Metamodelling techniques in multidimensional optimality analysis for linear programming

Response surface methodology (RSM) and kriging are used to develop a methodology for optimality analysis of linear programs (LPs). Using these techniques, metamodels are developed to predict the optimal objective function value of an LP for various levels of the constraints. These metamodels are valid over multiple critical regions, eliminating the usual requirement of determining which critical region contains the right-hand-side vector of interest. The metamodels are used to determine the responsiveness of the optimal objective function value to changes in the right-hand-side vector while illuminating key relationships between the objective function value and the elements of the right-hand-side vector. In some cases, the metamodels can actually be used as a surrogate model for the entire LP model. The metamodels are tested by comparing the predictions to the optimal solutions obtained by solving the linear programming model. This paper provides a description of the methodology as well as the results from three test problems.