Robust optimization under correlated polyhedral uncertainty set

• A new uncertainty set named correlated polyhedral uncertainty set is developed.
• The proposed set is advantageous when correlations exist among uncertain coefficients.
• The robust counterpart of a LP problem is developed under the proposed uncertainty set.
• The results of solving sample robust problems are discussed.
• The application of the proposed method in real problems are described.

Uncertain data in practical optimization problems led to emerge of robust optimization approaches, whereby solutions with more stable quality against perturbations are constructed. Furthermore, to avoid over-conservatism, different kinds of uncertainty sets are introduced. In most of these approaches, uncertain coefficients of the problems are assumed to be independent. While in practice, these coefficients are often influenced by several common uncertainty sources which cause dependency among uncertain coefficients. In this research, a new uncertainty set based on estimated correlation matrix of uncertain coefficients is introduced. It is followed by a robust counterpart formulation of the problem using the proposed uncertainty set. To evaluate the performance of the proposed model it is applied on a couple of uncertain optimization problems. The experimental results revealed that when significant correlations between the coefficients exist, the performance of the proposed method is superior to that of the traditional polyhedral uncertainty set. The results are discussed and concluding remarks are made.