Frontiers in Business, Economics and Management 
ISSN: 2766-824X | Vol. 12, No. 2, 2023 

 

1 

Financing	Mechanism	Design	of	Small,	Medium	and	
Micro	Manufacturing	Enterprises	with	Capital	
Constraints	in	Different	Life	Cycle	Stages	
Junhong Chen, Yonglong Wang* 

1 School of Business Administration, Chongqing Technology and Business University, Chongqing, 400067, China 
* Corresponding author: Wang Yonglong (Email: wyl@ctbu.edu.cn) 

 

Abstract: In order to solve the problem that manufacturers have sufficient funds when producing traditional products and lack 
of funds when producing green products, this paper considers three financing strategies: no financing, bank loan financing and 
internal financing, and constructs centralized decision-making and manufacturer-led Stackelberg game model. It is found that 
the wholesale price, production input, green input level and supply chain profit of the three financing methods are not optimal 
under the manufacturer-led decision-making. On this basis, aiming at the overall profit under centralized decision-making, this 
paper designs the combined contract of "revenue sharing contract + two-part cost + green cost sharing" to coordinate the supply 
chain, and puts forward the scope of optimal coordination of the combined contract under three financing models. 

Keywords: Financing optimization, Capital constraints, Green supply chain. 
 

1. Introduction  
Due to the global awareness of environmental deterioration 

and energy exhaustion [1], in recent years, in order to protect 
the environment, save resources and build a sustainable green 
economic system, countries have successively introduced 
relevant policies to promote the rapid development of the 
green economic system. In December 2019, the European 
Commission announced the European Green Deal to combat 
climate change and promote sustainable development. In 
February 2021, The State Council issued the Guiding 
Opinions on Accelerating the Establishment of a sound Green 
low-carbon Circular Development economic System, 
pointing out that it is necessary to establish a sound green 
low-carbon circular development economic system, ensure 
the realization of carbon peak and carbon neutrality goals, and 
promote China's green development to a new level. In 
February 2022, the U.S. Department of Energy released a 
Strategy to Protect Supply Chains for a Clean Energy 
Transition, including increasing domestic raw material supply 
to expand domestic manufacturing capacity, increasing clean 
energy deployment, attracting skilled U.S. clean energy 
workforce, and enhancing supply chain information and 
decision-making capabilities. In this context, more and more 
enterprises are slowly shifting from the traditional supply 
chain to the green supply chain, and constantly increasing the 
level of product green related technology investment, in order 
to improve their competitive advantage. For example,GAC 
Honda Automobile Co., Ltd launched the "green service" 
project, requiring dealers to adopt new equipment, new 
materials and new processes that are conducive to 
environmental protection [2]. H&M, a well-known fast 
fashion retailer, applies carbon emission reduction technology 
to reduce pollutant emissions in the manufacturing process 
and improve its competitiveness [3]. All these indicate that 
the implementation of green supply chain management by 
enterprises has become an inevitable trend [2]. 

However, in the process of implementing green supply 
chain management, enterprises, on the one hand, face 

financial constraints due to the high investment in technology 
related to the production of green products; on the other hand, 
enterprises will increase additional costs when implementing 
green supply chain, which leads to a certain conflict of 
interest distribution between upstream and downstream 
enterprises [4]. Therefore, for the green supply chain 
composed of manufacturers and retailers, it is of great 
practical significance to study the coordination contract 
mechanism under different financing decisions. 

