Dynamic production inventory model

A lot of companies have own production inventory. In this paper we assume a dynamic model of production inventory. For solving a model of production inventory system we use a necessary condition of optimal control theory in this paper. In the first part of the paper we introduce the theory of inventory in short, and about the expenditures, which belongs to the inventory. In the next one we give some theoretical background for theory of optimal control and its necessary conditions. For dynamic model we use Hamiltonian function and the necessary condition for its extremes. With this function we can solve the dynamic problem as a static one in every time period. In the last part we present a model of production inventory. This model is a bounded control and we are minimizing the cost of production and at the same time keep the production as close as possible to its goal level. We assume one control and one state variable with one difference equation for changing state variable in time. The state variable is production inventory of the company and the control variable is production level. In the end of this paper we show what happens if some parameters of the problem are changing.