Application of Linear Programming to Financial Budgeting and the Costing of Funds

Abstract

T HE purpose of this paper is to explore ways in which the theorems and computational apparatus of linear programming might be brought to bear on the allocation of funds within an enterprise. The rational deployment of a firm's resources requires (simultaneous) consideration of at least the following closely related questions. 1. Given the structure of the firm's assets, what operating program-in the sense of plans for production, purchases, and sales over the relevant planning interval-will the firm the greatest prospective net returns in the light of its profit and other objectives? That linear programming can contribute to a solution here has been amply demonstrated by its many successful applications to such planning problems (some quite large) in a variety of contexts.' For a number of reasons reported applications have so far been concentrated heavily in the production area; but, as we shall try to show, there is no reason why the same techniques cannot be used for financial planning or, more to the point, joint operating and financial planning. 2. What is the yield to the firm of each of the various possible changes in its asset structure, assuming that these assets are employed to maximum advantage? Here linear programming offers a way of bypassing some of the technical difficulties which have been encountered in connection with attempts to evaluate projects (as prosposed, e.g., in [16] or [21]) on the basis of their rates of return.2 In addition, with a programming formulation, some of the harder parts of the task of tracing through the interactions of proposed investments with each other and with existing facilities can be left to the mathematics. 3. What is, the opportunity cost of funds in the firm, in the sense of the prospective rate of on an increment of funds committed to the enterprise * This paper is a revised version of an ONR research report which was first presented at the Symposium on Operational Models, jointly sponsored by the Chemical Corps Engineering Command and New York University held at Army Chemical Center, Maryland, January 17, 1957. Part of the research underlying this paper was undertaken for the project Planning and Control of Industrial Operations at Carnegie Institute of Technology and part for the project Methodological Aspects of Management Research at Purdue University. Both projects are under contract with the United States Office of Naval Research. Reproduction of this paper in whole or in part is permitted for any purpose of the United States government, Contract Nonr-760-(01), Project NRO47-011, and Contract Nonr-1100-(05), Project NR047-016.