The research related to this paper mainly involves two 
aspects: (1) The research on green supply chain financing. 
Zhang Daru et al. [5] constructed a green supply chain 
consisting of a single financially constrained manufacturer 
and a single retailer, and studied the impact of trade credit 
loan and bank loan on pricing decisions and profits of 
manufacturers and retailers. Jin Yaqi et al. [6] studied the 
green product investment and financing decision of suppliers 
under the single financing channel of bank credit and the 
mixed financing channel of retailers paying part of the loan in 
advance and bank credit. Wang Wenli and Zhang Ruizhen [7] 
studied the optimal decision and profit of both sides of the 
supply chain under green credit and prepayment financing, 
considering the situation of suppliers with financial 
constraints and risk of R&D failure to conduct green product 
R&D. An et al. [8] constructed a supply chain consisting of a 
manufacturer with limited capital and a supplier with 
sufficient capital facing uncertain demand, and studied how 
the supply chain chooses green credit financing and trade 
credit financing under the hard constraint of carbon emission. 
Wu et al. [9] studied the optimal pricing, optimal emission 
reduction and ordering decision under commercial credit and 
bank credit respectively in the green supply chain with 
financial constraints of retailers. (2) Related research on green 
supply chain coordination. Sun Jiayi [10] and other scholars 
have studied the decision-making and coordination problems 
of low-carbon closed-loop supply chain with government 
subsidies and equity cooperation. Yu Nana and Yuan 
Shuaipeng [11] designed a joint contract consisting of 
revenue sharing and cost sharing, and studied the 



 

2 

coordination problem of closed-loop supply chain with 
differential pricing, considering the carbon emission 
reduction implemented by manufacturers and the low carbon 
preference of consumers. Under the carbon cap-and-trade 
mechanism, Tai Xianghui and Li Fang [12] discussed the 
relationship between carbon emission reduction rate, sales 
price, supply chain profit and consumers' low-carbon 
preference under decentralized and centralized decision-
making, and coordinated the supply chain through contracts. 
Pan Chen et al. [13] studied the selection of different cost-
sharing contracts in a green supply chain consisting of a 
manufacturer and a retailer. Peng et al. [14] studied the 
optimal decision-making of supply chain production, pricing 
and carbon emission reduction under decentralized and 
centralized decision-making, and the research results showed 
that quantity discount contracts can effectively coordinate 
low-carbon supply chains. 

Through the above literature review, it can be found that 
the research on green supply chain financing and the research 
on green supply chain coordination rarely focus on medium 
and micro manufacturing enterprises.However, in 
reality,medium and micro manufacturing enterprises are 
universal, and are an important pillar of the national economy. 
Therefore, this paper constructs a two-level supply chain 
consisting of a single financially constrained manufacturer 
and a single retailer. Among them, manufacturers can choose 
to produce traditional products or green products, the 
production of traditional products have sufficient funds 
without financing, but the production of green products face 
financial constraints, manufacturers can choose bank loans or 
internal financing financing methods to solve their own 
shortage of funds. Based on the above background, under the 
three models of no financing, bank loan and internal financing, 
this paper studies the optimal decision of product green input 
level, production input amount and supply chain profit under 
manufacturer-led decentralized decision making. On this 
basis, this paper takes the overall profit under the centralized 
decision-making as the goal, and designs a combined contract 
of ' revenue sharing contract + two costs + green cost sharing 
' to coordinate the supply chain. 

2. Problem Description and Model 
Assumptions 

2.1. Problem Description 
Consider a two-level supply chain consisting of a 

manufacturer and a retailer. In a two-level supply chain, the 
manufacturer wholesales the product to the retailer at the 
price 𝑝 , while the retailer sells the product directly to the 
market at the price 𝑤. The manufacturer holds the decision 
to produce the product, and can choose to produce traditional 
products or green products during production. When 
manufacturers choose to produce traditional products, they 
have sufficient funds and do not need financing, but when 
manufacturers choose to produce green products, they will 
face a shortage of funds. At this time, manufacturers can 
choose bank loans or internal financing of retailers to solve 
the problem of financial constraints. In this case, this paper 
considers the financing optimization mechanism design of 
small, medium and micro manufacturing enterprises under the 
non-financing model, bank loan model and internal financing 
model. 

