Anwendungen des Maximumprinzips im Operations Research, Teil 1

Abstract

Optimal control theory treats the steering of dynamical systems with the aim to reach a desired target. The problem of dynamic system optimization is to find the functions which will optimize a given objective functional subject to certain constraints. The purpose of the present paper is to provide an elementary approch to the maximum principle as well as to its economic interpretation. The calculation of optimal control trajectories is illustrated by some simple examples in cash management, production and investment planning, advertising and pricing, and science policy. Moreover, without claiming completeness some further applications of the deterministic maximum principle in operations research are reviewed. The use of the maximum principle provides a significant advantage compared with dynamic programming, namely the possibility to gain qualitative insights into the structure of solution paths and thus to draw interesting economic conclusions without performing a complete analysis of the control problem. © 1982 Springer-Verlag.