Robust optimization of large-scale systems

John M. Mulvey, Robert J. Vanderbei, Stavros A. Zenios

Research output: Contribution to journalArticlepeer-review

1521 Scopus citations


Mathematical programming models with noisy, erroneous, or incomplete data are common in operations research applications. Difficulties with such data are typically dealt with reactively-through sensitivity analysis-or proactively-through stochastic programming formulations. In this paper, we characterize the desirable properties of a solution to models, when the problem data are described by a set of scenarios for their value, instead of using point estimates. A solution to an optimization model is defined as: solution robust if it remains "close" to optimal for all scenarios of the input data, and mndel robust if it remains "almost" feasible for all data scenarios. We then develop a general model formulation, called robust optimization (RO), that explicitly incorporates the conflicting objectives of solution and model robustness. Robust optimization is compared with the traditional approaches of sensitivity analysis and stochastic linear programming. The classical diet problem illustrates the issues. Robust optimization models are then developed for several real-world applications: power capacity expansion; matrix balancing and image reconstruction; air-force airline scheduling; scenario immunization for financial planning; and minimum weight structural design. We also comment on the suitability of parallel and distributed computer architectures for the solution of robust optimization models.

Original languageEnglish (US)
Pages (from-to)264-281
Number of pages18
JournalOperations Research
Issue number2
StatePublished - Mar 1 1995

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Management Science and Operations Research


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