2.2. Model Assumptions 

In this paper, 𝜋  represents the profit of supply chain 
member 𝑖 when it chooses decision mode 𝑗 under model 𝑔, 
where 𝑖 ∈ 𝑀, 𝑅, 𝑆   represents manufacturer, retailer and 
supply chain system respectively; 𝑗 ∈ 𝐴, 𝐵, 𝐶   represents 
no financing model, bank loan model and internal financing 
model; 𝑔 ∈ 𝐼, 𝐷, 𝑁   represents centralized decision-
making, decentralized decision-making and combined 
contract decision-making respectively. In addition, based on 
the actual situation, without losing the premise of generality, 
this paper puts forward the following hypothesis: 

(1)The price for products is affected by the randomness of 
the production input, immediate factor of output,green input 
level, and market price, that is, ( )t t tp a q e        . 
Here,𝑡 ∈ 1,2,3  represents chain 1 (no financing), chain 2 
(bank loan), chain 3 (internal financing),the mean and 
variance of 𝜀 are 1u and 𝛿 , the mean and variance of   
are 2u and 0, respectively; 𝑎 is the scale of market demand; 
𝑞  is the production input; 𝑒  is the level of green; and the 
green input cost is 𝐶 𝑒 𝑒  . 

(2)Under decentralized decision-making, the manufacturer 
is the leader of the Stackelberg game and the retailer is the 
follower. 

(3)The interest rate paid by the manufacturer for internal 
financing with the retailer is the same as the interest rate paid 
by the manufacturer for choosing a bank loan. 

(4) Market information is symmetrical and complete, and 
all decision-making members of the supply chain are risk-
neutral decision-makers. 

3. No Financing (Model A) 
Under the no-financing model, manufacturers only produce 

traditional products and have sufficient funds, the expected 
profit functions of manufacturers, retailers and supply chains 
can be obtained as follows: 

 

11 1( )( )
A
M c q uw                  (1) 

 

2 2
1 2 1 1 1 1 1 1( )( )

A
R a q u w q u uq u         (2) 

 

1

1

1

1 2 1 1

2 2
1 1 1 1

( )( )

( )( )

A
S a q u w q u

w c q u u q u

p

d

= - + - +

+ - + - - -
      (3) 

3.1. Decentralized Decision-making 
Under the decentralized decision-making, the Stackelberg 

game is played between manufacturer and retailer.The order 
of the manufacturing supply chain decision is as follows: First, 
the manufacturer decides the wholesale price 𝑤1 of the 
product to the retailer ; Secondly, the retailer decides its 
production input 𝑞1according to the manufacturer's decision, 
and solves equations (1) and (2) by backward derivation, the 
optimal wholesale price 𝑤1

∗ and optimal production input  
𝑞1

∗of the manufacturer and retailer can be obtained as follows: 



 

3 

*

2

1

*

1 2

1

1
( )

2
1

( 4 )
4

D

D

w a c u

a c u uq

  


















 

By substituting the optimal wholesale price  𝑤1
∗and the 

optimal production input 𝑞1
∗ into (1) and (2), the optimal 

expected profit of the manufacturer 𝜋 ∗ and the optimal 
expected profit of the retailer  𝜋 ∗are respectively: 

2

2

*
2

* 2 2

1
( )

8
1

[ 16
1

( ) ]
6

AD
M

AD
R

a c u

ua c



 


  


  


 
 

3.2. Centralized Decision-making 
Under the centralized decision-making, the manufacturer 

and the retailer belong to a unified whole, and the profit of the 
whole supply chain system is maximized by determining the 
optimal production input 𝑞1

∗. At this time, the expected profit 
of the supply chain is expressed as (3). The first-order 
condition of production input 𝑞1 is obtained by equation (3), 
and the optimal production input 𝑞1

∗is obtained as follows : 

*
1 1 2

1
( 2 )

2
Iq a c u u   

 

By substituting the optimal production 𝑞1
∗ input into (3), 

the optimal expected profit 𝜋 ∗  of the supply chain is 
obtained as follows: 

* 2 2
2

1
( )

4
AI
S a c u    

 

Proposition 1: Under the non-financing model, compared 
with the decentralized decision-making, the centralized 
decision-making can promote the increase of production input, 
that is 𝑞1

∗ 𝑞1
∗. So decentralized decision-making cannot 

coordinate the supply chain. 

