Abstract
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*n is 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 47-56 |
| Number of pages | 10 |
| Journal | Operations Research Letters |
| Volume | 24 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 1999 |
Funding
David Morton's research was partially supported by the Summer Research Assignment program at The University of Texas at Austin and by the National Science Foundation through grant DMI-9702217. Kevin Wood's research was supported by the Air Force Office of Scientific Research and the Office of Naval Research. The authors thank John Birge, Julia Higle, and Suvrajeet Sen for valuable discussions, thank Andrzej Ruszczyński and Artur Świetanowski for access to their regularized decomposition code and thank the associate editor, David Goldsman, for many helpful comments.
ASJC Scopus subject areas
- Software
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics