Today's computers

always a good way is not to see when a solution is optimal, straight as it regarded, nor there is always a good human understanding way of finding it. It is also important to determine that it is not necessary for someone to settle the work in order an optimal solution to find real. If the model and the mathematical model represent the which is the basis problem correctly, the computer finds it. During it to be can a worrying, in order to retire, being able not do the process of finding an answer in such a way to a computer can be extremely expensive. An increase $6 million over $46 million solution represents an improvement of 13 per cent. Many of us jump over fast past the delimitations and the assumptions in our adoption of resolutions carefully understand and leap right to the release badly defined problems. Management scientists do the straight opposite. Confronted with the meeting of a decision, they spend their whole time on the delimitations and the assumptions and let the computer do, what it is the good on-solved problem. While problems keep larger, it becomes impossible for everyone to the account for the many controversies delimitations and the assumptions. Today's computers could treat you easily a problem for our CFO with 10 million projects and million delimitations. * * * although the term basis of communism philosophy descends of Karl Marx was Vladimir Lenin for getting it to the life responsible. Marx expressed a philosophy; Lenin had to find out, like one her into a working form converts of the government. Nevertheless on the eve of the october revolution, it was free this Lenin had to prepare the details. In a letter only hours before Bolshevik written troops shifted on the city of Petrograd, it locked up, „the point of the ascent are the seizure of the energy; afterwards we see, what we with it to do to be able. “Soviet mathematician and economist Leonid Kantorovich were one of those individuals pointed with which find out to do with the Soviet economy a work too. „For first time in history, “Kantorovich in its assumption lecture for the Nobel Prize said 1975 in the national economy, „developed all means of production discharged in the possession of the people and there the necessity at the centralized and standardized control of the economy of the considerable country.
“Differently than capitalistic national economies, those use prices manufactured by the free market, in order to determine, what keeps produced (the high prices, which cause larger production, low prices, less), production in the Soviet economy depended of the direction of the communist party. Someone somewhere had to decide you, what it receives formed and whom received, it to use. For Kantorovich central planning provided a new way of regarding economically before problems, as it drew after its formal training as a mathematician. In the west, mathematics won fast a predominating in the study of the national economy. If economic, conditions in the mathematical expressions could be expressed, then economic questions could be answered by obviously arranged deductive argumentation. Economists could agree over their mathematical of other opinion to be assumptions, but to be there over that the assumptions did not know an argument would finally lead. As everything it functions • 51 although the problems of Kantorovich and its confronted colleagues of orders of were the size of, those as the CFO problem, the philosophy is larger, was the same. The Soviets limited means had in the kind of the factory capacity, nature resources and work on you and the communist party had objectives, them in the kind of to obtain wanted food and materials production. The question was, like one maximally it obtains objectives with satisfying their limit aids delimitations. Kantorovich developed first a mathematical method for finding the optimal solutions to the problems likes you the CFO problem when working for the laboratory of veneer wood confidence.
the most intensive halfdecade closed 1939 straight as Stalin of the clearing during its rule over the communist party, Kantorovichs method in a brochure was published off, those the mathematical method of production called planning and organization. The relevant climate on the Soviet given connection, the work remained a western scholar unknown for many years. If he discovered his method, discovered Kantorovich also an extraordinary property of problems likes the CFO problem. With looking for optimal solution, its method found also special shade prices, to one for each aid delimitation. In the CFO problem gives it to two such delimitations, the $26 million of capital available now and the $12 million of the capital available in six months. The shade prices for these delimitations are $0,4 million and $3 million, and/or. What are these shade prices? Too this question, attempt using it answers, in order to compute the profitability of each project, which regards the CFO. E.G., using the shade prices which are the costs of the assumption the first project? Project now uses 11 units capital and three units capital in six months. „The costs of “this project using the shade prices (11 ✕ 0,4) + (3 ✕ 3) = $13,4 million. The return on the project is $16 million, thereby „the profit “$16 million actual $13,4 million = $2,6 million. At least regarding the shade prices, we find that the first project is profitable. If you consider that in our optimal solution to the problem of the CFOS (x1 = 1, x2 = 3/4, x3 = 0, x4 = 1 and x5 = 1/4), we decided to accept us the first project in its entireness. In relation to our shade prices this is meaningful. If the project is profitable, we should take up as much of it us, as possible. Extension on this fundamentally idea of measuring of profitability, fails it, that, if we can ourselves a suggested solution for the problem of the CFOS have and shade prices find to meet following profitability conditionally, then must our suggested solution be optimal (the fact that this is not applicable lies on the hand and requires mathematical derivative): 1. Projects, which are completely taken up, are profitable (or to have it a profit of 0). 2. Projects, which are not taken up, are unprofitable (or to have it a profit of 0). 3. All possible projects, which are taken up in a partial amount, are profitability. Regarding project 2, we find that the optimal solution x2 = 3/4. has. The costs is (10 ✕ 0,4) + (4 ✕ 3) = $16 million, and the profit is $16 million - $16 million = $0, as expects. Project 3, which is not taken up, has the costs (5 ✕ 0,4) + (5 ✕ 3) = $17 million and the profit $15 million - $17 million = - $2 52