# American Institute of Mathematical Sciences

November  2021, 17(6): 3027-3047. doi: 10.3934/jimo.2020106

## Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing

 1 School of Business Administration, Hunan University, Changsha, Hunan Province 410082, China 2 School of Business, University of International Business and Economics, Beijing 100029, China 3 School of Foreign Language, Jingdezhen Ceramic Institute, Jingdezhen, Jiangxi Province 333403, China 4 School of Business Administration, Hunan University, Changsha, Hunan Province 410082, China

* Corresponding author: yefangyu@hnu.edu.cn (Fangyu Ye)

Received  August 2019 Revised  March 2020 Published  November 2021 Early access  June 2020

Fund Project: The research was supported by the National Natural Science Foundation of China under Grant Nos. 71571065 and 71521061.

In this study, we consider a two-echelon supply chain, where two capital constrained suppliers compete to sell their products through a common retailer. The retailer may provide advance payment to one or two suppliers. We show that whether the retailer considers merging with only one supplier depends upon the revenue sharing ratio and the additional administrative costs of the revenue sharing contract. Meanwhile, the supplier who drops out of the market may adopt a hybrid financing scheme by combining bank credit with equity financing to return to the market. We find that the deselected supplier can be allowed to participate in the market when the bank loans ratio is below a certain threshold. We further investigate the impact of the bank loans ratio and competition intensity on the players' decisions and profits. In addition, we find that there exists an optimal bank loans ratio for the deselected supplier. Specifically, it is optimal for the deselected supplier to adopt pure bank credit if the production cost is sufficiently low.

Citation: Qiang Yan, Mingqiao Luan, Yu Lin, Fangyu Ye. Equilibrium strategies in a supply chain with capital constrained suppliers: The impact of external financing. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3027-3047. doi: 10.3934/jimo.2020106
##### References:

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##### References:
The evolution process of the three different strategies
The Pareto Zone
Wholesale price changes with $\theta$
Retailer's profit changes with $\theta$
Supplier's profit changes with $\theta$
Wholesale price changes with $b$
Retailer's profit changes with $b$
Order quantity changes with b
Retailer’s profit changes with b
Supplier’s profit changes with b
Notations and explanations
 Notation Explanation $b$ Competitive intensity of the products, where $0\leq b\leq 1$. $c$ Unit production cost. $\theta$ Bank loans ratio, where $0<\theta<1$. $r_f$ Interest rate of bank loans. $\lambda$ Revenue sharing ratio. $p_i^j$ Retailer's retail price for product $i$ in Strategy $j$, where $i=1$ and $2$, and $j=AA,A$ and $AE$. $w_i^j$ Wholesale price charged by $S_i$ in Strategy $j$. $q_i^j$ Retailer's order quantity from $S_i$ in Strategy $j$. $k_1$ Retailer's additional administrative costs associated with the revenue sharing contract in Strategy $A$. $k_2$ Supplier $S_1$'s additional administrative costs associated with the revenue sharing contract in Strategy $A$. $\pi_R^j$ Retailer's profit in Strategy $j$. $\pi_{S_i}^j$ Supplier $S_i$'s profit in Strategy $j$.
 Notation Explanation $b$ Competitive intensity of the products, where $0\leq b\leq 1$. $c$ Unit production cost. $\theta$ Bank loans ratio, where $0<\theta<1$. $r_f$ Interest rate of bank loans. $\lambda$ Revenue sharing ratio. $p_i^j$ Retailer's retail price for product $i$ in Strategy $j$, where $i=1$ and $2$, and $j=AA,A$ and $AE$. $w_i^j$ Wholesale price charged by $S_i$ in Strategy $j$. $q_i^j$ Retailer's order quantity from $S_i$ in Strategy $j$. $k_1$ Retailer's additional administrative costs associated with the revenue sharing contract in Strategy $A$. $k_2$ Supplier $S_1$'s additional administrative costs associated with the revenue sharing contract in Strategy $A$. $\pi_R^j$ Retailer's profit in Strategy $j$. $\pi_{S_i}^j$ Supplier $S_i$'s profit in Strategy $j$.
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