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 model 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.

We develop a framework for combining strategic benchmarking with efficiency benchmarking of the services offered by bank branches. In particular, a cascade of efficiency benchmarking models is developed guided by the service-profit chain. Three models---based on the nonparametric technique of Data Envelopment Analysis---are developed in order to implement the framework in a practical setting: (i) an operational efficiency model, (ii) a service quality efficiency model, and (iii) a profitability efficiency model. The use of the models is illustrated using data from the branches of a commercial bank. Empirical results indicate that we gain superior insights by analyzing simultaneously the design of operations together with the quality of the provided services and profitability, rather than by benchmarking these three dimensions separately. Relationships are also established between operational efficiency and profitability, and between operational efficiency and service quality.banking services, DEA, efficiency, profitability, service quality

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