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This article presents the simplex method for optimum time coordination of directional overcurrent relays. The main contribution of this article is the application of the simplex method in spite of the inherent unsuitability of the problem. This is achieved by applying the simplex algorithm to the dual of the problem. Furthermore, there are reductions in the number of calculations and memory requirement, as the artificial variables need not be introduced. A comparison with other variants of the simplex algorithm and the genetic algorithm is also presented. It has been shown that the proposed method is applicable for finding the optimum coordination, even when a variety of overcurrent relays is present in the system.