Ijeart02508

International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

Considering fairness preference in the supply chain carbon emissions decision analysis HUANG Xiang-yi Abstract—Under

linear

demand

common

conditions,

problems

facing

mankind,

and

assuming there is a two-echelon supply chain

representatives from 195 countries as well as

carbon emission reduction system composed of a

from the European Union attended the 21st UN

supplier and a retailer, we introduce the Nash

General Assembly on Climate Change in Paris,

Bargaining fair Solution into the model, engage in

France, and finally reached a new global climate

case studies to examine the supplier's optimal

agreement. “The Paris agreement" points out

wholesale price and his optimal carbon emission

that countries would not only strengthen the

reduction as well as the retailer's optimal retail

global response to the threat of climate change,

price. For that reason, we consider three different

control the global average temperature rise

cases such as the retailer having fairness preference,

comparatively with pre-industrial levels within 2

the supplier having the fairness preference and

degrees Celsius, but also take measures to

both of them enjoying fairness preference at the

control the temperature rise level within 1.5

same time. The study found out that both supplier’s

degrees

wholesale price and retailer’s sales price are

stipulates that the different parties would have to

affected either by their own fairness preference or

participate in the global action on responding to

by that of the other party, more important in the

climate change in a "self-contribution" way.

game the supplier will not actively take the

Developed countries will continue to take the

initiative to reduce carbon emissions since the

lead in emissions reduction, provide capital,

volume will progressively decrease as a supply

technology and capacity building to support

chain entity’s fairness preference degree increases.

developing countries to mitigate and adapt to

Celsius.

climate

change.

Besides,

China

as

the

a

agreement

responsible

Key words —supply chain; carbon emission;

developed country, early by the eve of the 2009

fairness preference; Nash bargaining

Climate Change Conference in Copenhagen, has made a responsible commitment to the world: by

I.

INTRODUCTION

2020,

China's

carbon

dioxide

emissions

percentage in its unit GDP will reduce 40% -

Faced with an increasingly serious problem

45% compared to 2005.

of global warming, reduce carbon dioxide emissions has become a consensus of the

La Roche et al pointed out that more and

international community. However, the current

more consumers are conscious of the importance

situation

not

of green consumption and wish to buy green

satisfactory; according to the United Nations

products, even at a higher cost [1]. Li et al

Environment Program (UNEP) “Emissions gas

argued that in a new mode of economic growth,

report” published in 2013, the world total carbon

people during shopping give priority to goods

dioxide emissions volume should not exceed 44

produced

billion tons by 2020. Yet, the data has reached

regulations. Therefore, the study of decisions on

50.1 billion tons in 2010 and if this issue is not

the supply chain carbon emissions reduction is

controlled, it is expected to reach 590 million

of high significance for enterprises [2].

about

carbon

emissions

is

under

environmental

protection

tons by 2020. Therefore, we are urged to take

Choi et al studied the problem of the supply

further measures to reduce carbon dioxide

chain pricing game based on a two-echelon

emissions. Faced such a serious situation, all

supply chain made up of two suppliers and a

countries are seeking cooperation to address

retailer

27

[3].

Zhang

et

al

discussed

the

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

single-cycle green supply chain pricing decisions

decision makers would also focus on an

and coordination problems under the coexistence

equitable distribution of benefits, and fairness

of non-green products and green products

preference can affect decision-making behavior

market demand[4].Xu et al based on the game

of the economic entity [15]. Cui et al studied the

theory, studied the decision making problem in a

effect of fairness preference on the coordination

closed loop supply chain where the supplier is in

of supply chain when there is certainty in the

the dominant position[5]. Qian et al studied in

demand [16]. Wei et al discussed optimal pricing

the case of decentralized decision making, the

strategies in a dual-channel supply chain with

optimal ordering policy and pricing decision

fairness preference and risk aversion [17]. In the

problem on the basis of a supply chain system

case of nonlinear demand, Caliskan–Demirag

which consists of one manufacturer and two

discussed the effect of fairness preference on the

retailers [6]. Wang et al studied the problem of

coordination of the supply chain when one of the

optimal decision making, when the market

main body of the chain has fairness preference

demand is affected by price and advertisement

[18]. Ho et al studied the effects of different

investment, on a supply chain composed of

types of fairness preference on a supply chain

traditional retail channels and direct sales

system based on a chain composed of one

channels [7].

supplier and two retailers [19]. Under a

Benjaafar et al considered the factors

non-linear demand constraint, Wei et al used

affecting carbon emission reduction in the

fairness preference theory to study the problem

supply chain system, and studied the low carbon

of the coordination of supply chain [20]. Zhang

supply chain operation [8]. Zhang et al

based

et al used the game theory to analyze

on the newsboy model, studied the optimal

corresponding pricing decision models, and

production strategy under the constraint of

studied the closed-loop supply chain pricing

carbon emissions [9]. Jaber et al studied the

considering

problem of cooperation between supply chain

decision-making

members in the case of a carbon transaction [10].