3.3. Combined Contract Decision-making 
It can be seen from proposition 1 that under the 

decentralized decision making, the production input of the 
manufacturer cannot reach the optimal level under the 
centralized decision making. Therefore, this section 
constructs a combined contract of "Revenue sharing contract 
+ two-part fee + green cost sharing" to coordinate the supply 
chain, which is marked (∅,𝑘,𝑇,  , w ). Specifically: (1) the 
manufacturer will share the ∅ (0 <∅ < 1) times of its own 
income with the retailer, and the retailer will also share the 
green production cost of the manufacturer 𝑘(0 <𝑘< 1) times, 
in order to encourage the manufacturer to improve the green 
level of the product, and the retailer will also provide financial 
support 𝑇 for the manufacturer to improve the production 
equipment and other costs; ② (0 <  < 1) is a multiple of 
the expected profit in the supply chain, and 𝑤  is the 
manufacturer's wholesale price per unit of product. 

Under this mechanism, the expected profit function of the 
manufacturer and retailer in the non-financing model is as 
follows: 

1 1 1(1 )( )( )
AN
M w c q u Tp f= - - + +  

1 2 1 1 1 1 1

2 2
1 1 11

[( )( )

] ( )( )

R
AN a q u w q u u q

u c q u Tw

p

d f

= - + - + -

- - + - + -  

Under the combined contract decision-making, the first 

derivation of production input 𝑞1 is obtained.Let 
1

0, 

and the optimal production input 𝑞1
∗is: 

*
1 1 2 1 1

1
( 2 )

2
Nq a u u w c w      

 

Proposition 2: Under the combined contract, if the 
contract parameters meet the following conditions, the 
combined contract can effectively coordinate the studied 
supply chain, that is, ∅ 1. 

At this time, the expected profits of manufacturers and 
retailers are : 

**

* *

*1

AN AI
M S

AI AI
R S
AN

S

T T

T T

 

   

   


     （ ）  
Proposition 3: In the case of supply chain coordination, if 

the financial support meets the following conditions, the 
expected profits of manufacturers and retailers will be 
improved by Pareto. 

2 2
2 2

1 3
( ) ( )

8 16
a c u T a c u     

 

Certificate 
(1) That is,∅ 1is substituted into 𝑞1

∗, it can be found that 
𝑞1

∗ 𝑞1
∗, so the supply chain is coordinated 

(2) The constraint conditions for manufacturers and 
retailers to participate in combined contracts are 𝜋 ∗

𝜋 ∗, 𝜋 ∗ 𝜋 ∗  respectively, and the result of 
proposition 2 can be obtained by combining the expected 
profits of manufacturers and retailers under decentralized 
decision-making. 

4. Bank Loan (Model B) 
Under the bank loan model, the manufacturer only 

produces green products, and the manufacturer is faced with 
financial constraints. The manufacturer solves the problem of 
insufficient funds by borrowing from the bank, and the 
expected profit function of the manufacturer, retailer and 
supply chain can be obtained as follows: 

 

 
2

1 1 21( )( ) (1 )
B
M c q u rw e             (4) 

         

2 2 2 2 2 1

2 2
1 2 1

( )( )BR a q e u w q u

u q u

p

d

= - + + - +

- - -
    (5)   

 
2

2 1 2

2 2
2 2 2 2 2 1 1 2 1

2( )( ) (1 )

( )( )

B
S c q u r e

a q e u w q u u q u

wp

d

= - + - + +

- + + - + - - -
 (6) 

 



 

