An extensive simplex method for mapping global feasibility

Understanding the global feasibility of engineering decision-making problems is fundamental to the synthesis of rational engineering decisions. An Extensive Simplex Method is presented to solve the global feasibility for a linear decision model relating multiple decision variables to multiple performance measures, and constrained by corresponding limits. The developed algorithm effectively traverses all extreme points in the feasible space and establishes the graph structure reflecting the active constraints and their connectivity. The algorithm demarcates basic and nonbasic variables at each extreme point, which is exploited to traverse the active constraints and merge the degenerate extreme points. Finally, a random model generator is presented with the capability to control the matrix sparseness and the model degeneracy for an arbitrary number of decision variables and performance measures. The results indicate that all these model properties are significant factors which affect the total number of extreme points, their connected graph, and the global feasibility.