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An algorithm for ranking the basic feasible solutions corresponding to a linear programming problem in increasing order of the linear objective function is described. An application of this algorithm for obtaining the minimal cost solution to a fixed charge problem is given. This algorithm can be applied in general to solve any fixed charge problem. However, the algorithm works efficiently when the problem is nondegenerate and the range in the values of the variable costs is large compared to the fixed charges. This algorithm can also be applied when the fixed charge part of the cost function is replaced by a concave function.
Katta G. Murty (Mon,) studied this question.