Dual Simplex

The dual simplex algorithm is an attractive alternative method for solving linear programming problems. Since the addition of new constraints to a problem typically breaks primal feasibility but not dual feasibility, the dual simplex can be deployed for rapid reoptimization, without the need of finding new primal basic feasible solutions. This is especially useful in integer programming, where the use of cutting plane techniques require the introduction of new constraints at various stages of the branch-and-bound/cut/price algorithms. In this article, we give a detailed synopsis of the dual simplex method, including its history and relationship to the primal simplex algorithm, as well as its properties, implementation challenges, and applications