling and Optimization in Engineering Design,” Proceeding of the Industrial Engineering Research Conference, Orlando, 19-21 May 2002.