Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
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An equality constrained optimization problem equivalent to the transportation problem with m sources and n destinations is described. The optimality condition and some algebraic characterizations of the problem are investigated using its Hessian matrix. In addition, several algebraic characterizations of an equivalent case of the transportation problem are given using the spectral decomposition and generalized inverses of its coefficient matrix. It is shown that the transportation problem and its equivalent case have common algebraic characterizations.