چکیده:
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
17th 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 20th
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.
خلاصه ماشینی:
"During these years, the economists who were interested in the models of Optimal Growth Economy which (Ramsey), and experts of management who favored Dynamic Programming in discrete form used these methods.
This optimization is independent of time; however, in dynamic programming all variable S are functions of time and the optimal path is obtained by control problem (5).
Uzawa reaches the following control problem in his article titled Optimum Technological Change: an Aggregative Model of Economic Growth[17]: (18) Where , is aggregate production function at each moment of time, , and the state of Technological knowledge at time, , is represented by the efficiency in labor, , it means is labor efficiency, out put per capita, aggregate capita labor ratio, labor allocation productive sector, investment ratio, and is the interest rate.
Temporal Aggregation in Multi-sector Economy with Endogenous Growth[19], published in the Journal of Economic Dynamic and Control in 2001, reference the Model is: of increase labor efficiency equal the rate of increase the capital labor ratio, .
Temporal Aggregation in Multi-sector Economy with Endogenous Growth[19], published in the Journal of Economic Dynamic and Control in 2001, reference the Model is: dt 0 0 Since and Equation 10 (Bellman Equation) change to: (22) and the boundary condition remains, as before: To clarify the issue we refer to a model by Metron[20], concerns allocating of personal wealth among current consumption, risk averse investment and riskul investment without transaction costs."