A Note About Kantorovich's Paper, “Mathematical Methods of Organizing and Planning Production”

Discussion on two early papers of Professor Kantorovich, from 1939 and 1949, that proved to be remarkable documents in the history of management science, of linear programming, and of economic theory in general. The 1949 paper discusses transportation models for a single commodity and for many commodities (including empty vehicles), and a single-commodity model for a capacitated network, with applications to sections of the Russian railroad network. All problems considered in the 1939 paper reprinted in this issue are what would now be called linear programming problems. The coefficient matrices of the problems labeled “A” and “B” exhibit special structures somewhat similar to that of the transportation problem matrix. Problem “C,” while appearing still to have a somewhat special structure, is in fact equivalent to the general linear programming problem.