供应商融资中买方的最优担保策略

doi:10.16381/j.cnki.issn1003-207x.2020.1440

摘要/Abstract

摘要：

在两级供应链中，零售商需要向供应商采购产品以满足随机的市场需求，供应商需要在市场需求观测到之前进行备货。供应商的自有资金是有限的，在必要时可向银行借款。在完全竞争的资本市场中，银行会根据贷款数量以及相应的风险决定其利率，使其期望回报率等于无风险利率。为了降低供应商的融资成本，促使其提高备货量，零售商有动机为供应商提供贷款担保。供应商和零售商进行Stackelberg博弈，首先由零售商决定采购价格和担保比例，然后由供应商决定备货量。供应商和零售商均为风险中性的决策者，以最大化自身期望利润为目标。研究结果表明：对给定的采购价格和担保比例，供应商的期望利润是其备货量的拟凹（quasi-concave）函数，其最优备货量是唯一的。零售商的最优策略是提供全额担保，零售商的最优期望利润是供应商自有资金的减函数。本文还讨论了存在破产成本的情形，发现破产成本不利于零售商，但不会改变零售商的最优担保策略。

关键词: 资金约束, 供应商融资, 买方担保, 有限担保比例, 破产成本

Abstract:

In a bilateral supply chain， the retailer sources product from the supplier to satisfy the random demand. The supplier needs to produce the product before the demand is realized. The supplier is financially constrained and can borrow money from the bank if necessary. As the capital market is perfectly competitive， the bank will determine the interest rate based on the loan amount and the associated risk so as to maintain its expected return rate equal to the exogenous risk-free rate. In order to reduce the financing cost of the supplier and induce him to produce more product， the retailer has a motivation to provide a （partial or full） guarantee for the supplier’s loan. A key feature of our model is that the guarantee is not a hard constraint of the loan amount， i.e.， the supplier can borrow as much as he needs， regardless of the retailer’s guarantee proportion. The retailer and supplier play a Stackelberg game. The retailer needs to decide the purchasing price and guarantee proportion as a leader， and then the supplier determines the production quantity as a follower. Both the retailer and supplier are risk-neutral profit maximizers. By backward induction， the supplier’s decision is studied， and then retailer’s problem is considered.For any given purchasing price and guarantee proportion， the supplier’s expected profit is quasi-concave in the production quantity， and thus his optimal-response production quantity is unique. The retailer’s optimal policy is to provide a full guarantee for the supplier’s loan. The retailer’s guarantee will not change he financing cost of the whole supply chain， but can shares the supplier’s financing cost. By providing a full guarantee， the retailer can maintain the supplier’s production quantity unchanged while offering a lower purchasing price. The overall effect of full guarantee is beneficial to the retailer. In other words， a full guarantee causes larger financial loss but brings higher sales profit to the retailer. The retailer’s optimal expected profit is demonstrated to be decreasing in the supplier’s internal capital. Thus， the retailer will be better off to work with a less wealthy supplier. Finally， the bankruptcy cost is incorporated into the model. It turns out that the presence of bankruptcy cost is unbeneficial to the retailer， but will not change the retailer’s guarantee policy.

Key words: capital constraint, supplier finance, buyer guarantee, limited guarantee proportion, bankruptcy cost

中图分类号:

F252

李沿海,赵玲. 供应商融资中买方的最优担保策略[J]. 中国管理科学, 2023, 31(10): 12-19.

Yan-hai LI,Ling ZHAO. The Buyer's Optimal Guarantee Policy for a Financially Constrained Supplier[J]. Chinese Journal of Management Science, 2023, 31(10): 12-19.

图/表 1

表1

变量符号及其意义"

变量	含义
c	生产成本
p	市场售价
$κ$	供应商的自有资金
$r f$	无风险利率
w	采购价格，满足 $c 1 + r f ≤ w ≤ p$
q	供应商的备货量
r	银行贷款的利率
θ	$1 - θ$ 为零售商的担保比例，满足 $θ ∈ 0,1$
ρ	$ρ ? c q - κ 1 + r / w$ ，满足 $ρ < q$
D	随机的市场需求
$f ?$	需求D的概率密度函数
$F ?$	需求D的概率分布函数
$F ˉ ?$	$F ˉ x ? 1 - F x$ ，满足 $F ˉ 0 = 1$
$z ?$	$z x ? f x / F ˉ x$ ，增函数
$π$	供应商的期望利润
$Π$	零售商的期望利润

