Dynamic von Neumann model is considered in this work. This model describes development of some industries and technological processes. Optimization tasks in the model are considered. The difference from classical model is additive restriction: variables must be integer.

The dynamic optimization task is formally described. Two algorithms solving this task are constructed. The first algorithm is approximate. It is algorithm of continualization of discrete optimization task. The second algorithm is based on the dynamic programming method. Complexity of these algorithms is evaluated.

A program realizing these algorithms is written. It is a program on the C++ language using the Clp library. Computational experiment is done. This experiment analyses and compares parameters of these algorithms. Calculations was complex, and thus a cloud was used for calculations.

It was found that complexity of the algorithms grows exponentially by time. It was predicted theoretically. In addition, it was found that optimal values of the objective function are very valuable and depends of parameters of input and output matrices. Thus a time of execution for dynamic programming algorithm is also very valuable and also depends of parameters of these matrices. Dependence of average values of objective function from matrices dimensions is small and its dependence of time is big. However real economical growth is rather slow often. By this reason, a time of program execution also grows rather slow.

A leak of this work: in the computational experiment average values for all possible tasks are considered. They include tasks that have solutions growing very fast and degenerate problems with zero solution. But real tasks in economical practice are "intermediate": tasks are not degenerate but their solutions grow slowly.

This work is a complete scientific research and can get excellent mark.