Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 10, No. 1, 2023 

 

149 

Research	on	the	Optimal	Strategy	of	Supply	Chain	
System	Considering	Carbon	Emission	Reduction	Level	
Jing Wang*, Fengshan Si, Zhen Yu 

School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China 
* Corresponding author: Jing Wang (Email: crystalstella@126.com) 

 

Abstract: In response to the decision-making problem of a secondary supply chain system composed of manufacturers and 
retailers, the optimal strategy of a master-slave game was studied, considering carbon emissions reduction. We compared and 
analyzed the differences in optimal strategies with and without coordination mechanisms, and explored the impact of sensitivity 
on the optimal strategy. Research has shown that the optimal profit of manufacturers and retailers under coordination mechanisms 
is greater than that without coordination mechanisms; Wholesale prices, carbon reduction levels, retail prices, and manufacturer 
profits are all negatively correlated with price sensitivity and positively correlated with carbon reduction sensitivity, while retailer 
profits are the opposite; There is an optimal cost sharing ratio that maximizes retailer profits. 

Keywords: Supply chain system, Carbon reduction, Optimal strategy, Game. 
 

1. Introduction 
With the proposal of carbon peaking and carbon neutrality 

strategies, the issue of supply chain carbon reduction has 
attracted the attention of scholars. A large number of scholars 
considered the impact of consumers' environmental 
awareness and low-carbon preference on the degree of carbon 
emission reduction and decision-making in the supply chain. 
Liu et al. [1] discussed the impact of carbon emission 
reduction cost sharing on the profit of the supply chain based 
on the carbon emission trading mechanism and consumers' 
low-carbon preference. Research shows that the increase of 
consumers' preference for low-carbon products can improve 
the income of supply chain enterprises, retailers have seen an 
increase in order quantity and profits. Han et al. [2] 
respectively established a Stackelberg game model under 
centralized decision-making, decentralized decision-making 
and revenue sharing contracts, and studied the impact of 
consumer environmental awareness and carbon emission 
reduction costs on the emission reduction efforts of upstream 
manufacturers in the supply chain under the carbon tax 
policies. The study found that enhancing consumer 
environmental awareness is conducive to improving the total 
revenue of the supply chain, while increasing carbon emission 
reduction costs will damage the profits of supply chain 
members. Zhang and Qin [3] studied the cooperative strategy 
of carbon reduction among supply chain members in a three-
level supply chain consisting of a manufacturer, a 
transportation enterprise, and a retailer, considering carbon 
limit trading policies and consumer environmental awareness. 
The proposed cost sharing contract can achieve Pareto 
improvement, while the two-part pricing contract can achieve 
Pareto optimization. On this basis, they also studied the 
pricing, carbon emission reduction and social welfare 
decisions of the supply chain system, considering transport 
carbon emissions and social welfare factors under the carbon 
tax policy, and proposed a cross ownership contract for 
coordination and optimization[4]. 

In addition, scholars have also conducted research on the 
coordination and optimization of low-carbon supply chains. 
Yin and Liu [5] explored the impact of carbon emission 

trading policies on carbon emission reduction decisions and 
coordination strategies in the closed-loop supply chain of new 
energy vehicles in the three-level supply chain participated by 
recyclers, and designed a revenue cost sharing contract based 
on the decentralized decision-making model. The results 
show that the contract can achieve complete coordination of 
the supply chain by reasonably setting the revenue and cost 
allocation ratio. Zhu et al. [6] explored the impact of retailers' 
horizontal and vertical fairness awareness on carbon 
reduction and pricing decisions in dual channel supply chains, 
taking into account consumer channel preferences, based on 
carbon tax policies. They utilized two pricing contracts to 
achieve a win-win situation for supply chain members. 

In summary, scholars have achieved rich research results 
on consumer low-carbon preferences, carbon emissions 
reduction, supply chain decision-making and coordination, 
which lays a solid foundation for this study. On the basis of 
existing research, this paper compares and analyzes the most 
effective strategies with and without coordination 
mechanisms, and provides an analytical formula for the most 
effective strategies; On the other hand, the impact of price 
sensitivity and carbon emission reduction level sensitivity on 
the optimal strategy was explored through numerical 
simulation. 

2. The Model 
This paper studies a secondary supply chain system 

consisting of a manufacturer and a retailer. Among them, the 
manufacturer is responsible for the product, the production 
cost per unit product is c  , the carbon emission reduction 
level is e , the product is sold wholesale to retailers at price 
w  , the retail price is p  , and the market demand for the 
product is q . 

