Model of stochastic spanning revenue-sharing contracts for multi-echelon supply chains

We consider a stochastic demand problem under a fixed-price newsvendor setting. We investigate revenue-sharing contract models that could be implemented to coordinate all supply chain actors in a decentralized decision-making supply chain in order to act together coherently. We develop and compare two revenue-sharing contract models: a pairwise contract model between two players in each echelon and a spanning contract model that covers all echelons. In the last model, we assume that the most downstream entity initiates a single contract involving all upstream entities. Our numerical experiments show that in the decentralized condition, the most upstream entity will have the biggest percentage of revenue, while the most downstream one will receive the smallest. We also demonstrate that in these two types of contracts, all of the entities could have a bigger profit in the decentralized condition than that in the centralized one.