The control problem and Dynamic programming is a powerful tool in economics and management. We review the dynamic programming problem from its beginning up to its present stages. A problem which was involved in physics and mathematics in I 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” century. This branch of Mathematics stated its actual development under the name control problem from the second half of 20th century. Its solution was made possible through the dynamic programming method, and maximum principle. Experts in economics and management started using these methods. Then In various works from the 1970s. The stochastic optimum control was used. In this paper we will consider from the first article in maximizing the profit of a firm up to its recent applications in economics and management.
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