Kornai János: “Mathematical Programming Models in Industrial Development Planning“, Industrialization and Productivity, UNIDO Bulletin, New York, UN, 1975, Vol. 22.
Mathematical programming models in industrial development planning by Janos KORNAI* Introduction This article is based on the models employed in Hungary since the late 1950s for the mathematical planning of industrial development. In constructing the models, the special conditions of the country had to be considered, of course. Hungary has a centrally planned economy; the five-year economic plans contain detailed estimates covering most industrial investment projects. It is a country in which agriculture still plays the major role, but in which manufacturing has developed at an accelerated rate over the past 10-20 years. The Government has set itself the task of improving the country’s position in the international division of labour and achieving a high growth rate. The endowments and problems of Hungary are similar to those of a number of other countries. Therefore, the mathematical models employed in Hungary should also be useful beyond its frontiers. Although the concrete structure and numerical data of these models reflect the special characteristics of that country, numerous features of the mathematical planning methodology evolved there are generally applicable. These features of general validity will be stressed in this article. It is the author’s intention that the reader should become acquainted, not just with the Hungarian methods but with a tested methodology that may be applied in any country. This article first describes the programming model of one sector, then explains the linking of the models of several sectors and the methods of their collective planning. Next, the application possibilities of the models are described, and finally, some of the special difficulties encountered in model construction are discussed. It is assumed throughout that the reader has a knowledge of the conceptual apparatus of mathematical programming and of matrix algebra. I. The sector model Suppose that a group of mathematical planners is assigned to construct a model of the development plans for one of the country’s industrial sectors; it does not, at the moment, matter which. They must first ask themselves what questions they are trying to answer with the aid of the model. We shall call these questions “decision problems”. A. Decision problems The type of model to be described below is designed to give a simultaneous answer to the following eight decision problems: 1. What products should the sector be able to produce? What should the product pattern of the sector’s total output be? How much of each product should the sector produce? The problem here is not to determine the production programme of a factory in full detail for years or decades in advance. This will be worked out in due course by the factory’s programming department in yearly or monthly breakdowns. In our problem, the products have to be aggregated into product groups that must be distinguished from each other from the point of view of investment decisions. Thus, in the model of the metallurgical sector we must plan the quantity of crude iron, steel, plate etc. that the country should produce. However, it will not be necessary to decide on the proportion of the plates of 5-mm and 6-mm thickness. The former, more general proportions affect investment; the latter, more detailed proportions affect only the specific structure of production carried out on the basis of a given investment capital and so do not fall within the scope of long-term industrial development planning. Decision problem 1 is thus the determination of the output structure of production. 2. The first problem was what to produce and how much of it. However, the question, How should ♦Computing Centre of the Hungarian Academy of Sciences, Budapest.