Stackelberg theory, researchers studied the

Zhang et al studied yield, pricing and profits

impact of the fairness concern on the supply

issues under different cooperation mechanisms

chain subjects’ decision-making when retailers

on the basis of a three-level supply chain [11].

and suppliers have fair concern [22].

fairness [21].

concerns On

the

behavior basic

of

Song et al based on the newsboy model

Currently, several research articles have

discussed the mandatory emission reductions,

discussed about fairness from the equitable

carbon taxes and the total amount restriction

allocation of carbon emissions rights and carbon

impacts on the optimal decision [12].Wang

emissions trading fairness aspects. Haddad et al

investigated the optimal contracts and the

compared the cap-and-trade model with the

manufacturer’s pricing strategies based on a

greenhouse gas emissions trading reduction

supply chain consisted of a single-manufacturer

model based on applicability and fairness criteria

and single-retailer [13]. Li et al took a

[23]. Onigkeit et al studied the carbon trading

two-echelon supply chain system as research

system considering fairness factors [24]. Zhang

object to discuss the impact of the carbon tax

et al studied efficiency and fairness in Chinese

policy on the decisions of the supply chain

provinces carbon emission rights allocation

companies [14].

problems [25]. Zhao studied the problem of

Some behavioral economists show that

international aviation carbon emissions rights

decision makers tend to have fairness preference,

fair allocation. Based on the responsibility

and while thinking about their own interests, the

principle, Zhao advanced a method for fair

28

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

allocation of international aviation emissions

emission reduction,  represents the

rights [26].

carbon

emission

reduction

effect

coefficient, with a  0 , b  0 ,    ,

The main issues discussed in the articles

e.

C. The supplier's

mentioned above are fair distribution and transaction from a general aspect. However, fairness in the supply chain is very different. It is

reduction cost is

mainly about fairness is what is gained after

carbon

e 2

emission

2

,and the carbon

comparison with another subject of the supply

emission reduction cost coefficient is

chain or oneself; few papers have been published

 (   0 ).

about carbon emissions and fairness preference

D. The retailer’s profit function is ; the  r  ( p  w)(a  bp   e)

in the supply chain. Li et al in a low-carbon environment, studied the influence of different

supplier’s

agreements on the supply chain coordination when retailers have fairness preferences, and

profit

function

 s  ( w  c)(a  bp   e) 

especially the issue of pricing agreement when

e

is

2

2

; and

the supplier has fairness preferences [27]–[28].

the supply chain profit function is

Based on the case where the supplier has the

  ( p  c)(a  bp   e) 

fairness preference, Lin studied the influence on the supply chain members pricing decisions and

 e2 2

.

E. The subscript rn represents only the

on emission reduction level [29].

retailer with fairness preference. The

On the basis of the above documents, this

subscript sn represents only the

paper considers a supplier carrying carbon

supplier with fairness preference. The

emissions reduction, explores the effect of

subscript bn represents both retailers

fairness preference coefficient on the decisions

and suppliers with fairness preference

of supply chain members in three different cases

at the same time. The superscript *

such as the supplier with fairness preference, the

represents the optimal solution.

retailer with fairness preference and both III.

supplier and retailer having fairness preferences

THE SUPPLY CHAIN SUBJECTS DO NOT HAVE FAIRNESS PREFERENCE

at the same time by using the Nash bargaining fair solution.

When the supply chain subjects do not have fairness preference, it is applied between the

II.

