Initial funds are distributed between the two companies over n years. Income earned in a k-end of the business year, I and II, depending on the means Xk and yk, respectively, allocated to the enterprises I and II in the k-th year, and the amount of investment in the enterprise funds I and II, respectively, over the previous k -1 years. Of these same factors also depends amount of funds that are returned at the end of each year and are redistributed in the next planning period. New tools are not available, the income is not put into production.
Stocks - is any money or goods that are periodically replenished (produced, delivered, and so on) and some time maintained for the purpose of spending in subsequent periods.
Required to find the optimal way to allocate resources among enterprises-I and II on the n years.
The class of problems in which one considers the optimal inventory control, is the most characteristic feature of dynamic programming. This is due to the fact that the problems of inventory management process unfolds naturally over time, and the control is precisely in the fact that a decision on a given interval of time is taken in view of the state reached by the system in the previous periods. Furthermore, these problems are related, as a rule, the discrete nature of the variables and, therefore, difficult to solve by other methods. Finally, a very important fact is that the form of task dependencies for each time period is relatively simple (often linear -), which facilitates the solution of a particular problem of optimization at each step, while a one-time solution to a common problem with a large number of variables (for many periods of time and piece-wise linear or nonlinear objective function for the whole process) is quite complex.
The problem of inventory management is one of the most important areas of practical application of economic-mathematical methods, including mathematical programming methods. We restrict the analysis of some simple problems to illustrate their solutions using dynamic programming.
In formulating the objectives of inventory management using such concepts.