Allocation of Repairable and Replaceable Components for a System Availability Using Selective Maintenance with Probabilistic Maintenance Time Constraints
Irfan Ali, Mohammed Faisal Khan, Yashpal Singh Raghav, Abdul Bari
DOI: 10.4236/ajor.2011.13016   PDF    HTML     5,423 Downloads   9,516 Views   Citations


In this paper, we obtain optimum allocation of replaceable and repairable components in a system design. When repair and replace time are considered as random in the constraints. We convert probabilistic constraint into an equivalent deterministic constraint by using chance constrained programming. We have used the selective maintenance policy to determine how many components to be replaced & repaired within the limited maintenance time interval and cost. A Numerical example is presented to illustrate the computational procedure and problem is solved by using LINGO Software.

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I. Ali, M. Faisal Khan, Y. Raghav and A. Bari, "Allocation of Repairable and Replaceable Components for a System Availability Using Selective Maintenance with Probabilistic Maintenance Time Constraints," American Journal of Operations Research, Vol. 1 No. 3, 2011, pp. 147-154. doi: 10.4236/ajor.2011.13016.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] 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.
[2] C. R. Cassady, E. A. Pohl and W. P. Murdock, “Selective Maintenance Modeling for Industrial Systems,” Journal of Quality in Maintenance Engineering, 2001, Vol. 7, No. 2, pp. 104-117. doi:10.1108/13552510110397412
[3] C. R. Cassady, W. P. Murdock and E. A. Pohl, “Selective Maintenance for Support Equipment Involving Multiple Maintenance Actions,” European Journal of Operational Research, Vol. 129, No. 2, 2001, pp. 252-258. doi:10.1016/S0377-2217(00)00222-8
[4] 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
[5] A. Prekopa, “Stochastic Programming,” Series: Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, 1995.
[6] A. Charnes and W. W. Cooper, “Deterministic Equivalents for Optimizing and Satisfying under Chance Constraints,” Operations Research, Vol. 11, No. 1, 1963, pp. 18-39. doi:10.1287/opre.11.1.18
[7] S. S. Rao, “Optimization Theory and Applications,” Wiley Eastern Limited, New Delhi, 1979.
[8] A. Prekopa, “The Use of Stochastic Programming for the Solution of the Some Problems in Statistics and Probability,” Technical Summary Report #1834, University of Wisconsin-Madison, Mathematical Research Center, Ma- dison, 1978.
[9] S. Uryasev and P. M. Pardalos, “Stochastic Optimization,” Kluwer Academic Publishers, Dordrecht, 2001.
[10] F. Louveaux and J. R. Birge, “Stochastic Integer Programming: Continuity Stability Rates of Convergence,” In: C. A. Floudas and P. M. Pardalos, Eds., Encyclopedia of Optimization, Vol. 5, Kluwer Academic Publishers, Dordrecht, 2001, pp. 304-310.
[11] G. B. Dantzig, “Linear Programming under Uncertainty,” Management Science, Vol. 1, No. 3-4, 1955, pp. 197-206. doi:10.1287/mnsc.1.3-4.197
[12] A. Charnes and W. W. Cooper, “Chance Constrained Programming,” Management Science, Vol. 6, No. 1, 1959, pp. 73-79. doi:10.1287/mnsc.6.1.73
[13] V. A. Bereznev, “A Stochastic Programming Problem with Probabilistic Constraints,” Engineering Cybernetics, Vol. 9, No. 4, 1971, pp. 613-619.

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