Estimating the efficient frontier of a probabilistic bicriteria model

Tara Rengarajan*, David P. Morton

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


We consider a problem that trades off cost of system design with the risk of that design, where risk is measured by the probability of a bad event, such as system failure. Our interest lies in the problem class where we cannot evaluate this risk measure exactly, even for a given system design. We approach this problem via a bicriteria optimization model, replacing the risk measure by an Monte Carlo estimator and solving a parametric family of optimization models to produce an approximate efficient frontier. Optimizing system design with the risk estimator requires solution of a mixed integer program. We show that we can minimize risk over a range of cost thresholds or minimize cost over a range of risk thresholds and we examine associated asymptotics. The proximity of the approximate efficient frontier to the true efficient frontier is established via an asymptotically valid confidence interval with minimal additional work. Our approach is illustrated computationally using a facility-sizing problem.

Original languageEnglish (US)
Title of host publicationProceedings of the 2009 Winter Simulation Conference, WSC 2009
Number of pages11
StatePublished - 2009
Event2009 Winter Simulation Conference, WSC 2009 - Austin, TX, United States
Duration: Dec 13 2009Dec 16 2009

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736


Other2009 Winter Simulation Conference, WSC 2009
Country/TerritoryUnited States
CityAustin, TX

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Science Applications


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