PROBLEM DESCRIPTION AND HYPOTHESIS

supplier and the retailer a Stackelberg game, the

A. The supply chain consists of a

supplier decides his wholesale price and the

supplier s and a retailer r. c represents

quantity of carbon emission reductions before

the Unit Production Cost of the

the retailer decides his sales price. The purpose

supplier. w represents the wholesale

of the supplier’s and retailer's decision is to

price of the supplier. p represents the

maximize their profit. Using the inverse method,

retailer's sales pwc0

the first derivative and the second derivative of

price

with

the retailer's profit function are as following:

B. The market demand is a linear function D  a  bp   e ,a represents

 r  r  2b  2bp  bw   e+a , p p 2 2

the basic market demand, b represents

 2 r  0 , the retailer has the optimal p 2

the price impact’s coefficient, e represents the unit product carbon

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

pricing p

IV.

 r 0, p

When

NASH BARGAINING FAIR SOLUTION

Indeed, fairness has relative characteristics, the strength and contribution of the supply chain

bw+ e+a p 2b

members affect fairness in profit distribution. So,

(1)

the use of the Nash bargaining fair solution

Replacing (1) in  s , we obtain the first

considering the strength or the contribution of the members of the supply chain reflects fairness

derivative and the second derivative of the

relativity, and discredit previous researches

supplier's profit function.

about fairness in the supply chain that consider

 s 1 1 1  s  b  bc  bw   e+ a , w2 w 2 2 2 2

absolute fairness limitations.

In this paper, Nash bargaining fair solution

 2 s  0 , the supplier has the optimal w 2

is introduced as a reference solution helping the supply chain subjects to perceive fairness.

pricing w

Assuming the fair solution of Nash bargaining is

 When s  0 , w w=

 r and s , according to the literature [30] when

bc+ e+a 2b

the supply chain subjects have fairness

(2)

preference, the utility function of the supply

  s 1 1   c + w   e , 2s   e e 2 2 2

chain subjects is

U r   r  r ( r   r )  (1  r ) r  r  r

 2 s  0 , the supplier has the best carbon e 2

U s   s  s ( s   s )  (1  s ) s  s  s

emissions e When

 s 0, e

  w  c e 2

U  Ur  Us The fair solution for retailers and suppliers is then

(3)

From (2) and (3) are obtained the optimal wholesale price of the supplier and the optimal carbon emission reduction:

w*  e* 

2bc  c 2  2a 4b   2

(4)

  a  bc  4b   2

(5)

V.

r 

1  r  2  r  s

s 

1  s  2  s  r

CONSIDERING ONLY THE RETAILER HAVING FAIRNESS PREFERENCE

When only the retailer has fairness preference, s  0 . His utility function is then

Introduce (4) (5) into (1), to obtain the optimal price of retailer,

U r  1  r   r 

bc  c 2  3a p  4b   2 *

r 1  r   2  r

 (1  r )( p  w)(a  bp   e)

Because p*  w *  c   , e*  0 , and the



market demand being very high, without loss of

r (1  r )  1  ( p  c)(a  bp   e)   e 2  2  r  2 

The supplier does not have fairness

generality, so 4b   2 Should be greater than 0.

preference, so the supplier's utility function is Us   s Proposition 1: When only the retailer has

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

fairness preference, the retailer's utility function

U s  0, e

When

and the supplier's utility function are strictly

( w  c) 2

concave functions, the best price prn* of the

e

retailer drives U r get the maximum

Respectively (7) (8), the optimal wholesale

* prn 

value ,and

bcr  3ar  2bc  2c  6a . The 2(2br  4b   2 ) 2

price and the optimal carbon reduction are obtained

supplier's optimal wholesale price and optimal

when

wrn 

 rn

respectively w and e drive Us value to the

ern 

2bcr  2bc  c 2  2a , 2br  4b   2

 a  bc   2br +4b  

2

r

0,

* ern

r

0,

prn* 0 r



4b 2  a  bc 

 2b

r

 4b   2 

2

With p  c , so a  bc   Obviously (6)

the

r

0

ern* and prn* on r are obtained.

1 1  1 U s  ( w  c)  b（  （wb   e  a）   e 2 r c  w） 2 4  2

and

* wrn

In the same way, the partial derivatives of

function as follows.

* ern

r

second



2 b  a  bc 

 2b

r

 4b   2 

2

* 3 2  a  bc  prn  r 2  2b  4b   2 2 r

 Us  Us  0,    0 2 w e 2 U s is a strictly concave function, the 2

Obviously

supplier can get the best wholesale price and the optimal carbon emission reduction.

* ern

r

0,

prn* 0 r

Completed.

U s  0, w

bcr  bc   e  a b(2  r )

* wrn

Conclusion 1

r

If we replace (6) in U s , we will get a

w

Completed.

