Kornai János: “Man-Machine Planning“, Economics of Planning, 1969, Vol. 9, No. 3, pp. 209-234. Original: 5.42, in Hungarian, 1969.
ECONOMICS OF PLANNING Vol. 9, No. 3, 1969 Printed in Norway Man-machine planning1 J. Kornai2 Institute of Economics Hungarian Academy of Sciences, Budapest 1. INTRODUCTION For the solution of large-scale linear programming problems, it may be useful to resort to what have been called decomposition algorithms. A number of methods have been developed in recent years. Experience has shown, however, that slow convergence to the optimum is a common characteristic of all these methods.3 In the following, an approximation method for solving decomposable problems is presented.4 The underlying mathematical concept is not original; the procedure may be considered as a naive heuristic variant of the Dantzig-Wolfe [2] decomposition algorithm (hereafter, the D-W method.) It cannot guarantee that the optimum of the original, undecomposed problem will be reached. It may, however, help to obtain as early as the first iteration programs with a comparatively favorable objective function value, which also lend themselves readily to practical interpretation. The subject is treated as follows: In Chapter 2, definitions are given and assumptions presented. Chapter 3 describes the approximation method in general form. Chapter 4 recommends some computational “tricks” to increase the efficiency of the 1 I am grateful to I. Danes, T. Lipták, B. Martos, R. Norton for useful comments. 2 The author is Professor of Economics at the Institute of Economics, Hungarian Academy of Sciences, Budapest. 3 No investigations are known to have been carried out thus far with the aim of comparing, on the basis of genuinely representative computation series (i.e., problems of sufficient size and variety of structure), the practical computational efficiency of the various non-decomposition, and decomposition, exact and approximative methods of linear programming. 4 For a first description see [4].