Improved Benders decomposition approach to complete robust optimization in box-interval

Abstract

Robust optimization is based on the assumption that uncertain data has a convex set as well as a finite set termed uncertainty. The discussion starts with determining the robust counterpart, which is accomplished by assuming the indeterminate data set is in the form of boxes, intervals, box-intervals, ellipses, or polyhedra. In this study, the robust counterpart is characterized by a box-interval uncertainty set. Robust counterpart formulation is also associated with master and subproblems. Robust Benders decomposition is applied to address problems with convex goals and quasiconvex constraints in robust optimization. For all data parameters, this method is used to determine the best resilient solution in the feasible region. A manual example of this problem's calculation is provided, and the process is continued using production and operations management–quantitative methods (POM-QM) software.