| Popis: |
A matrix N is Leontief if it has exactly one positive entry per column and there exists a nonnegative x such that Nx > 0. A Leontief flow problem is a linear-programming problem of the form min{c^Tx |nx = b; x >= 0}, where N is a certain type of Leontief matrix. It is shown that for b > 0 this problem can be solved in O (n^2UlognpU) pivots by the simplex method using Dantzig's rule for choosing the entering variable, where n is the number of variables, p is the largest entry of N in absolute value, and U is a valid upper bound on any extreme-point solution. Classes of problems where this is a strongly polynomial bound are identified. |
Full Text from ScienceDirect