* wrn

U r  0, p

bcr  bwr  2bw  2 e  2a prn  4b

When

bcr  3ar  2bc  2c 2  6a 2(2br  4b   2 )

Prove: The partial derivative of wrn* on r

function, and the retailer has the best price.

2

(9) (10)

2br +4b   2

* prn 

U r is a strictly concave

The first derivative derivative of U s are

2bcr  2bc  c 2  2a 2br  4b   2

retailer has fairness preference.

。

r (1  r )(bp   e  a  ( p  c)b) 2  r

When

fairness

retail price of retailer are obtained when the

derivative of the Ur U r  (1  r )(bp   e  a)  (1  r )( p  w)b p

 2U r 0 p 2

has

Introduce (9) (10) into (6), the optimal

Proof: The first derivative and the second



retailer

 a  bc  

ern 

maximum and wrn 

the

preference.

carbon emission reduction which are  rn

(8)

Conclusion 1 indicates that the supplier's wholesale price and carbon emission reduction are influenced by the retailer fairness preference

(7)

degree and reduced with the increase of retailers’

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

fairness preference. As for the retailer’s selling

 Ur  -2b  0 U r is a strictly concave p 2 2

price, it decreases with the increase of his own fairness preference. It suggests that when the retailers has fairness concerns, the supplier

function, and the retailer has the best price.

reduces the wholesale price, transferring some of

With

U r  0, p

p

bw+ e+a 2b

his profits. At the same time, due to the decrease of the wholesale price, the supplier will not take the initiative of emission reduction, so as to

Introduce (11) into U s , we obtain the first

reduce cost, while retailers would lower their

derivative and the second derivative of U s .

selling prices to expand the demand for commodities, and to ensure the supply chain

 2U s b(s2  5s  4)  2  2  s  w2

members fair profit distribution.

VI.

CONSIDERING ONLY THE SUPPLIER HAVING

 2U s  2 s2  4bs   2 s  4b  2  2  s  b e2

FAIRNESS PREFERENCE

When we consider that only the supplier has fairness preference, r  0 , the utility

 2U s  2U s  0, 0 2 w e 2 So U s is a strictly concave function, the

function of the retailer is U r   r , the utility function

of

the s 1  s  U s  1  s   s   2  s

supplier

supplier can get the optimal wholesale price w and the optimal carbon emission reduction e

1    (1  s ) ( w  c)( a  bp   e)   e 2  2  



when the supplier has fairness preference. U s U s  0 and  0 , the optimal w e

s (1  s )  1  ( p  c)(a  bp   e)   e 2   2  s  2 

wholesale price and the optimal carbon reduction are :

Proposition 2: When only the supplier has fairness preference, the utility functions of the

 wsn 

retailer and the supplier are strictly concave

 esn 

functions, and the retailer’s optimal price prn* drives * psn 

 a  bc  

(12) (13)

bs  4b   2

Introduce (12) (13) into (11), the optimal

as  bc  c  3a , The supplier's bs  4b   2

retail price of retailer are obtained when the

2

retailer has fairness preference. * psn 

emission reduction which are respectively wrn

as  2bc  c 2  2a bs  4b   2

 a  bc   bs  4b   2

as  bc  c 2  3a bs  4b   2

Completed

and ern make of U s value the maximum one, and

 esn 

as  2bc  c 2  2a bs  4b   2

value to the maximum ,and

Ur

optimal wholesale price and optimal carbon

 wsn 

(11)

Conclusion 2:

* esn

s

When  2  2b ,

,

2b   2  4b ,

.

Proof: the first derivative and the second derivative of U r are:

* wsn  0 , when s

* wsn 0; s

When  2  b ,

32

0

* psn   ,when  2  b , s

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International Journal of Engineering and Advanced Research Technology (IJEART) ISSN: 2454-9290, Volume-2, Issue-4, April 2016

* psn 。 s

* psn p*   ; when  2  b , sn   . s s

* esn

Prove:

  bc  a  b



s

 b

s

Obviously

e

* sn

s

 4b   2 

Completed.

