1912 65438+10/9, Leonid Kantrovich was born in a doctor's family in Petersburg, Russia.

1926, Kantrovich graduated from high school and was admitted to the Mathematics Department of Leningrad University. When he was in college, he liked function theory best. Kantorovich cultivated his research ability in this field and wrote many papers. At that time, because there were few domestic publications, he sent them abroad for publication. 1930 graduated from Kantrovich University and submitted two excellent papers to the first all-Soviet Mathematics Conference.

Before 1975, almost all the winners of the Nobel Prize in Economics were economists from Western Europe and North America. However, in 1975, the former Soviet scholar Leonid Kantrovich won this honor. He won this prize because he pushed the traditional economic problem of optimal utilization of resources from qualitative research and general quantitative analysis to the realistic measurement stage; It has made a pioneering contribution to the establishment and development of linear programming method, an important branch of modern economic applied mathematics.

In scientific research, the most taboo is "one mountain looking at another." Kantrovich is not like this. He focuses on analytic function theory. Analytic function theory is the main branch of complex function in function theory. 1934, after graduating from Kantrovich University for four years, he was promoted to be a professor at Leningrad University with excellent mathematics results. 23-year-old, got his doctorate without defending his thesis.

Kantorovich then continued to delve into functional analysis. Functional analysis is an abstract space theory about functions. He studied closely around function theory, analytic function theory and functional analysis step by step, which laid a solid foundation for his great contribution to mathematics and economics later.

China has two idioms: "Perseverance" and "Dripping water wears away a stone". This just sums up Kantrovich's excellent temperament in his youth.

1937, the laboratory of the All-Soviet Plywood Trust Center put forward a production problem to the Institute of Mathematics and Mechanics of Leningrad University, where Kantrovich is located: there are eight machine tools, which need to produce five different types of plywood, and each machine tool has different abilities to produce these five types of plywood. Machine tool A is good at producing this model and machine tool B is good at producing that model. How to allocate the tasks of each machine tool reasonably, so as to maximize the total output of each plywood and make its output reach a predetermined proportion for supporting use?

The functional analysis studied by Kantorovich is a very abstract mathematical theory. Faced with the above production problems, he did not abandon his attitude, but studied it with great enthusiasm.

Kantorovich gave full play to his mathematical talent, and finally put forward a simple and effective calculation method, "multiplier method". The essence of this method is that it does not need to solve m unknown variables, but only needs m multipliers λ to solve the whole problem.

1938, Kantorovich first proposed this method for solving linear programming problems-the multiplier method, which was a great achievement, and opened the door for solving optimization programming problems. This has a far-reaching impact on the development of modern applied mathematics and economics. At this time, Kantrovich was only 26 years old. Simplex method, which is often used to solve linear programming problems, was invented by American mathematicians Denzel and Huo Weici in 1947, nearly ten years later than Kantrovich.

1949, the former Soviet government awarded him the Kantrovich Stalin Prize in recognition of his achievements in mathematical research.

In the face of honor, Kantrovich did not rest on his laurels, but moved on. He explored how to organize and plan production optimally for a single enterprise, and then rose to a higher level, that is, how to implement optimal planning management for the whole national economy and how to realize the optimal utilization of resources within the whole national economy.

As early as 65438+70s, Adam Smith, a British classical economist, put forward the role of "invisible hand" in resource allocation and production regulation in The Wealth of Nations. His "invisible hand" reflects the role of price mechanism under the condition of free competition. Since then, many economists around the world, such as Marshall and Pigou in the United States, Pareto and Barron in Italy, have discussed the optimal allocation and utilization of resources. However, these studies only stay in theoretical explanation and general mathematical expression.

Kantorovich established a linear mathematical model for optimal utilization of resources, and applied the method of solving multipliers to solve various multipliers. These multipliers are a measure of resource scarcity, and a measure of labor consumption when enterprises adopt different resources and choose different production methods. He called these multipliers "objectively constrained valuation" in the sense of economics.

1965, in recognition of his achievements in applying mathematical methods in economic analysis and planning, the Soviet government awarded him the Lenin Prize.

Some people commented that looking back on Kantrovich's life will make people see how he used mathematics to create a powerful branch of economics.

1975, 63-year-old Kantrovich and American economist Kupmans won the Nobel Prize in Economics. When receiving the prize, he delivered a speech entitled "Application of Mathematics in Economy: Achievements, Difficulties and Prospects". He said: "The application of mathematical methods in the economy will not live up to our hopes for it, and it will make great contributions to economic theory and practical work."