4 

4.1. Decentralized Decision-Making 
Under decentralized decision-making, the Stackelberg 

game is played between manufacturer and retailer.The order 
of the manufacturing supply chain decision is as follows: First, 
the manufacturer decides the wholesale price 𝑤2  and the 
green input level 𝑒2 ; Secondly, the retailer decides its 
production input 𝑞3according to the manufacturer's decision, 
and then uses the backward derivation method to solve 
equations (4) and (5), the optimal wholesale price 𝑤2

∗, the 
optimal green input level 𝑒2

∗ and the optimal production 
input 𝑞2

∗ of the manufacturer and retailer can be obtained as 
follows: 

2

* 2
2

2

2
2 1

4 (1 ) (3 4 ) 4(1 )

7 8

7 8
2( )(1 ) (7 8 )

7 8

D

D

D

w
a r c r r u

r
a c u

e
r

a c u r r u

r
q














    



 



  




 


 

By substituting the optimal wholesale price  𝑤2
∗  ,the 

optimal green input level 𝑒2
∗ and the optimal production 

input 𝑞2
∗ into (4) and (5), the optimal expected profit of the 

manufacturer 𝜋 ∗  and the optimal expected profit of the 
retailer 𝜋 ∗ are respectively: 

2
* 2

22
* 2

2

(1 )( )

7

( (

8

4( ) 1 )

7 8

7 8 )

( )

BD
M

BD
R

r a c u

r

u ra c r

r




 

   
 


   

 

 
 

4.2. Centralized Decision-Making 
Under centralized decision-making, the manufacturers and 

the retailers belong to a unified whole and maximize the 
profits of the entire supply chain system by determining the 
optimal green input level 𝑒2

∗and the optimal production input 
𝑞2

∗. At this time, the expected profit of the supply chain is 
expressed as formula (6), and the first-order and second-order 
conditions of green input level 𝑒2and production input 𝑞2 
are obtained by formula (6). It can be seen that 𝜋  is the joint 

concave function of ( 𝑒2 , 𝑞2 ). By solving 
2

0  and  

2
0  jointly, the optimal green input level 𝑒2

∗ and 

production input 𝑞2
∗of the manufacturer can be obtained as 

follows: 

* 2
2

* 2 1
2

3 4
2( )(1 ) (3 4 )

3 4

I

I

a c u
e

r
a c u r r u

q
r

 
 


     

 

 

By substituting the optimal green input level 𝑒2
∗ and the 

optimal production 𝑞2
∗ input into (6), the optimal expected 

profit 𝜋 ∗ of the supply chain is obtained as follows: 

2 2 2
* 2 2( ) (1 ) (3 4 )

3 4
BI
S

a c u r ru r

r




     



 

Proposition 4: Under the bank loan model, compared with 
the decentralized decision-making, the centralized decision-
making can increase the production input and the green input 
level, that is, e ∗ e ∗, q ∗ q ∗ . So decentralized 
decision-making cannot coordinate the supply chain. 

4.3. Combined Contract Decision-Making 
It can be seen from proposition 4 that under the 

decentralized decision making, the production input and 
green input level of the manufacturer cannot reach the optimal 
level under the centralized decision making. Thus, like 
section 3.3 composite contract decisions, this section 
coordinates the supply chain by building composite contract 
decisions. Under this mechanism, the expected profit function 
of the manufacturer and retailer in the bank loan model is as 
follows: 

2 1

2 2
2

2

2

(1 )[( )( )

(1 ) ] (1 )

BN
M c q u

r e k r e T

wp f= - - +

- + + + +  

2 2
2 2 2 2 2 1 1 2 1

2 2
2 12 2 2

( )( )

[( )( ) (1 ) ] (1 )

