A risk-averse stochastic program for integrated system design and preventive maintenance planning

Xiaoqiang Bei, Xiaoyan Zhu, David W. Coit

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


The failure of high-consequence systems, such as highspeed railways, can result in a series of severe damages. Due to the volatility of real circumstances, stochastic optimization methods are needed to aid decisions on reliability design and maintenance for the high-consequence systems. Traditionally, risk-neutral approaches are used by considering the expectation of random variables as a preference criterion. The risk-neutral approaches may achieve the solutions that are good in the long run but do not control poor results under certain realizations of random variables. From a perspective of risk analysis, such solutions are not acceptable for high-consequence systems. To address this issue, this paper uses the conditional value at risk (CVaR) to more properly account for some of the worst realizations of random future usage scenarios, and then proposes a risk-averse two-stage stochastic programming model to simultaneously determine the numbers of components in each subsystem and preventive maintenance time intervals for the high-consequence systems that are exposed to uncertain future usage stresses. The proposed stochastic programming model can be converted to a nonconvex mixed-integer nonlinear programming (MINLP) model. To solve the model, we derive the analytical properties of the recourse function and the closed form of CVaR and then design a decomposition algorithm. Numerical examples demonstrate the proposed risk-averse stochastic approach and the effectiveness of incorporating the CVaR in modeling. The results show the research problem significantly benefits from the proposed approach. Furthermore, the robustness of the optimal system design and maintenance plan under different profiles of future usage scenarios is addressed.

Original languageEnglish (US)
Pages (from-to)536-548
Number of pages13
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Jul 16 2019

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management
  • Industrial and Manufacturing Engineering


  • Preventive maintenance
  • Redundancy allocation
  • Reliability
  • Risk-averse two-stage stochastic programming
  • Uncertain future usage stresses


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