An exact algorithm for cost minimization in series reliability systems with multiple component choices
In this paper, we present an exact method for cost minimization problems in series reliability systems with multiple component choices. The problem can be modelled as a nonlinear integer programming problem with a nonseparable constraint function. The method is of a combined Lagrangian relaxation an...
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| Vydáno v: | Applied mathematics and computation Ročník 181; číslo 1; s. 732 - 741 |
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| Jazyk: | angličtina |
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01.10.2006
Elsevier |
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| ISSN: | 0096-3003, 1873-5649 |
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| Abstract | In this paper, we present an exact method for cost minimization problems in series reliability systems with multiple component choices. The problem can be modelled as a nonlinear integer programming problem with a nonseparable constraint function. The method is of a combined Lagrangian relaxation and linearization method. A Lagrangian bound is obtained by solving the dual of a separable subproblem. An alternative lower bound is derived by 0–1 linearization method. A special cut-and-partition scheme is proposed to reduce the duality gap, thus ensuring the convergence of the method. Computational results are reported to show the efficiency of the method. |
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| AbstractList | In this paper, we present an exact method for cost minimization problems in series reliability systems with multiple component choices. The problem can be modelled as a nonlinear integer programming problem with a nonseparable constraint function. The method is of a combined Lagrangian relaxation and linearization method. A Lagrangian bound is obtained by solving the dual of a separable subproblem. An alternative lower bound is derived by 0–1 linearization method. A special cut-and-partition scheme is proposed to reduce the duality gap, thus ensuring the convergence of the method. Computational results are reported to show the efficiency of the method. |
| Author | Ruan, Ning Sun, Xiaoling |
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| Cites_doi | 10.1109/24.510811 10.1109/TR.1986.4335497 10.1109/24.75341 10.1080/00207728008967030 10.1109/TR.1978.5220401 10.1007/s10898-005-1678-6 10.1109/TR.1983.5221520 10.1287/opre.47.6.899 10.1080/07408170108936895 10.1016/S0305-0548(00)00089-7 10.1016/0167-6377(95)00009-9 10.1023/A:1016541912439 10.1023/A:1008325116400 10.1109/24.914551 10.1109/24.784268 10.1016/S0377-2217(99)00330-6 10.1016/S0096-3003(99)00217-9 |
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| Keywords | Reliability system Cost minimization Branch-and-bound method Multiple component choice Lagrangian bound Lower bound Branch and bound method Non linear programming System reliability Algorithm Integer programming Efficiency Applied mathematics Relaxation method Lagrangian method |
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| SubjectTerms | Branch-and-bound method Calculus of variations and optimal control Cost minimization Exact sciences and technology Lagrangian bound Mathematical analysis Mathematics Multiple component choice Numerical analysis Numerical analysis. Scientific computation Numerical methods in mathematical programming Numerical methods in mathematical programming, optimization and calculus of variations Reliability system Sciences and techniques of general use |
| Title | An exact algorithm for cost minimization in series reliability systems with multiple component choices |
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