Conclusions 2 indicates that the retailer’s

2

selling price are influenced by the supplier fairness preference degree, increases with the

0

increase of the supplier fairness preference when

w 2b c  bc   2ab  a   2 s bs  4b   2  * sn



2

2

2

2

 2 (bc  a)  2b 2 (a  bc)

 b

s

 4b   2 

2



2

 2  b , and decreases with the increase of the

(a  bc) (2b   2 )

b

s

 4b   2 

2

the supplier's wholesale price and carbon emission are influenced by his own fairness preference, carbon emission reduction reduces with the increase of his own fairness preference ; the supplier's wholesale price increases with the increasing of his fairness

p b 2 c 2 bc 2  ab 2 a  2  2 s  b  4b   2  * sn

s



  a  bc   b   2 

 b

s

 4b   2 

supplier’s fairness preference when  2  b ;

2

although 4b   2   ,it cannot guarantee

preference when  2  2b , and decreases with the increase of his fairness preference

2b   2   and b   2  0 ,So the relationship

when

2b   2  4b .

between wsn* and s 、 e* and s requires further VII.

analysis:

THE SUPPLIER HAS FAIRNESS PREFERENCE

When b   2   , precisely when  2  b ,

When both the retailer and the supplier

because b and  are constants higher than zero, so 2b   2   , at this time

have fairness preference, their utility functions

w  , s * sn

are respectively: U r  1  r   r 

p ; s * sn

r 1  r   2  r  s

 (1  r )( p  w)(a  bp   e)

When b   2    2b   2 , when b   2  2b ,

CONSIDERING BOTH THE RETAILER AND



precisely

* wsn p*  0 , sn   ; s s

U s  1  s   s 

* wsn p*  0 , sn   . s s

In summary, when  2  2b , when 2b   2  4b ,

s 1  s   2  s  r

1    (1  s ) ( w  c)( a  bp   e)   e 2  2  

When 2b   2  0  4b   2 , precisely when 2b   2  4b ,

r (1  r )  1  ( p  c)(a  bp   e)   e 2   2  r  2 



* wsn 0 ; s

s (1  s ) 2  s  r

1 2  ( p  c)(a  bp   e)  2  e   

Proposition 3: When the retailer and the supplier has fairness preference, their utility

* wsn  0 ; when  2  b , s

functions are strictly concave functions, and the optimal price prn* of retailers drives U r to obtain

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a maximum value , the supplier's optimal

2(a  bc) (16) br s  4br  2bs  8b  2 2

* ebn 

wholesale price and optimal carbon emission

Introduce (15) (16) into (14)

wrn and ern allow give the maximum value of U s .

pbn* 

Proof: Let us find the first derivative and the second derivative of the U r .

ar s  bcr  3ar  2as  2bc  2c 2  6a br s  4br  2bs  8b  2 2

Completed

 U r 2br s  4br  2bs  4b  0 2  r  s p 2

Conclusion 3:

U r is a strictly concave function, and the

Prove:

2

* 2  a  bc  bs  4b  ebn  r  b   4b  2b  8b  2 2 2 r s r s

retailer has the optimal price when both the retailer and the supplier have fairness preference.

When pbn 

* ebn e*  0 , bn  0 . r s

U r 0 p

* 2  a  bc  br  2b  ebn  s  b   4b  2b  8b  2 2 2 r s r s

bcr  bwr  bws   es  as  2bw  2 e  2a (14) 2  s  2  b

Introduce (11) into U s , the first derivative

obviously

and the second derivative of U s are as follows:

* ebn e*  0 , bn  0 。 r s

Certificate completed

 2U s b(s 2  5s  4)(2  r  s )  2 w2 2  2  s 

Conclusions 3 indicates that when both the retailer and the supplier have fairness preference,

 2U s 2bs r   2s 2  2br  4bs   2s  4b  e2 2  2  s  r  b

the supplier's carbon emission reduction volume

 Us  Us  0, 0 2 w e 2 In this case, U s is a strictly concave function,

well as his own fairness preference. It shows that

and the supplier can get the optimal wholesale

in order to gain more profits, the supplier will

price as well as the optimal carbon emission

reduce carbon emission reduction.

reduction when both the retailer and the supplier

Conclusions4: when r 

2

reduces with the increasing of the retailer’s as

2

when members of the supply chain have fairness preference, it happens a fierce game. Generally,

have fairness preference.