R
BN a q e u w q u uq u

c q u r e r Tw k e

p d

f

= - + + - + - - - +

- + - + - + -  

Under the combined contract decision-making, the first-
order and second-order conditions of green input level 𝑒2 
and production input 𝑞2 are obtained, and it can be seen that 
𝜋  is the joint concave function of (𝑒2,𝑞2). By solving the 

sum jointly, let 
2

0,
2

0, the optimal green input 

level 𝑒2
∗ and production input 𝑞2

∗ of the manufacturer can 
be obtained as follows: 

* 2 2 2
2

1 1

* 2 2
2

1 4 (1 ) 4(1 )

4 ( )(1 ) 2(1 )( )

[ ( 1 ) ]

1 4( )(1 )

N

N

a u w c w
e

k r r

u u k r r k

a u w c
q

k r

f f

f

f f

f f

f

ì + - - +
=ï
- + + + +ï

ï
- - + + + +í

ï
+ + - + -ï

=ï
- + + +î

 

Proposition 5: Under the combined contract, if the 
contract parameters meet the following conditions, the 
combined contract can effectively coordinate the studied 
supply chain, that is, ∅ 1, 𝑘 0. 

At this time, the expected profits of manufacturers and 
retailers are : 

*

* *

* *(1 )

BN BI
M S

BI BI
R S
BN

S

T T

T T

 

   

   


      
Proposition 6: In the case of supply chain coordination, if 

the financial support meets the following conditions, the 
expected profits of manufacturers and retailers will be 
improved by Pareto. 

2
2

2 3 2
2

2

(1 )( )

7 8

(37 121 132 )48 )

(3 4 )( 8 )

(

7

r a c u
T

r

r r r a c u

r r

+ - +
£ £

+

+ + + - +

+ +
 

Certificate 



 

5 

(1) That is,∅ 1, 𝑘 1is substituted into 𝑒2
∗and 𝑞2

∗, it 
can be found that 𝑒2

∗ 𝑒2
∗, 𝑞2

∗ 𝑞2
∗, so the supply chain 

is coordinated 
(2) The constraint conditions for manufacturers and 

retailers to participate in combined contracts are 𝜋 ∗

𝜋 ∗, 𝜋 ∗ 𝜋 ∗  respectively, and the result of 
proposition 4 can be obtained by combining the expected 
profits of manufacturers and retailers under decentralized 
decision-making. 

5. Internal Financing (Model C) 
Under the internal financing model, the manufacturer only 

produces green products and faces the problem of fund 
shortage. The manufacturer solves the problem of fund 
constraint by borrowing from retailers (internal financing). In 
this case, the expected profit function of the manufacturer, 
retailer and supply chain can be obtained as follows: 

 
2

3 1 33( )( ) (1 )
C
M c q u rw e              (7)   

                                    
2 2 2

3 2 3 3 1 1 33 1 3( )( )
C
R qa e u w q u uq u re            (8)   

                                            
2 2 2

3 1 1 3 1 3

3 3 2

3

3 3 1

( )( )

( )( )

C
S c q u uq u e

a q e w q u

w

u

p d= - + - - - -

+ - + + - +
  (9)  

                

5.1. Decentralized Decision-making 
Under decentralized decision-making, the Stackelberg 

game is played between manufacturer and retailer.The order 
of the manufacturing supply chain decision is as follows: First, 
the manufacturer decides the wholesale price 𝑤3  and the 
green input level 𝑒3 ; Secondly, the retailer decides its 
production input 𝑞3according to the manufacturer's decision, 
and then uses the backward derivation method to solve 
equations (7) and (8), the optimal wholesale price 𝑤3

∗, the 
optimal green input level 𝑒3

∗ and the optimal production 
input 𝑞3

∗of the manufacturer and retailer can be obtained as 
follows: 

2

* 2
3

3

3
2 1

4 (1 ) (3 4 ) 4(1 )

7 8

7 8
2( )(1 ) (7 8 )

7 8

D

D

D

w
a r c r r u

r
a c u

e
r

a c u r r u

r
q














    



 



