This Bachelor thesis examines an optimal control problem out of the
Supply Chain Management, which can be solved analytically with
Pontryagin’s maximum principle. The used model describes the cooperation
of a manufacturer and his supplier in a Supply Chain. It is investigated,
whether measures to improve supplier development could lead to an increase
in the single market players’ profits and which influence it has on the
total profit of the value chain. Therefore several optimal control problems
are formulated and solved. In particular a factor for the division of the
costs of the supplier development is determined, so that the cooperation
leads to a maximal possible profit in total. The focus is laid on a
detailed and mathematically precise presentation of the way of solving the
problem. After finding a mathematical solution, that one is interpreted
economically to gain a recommended course of action. To solve the optimal
control problem Pontryagin’s maximum principle for fixed termination
times and free finite condition on the right side is used. The theorem is
deduced from Pontryagin’s maximum principle for free termination time
with given finite condition.