Linear Programming in Finance, Accounting and Economics

Sijia Lu 7289928683

Summary

This article is literatures review about five articles or blog posts, which apply linear programming to Finance, accounting and economics. The mathematical method is found of crucial importance in all those fields. The paper reveals how assumptive inference in linear programming throws lumination upon reasonable practice, and how empirical data supports all those theories.

Keywords: finance; accounting; economics; geradlinig programming; expenditure analysis

Linear Programming in Finance

" Application of Linear Programming to Financial Budgeting and the Being of FundsвЂќ explored tips on how to allocate cash in an enterprise by applying thready programming. As Charnes, Cooper and Callier analyzed, in least 3 problems are to get considered to resolve the allowance problem: 1) Plans intended for production, acquisitions, and product sales under selected structure in the firm's possessions, in order to maximize its revenue or reach other goals. 2) The change of the firm's revenue per device change in the structure of the assets. 3) Opportunity cost of the business funds. This article starts with a simple example with one commodity and 1 warehouse. Allow B be the set warehouse potential, A always be the initial stock of inventory in the stockroom, xj become the amount being sold in period j, yj be the quantity to be bought from period t, pj be the product sales price every unit in period l, and cj be the purchase price per unit in period j, then we have

due to the cumulative sales restriction;

due to the factory capacity constraint;

due to the buying constraint;

due to the offering constraint; and

with our aim of increasing

The dual problem is likewise obvious. You should minimize

subject to

and to

in which

As we learned, " dual theorem of linear programmingвЂќ says the two ideal values of the original trouble and the dual problem must be equal. Making use of this theorem, the authors after that reached a fresh method of evaluating assets. Because

,

we have

in which the two sides need to have the same products of evaluate. So it is right now obvious that t*k presents the value per unit of net stockroom capacity and u*k presents the value per unit of initial products on hand in the warehouse. Similarly, consider the financial problem, which includes liquidity restrictions as

wherever j-Оµrepresents obligations and j-r represents receipts, M0 is definitely the initial money available and M is the balance the firm preferred the maintain. By analyzing the dual problem on this, we can get corresponding dual variables for the problem referred to as, say, vk. Again, from your equality all of us found prior to, we can find out that the two sides with the equation have a similar units of measure. It can be then noticed that the v's should be us dollars per product time per dollar spent.

The value of resources or opportunities is of important importance to any business. В So far, by applying the dual theorem, Charnes, Cooper and Miller have created a new method of considering assets or investments. This technique of evaluating is also easy to find out answers. It is brilliant to examine the units of measure instead of try to solve the specific concerns. The interesting thing is that in practical problems, we are able to find accurate meanings of theoretical dual variables.

Then the authors mixed the two former problems together to get a more practical case вЂ“ a stockroom problem with financial constraints. Hence the following fresh constraints are added:

Now if we establish

We'll find the new dual problem:

Below, V1 is a incremental cumulative internal yield rate. Or it is the opportunity price the capital used вЂ“ " it reveals the net total which an additional dollar used the company will accumulate if still left to mature to the end of the planning horizon. вЂќ This is also easy to understand in terms of economics, maximizing earnings can be the same as minimizing the opportunity costs.

The content then experienced several functional problems making use of the dual adjustable evaluating technique....

References: " Application of Geradlinig Programming to Financial Spending budget and the Costing of FundsвЂќ, A. Chares, W. Watts. Coopers, and M. They would. Millerss, The Journal of Business, Volume. 32, Number 1, Jan., 1959 (pp. 20-46)В В

" A Geradlinig Programming Style for Spending budget and Financial PlanningвЂќ, Sumado a. Ijiri, N. K. Levy, and R. C. Lyon, Journal of Accounting Analysis, Vol. one particular, No . a couple of, Autumn, 1963, (pp. 198-212)В

" Prices and Incomes in Thready Programming ModelsвЂќ, John L. Duloy and Roger M. Norton, American Journal of Agricultural Economics, Vol. 57, No . four, Nov., 1975 (pp. 591-600)

" Endogenous Type Prices in Linear Development ModelsвЂќ, Philip B. 3rd there’s r. Hazell, American Journal of Agricultural Economics, Vol. 61, No . 3, Aug., lates 1970s (pp. 476-481)

" Optimum Portfolios Using Linear Programming ModelsвЂќ, C. Papahristodoulou and E. Dotzauer, The Journal of the Detailed Research Society, Vol. fifty-five, No . 14, Nov., 2005 (pp. 1169-1177)