On A Complex Microeconomical Model For The Optimal Control Of A Concern

A state constrained optimal control problem in economics with four linear control variables is discussed. First of all, the complex model of a concern is introduced and a suitable choice of the model functions and the model parameters is investigated. This means the adjustment of initial data as well as the storage charges and the introduction of a price function depending on the trade cycle. To solve the optimal control problem, direct and indirect methods can be used. With the help of a direct approach, for example the direct collocation method DIRCOL, it is possible to solve the problem fast and easily, without any knowledge of the necessary conditions of optimal control theory. Moreover, the direct method provides good initial estimations which can be improved w.r.t. accuracy and reliability by an indirect method, e.g. the indirect multiple shooting method MUMUS. Furthermore, a brief outline about the theoretical analysis of the state constrained optimal control problem - including the derivation of necessary conditions - and its numerical solution by means of the indirect method is represented. Besides, the complex switching structure of the optimal controls , which results from the appearance of singular subarcs and overlapping boundary arcs of two active state constraints, is remarkable.