Risk Migration In Supply Chain Inventory Financing Service

doi:10.4236/jssm.2011.42026

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Journal of Service Science and Management, 2011, 4, 222-226

doi:10.4236/jssm.2011.42026 Published Online June 2011 (http://www.SciRP.org/journal/jssm)

Risk Migration in Supply Chain Inventory

Financing Service

Zheng Qi n1, Xiaochao Ding2

1School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, China; 2Informa-

tion Engineering College of Yangzhou University, Yangzhou, China.

Email: {morris.brenna, federica.foiadelli, dario.zaninelli}@polimi.it, [email protected]

Received January 17th, 2010; revised March 17th, 2011; accepted April 7th, 2011.

ABSTRACT

Inventory financing affects the risks o f both for banks and supply cha in co mpa nies. Trad itio nally, su pp ly chain research

focus more on material flow than financial. We construct a supply chain financing risk-information migration model

(RMM). In this mod el , we discussed the preconditions to adopt inventory financing when the enterprises are facing cash

constraints. And we simulated th e whole operate of supply chain and bank beha vior with Matlab. The simulatio n result

shows if loan conditions are satisfied, the total risk value is reduced. Risk migration happens in the financing process.

In this process, information-risk proportions are more reasonable.

Keywords: Supply Chain, Inventory Financing, Value of Risk

1. Introduction

Modern corporate finance theory is founded on the

proposition that financial capital is supplied to firms by

investors who have an “expectation of return”, and that,

Cavinato (1991) research show supply chain can reduce

cost, improve quality and make lead time shorter [1],

thus it can improve competence of the whole supply

chain. In traditional supply chain, researchers focus more

on material flow than cash flow. It is essential to corpo-

rate supply chain research with finance theory. Recipro-

cally, such expectation represents the firm’s “cost of fi-

nancial capital” optimization along with materials in

supply chain operation. We observe that supply chain

theory begins with “irrelevancy” pronouncements about

a firm’s value being independent of its supply chain op-

timization. Risk sharing in supply chain financing, which

are ignored in most supply chain optimization, in re-

sponse to these unrealistic assumption, theoretical de-

velopment has subsequently come to be directed at pro-

viding models that are descriptive of the way corporate

financial with supply chain [2]. To this end, supply ch ain

financial has increasingly been recognized as first order.

Supply chain structure is defined as the associations

among supply chain members [3]; this structure can

benefit both vertical and horizontal connected companies

[4]. Aberdeen Group defines Supply Chain Finance (SCF)

as “a combination of Trade Financing provided by a fi-

nancial institution, a third-party vendor, or a corporation

itself, and a technology platform that unites trading part-

ners and financial institutions electron ically and provides

the financing triggers based on the occurrence of one or

several supply chain events.” Banks can offer SCF solu-

tions that enable their customers to lower costs and create

financial stability in their end-to-end supply chain-and

create deeper and broader customer relationships in the

process.

Inventory financing is a kind of supply chain finance,

which is banking line of credit secured by the company’s

inventory. Companies with tangible inventory and a

proven sales history and good credit since lenders aren't

really interested in taking possession of your inventor y if

you can't make your loan payments. John A. Buzacott &

Rachel Q. Zhang (2004) researched on the deposit and

loan decision process of supply chain companies and

banks [2]. N. R. Srinivasa Raghavan and Vinit Kumar

Mishra (2009) consider a two-level supply chain with a

single retailer and a manufacturer, where both the firms

are facing financial constraints and cannot produce/order

their optimal quantity [5].

A commonly held opinion is that the low level of

long-term profit rates could be largely explained by a

decline in the compensation for risk. This opinion is

The work is supported by China National Nature Science Foundation

under Grant 70971083.

Risk Migration in Supply Chain Inventory Financing Service

223

supported by a great deal of empirical work devoted to

the measurement of bond risk premium and the analysis

of their dynamics [6]. While financing a firm, although a

lender tries to perceive its exposure to default risk by

looking into borrower’s accounts, due to lack of proper

information, the buying or selling cap acities of preceding

or following stakeholders, as in manufacturer and its re-

tailer of supply chain remain unkn own. Lend er’s analysis

is then based on certain assumptions. This lack of infor-

mation is a reality, especially fo r small firms that are not

publicly listed.

The paper is organized as follows. In Section 2 we in-

troduce basic notation, terminology and assumptions.

The risk information migration model RMM model and

solutions is presented in Section 3. We discuss inference

and parameter estimation for RMM and presented ex-

periment results in Section 4. Finally, Section 5 presents

our conclusions.

2. Assumptions, Notations

For simplicity we assume that both the firms have no

other assets but the cash available with them before they

commence their respective activities. Both manufacture

and retailer have no fix asset such as land, buildings,

machines etc. Account payable, account receivable, cash,

inventory and short term borrowing are considered in the

model. r

q are predicted based on constant elasticity

form. The expected quantity of production is equal with

mathematical expectation of r

q (



qEq

). Because

of cash constrain ts and ability to get loan from bank, real

quantity is less than expected quantity. Manufacture

firstly predicts the retailer’s purchasing before producing,

and decides a price m

p of finished product. Based on

the cash constraints of manufacture, im

L will be decided.

