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An exact solution to the problem of transmission line losses with respect to load scheduling is becoming more and more important in view of the large size of the systems. A formulation for this, including the system constraints as a nonlinear programming problem, was first proposed by Carpentier. It is shown that the dimension of the problem can be reduced by considering bus voltage variables alone as problem variables. A penalty function approach for the solution of this problem is described which is computationally more efficient than some of the earlier methods. Finally, two methods for computing the optimal solutions for small changes in loads are described.