表1

参考文献 32

1	Yi Zelong， Wang Yulan， Chen Yingju. Financing an agricultural supply chain with a capital-constrained smallholder farmer in developing economies ［J］. Production and Operations Management， 2021， 30（7）： 2102-2121.
2	Tunca T I， Zhu Weiming. Buyer intermediation in supplier finance ［J］. Management Science， 2018， 64（12）： 5631-5650.
3	Yan Nina， Sun Baowen， Zhang Hui， et al. A partial credit guarantee contract in a capital-constrained supply chain： financing equilibrium and coordinating strategy ［J］. International Journal of Production Economics， 2016， 173： 122-133.
4	Li Bo， An Simin， Song Dongping. Selection of financing strategies with a risk-averse supplier in a capital-constrained supply chain ［J］. Transportation Research Part E： Logistics and Transportation Review， 2018， 118： 163-183.
5	Jin Wei， Zhang Qinhong， Luo Jianwen. Non-collaborative and collaborative financing in a bilateral supply chain with capital constraints ［J］. Omega， 2019， 88： 210-222.
6	Beranek W. Financial implications of lot-size inventory models ［J］. Management Science， 1967， 13（8）： 401-408.
7	Hu Qiaohai， Sobel M J. Echelon base-stock policies are financially sub-optimal ［J］. Operations Research Letters， 2007， 35（5）： 561-566.
8	Xu Xiaodong， Birge J R. Operational decisions， capital structure， and managerial compensation： a news vendor perspective ［J］. The Engineering Economist， 2008， 53（3）： 173-196.
9	Buzacott J A， Zhang R Q. Inventory management with asset-based financing ［J］. Management Science， 2004， 50（9）： 1274-1292.
10	Dada M， Hu Qiaohai. Financing newsvendor inventory ［J］. Operations Research Letters， 2008， 36（5）： 569-573.
11	Alan Y， Gaur V. Operational investment and capital structure under asset-based lending ［J］. Manufacturing & Service Operations Management， 2018， 20（4）： 637-654.
12	张义刚，唐小我. 供应链融资中的制造商最优策略［J］. 系统工程理论与实践， 2013， 33（6）： 1434-1440.
	Zhang Yigang， Tang Xiaowo. Manufacturer’s optimal policies in supply chain finance ［J］. Systems Engineering - Theory & Practice， 2013， 33（6）： 1434-1440.
13	白世贞，徐娜，鄢章华. 基于核心企业回购担保的存货质押融资决策分析［J］. 中国管理科学， 2012， 20（S1）： 309-314.
	Bai Shizhen， Xu Na， Yan Zhanghua. Research on decisions on inventory financing based on core enterprise’s buy-back guarantee ［J］. Chinese Journal of Management Science， 2012， 20（S1）： 309-314.
14	王文利，骆建文. 零售商提前支付与贷款担保下的供应商融资策略［J］. 管理工程学报， 2013， 27（1）： 178-184.
	Wang Wenli， Luo Jianwen. Strategies for financing suppliers based on retailers' prepayment and loan guarantee ［J］. Journal of Industrial Engineering & Engineering Management， 2013， 27（1）： 178-184.
15	Lin Qiang， Xiao Yang. Retailer credit guarantee in a supply chain with capital constraint under push & pull contract［J］. Computers & Industrial Engineering， 2018， 125： 245-257.
16	Xu Song， Fang Lei. Partial credit guarantee and trade credit in an emission-dependent supply chain with capital constraint［J］. Transportation Research Part E： Logistics and Transportation Review， 2020， 135： 101859.
17	Zhou Weihua， Lin Tiantian， Cai Gangshu. Guarantor financing in a four-party supply chain game with leadership influence［J］. Production and Operations Management， 2020， 29（9）： 2035-2056.
18	Tang C S， Yang S A， Wu Jing. Sourcing from suppliers with financial constraints and performance risk［J］. Manufacturing & Service Operations Management， 2018， 20（1）： 70-84.
19	Li Yanhai， Gu Chaocheng， Jinwen Ou. Supporting a financially constrained supplier under spectral risk measures： the efficiency of buyer lending［J］. Transportation Research Part E： Logistics and Transportation Review， 2020， 136： 101894.
20	Gupta D， Chen Yibin. Retailer-direct financing contracts under consignment［J］. Manufacturing & Service Operations Management， 2020， 22（3）： 528-544.
21	Deng Shiming， Gu Chaocheng， Cai Gangshu， et al. Financing multiple heterogeneous suppliers in assembly systems： buyer finance vs. bank finance［J］. Manufacturing & Service Operations Management， 2018， 20（1）： 53-69.
22	李沿海，顾超成，邓世名. 装配系统中的供应商融资：银行贷款 vs 买方预付款［J］. 运筹与管理， 2018， 27（11）： 157-162.
	Li Yanhai， Gu Chaocheng， Deng Shiming. Financing the suppliers in assembly system： bank lending vs advance payment［J］. Operations Research and Management Science， 2018， 27（11）： 157-162.
23	Reindorp M， Tanrisever F， Lange A. Purchase order financing： credit， commitment， and supply chain consequences［J］.Operations Research， 2018，66（5）： 1287-1303.
24	Zhao Lima， Huchzermeier A. Managing supplier financial distress with advance payment discount and purchase order financing［J］. Omega， 2019， 88： 77-90.
25	Kouvelis P， Zhao Wenhui. The newsvendor problem and price-only contract when bankruptcy costs exist ［J］. Production and Operations Management， 2011， 20（6）： 921-936.
26	Yang S A， Birge J R. Trade credit， risk sharing， and inventory financing portfolios［J］. Management Science， 2018， 64（8）： 3667-3689.
27	Kouvelis P， Zhao Wenhui. Supply chain contract design under financial constraints and bankruptcy costs［J］. Management Science， 2016， 62（8）： 2341-2357.
28	Xiao Shuang， Sethi S P， Liu Mengqi， et al. Coordinating contracts for a financially constrained supply chain［J］. Omega， 2017， 72： 71-86.
29	Chod J. Inventory， risk shifting， and trade credit［J］. Management Science， 2017， 63（10）： 3207-3225.
30	Lariviere M A. A note on probability distributions with increasing generalized failure rates［J］. Operations Research， 2006， 54（3）： 602-604.
31	Gerchak Y， Wang Yunzeng. Revenue-sharing vs. wholesale-price contracts in assembly systems with random demand［J］. Production and Operations Management， 2004， 13（1）： 23-33.
32	Lariviere M A， Porteus E L. Selling to the newsvendor： an analysis of price-only contracts［J］. Manufacturing & Service Operations Management， 2001， 3（4）： 293-305.

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