Bank will evaluate the risk and give a max loan available

for bank. Retailer predicts a market demand and purchase

from manufacture. At any time, cash owned by manu-

facture and retailer greater than zero, or they will bank-

rupt.

VaR is adopted to calculate risk value of manufacture

and bank loan. It is equal the maximum loss from the

specific confidence level. Based on Jorion, 1997, we can

calculate VaR with Equations (1) and (2) [7].



VaR E





(1)



VaR E





(2)

A simple two-stage supply chain is considered that

consisting of a single manufacturer and a retailer. Manu-

facture produces goods at a constant rate and ships it to

retailer with zero lead time. Retailer is of the classical

newsvendor type. Retailer returns the defective quantity

to manufacture who is liable to compensate for it at the

end of the period. One bank provides loans to both manu-

facture and retailer if they applied and passed evaluation

of risk level.

i Interest rate of bank

'i Interest rate of deposit where ii



Current cash of manufacture

Price of raw material manufacture bought from supplier





It Raw material inventory of manufacture

c Production cost of manufacture



 Expected profit without inventory finance



Real profit without inventory finance



 Expected profit with inventory finance



Real profit with inventory finance

 Expected quantity of product being produced by manu-

facture

q Real quantity need to be produced by manufacture

q Retail quantity being sold

Price of raw material

Price of product manufacture selling to retailer

Current cash of retailer



Coefficient of labor changing to product

y Account receivable of manufacture

y Account receivable of retailer

After risk evaluation, lend available from bank to

manufacture

After analysis of market information, load applied from

manufacture to bank

z Accounts payable of manufacture

z Accounts payable of retailer

Finished product inventory of manufacture

VaR Value at risk of retailer in borrowing from bank

VaR Value at risk of manufacture in borrowing from bank



The portion of VaR of bank loan after standardized



The portion of VaR of manufacture earnings after stan-

dardized

3. The Model

3.1. Bank Profit from Loan

The cost of bank cash is equal'i, thus the cost of manu-

facture cash is i. Based on maximum expectation of

return principle, we can easily get condition of ii





The bank can predict the payable of manufacture after

one period of product time.





min ,

mmrm

Payableq qp (3)

If manufacture apply loan from bank without mortgage,

the expected profit of bank as follow:















min1,min,1 '

Lom mrmom

Li qqpLi







 (4)

By the profit function 4, when









Risk Migration in Supply Chain Inventory Financing Service

224



min ,

mr m

qqp

 bank can get more profit by improve

L. When







1min,

omm rm

Li qqp , no matter how

much bank loans, bank will loss profit. So the maximize

bank profit and exist condition s show as follow:











maxmin , 1

min ,1

1min, 1'

Lmr

omm rm

omm rmom

qq i

Lqqpi

Li qqpLi















 









(5)

When adding inventory mortgage to exist bank profit

functions, we can get the object function of bank profit

is:









'min (1),min{,}

min ,

omm rm

rrmf fmom

fmmm r

Li qqp

IsI Li

Iq qq







 











(6)

In a similar way, we can get the maximum profit of

bank when manufacture applied inventory mortgage.















max'min ,1

min,/ 1

1min,

Lmrmffm

ommrmf fm

ommrmr rmffm

qqp sIi

LqqpsIi

Li qqpsIsI

















 











(7)

3.2. Manufacture Profit from Production

Manufacture decides the expected most profit produce

quantity m

. Then manufacture will apply a loan ofim

the received loan of manufacture is



min ,

momim

LLL.

We can get profit of manufacture as follow:







min ,

mmrmlrmmm

qqpc pqiL





(8)

L is used to conquer the shortage of cash, because

, manufacture will maximize the usage of cash

available of its own, at the end of production period,

x. The initial cash of manufacture is 0m

. By bor-

row from bank, manufacture have more opportunities to

maximize m





mmmmmim

mm mm

ml rm

qp cq iL

cq xL

ccp

















(9)



mmmmmim

mm mim

qp cq iL

qp xiL









(10)



mmmmmim

m mmmmmm

mm mm

qp cq iL

qp cq icqx

qp ciix





 







(11)

From Equations (10) and (11), we can get the precon-

ditions of loan are 0mm m

qp x and





pc i

When the maximize profit is satisfied,





max ,0

imm mm

Lcqx

3.3. RMM Model and Conditions

Based on the analysis both of bank and manufacture de-

cisions, the cash investment and VaR value of both bank

and manufacture should be balanced, we conclude the

following RMM model:





min mm bm

VaRxVaR L (12)

Subject to:















min{, }1

1min,

max ,0

min(1),min,1'

()

ommrmf fm

ommrmr rmffm

imm mm

mmmmmim

Lom mrmom

LLL

MMM

LqqpsIi

Li qqpsIsI

Lcqx

qp cq iL

Li qqpLi

VaR E









 































(13)

