Studies in the mathematical theory of decentralized resource-allocation

Abstract: (This dissertation was submitted, in May 1971, to the Graduate School of Business, Stanford University. It was published by EFI in June 1972.)This is a research report about decentralization in economic systems. Decentralization is an important management technique with obvious advantages and disadvantages to the management practitioner. There is a rather large body of literature which deals with practical aspects of decentralization: the proper degree of centralization or decentralization in large organizations, how best to design decentralized administrative systems, etc. This report does not belong to that body of literature, that may as well be admitted at once. Rather, this report is a more theoretical discussion of some facets of decentralization in economic systems. However, it was written in the hope that theoretical discussions of this kind will nevertheless provide insights of value for practical decision-making in organizations.The first half of this research report investigates the applicability of some different decentralization principles, or methods, such as the price mechanism, which have been proposed in the literature. This is done within the context of a highly simplified and idealized model organization.It will become evident to the reader that decomposition theory of mathematical programming plays a very important role in this report. A new decomposition algoritm for linear programming problems is also given in the report.