Abstract: With the development of modern logistics industry, business process outsourcing for example transporting and so on has been the trend of enterprise for market competition nowadays. Supply chain models including the third-party logistics service provider (3PL) is more practical and theoretical significance.But the existing literatures rarely consider the effect of the 3PL provider to the supply chain for the deteriorating items with time-varying. Based on this, a three-level supply chain model including the 3PL for deteriorating items with time-varying demand model is developed. Dynamic game theory is used to solve the decentralized optimal solution. The research shows that compared with the transportation costs borne separately by the manufacturer,the transportation costs borne by the 3PL provider will make the order cycle shorter and will reduce the quantity of order in a single cycle. Optimal solutions under the decentralized and the centralized are compared, the conclusion implies that considering the total system profit,the centralized decision can't make this supply chain reach coordination. Finally, a numerical example is provided to support the findings.

Key words: deteriorating items, third-party logistics, game theory, time-varying demand, supply chain coordinating