Considering simultaneously

U s  0 and w

when r 

U s  0 , let us find the optimal wholesale price e

p* 2 2  2 , bn  0 ; s b

p* w* 2 2  2 , bn  0 and bn  0 。 s s b

Prove: * pbn 2 2 (a  bc)(s  3)  r  b   4b  2b  8b  2 2 2 r s r s

and the optimal carbon reduction of the supplier. * wbn  (bcr 2 s  ar s 2  4bcr 2

wbn* 1   (a  bc)(br 2 s3 2 r  2       b   4b  2b  8b  2 2 2 r s r s r s

4bcr s  4ar s  2as 2  12bcr  4bcs

8b r 2 s 2  4b  r s3  2 0b r2 s 3 b2

2c 2 r  2c 2 s  4ar  8as  8bc  4c 2

8a )

1 (2  r  s )(br s  4br  2bs  8b  2 2 )

r 2 s b4

3

s 1b6

2

 8b 0

r

2 2 s 3  32bs 2  8 2 s 2  64br  80bs  8 2 s  64b )

(15)

* pbn w*  0 , bn  0 r r

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*   r  2  (a  bc)(br  2b  2 2 ) pbn  s  b   4b  2b  8b  2 2 2 r s r s

r 

, (a  bc) (br  2b  2 ) A  B  w  s (1  r  s ) 2 (br s  4br  2bs  8b  2 2 ) 2

b (s  6)

* wbn

2

* bn

2bs  8b  2 2  2b 2s2  8b 2s  16b 2 2  8b 2  4 2

s

 0 .But

because

when s  0 ,

2bs  8b  2 2  2b 2s2  8b 2s  16b 2 2  8b 2  4 2 b (s  6)

A  2r2 s  r 2 s 4 2 r 8 r s2 2 s1 2 r 8 s 8 B  b (r 3s 2  6r 3s  5r 2s 2  8r 3  28r 2s  8r s 2  36r 2

, r 

40r s  4s  48r  16s  16)

and

r  0



,so

2bs  8b  2 2  2b 2s2  8b 2s  16b 2 2  8b 2  4 2 b (s  6)

2

Since

we

cannot

untenable,

is

judge

whether

r 

br  2b  2 2 and (br  2b  2 2 ) A  B 

2bs  8b  2 2  2b 2s2  8b 2s  16b 2 2  8b 2  4 2 b (s  6)

are positive or negative, we need to categorize

is then permanently tenable. So when r  0 ,

the analysis. Firstly, let us examine the positive

s  0 ,

and negative cases for br  2b  2

2

sales price is influenced by some parameters. It

2  2 , since a  bc is positive, so b

increases with the increase of supplier's fairness preference when r 

* pbn  0 ; when br  2b  2 2  0 , precisely s

p  0; s

when r  we

(br  2b  2 2 ) A  B

discuss

fairness preference, and increases with the

:

increase of his own fairness preference.

VIII.

r  0 , we ignore the two negative values,

,

more clearly the results, we will use a numerical example to analyze the results of the optimal

b (s  6)

decision in this section. Suppose a  300 , b  10 ,   5 , c  4 ,   2 . We introduce these

when

parameters into the above model, and through

2bs  8b  2 2  2b 2s2  8b 2s  16b 2 2  8b 2  4 2

Maple software obtain the optimal decisions.

b (s  6)

w

* bn

s

0

NUMERICAL SIMULATION

In order to discuss the model and illustrate

2bs  8b  2 2  2b 2s2  8b 2s  16b 2 2  8b 2  4 2

, r 

2 2  2 ; the supplier's wholesale b

price reduces with the increase of retailer's

When (br  2b  2 2 ) A  B   , with

r 

2 2  2 , and reduces with b

the increase of supplier's fairness preference

* bn

Next

0.

Conclusions 4 indicates that the retailer’s

2

when,

s

Completed.

When br  2b  2 2  0 , precisely when

r 

* wbn

Using the given parameters, let us firstly simulate the retailer having fairness preference.

;When

The retailer's level of fairness preference would impact the supplier's carbon emission reduction,

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wholesale price and the retailer's sales price.

when

As shown in Figure 1:

* wsn   and s

  4 , b   2   and

* psn   , results are in Figure 3; s

Figure

4

shows

2b   2  0  4b   2

 7

when and

w 0 s * sn

, and

* psn ; s

Figure 1:The relationship between carbon emission reduction, wholesale price, sales price and the fairness preference of the retailer

Figure 1 shows that the supplier's carbon emission reductions, wholesale prices and retail price reduce with the increase of the retailer's level of fairness preference. As well, with the increase of the level of fairness preference, the

Figure 2: The relationship between carbon emission

supplier's carbon emission reduction, wholesale

reduction, wholesale price, sales price and the degree of

price and retail price reduction trends tend to

fairness preference of suppliers ( b   2    2b   2 )

slow. It shows that with the increase of the degree of retailer's fairness preference, the supplier will reduce the wholesale price to meet the requirements of the retailer's profit, and reduce his own carbon emission to save costs.

