Open AccessA probabilistic lower bound for two-stage stochastic programs
Author(s) -
George B. Dantzig,
Gerd Infanger
Publication year - 1995
Language(s) - English
Resource type - Reports
DOI - 10.2172/656786
Subject(s) - upper and lower bounds , mathematics , probabilistic logic , monte carlo method , confidence interval , mathematical optimization , value (mathematics) , interval (graph theory) , statistics , combinatorics , mathematical analysis
In the framework of Benders decomposition for two-stage stochastic linear programs, the authors estimate the coefficients and right-hand sides of the cutting planes using Monte Carlo sampling. The authors present a new theory for estimating a lower bound for the optimal objective value and they 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