Abstract: When a retailer confronts with the fund shortage problem, the retailer often uses supply chain financing. As an innovative mode of supply chain financing, third part logistics (3PL) firm financing service has been practiced over the recent years. Moreover, the capital-constrained retailer often has loss aversion behavior because of the demand uncertainty. Therefore, it is worth to study the operational and coordination strategies of supply chain with a loss-averse retailer under 3PL firm financing service.
In this paper, it is assumed that the supply chain comprises a 3PL firm and a capital-constrained retailer who is loss aversion. a two-stage Stackelberg game between the 3PL firm (Stackelberg leader) and the retailer (Stackelberg follower) is considered. The 3PL firm offers transportation service and financing service to the capital-constrained retailer. Furthermore, the Stackelberg games are analyzed and obtain the 3PL's optimal interest rate and the retailer's optimal ordering quantity under the decentralized situation and the optimal ordering quantity for the supply chain under the centralized situation, are obtained respectively. Comparing the retailer's optimal ordering quantity between the decentralized situation and the centralized situation, a transfer payment contract is designed that may realize the supply chain coordination under 3PL firm financing service. Finally, some numerical studies are conducted to show the impacts of the retailer's initial capital on the retailer's profit, the 3PL's profit and the profit of the entire supply chain, and to analyze the impacts of transfer payment amount on the 3PL's profit and the retailer's profit.
Some important conclusions are obtained through the theoretical analysis. First, when the retailer's initial capital is more than the certain threshold, the optimal ordering quantity of the loss-averse retailer under 3PL firm financing service is more than that of a well-funded retailer. Second, when the retailer's initial capital changes within certain range, 3PL firm financing service can make the 3PL firm and the loss-averse retailer both obtain Pareto improvements, but the 3PL firm financing service does not coordinate the supply chain. Third, when the transfer payment contract between the 3PL firm and the loss-averse retailer meets a certain condition, the capital-constrained supply chain can obtain the whole coordination.
Two useful managerial implications are obtained based on our study. On the one hand, the 3PL firm offers financing service to the capital-constrained retailer, which can not only increase the ordering quantity and the retailer's profit, but also increase the profit of the whole supply chain through a suitable interest rate. That is to say, the 3PL firm financing service becomes a new incentive mode to improve the supply chain's performance effectively. On the other hand, 3PL firm financing service can improve his profit and the competitive marketplace. If the 3PL firm cooperates with the retailer, they can jointly determine a suitable transfer payment contract, which can realize a win-win situation for all the supply chain members.

Key words: the third logistics (3PL), capital-constrained, supply chain coordination, loss-averse, transfer payment contract