A revisit to the markup practice of irreversible dynamic pricing

We consider an irreversible dynamic pricing situation in which a firm uses real-time inventory information to decide the most opportune time to raise its sales prices. Feng and Xiao (Oper Res 48:332-343, 2000b) has studied this problem along with the opposite markdown case. In quite symmetric fashions, they established the optimality of threshold policies for both cases. Though the earlier work has made dramatic advances in dynamic pricing and at the same time pioneered with many relevant techniques, we believe its treatment of the markup case warrants some revision. In particular, we find it is in possession of an erstwhile-unknown complementarity property between price flexibility and inventory, whose counterpart is not true for the markdown case. This property is needed in the derivation leading to the optimality of a threshold policy. Our development also allows demand to be time-dependent in a product form, and naturally leads to an efficient policy-computing algorithm.