# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021104
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## Financing and ordering decisions in a capital-constrained and risk-averse supply chain for the monopolist and non-monopolist supplier

 1 School of Business Administration, Hunan University, Changsha, Hunan Province 410082, China 2 School of Marketing and Logistics Management, Nanjing University of Finance and Economics, Nanjing, Jiangsu Province 210023, China

* Corresponding author: ottoyang@126.com (Honglin Yang)

Received  December 2020 Revised  March 2021 Early access May 2021

Fund Project: This research is supported by the National Natural Science Foundation of China under Grant Nos. 72071072, 71901117 and 71790593 and by the Ministry of Education in China of Humanities and Social Science Project under Grant No. 19YJC630242

The paper focuses on a supply chain consisting of one supplier and one capital-constrained retailer. The retailer can solve the limited working capital problem through a bank, an investor, or its supplier. When facing business risks brought by uncertain demand, the retailer and the supplier are risk-averse behavior. To better explore the financing decision, we consider the supplier has two different cases: monopolist firm and non-monopolist firm. We first use the CVaR criterion to incorporate the members' risk-averse behavior into the objectives function. Then the equilibrium results of the supply chain are derived under three financing schemes, respectively. Our analysis finds when the supplier is a relatively low risk-averse monopolist firm, trade credit financing is the unique financing equilibrium. When the supplier is a relatively high risk-averse monopolist firm and non-monopolist firm, schemes, if the valuation level is relatively low, all members prefer bank credit financing. Otherwise, the members prefer equity financing. By tuning the valuation level, we obtain the conditions in which the supply chain realizes Pareto improvement relative to the other two financing schemes. Finally, we use numerical analysis to verify the above theoretical results.

Citation: Zhiyuan Zhen, Honglin Yang, Wenyan Zhuo. Financing and ordering decisions in a capital-constrained and risk-averse supply chain for the monopolist and non-monopolist supplier. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021104
##### References:

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##### References:
The retailer's optimal order quantity with $\eta_r$
The retailer's CVaR with $\eta_r$
The retailer's optimal order quantity with $w$
The retailer's CVaR with $w$
The supplier's CVaR with $w$
Difference of the supplier's CVaR with $\eta_s$
Expected profit and difference of CVaR with $a$
$V(q)$
Notation and Definition
 Notation Definition $p$ Unit retail price. $c$ Unit production cost. $A$ Retailer's fixed asset. $w_{i}$ Unit wholesale price, where $i=I, B, T$ represents three cases under EF, BCF and TCF, respectively. $q_{i}$ Retailer's order quantity. $x$ Uncertain demand. $\eta_{j}$ Risk-averse coefficient, where $j=r, s$ represents the retailer and the supplier, respectively. $a$ The valuation level. $\pi_i$ Retailer's profit function. $\Pi_i$ Supplier's profit function. $\Omega_I$ Investor's expected profit. $r_{f}$ The risk-free interest rate. $r_{B}$ The interest rate charged by the bank to the retailer. $r_{s}$ The interest rate charged by the supplier to the retailer.
 Notation Definition $p$ Unit retail price. $c$ Unit production cost. $A$ Retailer's fixed asset. $w_{i}$ Unit wholesale price, where $i=I, B, T$ represents three cases under EF, BCF and TCF, respectively. $q_{i}$ Retailer's order quantity. $x$ Uncertain demand. $\eta_{j}$ Risk-averse coefficient, where $j=r, s$ represents the retailer and the supplier, respectively. $a$ The valuation level. $\pi_i$ Retailer's profit function. $\Pi_i$ Supplier's profit function. $\Omega_I$ Investor's expected profit. $r_{f}$ The risk-free interest rate. $r_{B}$ The interest rate charged by the bank to the retailer. $r_{s}$ The interest rate charged by the supplier to the retailer.
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