A discussion of recent proposals by Gomory and others for solving linear programs involving integer-valued variables. Problems that can be reduced to this class, and thereby solved, are reviewed. It is significant that the reduction can be made for problems involving multiple dichotomies and k-fold alternatives. These problems include those with discrete variables, nonlinear separable minimizing functions, conditional constraints, global minimum of general concave functions, and combinatorial problems such as the fixed-charge problem, traveling-salesman problem, orthogonal latin-square problems, and map-coloring problems.
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