Optimal periodic control strategies in a dynamic pricing problem†

This paper considers an application of control theory to management decision problems. The formulation of optimal periodic control is employed in studying the so-called intertemporal price discrimination problem. Previous static analyses of this problem have shown that the policy of switching between two certain price levels is more profitable than the optimal constant price. In the present paper the dynamics of the demand is modelled explicitly. Using this formulation the optimal dynamic solution to this problem can be found. A numerical example with three consumer groups is considered. The solution to this example shows that the optimal price patterns need not necessarily consist of only two price levels.