Structural properties of buyback contracts for price-setting newsvendors

This paper studies a buyback contract in the Stackelberg framework of a manufacturer (leader) selling to a price-setting newsvendor retailer (follower). Using an analytical model that focuses on a multiplicative demand form, we generalize previous results and produce new structural insights. A novel transformation technique first enables us to establish the unimodality of the profit functions for both channel partners, under relatively mild assumptions. Further analysis identifies the necessary and sufficient condition under which the optimal contract for the manufacturer (wholesale and buyback prices) is distribution free, i.e., independent of the uncertainty in customer demand. A specific instance of the above condition is also necessary and sufficient for a no-buyback contract to be optimal from the manufacturer's perspective. We then prove that the optimal performance of the decentralized channel for distribution-free buyback contracts depends only on the curvature of the deterministic demand part. In addition, some of the optimal decisions and relevant profit ratios for buyback contracts in our setting are shown to be identical to those for their deterministic price-only counterparts.