Optimization under uncertainty: State-of-the-art and opportunities

Nikolaos V. Sahinidis

Research output: Contribution to journalArticlepeer-review

Abstract

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space that is huge and frequently leads to very large-scale optimization models. Decision-making under uncertainty is often further complicated by the presence of integer decision variables to model logical and other discrete decisions in a multi-period or multi-stage setting. This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty. We discuss and contrast the classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. The advantages and shortcomings of these models are reviewed and illustrated through examples. Applications and the state-of-the-art in computations are also reviewed. Finally, we discuss several main areas for future development in this field. These include development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations.

Original languageEnglish (US)
Pages (from-to)971-983
Number of pages13
JournalComputers and Chemical Engineering
Volume28
Issue number6-7
DOIs
StatePublished - Jun 15 2004

Keywords

  • Approximation algorithms
  • Fuzzy programming
  • Global optimization
  • Stochastic dynamic programming
  • Stochastic programming

ASJC Scopus subject areas

  • General Chemical Engineering
  • Computer Science Applications

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