Based on the above description, the following assumptions 
are made for the model: 

(1) The higher the level of carbon reduction, the higher the 
degree of low-carbon of the product; In markets where 
consumers have a low-carbon preference, the product demand 
is positively correlated with the level of carbon reduction, 

0e  . 



 

150 

(2) This paper only considers the one-time carbon 
reduction costs invested by manufacturers (such as 
production process improvement, etc.), which are not related 
to the quantity of products. The cost of achieving carbon 

emission reduction e   is 
2 / 2e  , and    is the cost 

coefficient, 0  . 
(3) To ensure that manufacturer and retailer are profitable, 

it is necessary to meet 0p w c   . 
(4) This paper studies the Stackelberg game model, in 

which the manufacturer as the leader, first decides the 
wholesale price w  and carbon emission reduction level e ; 
Retailer as follower, decides the retail price p last . 

Based on the above description, the market demand 
function of the product is: 

 
q a p e               (1) 

 
where a   is the potential maximum demand for the 

product,   is the sensitivity coefficient of demand to price, 
and    is the sensitivity coefficient of demand to carbon 
emission reduction level. 

3. Model Analysis 
Suppose that both manufacturers and retailers are perfect 

rationality decision makers, and they can obtain all the 
information needed for decision-making. Manufacturers need 
to bear high carbon reduction costs in order to improve the 
carbon reduction level of their products. This paper considers 
two scenarios: there is no coordination mechanism, where the 
manufacturer bears the cost of carbon reduction alone, 
represented by subscript 1. There is a coordination 
mechanism, where retailers share the cost of carbon reduction, 
represented by subscript 2. In addition, the superscript * 

represents the optimal strategy, and m  and r  represent 
the profits of manufacturers and retailers, respectively. 

3.1. Manufacturers bear the cost of carbon 
reduction alone 

Under this uncoordinated mechanism, the profit functions 
of manufacturers and retailers are: 

 

2
1 1 1 1 1

1
( , ) ( )

2
m w e w c q e           (2) 

         

1 1 1 1( ) ( )r p p w q             (3)  
                          

Proposition 1: When 
2 4 0   , there are optimal 

strategies 
*
1w  , 

*
1e  , and 

*
1p   that maximize both the 

manufacturer's and retailer's profits. where 
2

*
1 2

2 2

4

c a c
w

  
 
 




, 
*
1 2 4

c a
e

 
 





, 

2
*
1 2

3

4

c a c
p

  
 
 


   

 

Based on the reverse solution method, first, according to 
the profit function Eq. (3) of the retailer, the optimal retail 

price 1 1 1( , )p w e   is obtained when ensuring 1r  
maximum. Secondly, bring it into the manufacturer's profit 

function Eq. (2), and obtain 
*
1w   and 

*
1e  when ensuring 

1m   maximum and condition (I):
2 4 0    is met. 

Finally, bring both into 1 1 1( , )p w e  to obtain 
*
1p . Based on

*
1w , 

*
1e  

and 
*
1p ,  the optimal profit is obtained as follows: 

 2
2

*
1

2( 4 )
m

a c


 
 


 


, 
 
 

2 2

2
*
1

2 4
r

a c


  

 





 

where manufacturers and retailers must meet condition (II) 

a c  to ensure * 1 0m    and 
*
1 0r    in order to 

profit. 

3.2. Retailers share the cost of carbon 
reduction  

Under this coordination mechanism, retailers share the cost 

of carbon reduction, the sharing ratio is  , (0,1] ..At 
this point, the retailer, as a follower, decides on the retail price 
c and the sharing ratio   . The profit functions of 
manufacturers and retailers are: 

2
2 2 2 2 2

1
( , ) ( ) (1 )

2
m w e w c q e           (4)         

2
2 2 2 2 2

1
( , ) ( )

2
r p p w q e            (5)         

Proposition 2: When 
23 8 0   , there are optimal 

strategies 
*
2w , 

*
2e , 

*
2p  

and 
*  that maximize the profits 

of manufacturers and retailers. where 

   
 

2
*
2 2

5 8

2 3 8
w

aa c c    
  






 
, 

 
2

*
2

2

3 8

a c
e

 
 





 ,
2

*

8





 ,  

   
 

2
*
2 2

3 3 8 3

4 3 8
p

a c a c    
  






 
 

Proof: According to the reverse solution method, due to 
2

2 2
2
2

( , )
02r

p

p








 , there is an optimal retail price 

that maximizes the retailer's profit. Let 2 2

2

0
( , )r p

p

 



