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Mathematical Problems in Engineering
Volume 2015, Article ID 396864, 16 pages
Research Article

A New Biobjective Model to Optimize Integrated Redundancy Allocation and Reliability-Centered Maintenance Problems in a System Using Metaheuristics

1Department of Industrial Engineering, Islamic Azad University, Science and Research Branch, Hesarak, Tehran 1477893855, Iran
2Center of Excellence in Advanced Manufacturing and Optimization, School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Received 5 February 2015; Revised 27 May 2015; Accepted 17 June 2015

Academic Editor: Babak Shotorban

Copyright © 2015 Shima MohammadZadeh Dogahe and Seyed Jafar Sadjadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A novel integrated model is proposed to optimize the redundancy allocation problem (RAP) and the reliability-centered maintenance (RCM) simultaneously. A system of both repairable and nonrepairable components has been considered. In this system, electronic components are nonrepairable while mechanical components are mostly repairable. For nonrepairable components, a redundancy allocation problem is dealt with to determine optimal redundancy strategy and number of redundant components to be implemented in each subsystem. In addition, a maintenance scheduling problem is considered for repairable components in order to identify the best maintenance policy and optimize system reliability. Both active and cold standby redundancy strategies have been taken into account for electronic components. Also, net present value of the secondary cost including operational and maintenance costs has been calculated. The problem is formulated as a biobjective mathematical programming model aiming to reach a tradeoff between system reliability and cost. Three metaheuristic algorithms are employed to solve the proposed model: Nondominated Sorting Genetic Algorithm (NSGA-II), Multiobjective Particle Swarm Optimization (MOPSO), and Multiobjective Firefly Algorithm (MOFA). Several test problems are solved using the mentioned algorithms to test efficiency and effectiveness of the solution approaches and obtained results are analyzed.