Nina Yan and Baowen Sun

Central University of Finance and Economics

Beijing 100081, China

(Communicated by Thomas Sharkey)

Abstract. In the supply chain nance (SCF) system composed of a capital-

constrained retailer, a manufacturer and a commercial bank, we design two

dierent limited nancing modes, namely, a nancing mode based on order and

on the capital-gap. Considering the retailer's capital constraint and bankruptcy

risk, we formulate a Stackelberg game in which the manufacturer acts as the

leader and analyze the optimal decisions for each participant. Finally, we

conduct numerical examples and make comparative analyses between these two

dierent nancing modes in terms of optimal ordering and pricing decisions,

as well as optimal expected prots. It is concluded that the optimal expected

prot of SCF under either nancing mode would be higher than that in the case

of no capital constraint or capital-constrained without nancing. Moreover, the

nancing mode based on order would encourage the manufacturer to earn more

and the nancing mode based on capital-gap would be more favorable to the

retailer.

1. Introduction. Supply chain nancing (SCF) is a nascent area emerging from

a growing appreciation for nancial 

ows by supply chain practitioners and by

researchers, which is also a response to an emerging need for banks to play a more

active role in the activities of suppliers and buyers. As a means of substituting for

lower credit availability, SCF is increasingly generating much enthusiasm among

small and medium enterprises (SMEs) and their corresponding banks. Dierent

from trade credit where one corporation extends his own credit to the upstream or

downstream partner allowing a delay payment, the role of SCF is to integrate bank

loans to optimize both the availability and cost of capital within a given buyer-seller

supply chain and create liquidity in the supply chain through various SCF solutions

(Hans and Moritz, 2009[7]; Caldentey and Haugh, 2009[4]).

Recently, SCF has increasingly received substantial interests among supply chain

practices and academic elds (Arnold and Minner, 2011[1]; Lee and Rhee, 2010[13],

2011[14]; Kouvelis and Zhao, 2011[9], 2012[10], and so on). The rst attempt to

incorporate asset-based nancing into production decisions is Buzacott and Zhang

(2004)[2]. They formulated and discussed the situation in which the capital

-constrained retailer nances from a prot maximizing bank that sets the interest

rate and loan limit. Dada and Hu (2008)[6] also analyze the decision of a capital-

constrained newsvendor who can borrow funds to make the procurement; from this

2010 Mathematics Subject Classication. Primary: 90B05; Secondary: 91A12.

Key words and phrases. Supply chain nancing, capital constraints, credit line, Stackelberg

game, demand uncertainty.

NINA YAN AND BAOWEN SUN

study we can observe a nonlinear loan schedule for dierent nancing modes. Lai

et al. (2009)[11] examine a Stackelberg game in the supply chain with nancial

constraints and addressed the eciency of a supply chain operated under dierent

ordering modes. They concluded that in the presence of nancial constraints, the

supplier prefers the preorder mode, while the combination mode is the most e-

cient mode for the whole supply chain. Srinivasa and Mishra (2011)[15] consider

a two-level supply chain with a single retailer and manufacturer, where both rms

are facing nancial constraints. They investigated how the lender's prot is related

to the cash position at the next level of the supply chain of the borrowers. Kouvelis

and Zhao (2012)[10] present a trade credit model to study the interaction of short-

term nancing and inventory decisions and make comparisons between trade credit

and bank nancing. We extend their bank nancing models to discuss the bank's

optimal decision making on the credit line under nite nancing schemes. Caldentey

and Chen (2011)[3] investigate the role of nancial service in a procurement con-

tract with a budget-constrained retailer. They focus on the internal nancing of

supplier's trade credit and external nancing of bank loans in which the lending

bank makes zero prot in a competitive nancial market. In contrast, a key feature

of our model is that we characterize the bank's optimal credit decision for maxi-

mizing his expected prot in the non-competitive nancial market under specic

nancing modes. Yang and Birge (2011)[16] discuss how to use the inventory -

nancing portfolio including cash, trade credit and short-term debt to work out a

nancial diversication solution to the capital-constrained supply chain. Although

we also try to formulate the supply chain nancing problem with bank loans, our

work diers from theirs as it is concerned about the internal supply chain nanc-

ing, such as trade credits without bank loans. Trade credit refers to an agreement

between the rm and a supplier where the supplier allows the rm to delay pay-

ment. Instead, we mainly focus on the external nancing of bank loans and assume

that the lending bank can endogenously determine the credit lines according to the

borrower's nancial position under given loan schemes, which is more realistic in

supply chain nancing practices. The most closely related papers are Chen and

Wang (2012)[5] and Jing et.al. (2012)[8]. Chen and Wang (2012)[5] investigated

the impacts of limited liability on the performance of SCF and shows that lim-

ited liability accounts for the reason why the retailer with a lower initial budget

initiates a higher ordering level under trade credit contract. Jing et.al. (2012)[8]

discuss the equilibrium in SCF with two credit schemes (bank or trade credit) and

show that bank credit nancing generally charges a lower wholesale price and thus

becomes more attractive than trade credit nancing for the retailer. Based on their

conclusions we extend our research on designing specic bank nancing modes and

further explore which one will be much more attractive under a given initial budget.

Although extensive work has been done to address issues of optimal strategies in

SCF, very little attention has been paid to how to determine the credit line, let

alone based on a specic nancing mode. While some of our analysis has a similar

avor to theirs, the key distinction is that we formally treat the bank as one of

the Stackelberg game players in a less-competitive nancial market and incorporate

specic nancing modes into optimizing ordering and pricing decisions. Moreover,

we assume that the endogenous credit line is decided by the bank to avoid over-

borrowing.

Because of the novelty of SCF, most research so far have only covered certain

parts of SCF and have left many research gaps, such