KSCE Journal of Civil Engineering

, Volume 21, Issue 6, pp 2226–2234 | Cite as

A mathematical programming model for solving cost-safety optimization (CSO) problems in the maintenance of structures

  • Sayed Madeh Piryonesi
  • Mehdi TavakolanEmail author
Structural Engineering


Cost-Safety tradeoff analysis is one of the most challenging tasks of structural maintenance. Undoubtedly, developing an economic and efficient schedule for structural maintenance and rehabilitation is highly acknowledged. While meta-heuristic optimization algorithms have been used widely to determine the best maintenance strategies to provide more economical structures, we present a mathematical programming model to overcome the limitations of previous studies. In this paper a Mixed Integer Non-linear Programming (MINLP) has been presented to find the optimal time of applying maintenance intervention in a deteriorating structure. While, considering the time value of money, postponing the maintenance actions will be more economic, this postponement may cause a decrease in the safety of structures. Due to this contradictory relation between the objectives, it is vital to find a reasonable trade-off between cost-safety. Our proposed approach considers different values of the discount rate of money. We apply our mathematical programming model to solve two optimization examples, which are found in the structural maintenance literature. It is shown that our proposed model is able to determine the optimal time of applying maintenance intervention to the structures with less total life cycle cost, and higher level of safety.


