The data of real-world optimization problems are usually uncertain, that is especially true for early stages of system design. Data uncertainty can significantly affect the quality of the nominal solution. Robust Optimization (RO) methodology uses chance and robust constraints to generate a robust solution immunized against the effect of data uncertainty. RO methodology can be applied to any ge...

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Optimization problems due to noisy data are usually solved using stochastic programming or robust optimization approaches. Both requiring the explicit characterization of an uncertainty set that models the nature of the noise. Such approaches tightly depend on the modeling of the uncertainty set. In this paper, we introduce a framework that implicitly models the uncertain data. We define the ge...

Optimal solutions of Linear Programming problems may become severely infeasible if the nominal data is slightly perturbed. We demonstrate this phenomenon by studying 90 LPs from the well-known NETLIB collection. We then apply the Robust Optimization methodology (Ben-Tal and Nemirovski [1-3]; El Ghaoui et al. [5,6]) to produce “robust” solutions of the above LPs which are in a sense immuned agai...

In this paper, we reformulate the conventional DEA models as an imprecise problem and propose a novel method for evaluating DMUs when inputs outputs are fuzzy and/or ordinal or vary in intervals. For purpose, convert all data into interval data. order to each number data, use nearest weighted approximation of numbers by applying weighting function, one. manner, could The presented determine eff...