A Probabilistic Lower Bound for Two-Stage Stochastic Programs

  • George B. Dantzig
  • Gerd Infanger
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 150)


In the framework of Benders decomposition for two-stage stochastic linear programs, we estimate the coefficients and right-hand sides of the cutting planes using Monte Carlo sampling. We present a new theory for estimating a lower bound for the optimal objective value and we compare (using various test problems whose true optimal value is known) the predicted versus the observed rate of coverage of the optimal objective by the lower bound confidence interval.


Master Problem Bender Decomposition Normal Deviate Variance Reduction Technique Bender Decomposition Algorithm 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Operations ResearchStanford UniversityStanfordUSA
  2. 2.The RAND CorporationSanta MonicaUSA
  3. 3.Department of Management Science and EngineeringStanford UniversityStanfordUSA

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