Abstract
In this paper we solve a problem of optimization and production planning using the optimal control methods and Pontryagin Maximum Principle. We propose an economic model and find an optimal plan of production for n products, to ensure the required quantity at specified delivery data with minimum cost of inventory and production. We prove that the economic system is not controllable, in the sense that we cannot reach any final stock quantity. Finally, we justify this construction with a numerical example.
Highlights
Control theory is frequently used in modelling and analysis of operational systems in production planning and logistics
LaValle [17] gave an unified treatment of control theory including control affine systems and Popescu [22] used the framework of Lie algebroids in the study of driftless control affine systems
One of the motivations for this work is the study of Lagrangian systems with some external constraints. These systems have a wide application in many different areas as optimal control theory, econometrics, cybernetics
Summary
Control theory is frequently used in modelling and analysis of operational systems in production planning and logistics. One of the motivations for this work is the study of Lagrangian systems with some external constraints These systems have a wide application in many different areas as optimal control theory, econometrics, cybernetics. An overview of earlier research concerning optimal control theory applications in production economics is given. In the last part of the paper the complete solution of the problem is found, using a convenient change of variables for the system of differential equations generated by Pontryagin Maximum Principle.
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