Sun Jie, Ph.D., University of Washington, USA. He is currently an academician of Singapore-MIT, Associate Professor, Department of Decision Science, Singapore National University, Department of Decision-making, Department of Asia-Pacific Operations. He was held in Beijing Tsinghua University, University of Washington, USA and Northwestern United States. The research scope includes operational development, optimization, random decision making and e-commerce.
With the development and application of strong algorithms, the problem of linear planning can be solved is increasing. In history, there is no mathematical approach to creating such huge wealth like a linear planning, and there is such a direct impact on the process of history.
The size of modern companies is increasing, and management is increasingly complex. The analysis and judgment of management issues is performed by manpower. For example, the inventory and distribution of thousands of parts on automotive assembly lines, banks in the investment and management of multiple stock bonds, or the loading and unloading and scheduling of ports of portions, must be completed with the help of the computer. Computers always operate in accordance with some mathematical model. Therefore, modern entrepreneurs understand some mathematical models related to management should be very important. In this paper, it is a mathematical model called "Linear Plan". We don't introduce the specific content of this model, just talk about the history of this model and related stories. I hope that the reader can understand how to manage how to promote mathematics, and how the mathematics progress has promoted the management of innovation. From the military transfer to the commercial 20th century, the Academician Kanglovich, the Soviet Academy of Sciences, wrote a book, telling the math method of solving economic problems, which has been discussed. However, linear planning truly becomes a discipline and is applied, or starting from the Second World War. At that time, a batch of British scientists served in the army may, in order to keep their work, their work is called "linear planning", which is actually used in today. Thereafter, there are similar institutions in the US military. At that time, Danzg, who was served in the US Air Force, summed him to solve some methods of some management issues, and proposed "Single Method". This method has been confidential until 1947 after the war, when Danzg left the army, he transferred to the professor of Stanford University. At the same time, a group of scientists who transferred from the army to the business community, also put them in handling the methods studied in military issues, applied to the management of industrial and commercial, making the post-war management scientific and vigorous development. Plus high-speed computers, a large number of mathematical methods, are widely used in management. Condoovic has obtained the Nobel Prize due to the creation of this aspect; and Danzg has been hailed as the "linear plan". To illustrate what is linear planning, we will quote a problem with Dattsg to make an example. This problem is called "Square meals". In order to ensure the nutrition of soldiers, the US Air Force stipulates that a certain nutrient component, such as protein, fat, vitamin, etc., and has quantitative provisions. Of course, these nutrients can be provided by a variety of different foods, such as milk to provide proteins and vitamins, butter provide proteins and fat, carrots to provide vitamins, and so on. Due to the limited restriction of war conditions, the food type is limited, and it is necessary to reduce costs, so in a box of package, how to determine the number of foods, so that it can meet the needs of nutrients, but also reduce costs, and put these requirements Mathematical equation, solving with a simple form, it is the best meal scheme. Although modern management issues are thousands of variables, it is always necessary to use limited resources to pursue the largest profit or minimal cost, so many of them can always be in linear planning. In mathematics language, linear planning issues are extremely or minimal issues of linear functions under linear constraints. Linear planning issues, small only dozens of hundreds of variables, such as a meal problem, optional foods, and a large amount of millions of millions of variables. Although the computer is getting faster, there is always a problem that the computer can also solve the problem. Therefore, in the 1950s and 1960s, mathematicians are committed to the improvement of simple forms, so that they can solve increasing problems. This time can be said to be a simple era of simplicity. During this time, mathematician has also done a careful analysis of the advantages and disadvantages of the algorithm. Generally speaking, the computer always makes a question of the question of the problem with limited four operations (addition and subtraction). If the algorithm is good, you can measure the number of computers.
Given a problem, how many times need the computer you need to solve this problem? Of course, this number of calculations is related to the size of the problem. The bigger the problem, the more variables, the more computments needed. This number of computing is the dependence on the size of the problem, and it can be used to determine the good and bad of an algorithm. A good algorithm, the increase in the number of calculations is less sensitive to the problem. Converse, bad algorithm, when the problem is slightly bigger, the number of calculations increases, so it is not possible to solve big problems. According to this standard, it can be proved that a simple form is a bad algorithm. This result was obtained by two professors at Washington University in 1971. This caused a sensation at the theoretical community at the time. It turned out that we used such a single-style algorithm, it was actually a "bad" algorithm! Constantly explore better algorithms, have there any good algorithm for solving linear planning? This issue has two possible answers. One is that there is no, that is, the characteristics of linear planning itself determines that this problem is impossible to have a good algorithm. Another possible answer is there. That is to say, the linear plan is not so bad, or can have a good algorithm, but human beings have not found that algorithm. In 1979, a nameless Soviet mathematician Haki Yang, invented a new algorithm to solve the problem of linearization. He is theoretically proven that this "ellipsoid method" algorithm is a good algorithm. This makes a problem for the eight-year-old case, ie the linear planning has no good algorithm, completely solved. Harchi Yang himself is therefore a gun. On the other hand, his discovery has also aroused a new round of boom on linear planning research, quite a bit similar to the second battle. Many people come up with a growing problem to let the ellipsoid algorithm. Surprisingly, in all calculation experiments, the ellipsoidal law is in a simple hand. The so-called ginger is still old spicy, in theory "bad" single-form method, in practice, far better than the theoretical "good" ellipsoid method. This matter brings a huge spiritual crisis to mathematicians: the theory is not in line with the actual situation, is it our theory itself? If the theory is wrong, then in the past decade, we did a bunch of waste paper in this theoretical guidance. This confusion does not last too long. In 1984, a young researcher in Bell Lab, USA, claims that he invented a "inner point algorithm" in theory, in theory, in fact, actually faster than simple . His paper is published, it should be a good thing, but during a period, it has caused an academic debate. What is going on? The problem is enrolled in the confidentiality system implemented in the Bell Laboratory working in Kamar, making Kamar's details of his algorithm. Therefore, after reading his paper, he could only recognize his previous conclusions. Better than the simple method. In fact, some scientists have different results of the computer program trial in accordance with the theory of Carmaka, and the calculated results announced by Carmara. When a scientific experiment, you can't be regenerated by others, how do you determine the authenticity of this experiment? In order to eliminate the public's suspicion, Kamar came to the University of California to cooperate with graduate students, and made a set of public computer programs, including various details. The calculation results of this set of procedures, although Camar in the Bell Laboratory, but has exceeded a simple formwork on certain important issues. The doubts in the hearts of people have gradually eliminated. Kamar's internal point algorithm has been 16 years of history. In this 16 years, the internal point algorithm has a profound impact on linear planning research.
