An efficient algorithm to solve integer-programming problems arising in system-reliability design

IEEE Transactions on Reliability

Volumn 40, Issue 1, 1991, Pages 81-91

  Misra, Krishna Behari ^a   Sharma, Usha ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

Integer programming; Mixed integer programming; Mixed redundancy; Multi criteria optimization; Parametric programming; Reliability optimization; Zero One programming

Indexed keywords

MATHEMATICAL PROGRAMMING; OPERATIONS RESEARCH; REDUNDANCY; RELIABILITY - OPTIMIZATION;

MIXED REDUNDANCY; MIXED-INTEGER PROGRAMMING; MULTI-CRITERIA OPTIMIZATION; PARAMETRIC PROGRAMMING; SYSTEM-RELIABILITY DESIGN; ZERO-ONE PROGRAMMING;

SYSTEMS ENGINEERING;

EID: 0026139518     PISSN: 00189529     EISSN: 15581721     Source Type: Journal    
DOI: 10.1109/24.75341     Document Type: Article

References (25)

1. K.B. Misra, “On optimal reliability design: A review”, IFAC, 6th World Conference, Boston, Mass., USA, pp. 3.4.1–3.4.10, 1975 Aug.
2. F.A. Tillman, C.L. Hwang, W. Kuo, Optimization of System Reliability, 1980; Marcel Dekker.
3. K.B. Misra, “On optimal reliability design: A review”, System Science, vol 12, 1986, pp. 5–30.
4. A.J. Federowicz, M. Mazumdar, “Use of geometric programming to maximize reliability achieved by redundancy”, Operations Research, vol 19, 1968 Sept.-Oct., pp. 948–954.
5. K.B. Misra, J.D. Sharma, “A new geometric programming formulation for a reliability problem”, Int'l J. control, vol 18, 1973 Sep, pp. 497–503.
6. R. Gomory, An Algorithm for Integer Solutions to Linear Programs, Princeton IBM Mathematical Research Report, 1958.
7. D.M. Murray, S.J. Yakowitz, “Differential dynamic programming and Newton's method for discrete optimal control problems”, J. Optimization Theory and Applications, vol 43, 1984, pp. 395–414.
8. R.E. Bellman, E. Dreyfus, “Dynamic programming and reliability of multicomponent devices”, Operations Research, vol 6, 1958 Mar-Apr, pp. 200–206.
9. K.B. Misra, “Dynamic programming formulation of redundancy allocation problem”, Int'l J. Mathematical Education in Science and Technology, (UK), vol 2, 1971, pp. 207–215.
10. A.M. Geoffrion, “Integer programming by implicit enumeration and Bala's method”, Soc. Industrial and Applied Mathematics Review, vol 9, 1967, pp. 178–190.
11. J. Kelley, “The cutting plane method for solving convex programs”, J. Soc. Industrial and Applied Mathematics, vol 8, I960, pp. 708–712.
12. D.E. Fyffee, W.W. Hines, N.K. Lee, “System reliability allocation and a computational algorithm”, IEEE Trans. Reliability, vol R-17, 1968 Jun, pp. 64–69.
13. K.B. Misra, J.D. Sharma, “Reliability optimization of a system by zero-one programming”, Microelectronics and Reliability, vol 12, 1973 Jun, pp. 229–233.
14. E.L. Lawler, M.D. Bell, “A method for solving discrete optimization problems”, Operations Research, vol 14, 1966 Nov-Dec, pp. 1098–1112.
15. K.B. Misra, “A method of solving redundancy optimization problems”, IEEE Trans. Reliability, vol R-20, 1971 Aug.
16. K.B. Misra, “Optimum reliability design of a system containing mixed redundancies”, IEEE Trans. Power Apparatus and Systems, vol PAS-94, 1975 May-Jun, pp. 983–993.
17. Y. Nakagawa, “Studies on optimal design of high reliable system: Single and multiple objective nonlinear integer programming”, PhD Thesis, Kyoto University, Japan, 1978 Dec.
18. P.M. Ghare, R.E. Taylor, “Optimal redundancy for reliability in series system”, ORSA, vol 17, 1969 Sep, pp. 838–847.
19. J. Sharma, K. Venkateswaran, “A direct method for maximizing the system reliability”, IEEE Trans. Reliability, vol R-70, 1971 Nov, pp. 256–259.
20. K.B. Misra, “A simple approach for constrained redundancy optimization problems”, IEEE Trans. Reliability, vol R-21, 1972 Feb, pp. 30–34.
21. K.K. Aggarwal, J.S. Gupta, K. B. Misra, “A new heuristic criterion for solving a redundancy optimization problem”, IEEE Trans. Reliability, vol R-24, 1975 Apr, pp. 86–87.
22. Krishna B. Misra, “An algorithm to solve integer programming problems: An efficient tool for reliability design”, Microelectronics and Reliability (to appear).
23. M.S. Chern, R.H. Jan, “Parametric programming applied to reliability optimization problems”, IEEE Trans. Reliability, vol R-34, 1985 Jun, pp. 165–170.
24. U. Sharma, K.B. Misra, “Optimal availability design of a maintained system”, Reliability Engineering and System Safety, vol 20, 1988, pp. 146–159.
25. M. Sakawa, “Multi-objective reliability and redundancy optimization of a series parallel system by the surrogate worth trade off method”, Microelectronics and Reliability, vol 17, 1978, pp. 465–467.