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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 965835, 13 pages
http://dx.doi.org/10.1155/2012/965835
Research Article

Tractable Approximation to Robust Nonlinear Production Frontier Problem

1Department of Economic Mathematics, South Western University of Finance and Economics, Sichuan, Chengdu 610074, China
2Department of Mathematics, Sichuan University, Chengdu 610064, China

Received 4 September 2012; Accepted 24 September 2012

Academic Editor: Jen-Chih Yao

Copyright © 2012 Lei Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Robust optimization is a rapidly developing methodology for handling optimization problems affected by the uncertain-but-bounded data perturbations. In this paper, we consider the nonlinear production frontier problem where the traditional expected linear cost minimization objective is replaced by one that explicitly addresses cost variability. We propose a robust counterpart for the nonlinear production frontier problem that preserves the computational tractability of the nominal problem. We also provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.