Coordinating a Constrained Channel with Linear Wholesale Price Contracts

We show that when a supply channel is capacity-constrained and the constraint is tight, there is a set of linear wholesale price contracts that coordinates the channel while allowing the supplier to make a profit. We prove this for the one-supplier/one-newsvendor supply channel as well as the many-supplier/one-newsvendor channel configuration (with each supplier selling a unique product). We analyze how this set of wholesale prices changes as we change the channel’s capacity constraint. We also explore conditions under which these channel-efficient linear wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Lariviere and Porteus (2001) to allow for multiple suppliers as well as a capacity constraint at the newsvendor. Finally, we find the set of risk-sharing contracts (such as buy-back and revenue-sharing contracts) that coordinate a constrained supply channel and contrast that set with the set of risk-sharing contracts that coordinate an unconstrained channel.