 

obtain: 

2 2
2 2 2( , )

2

a w e
p w e

 


 
       (6) 

 

By introducing Eq.(6) into 2m  , when condition (III): 
2 4 (1 ) 0       is satisfied, the Hesse matrix is 

negative definite, and there exists an optimal wholesale price 
and carbon reduction level that maximizes the manufacturer's 



 

151 

profits. Combining 2 2 2

2

)
0

( ,m w e

w





  and 

2 2 2

2

)
0

( ,m w e

e





 yields: 

    
 

2

2 2

2 1 2

4
(

1
)

1
w

c a    

  


  







   (7) 

 

 22
(

( )
)

4 1

c
e

a 
 


 


 
 

       

(8) 

                   
Bringing Eq.(7) and Eq.(8) into Eq.(6) yields: 
 

    
 

2

2 2

1 3 1
(

4
)

1
p

c a    

  


  







  

(9) 

             
Bring Eqs.(7) - (9) into Eq.(5), and when condition (IV): 

  28 1 2 5 0       is met, there exists an optimal 
carbon reduction cost sharing ratio that maximizes retailer 
profits. The optimal sharing ratio is: 

 
2

*

8





              (10) 

 
By bringing Eq. (10) into Eqs. (7) - (9), we can obtain: 

 

   
 

2
*
2 2

3 3 8 3

4 3 8
p

a c a c    
  






 

  

  (11) 

         

 
2

*
2

2

3 8

a c
e

 
 





             (12) 

 

   
 

2
*
2 2

5 8

2 3 8
w

aa c c    
  






 

   

 (13) 

         
Bring Eq. (10) into the above conditions (III) and (IV) to 

obtain condition (V): 
23 8 0   . 

Based on Eqs. (4)-(5) and Eqs.(10)-(13), the optimal profits 
for manufacturers and retailers are: 

 

   
 

2 2

2

*
2

8

8 3 8
m

a c




  

  







        (14) 

 

   
 

2

2

*
2

2
8

16 3 8
r

a c




  

  








      (15)   

3.3. Comparative analysis 
According to propositions 1-2, the optimal strategy with or 

without coordination mechanism is shown in Table 1. 
 

Table 1. Optimal strategies in two cases 

 *w  *e  
*p  *  *m  

*
r  

N 
2

2

2 2

4

c a c  
 
 

  
2 4

c a 
 


  

2

2

3

4

c a c  
 
 
  

— 
 2

22( 4 )

a c 
 



  

 
 

2

22 4

a c  

 




 

Y 
   

 
2

2

5 8

2 3 8

a c a c    
  

  



  
2

2

3 8

a c 
 



  
   

 
2

2

3 3 8 3

4 3 8

a c a c    
  

  



 2

8




    
 

2 2

2

8

8 3 8

a c  

  

 


    

 
2 2

2

8

16 3 8

a c  

  

 


  

Notes: N represents no coordination mechanism, Y represents coordination mechanism. 
 

Theorem 1: When a c  , * *1 2p p  , 
* *
1 2w w  , 

* *
1 2e e ; When a c , 

* *
1 2p p , 

* *
1 2w w , 

* *
1 2e e .  

The optimal strategy difference between the two scenarios 
can lead to theorem 1. Theorem 1 indicates that when the 
market demand for products is high, the optimal wholesale 
price, optimal retail price, and optimal carbon emission 
reduction level under the coordination mechanism are greater 
than those without the coordination mechanism. When the 
market demand for a product is low, the result is the opposite. 

Theorem 2: When a c , * *1 2m m  , 
* *
1 2r r  .  

From Proposition 1, it can be inferred that a c  and 
theorem 2 indicate that the optimal profits of both 
manufacturers and retailers under a coordination mechanism 
are greater than those without a coordination mechanism. 
From the perspective of manufacturers and retailers, they 

prefer to achieve higher profits by establishing a cost sharing 
and coordination mechanism. 

4. Numerical Simulation 
In order to more intuitively demonstrate the impact of retail 

price sensitivity, carbon emission reduction level sensitivity, 
and coordination ratio on the optimal strategy, the parameter 
values are: 1a   , 0.8   , 0.6   , 0.4   , 

0.1c   , based on meeting the conditional assumptions, 
conditions (I), conditions (II), and conditions (V). At this 
point, there is 1 0.08a c   . According to theorem 1 
and theorem 2, the optimal strategies under the coordination 
mechanism is greater than those without the coordination 
mechanism. After calculation, the optimal strategies for the 
two cases are shown in Table 2. 

