Dynamic channel control and pricing of a single perishable product on multiple distribution channels

Abstract

This paper studies dynamic channel control and pricing of a single perishable product distributed through multiple channels with the objective of maximizing the total expected profit over a finite horizon. We consider two types of commissions, namely proportional and fixed commissions, on the third-party channels and utilize stylized linear functions to characterize dependent demand flows from different channels. We show that, the magnitude of the opportunity cost of capacity uniquely determines the optimal channel control, at any given inventory level and periods to go. Consequently, we are able to derive the optimal price offered on each channel as a function of the opportunity cost of capacity in closed form. This significantly reduces the computational complexity of the stochastic dynamic program when parameters are constant with time. When channels are independent, we provide a necessary and sufficient condition for the optimality of a nested channel control policy by commission rates. The same condition is also sufficient for the optimality of the nested channel control policy in a distribution system with two dependent channels. We then characterize the structural properties of the optimal pricing and channel control policies. Finally, we explore the impact of the substitution effect on the channel control through numerical studies and gain managerial insights.