Linear Programming in Finance, Accounting and Economics
Linear Programming in Finance, Accounting and Economics
Sijia Lu 7289928683
Abstract
This article is literatures review about five articles, which apply linear programming to Finance, accounting and economics. The mathematical method is found of crucial importance in those fields. The paper shows how theoretical inference in linear programming throws light upon realistic practice, and how empirical evidence supports those theories.
Keywords: finance; accounting; economics; linear programming; investment analysis
Linear Programming in Finance
“Application of Linear Programming to Financial Budgeting and the Costing of Funds” explored how to allocate funds in an enterprise by applying linear programming. As Charnes, Cooper and Miller analyzed, at least three problems are to be considered to solve the allocation problem: 1) Plans for production, purchases, and sales under certain structure of the firm’s assets, in order to maximize its profit or reach other objectives. 2) The change of the firm’s profit per unit change in the structure of the assets. 3) Opportunity cost of the firm’s funds.
The article starts with a simple example with one commodity and one warehouse. Let B be the fixed warehouse capacity, A be the initial stock of inventory in the warehouse, xj be the amount to be sold in period j, yj be the amount to be sold in period j, pj be the sales price per unit in period j, and cj be the purchase price per unit in period j, then we have
due to the cumulative sales constraint;
due to the warehouse capacity constraint;
due to the buying constraint;
due to the selling constraint; and
with our goal of maximizing
The dual problem is also obvious. It is to minimize
subject to
and to
where
As we learned, “dual theorem of linear programming” says that the two optimal values of the original problem and the dual problem should be equal. Using this theorem, the authors then reached a new method of evaluating assets.
Because
, we have
in which the two
Sijia Lu 7289928683
Abstract
This article is literatures review about five articles, which apply linear programming to Finance, accounting and economics. The mathematical method is found of crucial importance in those fields. The paper shows how theoretical inference in linear programming throws light upon realistic practice, and how empirical evidence supports those theories.
Keywords: finance; accounting; economics; linear programming; investment analysis
Linear Programming in Finance
“Application of Linear Programming to Financial Budgeting and the Costing of Funds” explored how to allocate funds in an enterprise by applying linear programming. As Charnes, Cooper and Miller analyzed, at least three problems are to be considered to solve the allocation problem: 1) Plans for production, purchases, and sales under certain structure of the firm’s assets, in order to maximize its profit or reach other objectives. 2) The change of the firm’s profit per unit change in the structure of the assets. 3) Opportunity cost of the firm’s funds.
The article starts with a simple example with one commodity and one warehouse. Let B be the fixed warehouse capacity, A be the initial stock of inventory in the warehouse, xj be the amount to be sold in period j, yj be the amount to be sold in period j, pj be the sales price per unit in period j, and cj be the purchase price per unit in period j, then we have
due to the cumulative sales constraint;
due to the warehouse capacity constraint;
due to the buying constraint;
due to the selling constraint; and
with our goal of maximizing
The dual problem is also obvious. It is to minimize
subject to
and to
where
As we learned, “dual theorem of linear programming” says that the two optimal values of the original problem and the dual problem should be equal. Using this theorem, the authors then reached a new method of evaluating assets.
Because
, we have
in which the two
References: “Application of Linear Programming to Financial Budgeting and the Costing of Funds”, A. Chares, W. W. Coopers, and M. H. Millerss, The Journal of Business, Vol.32, No.1, Jan., 1959 (pp. 20-46) “A Linear Programming Model for Budgeting and Financial Planning”, Y. Ijiri, F. K. Levy, and R. C. Lyon, Journal of Accounting Research, Vol.1, No.2, Autumn, 1963, (pp. 198-212) “Prices and Incomes in Linear Programming Models”, John H. Duloy and Roger D. Norton, American Journal of Agricultural Economics, Vol. 57, No. 4, Nov., 1975 (pp. 591-600) “Endogenous Input Prices in Linear Programming Models”, Peter B. R. Hazell, American Journal of Agricultural Economics, Vol. 61, No. 3, Aug., 1979 (pp. 476-481) “Optimal Portfolios Using Linear Programming Models”, C. Papahristodoulou and E. Dotzauer, The Journal of the Operational Research Society, Vol. 55, No. 11, Nov., 2004 (pp.1169-1177)