When the supplier has fairness preference, the supplier's degree of fairness will impact the supplier's carbon emission reduction, wholesale price and the retailer's sales price. Since b ,   , will impact the supplier's wholesale price, the retailer's sales price and the level of the supplier's fairness preference, I assume that b and  values do not change , consider  equal to

5,4

and

b   2    2b   2

7.

 5

When and

w 0 s * sn

Figure 3: The relationship between carbon emission

,

reductions, wholesale prices, sales price and the degree of fairness preference of suppliers ( b   2   )

and

* psn   , results are as shown in Figure 2; s

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supplier's fairness preference degree. It means that when his fairness preference grows, the supplier may try to get more profit by reducing carbon emissions cost and raising the wholesale price.

Figure 4 shows that both the retailer’s sales price, the supplier’s carbon emission reduction and the wholesale price decrease with the increase of the supplier’s fairness preference. It can also be seen from the figure that carbon emission

reduction

is

very

remarkable,

indicating that the supplier in order to obtain a higher profit will drastically reduce carbon emission reduction.

Figure 4: The relationship between carbon emission

When retailers and suppliers both have

reductions, wholesale prices, sales price and the degree of fairness preference of suppliers ( 2b    0  4b   ) 2

2

fairness preference, the retailer's and the

Figure 2 shows that both the retailer’s sales

supplier’s level of fairness would impact the

price and the supplier’s carbon emission

supplier's carbon emission

reduction decrease with the increase of the

wholesale price and the retailer's sales price . As

supplier’s fairness preference, and the supplier's

shown in Figure 5,6,7and 8:

reductions,

the

wholesale price increases with the increase of his fairness preference. Figure 2 also shows that when the supplier has fairness preference, the supplier may increase the wholesale price and reduce carbon emission reductions to get more profit. Besides, it can be seen from figure 2 that when the supplier has fairness preference, the decline of the supplier’s carbon emission reduction is more rapid than the increase of the supplier’s wholesale price , indicating that in order to get more profit, the supplier will reduce carbon emission reductions, meaning reduce costs rather than raising wholesale prices.

Figure 3 shows that both the retailer’s sales price and the supplier’s wholesale price increase with the increase of the supplier’s fairness

Figure

preference, and the supplier’s carbon emission

reductions and the degree of fairness preference of suppliers

reduction decreases with the increase of his own

and retailers

5:The

relationship

between

carbon

emission

fairness preference. We can also figure out that with

the

increase

of

supplier's

fairness

preference, the increasing rate of the wholesale price is higher than that of the retailer's sales price, the trend of the supplier's carbon emission reduction lowers as well with the increase of the

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Figure 8:The relationship between wholesale price and the degree of fairness preference of the suppliers and retailers

Figure 5 shows that the supplier’s carbon Figure 6:The relationship between the sales price and the

emissions reduction trend decreases with the

degree of fairness preference of the suppliers and retailers

increase of fairness preference degree of the

( r



supplier and the retailer; From figure 6 and

2 2) b 2

Figure 7, we can find out that the retailer's sales price will change if the level of the retailer's fairness preference changes. When the retailer’s fairness preference is r 

2 2  2 , it is obvious b

that the sales price decreases with the increase of the supplier's fairness preference degree ( r is unchanged) ; and when the retailer’s fairness preference is r 

2 2  2 , the retailer’s sales b

price increases with the increase of the supplier’s fairness preference. From Figure 8, we can figure out that the supplier’s wholesale price increases with the increase of the fairness preference degree of the retailer and the supplier.

IX.

CONCLUSION

Under linear demand condition, this paper Figure 7: The relationship between the sales price and the

applies Nash bargaining game theory to build a

degree of fairness preference of the suppliers and retailers

fairness concern framework, analyze the effect

( r  2

of fairness preference on retailer’s sales prices ,

2

b

2 )

the supplier’s carbon emission reduction and wholesale price by building models and carrying out case studies. The aim of these studies is to find out the optimal decision that are accurate in

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the following three situations: the retailer has

is a future direction for researches.

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