Liability cost sharing, product quality choice, and coordination in two-echelon supply chains

We consider a two-echelon supply chain in which an upstream manufacturer (M) and a downstream retailer (R) share the product liability cost caused by quality defects. We assume that M and R share the expected liability cost per unit of the low-quality product (the ULQ liability cost). We use two respective Stackelberg games to model two different channel leadership structures: the manufacturer-led Stackelberg (MS) and the retailer-led Stackelberg (RS). We first obtain the analytical subgame perfect equilibria for the games. Subsequently, we investigate the impacts of the ULQ liability cost sharing on the product quality and the pricing decisions and on the profitability for supply chain members and the entire supply chain in equilibrium. We find that (1) in response to a shift of the share of the ULQ liability cost from R to M, the leader M under the MS structure is able to use a higher wholesale price to transfer its increased ULQ liability cost completely to R without the need to improve its product quality, while the leader R under the RS structure would decrease its retail margin to incentivize M to improve its product quality; (2) such a shift of the ULQ liability cost sharing does not have any impact on the supply chain efficiency under the MS structure, but it enhances the supply chain efficiency under the RS structure; (3) despite the different responses of the leaders under the MS and the RS structures, we are able to establish a same set of contracts combining quantity discounts with quality improvement cost sharing to coordinate the supply chain, regardless of the channel leadership structures.