Kantorovich pushed the traditional economic problem of optimal utilization of resources from qualitative research and general quantitative analysis to the realistic measurement stage, and made a pioneering contribution to the establishment and development of linear programming method, an important branch of modern economic applied mathematics.

In the thought of real economics, Kantorovich first put forward a method to solve linear programming problems-solving multiplier method in 1938. This is a pioneering contribution to modern applied mathematics, and has since opened the door to solving the optimal planning problem. Using the multiplier method to solve linear programming problems has extensive and important application significance. Kantorovich pointed out that there are two ways to improve the labor efficiency of enterprises. One is the improvement of technology, and the other is the reform of production organization and planning. In the past, the latter method was rarely used because there was no necessary calculation tool. The multiplier method opens up a realistic prospect for solving linear programming problems and scientifically organizing and planning production. He extended this method to a series of practices. Such as rational distribution of machine tools and machinery, minimizing waste, making full use of raw materials and fuel, effectively organizing the transportation of goods, and arranging the layout of crops most appropriately. To sum up, the general procedure to solve this kind of problem is to establish a mathematical model first, that is, according to the conditions of the problem, express the quantitative relationship among production objectives, resource constraints and required variables with linear equations, and then solve the calculation. In some countries' mathematics and economics books, this kind of model is often called "mathematical model of Kantrovich problem".

The above research is about how to organize and plan production scientifically within an enterprise.

Later, when he was studying how to apply the linear programming method between the enterprise and the whole national economy, he realized that the multiplier λ-which he called the "balance index"-played a unique role in measuring the scarcity of resources, selecting the most reasonable mode of production, compiling the optimal plan of the national economy, and coordinating the overall interests of the country and the local interests of enterprises. So he changed the multiplier λ to "objectively limited valuation" (shadow price).

Objective constraint valuation includes the valuation of various products and the valuation of various resources. The so-called objective constraint evaluation of products is the complete labor consumption necessary to produce each product under the optimal scheme. It includes the consumption part of transferred materials and the newly added labor consumption part in production. The so-called objective constraint evaluation of resources is the amount of labor needed to save a certain resource of a unit under the optimal scheme; In other words, under the optimal scheme, the amount of labor that can be saved by using a certain resource of a unit.

The objective constraint evaluation proposed by Kantorovich can realize the optimal allocation and utilization of resources in the whole society. At this time, the whole society can achieve maximum production with the least labor consumption under the existing resources. The resulting production plan is called the optimal plan. Sometimes, target-constrained valuation is called optimal planned price.

This is the concrete embodiment of his innovation, popularization and development of the theory of optimal utilization of resources. According to the requirements and premises that the optimal plan must meet, he put forward the static and dynamic models of production planning. Static model is suitable for short-term planning, because the time is short and the production conditions can be assumed unchanged; Dynamic model is suitable for long-term planning, when production conditions (such as capital construction investment and exploitation of new resources) will change. Both static and dynamic models are linear programming problems, which are relatively simple and have the same solution method. However, dynamic models sometimes require special solutions. If the model contains few factors, dynamic programming can be applied.

Stochastic programming was put forward by Denzel 1955 in America. Kantorovich's contribution in this respect lies not in this new method itself, but in its application in making the optimal plan. In the linear programming model, there is a very important assumption, that is, the coefficient ai and the resource bi are positive data, that is to say, the planning agency has absolutely accurate information about the uncontrollable parameters of the model. Under the condition that the basic characteristics of the economic system will not change significantly, the above assumption can be established.

But in the long-term plan, mistakes will inevitably occur. Kantrovich believes that the future new technology, demand, natural resources, crop yield and consumption quota are all random variables, and only a possible numerical range can be known with a certain probability. If the randomness of uncontrollable parameters is not considered in long-term planning, planning decisions may make serious mistakes. In the study of stochastic programming, he proposed a two-stage stochastic programming model.

In his view, the positive model can't combine the two stages of the original plan and its adjustment, but the two-stage stochastic programming model can do this, that is, establish a model for selecting plans under uncertain conditions. The first stage is to minimize the expected cost of the implementation plan, and the second stage is to maximize the average effect obtained from the original plan and its adjustment. The idea of multi-stage stochastic programming model is similar to that of two-stage model.