Abstract
This paper deals with the problem of simultaneously determining the optimal price policy and production rate over a given planning horizon. For nonlinear demand functions and convex inventory and shortage cost functions the optimal solution paths are derived by using optimal control theory. The treatment of linear nonsmooth cost functions requires the use of a generalized maximum principle. The solution method is a phase portrait analysis providing insight into the optimal pricing and production policies as well as the resulting inventory paths. Moreover, it is shown that in the case of nonsmooth piecewise linear cost functions the equilibrium is approached within finite time although the model is nonlinear in the control variables. Finally it is illustrated that exogenous fluctuations in the demand rate (seasonal demand pattern) amount to cyclical optimal solutions.
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