Document Type : Original Article


1 Ph.D Student, Faculty of Industrial and Mechanical Engineering, Islamic Azad University, Qazvin Branch, Qazvin Iran.

2 Professor, Faculty of Management and Accounting, Shahid Beheshti University, Tehran, Iran.


The redundancy allocation problem is to find an optimal allocation of redundant components by considering a set of different constraints. Solving these problems is of great interest to various researchers due to its high mathematical complexity. In this research, the satellite attitude determination and control system are studied, and its components are introduced. Then, the reliability and cost of this system are modeled and optimized using a mathematical approach based on redundancy allocation. The model studied in this research pertains to the configuration of a series-parallel system operating within the precise context of a satellite attitude determination and control system. This paper introduces a novel approach to modeling a bi-objective problem and optimizing it using an exact solution method. The mathematical model presented in this paper is a mixed integer non-linear programming (MINLP). In this research, an heuristic method executed in 7 steps has been employed to achieve an exact solution to the problem. Based on this approach, the optimal values for system reliability and cost are determined under various objective weighting schemes.


Main Subjects

  1. Aggarwal, K. K. (1976). Redundancy optimization in general systems. IEEE Transactions on Reliability25(5), 330-332.
  2. Aggarwal, K. K., Gupta, J. S., & Misra, K. B. (1975). A new heuristic criterion for solving a redundancy optimization problem. IEEE Transactions on Reliability24(1), 86-87.
  3. Amiri, M., Azizi-Broujerdi, S., Poorbakhsh, H. (2014). Presenting a mathematical model to solve the multi-objective problem of selecting redundancy allocation strategy with the aim of maximizing reliability for K-out-of-N systems. The Journal of Industrial Management Perspective, 4(4), 117-134. (In Persian)
  4. Bulfin, R. L., & Liu, C. Y. (1985). Optimal allocation of redundant components for large systems. IEEE Transactions on Reliability34(3), 241-247.
  5. Busacca, P. G., Marseguerra, M., & Zio, E. (2001). Multiobjective optimization by genetic algorithms: application to safety systems. Reliability Engineering & System Safety72(1), 59-74.
  6. Cao, R., Coit, D. W., Hou, W., & Yang, Y. (2020). Game theory-based solution selection for multi-objective redundancy allocation in interval-valued problem parameters. Reliability Engineering & System Safety,
  7. Chambari, A., Rahmati, S. H. A., & Najafi, A. A. (2012). A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies. Computers & Industrial Engineering63(1), 109-119.
  8. Chern, M. S. (1992). On the computational complexity of reliability redundancy allocation in a series system. Operations research letters11(5), 309-315.
  9. Coit, D. W. (2001). Cold-standby redundancy optimization for nonrepairable systems. Iie Transactions33(6), 471-478.
  10. Coit, D. W., & Smith, A. E. (1996). Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on reliability, 45(2), 254-260
  11. Dobani, E. R., Ardakan, M. A., Davari-Ardakani, H., & Juybari, M. N. (2019). RRAP-CM: A new reliability-redundancy allocation problem with heterogeneous components. Reliability Engineering & System Safety, 191,
  12. Fyffe, D. E., Hines, W. W., & Lee, N. K. (1968). System reliability allocation and a computational algorithm. IEEE Transactions on Reliability17(2), 64-69.
  13. Gopal, K., Aggarwal, K. K., & Gupta, J. S. (1978). An improved algorithm for reliability optimization. IEEE Transactions on Reliability27(5), 325-328.
  14. Ha, C., & Kuo, W. (2006). Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems. European Journal of Operational Research171(1), 24-38.
  15. Hajiyev, C., & Bahar, M. (2003). Attitude determination and control system design of the ITU-UUBF LEO1 satellite. Acta Astronautica52(2-6), 493-499.
  16. Hsieh, Y. C. (2016). A two-phase linear programming approach for redundancy allocation problems. Yugoslav journal of operations research12(2).
  17. Khalili-Damghani, K., & Amiri, M. (2012). Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA. Reliability Engineering & System Safety103, 35-44.
  18. Misra, K. B. (1972). Reliability optimization of a series-parallel system. IEEE Transactions on Reliability21(4), 230-238.
  19. Mousavi, S. M., Alikar, N., Tavana, M., & Di Caprio, D. (2019). An improved particle swarm optimization model for solving homogeneous discounted series-parallel redundancy allocation problems. Journal of Intelligent Manufacturing, 30(3), 1175-1194.
  20. Nakagawa, Y., & Miyazaki, S. (1981). Surrogate constraints algorithm for reliability optimization problems with two constraints. IEEE Transactions on Reliability30(2), 175-180.
  21. Nakagawa, Y., & Nakashima, K. (1977). A heuristic method for determining optimal reliability allocation. IEEE Transactions on reliability26(3), 156-161.
  22. Ouyang, Z., Liu, Y., Ruan, S. J., & Jiang, T. (2019). An improved particle swarm optimization algorithm for reliability-redundancy allocation problem with mixed redundancy strategy and heterogeneous components. Reliability Engineering & System Safety, 181, 62-74.
  23. Radfar, A., Mohammaditabar, D. (2019). Bi-Objective Optimization of Vendor Managed Inventory Problem in a Multi Echelon Green Supply Chain. The Journal of Industrial Management Perspective, 9(3), 109-134. (In Persian)
  24. Sharma, J., & Venkateswaran, K. V. (1971). A direct method for maximizing the system reliability. IEEE Transactions on Reliability20(4), 256-259.
  25. Shoul, A., Amiri, M., Olfat, L., Khalili-Damghani, K. (2014). designing multi-period and multi-product supply chain network using a hybrid multi-objective mathematical programming approach and data envelopment analysis. The Journal of Industrial Management Perspective, 4(2), 117-137. (In Persian)
  26. Shrestha, A., Xing, L., & Liu, H. (2007, January). Modeling and evaluating the reliability of wireless sensor networks. In 2007 Annual Reliability and Maintainability Symposium(pp. 186-191). IEEE.
  27. Steyn, W. H. (1995). A multi-mode attitude determination and control system for small satellites(Doctoral dissertation, Stellenbosch: Stellenbosch University).
  28. Sun, M. X., Li, Y. F., & Zio, E. (2019). On the optimal redundancy allocation for multi-state series–parallel systems under epistemic uncertainty. Reliability Engineering & System Safety, 192,
  29. Tillman Tillman, F. A., Hwang, C. L., & Kuo, W. (1977). Determining component reliability and redundancy for optimum system reliability. IEEE Transactions on Reliability26(3), 162-165.
  30. You, P. S., & Chen, T. C. (2005). An efficient heuristic for series–parallel redundant reliability problems. Computers & operations research32(8), 2117-2127.
  31. Yun, W-Y. & Kim, J-W. (2004). Multi-Level Redundancy Optimization in Series Systems. Computers & Industrial Engineering; 46, 337-346.
  32. Zaretalab A, Hajipour V, Sharifi M, Shahriari, M.R (2015). A knowledge-based archive multi-objective simulated annealing algorithm to optimize series–parallel system with choice of redundancy strategies. Computer and Industrial Engineering, 80, 33-44.
  33. Zaretalab, A., Hajipour, V., & Tavana, M. (2020). Redundancy allocation problem with multi-state component systems and reliable supplier selection. Reliability Engineering & System Safety, 193,