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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Bibliographic Details
Published in:Applied mathematics and computation Vol. 181; no. 1; pp. 732 - 741
Main Authors: Ruan, Ning, Sun, Xiaoling
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.10.2006
Elsevier
Subjects:
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
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
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2006.02.001