Full versus partial coordination in serial N-echelon supply chains and a new profit-sharing contract

Despite the significance of full coordination of N-echelon supply chains in real-world decision-making situations, the relevant literature has rarely addressed this issue. Furthermore, there is a scarcity of mathematical models in the supply chain management literature for partially coordinated cases. To address these shortcomings, this study concerns both the full and partial coordination in serial N-echelon supply chains facing stochastic demand. In particular, three general cases including decentralized (no coordination), sub-supply chain coordination (partial coordination) and centralized (full coordination) cases are examined to support decisions on ordering and pricing. In addition, this study adds to the literature by investigating how to coordinate a serial N-echelon supply chain through a new spanning profit sharing contract, which can coordinate the entire supply chain through only one contract. Furthermore, we analytically prove the occurrence of externality benefit in partially coordinated cases, which is a paradoxical phenomenon suggesting that small coalitions are unstable. Two numerical examples extracted from the literature are given to verify the effectiveness and validity of the proposed contracts and models. The results show that the proposed contracts can be applied in a rather simple and convenient way and is reliable enough for use in real-world applications.