 
 
 
 



 

152 

Table 2. Optimal strategy values for two cases 

 *w  *e  
*p  *  *m  

*
r  

N 0.9000 0.6000 1.3000 —— 0.1840 0.1280 

Y 0.9547 0.7459 1.3821 0.1406 0.1966 0.1305 
Notes: N represents no coordination mechanism, Y represents coordination mechanism. 

 

4.1. The impact of price sensitivity coefficient 
 on the optimal strategy without 
coordination mechanism 

Calculate 0.225  from condition (I), where  starts 
at 0.25. The impact of   on the optimal strategy is shown 
in Figure 1. and Figure 2. 

 

 
Figure 1. The impact of   on the optimal prices and 

carbon reduction levels 

 
Figure 2. The impact of   on the optimal profits for 

manufacturers and retailers 
 
Figure 1 and Figure 2 indicate that as retail price sensitivity 

increases, wholesale prices, carbon reduction levels, and retail 
prices decrease, manufacturers' profits gradually decrease, 
retailers' profits gradually increase, and finally tend to be 
relatively stable. Therefore, retailers and consumers are more 
inclined towards high price sensitivity, while manufacturers 
are the opposite. 

4.2. The influence of sensitivity coefficient of 
carbon emission reduction level on the 
optimal strategy without coordination 
mechanism 

According to condition (V), it can be seen that

8 / 3 0.9238   , [0, 0.9]   is set here. 
Figure 3 and Figure 4 indicate that product demand is 

more sensitive to carbon reduction levels, leading to 
significant increases in wholesale prices, carbon reduction 
levels, and retail prices. Manufacturers' profits gradually 
increase, while retailers' profits continue to decline. This 
indicates that the low-carbon market (where consumers prefer 
low-carbon products) is more advantageous for 
manufacturers, but consumers need to pay relatively high 
purchasing costs. 

 
Figure 3. The impact of   on optimal prices and 

carbon reduction levels 
 

 
Figure 4. The impact of   on optimal profits for 

manufacturers and retailers 

o
p

tim
a

l s
tr

a
te

g
y

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0

0.5

1

1.5

2

2.5

w
1
*

e
1
*

p
1
*

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

m1
*

r1
*



 

153 

4.3. The influence of cost sharing coefficient on 
the optimal profits with coordination 
mechanism 

For clearer graphical display, set [0, 0.6]   here. 

 
Figure 5. The impact of   on the optimal profits  

for manufacturer 

 
Figure 6. The impact of   on the optimal profits  

for retailer 
 

Figure 5 shows that the higher the cost sharing ratio, the 
more profitable the manufacturer will be, but retailers cannot 
always increase the sharing ratio. According to theorem 2, 
cost sharing is beneficial for both manufacturers and retailers. 
Specifically, for retailers, there is an optimal sharing ratio that 
maximizes its profit, as shown in Figure 6. When

0.1406  , the maximum profit for the retailer is 0.1305, 
while the profit for the manufacturer is 0.1966, which is 
consistent with Table 1. 

5. Conclusions 
On the basis of considering the level of carbon emission 

reduction, the optimal strategy of the secondary supply chain 
system is studied in depth. By constructing the Stackelberg 
game model, the optimal strategy and the analytical formula 
of the optimal carbon emission reduction cost sharing ratio 

are given, ensuring the profit maximization of manufacturers 
and retailers. Research has shown that establishing a sharing 
and coordination mechanism for carbon emission reduction 
costs can help improve the profits of manufacturers and 
retailers. However, the optimal wholesale price, carbon 
reduction level, and retail price are influenced by the demand 
for products and are not related to the coordination 
mechanism. The sensitivity of demand to price is negatively 
correlated with manufacturers' profits, but positively 
correlated with retailers' profits. The sensitivity of demand to 
carbon reduction levels is positively correlated with 
manufacturers' profits, while negatively correlated with 
retailers' profits. There is an optimal cost sharing ratio for 
carbon reduction that enables manufacturers and retailers to 
achieve optimal profits. 

Acknowledgment 
The authors thank the reviewers for their careful reading 

and pertinent suggestions. This work was supported by the 
Natural Science Research Project of Education Department in 
Anhui Province (2022AH050589); the School-level Science 
Research Project of Anhui University of Finance and 
Economics (ACKYB22015). 

Conflicts of Interest 
The authors declare no conflict of interest. 

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