An Operator Theory of Parametric Programming for the Generalized Transportation Problem. I. Basic Theory

摘要

The paper gives a new organization of the theoretical results of the Generalized Transportation Problem with capacity constraints. A graph-theoretic approach is used to define the basis as an one-forest consisting of one-trees (a tree with an extra edge). Algorithmic development of the pivot-step is presented by the representation of a two-tree (a tree with two extra edges). Constructive procedures and proofs leading to an efficient computer code are provided. The basic definition of an operator theory which leads to the discussion of various operators is also given. In later papers the authors will present additional results on the operator theory for the generalized transportation problem based on the results in the present paper. (Author)