structural safety non-linear programming optimization reliability profile life-cycle cost maintenance 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alpsten, G. A. (1972). “Variation in mechanical and cross-sectional properties of steel.” Proc. Int. Conf. on Planning and Design of Tall Buildings, Lehigh University, Bethlehem, Vol. Ib, pp. 775–805.Google Scholar
  2. American Institute of Steel Construction (AISC) (2003). Steel Design Guide 3, Serviceability Design Considerations for Steel Buildings, 2nd Ed, Chicago, I. L.Google Scholar
  3. Barone, G., Frangopol, D. M., and Soliman, M. (2014). “Optimization of life-cycle maintenance of deteriorating bridges with respect to expected annual system failure rate and expected cumulative cost.” Journal of Structural Engineering, Vol. 140, No. 2, 04013043, DOI: 10.1061/(ASCE)ST.1943-541X.0000812.CrossRefGoogle Scholar
  4. Central Bank of IRI (2013). “Price Indices.” 〈〉 (November, 30, 2013).Google Scholar
  5. Chang, S. E. and Shinozuka, M. (1996). “Life-cycle cost analysis with natural hazard risk.” Journal of Infrastructure System, Vol. 2, No. 3, pp. 118–26, DOI: 10.1061/(ASCE)1076-0342(1996)2:3(118).CrossRefGoogle Scholar
  6. Cho, H. N., Choi, H. H., Kim, J. H., and Choi, Y. M. (2004). “An experience of practical reliability-based safety assessment and capacity rating.” KSCE Journal of Civil Engineering, Vol. 8, No. 1, pp. 65–73, DOI: 10.1007/BF02829082.CrossRefGoogle Scholar
  7. Choi, S. K., Grandhi, R., and Canfield, R. A. (2007). Reliability-Based Structural Design, Springer, New York, N.Y.zbMATHGoogle Scholar
  8. Der Kiureghian, A., Haukaas, T., and Fujimura, K. (2005). “Structural reliability software at the university of california, berkeley.” Journal of Structural Safety, Vol. 28, No. 1, pp. 44–67, DOI: 10.1016/j.strusafe.2005.03.002.Google Scholar
  9. Estes, A. C. (1997). “A system reliability approach to the lifetime optimization of inspection and repair of highway bridges.” PhD thesis, Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder.Google Scholar
  10. Estes, A. C. and Frangopol, D. M. (1999). “Repair optimization of highway bridges using system reliability approach.” Journal of Structural Engineering, Vol. 125, No. 7, pp. 766–75, DOI: 10.1061/(ASCE) 0733-9445(1999)125:7(766).CrossRefGoogle Scholar
  11. Frangopol, D. M. and Liu, M. (2007). “Maintenance and management of civil infrastructure based on condition, safety, optimization and life-cycle cost.” Structure and Infrastructure Engineering, Vol. 3, No. 1, pp. 29–41, DOI: 10.1080/15732470500253164.CrossRefGoogle Scholar
  12. Frangopol, D. M. and Maute, K. (2003). “Life-cycle reliability-based optimization of civil and aerospace structures.” Computers & Structures, Vol. 81, No. 11, pp. 397–410, DOI: 10.1016/S0045-7949(03)00020-8.CrossRefGoogle Scholar
  13. Frangopol, D. M., Strauss, A., and Bergmeister, K. (2009). “Lifetime cost optimization of structures by a combined condition-reliability approach.” Engineering Structures, Vol. 31, No. 5, pp. 1572–1580, DOI: 10.1016/j.engstruct.2009.02.036.CrossRefGoogle Scholar
  14. Furuta, H., Koyama, K., and Ohi, M. (2006). “Life-cycle cost analysis of bridges structures considering maintenance cost and seismic risk.” Advances in Reliability and Optimization of Structural Systems, Sorenson, J. D. and Frangopol, D. M. (Eds), Taylor & Francis Group, London, UK.Google Scholar
  15. Hawk, H. and Small, E. P. (1998) “The BRIDGIT bridge management system.” Structural Engineering International, IABSE, Vol. 8, No. 4, pp. 303–14, DOI: 10.2749/101686698780488712.CrossRefGoogle Scholar
  16. Hess, P. E., Bruchman, D., Assakkaf, I. A., and Ayyub B. M. (2002). “Uncertainties in material and geometric strength and load variables.” Naval Engineering Journal, Vol. 114, No. 2, pp. 139–165, DOI: 10.1111/j.1559-3584.2002.tb00128.x.CrossRefGoogle Scholar
  17. Highways Agency of United Kingdom (2001). Design manual for roads and bridges: The assessment of highway bridge structures, Highways Agency Standard for Bridge Assessment, BD21/01, London, UK.Google Scholar
  18. Hong, T., Chae, M. J., Kim, D., Koo, C., Lee, K. S., and Chin, K. H., (2013). “Infrastructure asset management system for bridge projects in South Korea.” KSCE Journal of Civil Engineering, Vol. 17, No. 7, pp. 1551–1561, DOI: 10.1007/s12205-013-0408-8.CrossRefGoogle Scholar
  19. Jahani, E., Shayanfar, M. A., and Barkhordari, M. A. (2013). “A new adaptive importance sampling Monte Carlo method for structural reliability.” KSCE Journal of Civil Engineering, Vol. 17, No. 1, pp. 210–215, DOI: 10.1007/s12205-013-1779-6.CrossRefGoogle Scholar
  20. Kaveh, A. (2014). Advances in Metaheuristic Algorithms for Optimal Design of Structures, Springer, Berlin.CrossRefzbMATHGoogle Scholar
  21. Kaveh, A., Motie Share, M. A., and Moslehi, M. (2012). “Magnetic charged system search: A new meta-heuristic algorithm for optimization.” Acta Mechanica, Vol. 224, No. 1, pp. 85–107, DOI: 10.1007/s00707-012-0745-6.CrossRefzbMATHGoogle Scholar
  22. Kim, H. J., Kim, H. K., and Park, J. Y. (2013). “Reliability-based evaluation of load carrying capacity for a composite box girder bridge.” KSCE Journal of Civil Engineering, Vol. 17, No. 3, pp. 575–583, DOI: 10.1007/s12205-013-0603-7.CrossRefGoogle Scholar
  23. Management and Planning Organization of Iran (2014). “Rules and regulations,” 〈〉 (August, 30, 2014).Google Scholar
  24. Marler, R. T. and Arora, J. S. (2004). “Survey of multi-objective optimization methods for engineering.” Structural Multidisciplinary Optimization, Vol. 26, No. 6, pp 369–395, DOI: 10.1007/s00158-003-0368-6.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Melchers, R. E. (2002). Structural Reliability Analysis and Prediction, 2nd Ed., John Wiley, Chichester, UK.Google Scholar
  26. Morcous, G. and Lounis, Z. (2005). “Maintenance optimization of infrastructure networks using genetic algorithms.” Automation in Construction, Vol. 14, No. 1, pp. 129–142, DOI: 10.1016/j.autcon. 2004.08.014.CrossRefGoogle Scholar
  27. Morcous, G., and Lounis, Z., and Cho, Y. (2010). “An integrated system for bridge management using probabilistic and mechanistic deterioration models: Application to bridge decks.” KSCE Journal of Civil Engineering, Vol. 14, No. 4, pp. 527–537, DOI: 10.1007/s12205-010-0527-4.CrossRefGoogle Scholar
  28. Neves, L. C. and Frangopol, D. M. (2005). “Condition, safety and cost profiles for deteriorating structures with emphasis on bridges.” Reliability Engineering and System Safety, Vol. 89, No. 2, pp. 185–198, DOI: 10.1016/j.ress.2004.08.018.CrossRefGoogle Scholar
  29. Neves, L. C., Frangopol, D. M., and Cruz, P. J. S. (2006). “Probabilistic lifetime-oriented multiobjective optimization of bridge maintenance. Single maintenance type.” Journal of Structural Engineering, Vol. 132, No. 6, pp. 991–1005, DOI: 10.1061/(ASCE)0733-9445(2006)132:6 (991).CrossRefGoogle Scholar
  30. Neves, L. C., Frangopol, D. M., and Petcherdchoo, A. (2006a). “Probabilistic lifetime-oriented multi-objective optimization of bridge maintenance: Combination of maintenance types.” Journal of Structural Engineering, Vol. 132, No. 11, pp. 1821–1834, DOI: 10.1061/(ASCE)0733-9445 (2006)132:11(1821).CrossRefGoogle Scholar
  31. Nowak, A. S. and Collins, K. R. (2012). Reliability of Structures, 2nd Ed., CRC Press, Boca Raton, F.L.Google Scholar
  32. Okasha, N. M. and Frangopol, D. M. (2009). “Lifetime-oriented multiobjective optimization of structural maintenance considering system reliability, redundancy and life-cycle cost using GA.” Structural Safety, Vol. 31, No. 8, pp. 460–474, DOI: 10.1016/j.strusafe.2009. 06.005.CrossRefGoogle Scholar
  33. Thompson, P. D. (1993). “The pontis bridge management system.” Pacific Rim Trans Tech Conference: International Ties, Management Systems, Propulsion Technology, Strategic Highway Research Program, Seattle, W.A. pp. 500-506.Google Scholar
  34. Wenzel, H. (2009). Health Monitoring of Bridges, 1st Ed, John Wiley and Sons, Ltd, New York, N.Y.CrossRefGoogle Scholar

Copyright information

© Korean Society of Civil Engineers and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.University of Toronto, School of Civil EngineeringTorontoCanada
  2. 2.Dept. of Construction Engineering and Management, School of Civil Engineering, College of EngineeringUniversity of TehranTehranIran

Personalised recommendations