The supplier's optimal guarantee policy in newsvendor finance

• Author: Yanhai Li,Xuan Jiang
• Date: 01 September 2020
• Published date: 01 September 2020
• DOI: http://doi.org/10.1111/itor.12757

Intl. Trans. in Op. Res. 27 (2020) 2370–2395

DOI: 10.1111/itor.12757

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The supplier’s optimal guarantee policy in newsvendor finance

Yanhai LiaandXuanJiang

b,∗

aSchool of Economics and Management, Fuzhou University, Fuzhou 350108, China

bSchool of Business Administration, Zhongnan University of Economics and Law, Wuhan430073, China

E-mail: xgliyh@163.com [Li]; judyx.jiang@foxmail.com [Jiang]

Received 25 November2018; received in revised form 1 November 2019; accepted 2 November 2019

Abstract

The retailer is a capital-constrained newsvendor and can borrow money from the bank if necessary. To

help the retailer get a bank loan at a lower interest rate, the supplier provides guarantee for the retailer’s

loan up to a prespecified amount. In a Stackelberg game, the supplier decides the wholesale price and the

guarantee amount as a leader, and then the retailer determines the order quantity and the amount of the

loan as a follower. The supplier is risk-neutral while the retailer’s risk preference is reflected by a spectral

risk measure (risk-neutral, risk-averse, or risk-seeking). For a given wholesale price and guarantee amount,

the retailer’s objective function is quasi-concave in the order quantity. The optimal solutions for the supplier

and the retailer are derived. The supplier’s expected profit with optimized wholesale price increases with the

guarantee amount, and thus the supplier’s optimal policy is to provide a full guarantee for the retailer’s loan.

When the supplier can limit his guarantee responsibility by a proportion of the outstanding loan obligation,

the supplier’s optimal policy is also to provide a full guarantee. Even if the retailerincurs bankruptcy costs in

the event of repaymentdefault, the supplier’s optimal guarantee policy remains the same in these two different

forms of limited guarantee. However, when the wholesale price is exogenous, that is, not a decision variable,

the full guarantee is not necessarily optimal for supplier.

Keywords:capital-constrained newsvendor; limited guarantee; spectral risk measure; supplier-guaranteed loan

1. Introduction

Many of the small- and medium-sized enterprises (SMEs) face capital constraints, and thus require

short-term financing to keep the business running. However, it is difficult for them to obtain

financial resources in the capital markets because of their low quality or history credit. This implies

that they have to bear high costs of financing. At the same time, the banks are interested in selecting

safe borrowers, thus engaging in secure and profitable transactions. This can be achieved through

loan guarantees, which is a common solution for credit enhancement. In such financing schemes,

when the original borrowercannot repay the loan and the respective interest in full, the guarantor is

∗Corresponding author.

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Y. Li and X. Jiang / Intl. Trans. in Op. Res.27 (2020) 2370–2395 2371

responsible for repaying the remaining balance. In addition to providing the lender a safety cushion,

the loan guarantee can induce the guarantor to select and monitor the borrower carefully in order

to control his own risk (Madajewicz, 2011).

In a supply chain, if the retailer’s order quantity is lowered by a high interest rate, the supplier’s

profit will be negatively affected. Generally, banks are willing to charge a lower interest rate under

the condition that the core enterprise in the supply chain underwrites its loan applications. This is a

common technique through which banks are balancing the risk and return of a loan. Consequently,

the suppliers with good credit might be motivated to guarantee for the retailers to reduce their

financing cost and alleviate the underinvestment problem. We refer to this financing scheme as a

supplier-guaranteed loan.

A guarantor does not always provide a full guarantee, thus sometimes it might provide a partial

guarantee for the original borrower’s loan. In a partial guarantee agreement, the guarantor covers

partially the risk within a certain prespecified guarantee level. In some cases, guarantors consider

that lenders should also assume a certain risk level, in order to create an incentive for the lender

to make the effort to screen loans carefully and take actions to maintain default rates down. In

fact, full guarantee and partial guarantee have coexisted for a long time. Partial guarantee schemes

have been commonly used by many mutual guarantee institutions (Busetta and Zazzaro, 2012) as

well as credit guarantee programs supported by governments aiming at alleviating SMEs financing

constraints (Honohan, 2010; Liang et al., 2017). Some entrepreneurs in China consider the partial

guarantee scheme as a flexible and popular agreement that can avoid incentive distortions usually

caused by the government guarantee schemes (Luo et al., 2016).

With the innovation and evolution of financial business modes, partial guarantee is adopted by

some commercial banks for supply chain finance. For example, an innovative scheme has been

undertaken by Evergrowing Bank (a Chinese commercial bank) that lent money to a financially

constrained retailer based on the credit guarantee of the upstream manufacturer (Yan et al., 2016).

More specifically, the retailer wanted to purchase equipment from a large manufacturer but lacked

the cash to pay for the order. Evergrowing Bank offered the retailer a loan conditional on the

promise of the manufacturer to repay part of the loan to the bank if the retailer’s bankruptcy

occurred. Similarly, some other Chinese commercial banks, such as Hua Xia Bank and ICBC

(Industrial and Commercial Bank of China), also provide loans to support SMEs based on the

partial credit guarantee of the core enterprises in supply chains (Li et al., 2018; Jin et al., 2019).

In a supplier-guaranteed loan program,the retailer and the supplier are engaged in both borrower–

guarantor and buyer–seller relationships. By providingguarantee for the retailer’s loan, the supplier

essentially shares the retailer’s financing cost and can induce the retailer to purchase more product.

At the same time, the supplier needs to undertake the risk of the retailer’s repayment default. In

a word, the supplier’s guarantee for the retailer’s loan raises complex effects on the interaction

between them. Intuitively, as the guarantee level becomes higher, the supplier bears more financial

risk but obtains more wholesale profit from the retailer. These two factors cannot be divided clearly

and may affect the supplier’s decision on the guarantee level in opposite ways. Thus, the ultimate

impact of the guarantee level on the supplier’s profit is not so straightforward. However, few papers

have studied the guarantee policy of the core enterprise in the supply chain from an operational

perspective.

For the last decade or so, the operations management literature has shown a significant influence

of risk preferences on the operational decisions. The financially constrained retailer faces the risk of

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