A retailer-supplier supply chain model with trade credit default risk in a supplier-Stackelberg game

- A retailer-supplier uncooperative replenishment model is formulated.
- In the model, demand and default risk are exponential functions of trade credit period.
- Optimal results for the decentralized decision and the centralized decision without trade credit are presented.
- The existence and uniqueness conditions of the optimal solution are derived under a supplier-Stackelberg.
- An example followed by sensitivity analysis is conducted to illustrate the proposed strategy and optimal solutions.

The purpose of this paper is to formulate a retailer-supplier uncooperative replenishment model with demand and default risk are functions of the trade credit period for determining the optimal trade credit period in a supplier-Stackelberg game. Firstly, we present optimal results for the decentralized decision and the centralized decision without trade credit. Secondly, we derive the existence and uniqueness conditions of the optimal solutions for the retailer and the supplier. Moreover, we develop a set of theorems and corollaries to determine the optimal solutions. Finally, we provide an example and sensitivity analysis to illustrate the proposed strategy and optimal solutions. Sensitivity analysis reveals that the total profit of the supply chain under a supplier-Stackelberg game is greater than that observed under a centralized decision only if the optimal trade credit period is not too short. This finding also reveals that the size of the trade credit period, demand, retailer's profit and supplier's profit have strong relationships with the increasing demand coefficient, wholesale price, default risk coefficient and production cost.