A Hierarchy of Bounds for Stochastic Mixed-Integer Programs

38 Pages Posted: 3 Jun 2009

See all articles by Burhaneddin Sandikci

Burhaneddin Sandikci

University of Chicago - Booth School of Business

Nan Kong

Purdue University

Andrew J. Schaefer

University of Pittsburgh

Date Written: June 3, 2009

Abstract

Strong relaxations are critical for solving deterministic mixed-integer programs. As solving stochastic mixed-integer programs (SMIPs) is even harder, it is likely that strong relaxations will also prove essential for SMIPs. We consider general two-stage SMIPs with recourse, where integer variables are allowed in both stages of the problem and randomness is allowed in the objective function, the constraint matrices (i.e., the technology matrix and the recourse matrix), and the right-hand side. We develop a hierarchy of lower and upper bounds for the optimal objective value of an SMIP by generalizing the wait-and-see (WS) solution and the expected result of using the expected value (EEV) solution. These bounds become progressively stronger but, generally, more difficult to compute. Our numerical study indicates that the bounds developed in this paper can be very strong relative to those provided by stochastic linear programming relaxations.

Suggested Citation

Sandikci, Burhaneddin and Kong, Nan and Schaefer, Andrew J., A Hierarchy of Bounds for Stochastic Mixed-Integer Programs (June 3, 2009). Chicago Booth Research Paper No. 09-21. Available at SSRN: https://ssrn.com/abstract=1413774 or http://dx.doi.org/10.2139/ssrn.1413774

Burhaneddin Sandikci (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Nan Kong

Purdue University ( email )

610 Purdue Mall
West Lafayette, IN 47907
United States

Andrew J. Schaefer

University of Pittsburgh ( email )

135 N Bellefield Ave
Pittsburgh, PA 15260
United States

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