3.4. Solutions to RMM Model

We use matlab simulate the whole manufacture, retail

and loan process with the model built above (Figure 1),

the process of simulation shows as Figure 2. The de-

mand for a consumer product and populate the model

with N consumers. The basic demand function for each

agent is well behaved:

DfP



 (12)

The i

are selected at random and represent the het-

erogeneous tastes of customers. The sum of the individ-

ual demands N



represents the whole market de-

mand. For fashion goods, the size of the market can be

assumed small compared to consumers’ incomes and can

therefore reasonably ignore the difficulties which the

Sonneschein, Mantel, Debreu theorems (for example

Sonnenschein 1972) raise for the shape of aggregate de-

mand functions [8]. The demand curves for each indi-

vidual customer are well behaved, and we assume that

the sum of these is also well-behaved.

We calculate VaR follow four steps as follow:

1) Based on Equation (12), calculate the market de-

mand series





122

rr rrn

qqq q and then we can get

expectations of





Eq (



qEq

which means the

manufacture can predict the market demand in the long

Risk Migration in Supply Chain Inventory Financing Service

225

DfP







（）

0mm

L

()

qEq







()

mtmmmmim

xpcqiL 

Figure 1. RMM model in simulation experiment.

ManufactureBank Retailer

DfP

()

qEq



122

{, ,}

rr rrn

qqq q

(/)

lrmmm

Ccp qx



 

min{, }

mr mffm

qqpsI







Figure 2. Flow of simulation experiment.

run);

2) Select data basing on cash constrain ed conditions of

0mm m

qp x and





pc i

3) Calculate



and m



based on Equations (5),

(6), (7) and (8) .

4) Calculate m

VaR and b

VaR based on Equations (1)

and (2).

Necessary and sufficient conditions on the bivariate

utility function v ary according to the conditions imposed

on the joint distribution of the risks. If only independent

risks are considered, then any utility function which is

concave in its first argument will satisfy the condition of

risk aversion. If risk aversion is required for all possible

pairs of risks, then the biv ariate utility function has to be

additively separable.

4. Experiments Results (Table 1)

The operating of supply chain is divided into a certain

number of periods and the model with suitable demand

forecasts is solved to yield scheduling/planning decisions

for each period, and only those belonging to the first pe-

riod are implemented. At the end of the first period, the

state of the system, including inventory levels, is updated

and the cycle is repeated with the horizon advanced by

Table 1. Typical data results of several experiments.

q m

VaR



VaR







40000 40 28 20 3256.23 5675.20 7846.01 1102.30 0.71 0.16

40000 80 50 40 1340.35 4521.32 5769.20 716.03 0.81 0.14

40000 40 30 28 4341.35 6512.20 7524.63 1341.24 0.63 0.17

30000 40 30 28 2571.92 4374.34 4529.84 857.34 0.64 0.16

30000 80 28 30 1136.22 2456.43 4281.23 910.20 0.79 0.27

30000 80 50 35 1263.28 4320.43 5472.21 702.16 0.81 0.14

Figure 3. Relation curves be twe e n pr oduc t quantity and VaR.

Risk Migration in Supply Chain Inventory Financing Service

226

one period considering the demand forecast for the new

period, which is now available. Therefore, the determi-

nistic formulation next described comprises a set of

planning periods, and only the first one includes the de-

tailed scheduling decisions with shorter time increments.

Such detail period moves as the model is solved in time,

thus the term rolling horizon.

Calculate VaR of both manufacture and bank, then

standardize VaRto [0,1], then we can get



LL L M

VaR VaR VaR



 basing on Equation (1) and

(2). Get



by 1



 , Table 1 shows the typical

data results of several experiments in computer simula-

tion when 01000

x、0.10i and '0.06i. With

different initial variables, the bank Va R will decrease

when adopt inventory mortgage, the potential profit is

growing. For the manufacture, after use inventory mort-

gage, VaR is larger than before. The potential income is

growing because bank can offer more loans which reduce

the manufacture shortage of cash, so the manufacture can

produce more to maximum profit.

When the manufacture satisfies 0mm m

qp x and



pc i

, accompany with market demand in-

creasing, the VaR of bank decrease because manufac-

ture’s capability of making profit. If using inventory

mortgage, the VaR value for manufacture is increasing

because more cash are put in producing and inven-

tory(Figure 3).

5. Conclusions

We discussed manufacture and retail supply chain struc-

ture which both facing cash-constrain and a bank that

finances the manufacturer. Supply chain inventory mort-

gage must satisfy preconditions of 0mm m

qp x and



pc i, that is member of supply chain will use

self-owned capital before using inventory mortgage, and

the cost of loan must less than the profit rate. In inven-

tory mortgage, both bank and manufacture are benefit

because the risk migration. After migration of risk, it is

more compatible with the information shared between

supply chain member and bank. For supply chain mem-

bers, they have more market information than bank in

production operate process, after sharing inventory in-

formation with bank, this reduce the bank shortage in-

formation. So the migration of risk can help optimize the

whole supply chain and bank.

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