Analyzing Risks Measurement and Transmission of Supply Chain with Retail

Price Fluctuation

Yonghong Li Lindu Zhao

2009-10-31

Contents

1. Introduction 2. Risks Model of a Supply Chain 3. Transmission Mode Analysis 4. Numerical Example 5. Conclusions and Extensions

1. Introduction

Knight the publication of risk, uncertainty and profit

March & Shapira et al.

define risks as uncertainties

Guo and Pu hold risks are the possibility of the risks outcome

Kaminsky & Reinhart

study the credit risk transfer between different countries

Beretta study the risk transmission of financial crisis between different countries and companies

1. Introduction

Kraljic propose a combination management framework of procurement

Hallikas divide risk factors of network of suppliers into four categories

Ojala and Hallikas analyze supplier investment risk, and how each could be managed

Wu et al. classify a broader set of supply chain risks as internal and external by the level of controllability

Li model supplier risk attitude with respect to risk aversion

Ye and Deng

analyze the transfer of costs structure when producers implemented VMI services, the transfer of costs structure would cause change of the profits

function of the main decision-making agents

1. Introduction

Wu & Olson consider three types of risk evaluation models within supply chains

Lee et al. consider pricing as a main cause of bullwhip effect, creates adverse effects such as excess inventories, backorders and inefficient use of resources.

Özelkan &Cakanyildirim analyze the impact of procurement price variability in the upstream of a supply chain on the downstream

Li & Zhao use the variances of profits of supplier and retailer to characterize their risk, respectively and analyze the transmission mode of risk by the

difference of variances of profits of retailer and supplier

Most papers generalize and introduce supply chain risk just from the micro level

Few papers analyze quantificationally the measurement methods, transfer process, and impact extent of risk in a supply chain caused by the fluctuation of price.

2. Risks model of a supply chain

c Production cost w Wholesale price

d Distribution price Retail price

QdThe orders of distributor Qr

The orders of retailer

M The purchases of supplier Market demand

a The maximum market demand b The price-sensitive coefficient

Figure 1. Supply chain flowing model without inventory

Supplier

Distributor

Retailer

Materials flow Capital flow

pdwc

To simplify the analysis, assumptions of the paper are as follows:

(1)The information of costs structure and market demand of supplier, distributor and retailer are perfect information, and all of the supplier, distributor and retailer are risk-neutral;

(2)The supplier, distributor and retailer are independent economic entities;

(3)The situations of out of stock and holding inventory are irrespective;

(4)The retail price is a random variable;

The market demand:

The relationships among the orders of retailer, distributor, purchases of supplier and the market demand:

a b

r dM Q Q

The variance of profits of retailer :

The variance of profits of distributor :

The variance of profits of supplier:

2 2( ) ( ) ( )DVar b d w Var

2 2( ) ( ) ( )SVar b w c Var

2 2 2 2( ) ( ) ( ) ( ) 2 ( ) ( ) ( )RVar b Var a bd Var b a bd Var Var

3. Transmission mode analysis

There is a ripple effect in a supply chain. Because of the ripple effect, the risk caused by a certain factor will flow along the supply chain when the factor of the chain flows. That is, the risk of downstream echelon caused by factors has changed, there are a series of ripple effects and it will cause the risk of upstream echelon arising from the relevant factors to change. There is reduction effect, invariable effect and amplification effect for the change.

Measuring the risk of retailer and distributor by the variances of profits, so the difference of risk is the difference of variances : 1V

1 ( ) ( )R DV Var Var 2 2 2( ) ( 2 )( ) ( ) 2 ( ) ( ) ( )b Var a bd bw a bw Var b a bd Var Var

The difference of risk between distributor and supplier is the difference of variances :

2V

22 ( ) ( ) ( )( 2 ) ( )D SV Var Var b d c d c w Var

Theory: In a three-supply chain system, a reduction effect on risks caused by retail price fluctuation takes place when the wholesale price and distribution price satisfy conditions of

21 1 1

2 0

w

dd c w

4. Numerical Example

Assume that the production cost and wholesale price are c=0.2, the maximum market demand and the price-sensitive coefficient are a=50 and b=0.1. The random variable subjects to the probability density function

1

( ) 3

0

p

f p p

1 2

2 3

p

p

others

Table 1. Expectations of retail price

The conditions of risks reduction effect is:15 1

{( , ) |1 1, 2 0, 1}22 5

ww d d w d

d

Figure 2. Cures of distribution price d, wholesale price w and differences

From the simulation model: when the wholesale price and distribution price satisfy certain

conditions in a three-echelon supply chain, risks of upstream echelon are lower than that of the downstream echelon and it is a reduction effect.

5. Conclusions and Extensions

Characterize the risks of supply chain members by variances of profits

Analyze the influence of distribution price and wholesale price on the transmission mode of risks caused by price fluctuation in a supply chain

When the distribution price and wholesale price satisfy certain conditions, the upstream will suffer lower risks caused by retail price fluctuation than the downstream echelon

Further research

to characterize the risk of multi-echelon supply chains

to research the risk of three-echelon supply chains with inventories

to measure the risk when considering the retail price as a random variable by other methods