Monte Carlo bounding techniques for determining solution quality in stochastic programs

  • Mak W
  • Morton D
  • Wood R
  • 123


    Mendeley users who have this article in their library.
  • 262


    Citations of this article.


A stochastic program SP with solution value z* can be approximately solved by sampling n realizations of the program's stochastic parameters, and by solving the resulting `approximating problem' for (x*n, z*n). We show that, in expectation, z*nis a lower bound on z* and that this bound monotonically improves as n increases. The first result is used to construct confidence intervals on the optimality gap for any candidate solution x to SP, e.g., x = x*n. A sampling procedure based on common random numbers ensures nonnegative gap estimates and provides significant variance reduction over naive sampling on four test problems.

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Get full text


  • Wai Kei Mak

  • David P. Morton

  • R. Kevin Wood

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free