  




 


 

By substituting the optimal wholesale price  𝑤3
∗  ,the 

optimal green input level 𝑒3
∗ and the optimal production 

input 𝑞3
∗ into (7) and (8), the optimal expected profit  of 

the manufacturer 𝜋 ∗ and the optimal expected profit of the 
retailer 𝜋 ∗ are respectively: 

2
* 2

2 2
* 2

2

2

( (

(1 )( )

7 8

( ) 4 9 4 )

7 8

7 8 )

( )

CD
M

CD
R

r

r a c u

r

a c u r r

r




 

   
 


    

 

 
 

5.2. Centralized Decision-Making 
Under centralized decision-making, the manufacturers and 

the retailers belong to a unified whole and maximize the 
profits of the entire supply chain system by determining the 
optimal green input level 𝑒3

∗and the optimal production input 
𝑞3

∗. At this time, the expected profit of the supply chain is 
expressed as formula (9), and the first-order and second-order 
conditions of green input level 𝑒3and production input 𝑞3 
are obtained by formula (9). It can be seen that 𝜋  is the joint 

concave function of ( 𝑒3 , 𝑞3 ). By solving 
3

0  and  

3
0  jointly, the optimal green input level 𝑒3

∗ and 

production input 𝑞3
∗of the manufacturer can be obtained as 

follows: 

*
3 2

*
3 1 2

1
( )

3
1

(2 2 3 2 )
3

I

I

e a c u

q a c u u


  


    


 

By substituting the optimal green input level 𝑒3
∗ and the 

optimal production 𝑞3
∗ input into (9), the optimal expected 

profit 𝜋 ∗ of the supply chain is obtained as follows: 

* 2 2
2

1
[( ]) 3

3
CI
S a c u      

Proposition 7: Under the internal financing model, 
compared with the decentralized decision-making, the 
centralized decision-making can increase the production 
input and the green input level, that is, e ∗ e ∗, q ∗ q ∗. 
So decentralized decision-making cannot coordinate the 
supply chain. 

5.3. Combined Contract Decision-making 
It can be seen from proposition 7 that under the 

decentralized decision making, the production input and 
green input level of the manufacturer cannot reach the optimal 
level under the centralized decision making. Thus, like 
section 3.3 composite contract decisions, this section 
coordinates the supply chain by building composite contract 
decisions. Under this mechanism, the expected profit function 
of the manufacturer and retailer in the bank loan model is as 
follows: 

2
3 1 3

2

3

3

(1 )[( )( ) (1 ) ]

(1 )

CN
M c q u r e

k r e T

wp f= - - + - +

+ + +  

2 2
3 3 2 3 3 1 1 3 1

2 2
3

2
3 3 1 3 3

( )( )

[( )( ) (1 ) ] (1 )

R
CN a q e u w q u uq u

re c q u r e k r e Tw

p d

f

= - + + - + - - -

+ + - + - + - + -  

Under the combined contract decision-making, the first-
order and second-order conditions of green input level 𝑒3 
and production input 𝑞3 are obtained, and it can be seen that 
𝜋  is the joint concave function of (𝑒3,𝑞3). By solving the 

sum jointly, let 
3

0,
3

0, the optimal green input 

level 𝑒3
∗ and production input 𝑞3

∗ of the manufacturer can 
be obtained as follows: 



 

6 

( ) ( )
* 2 3 3

3

* 2 3 3
3 1

1 4 1 4 1 4

2( )[( )(1 ) ]

1 4( )(1 ) 4

N

N

a u w c w
e

k r r

a u w w c k r r
q u

k r r

f f

f f

f f f

f

ì + - - +
=ï
- + + + - + +ïï

í
- + - + + + -ï

= -ï
- + + + -ïî

 

Proposition 8: Under the combined contract, if the 
contract parameters meet the following conditions, the 
combined contract can effectively coordinate the studied 
supply chain, that is, ∅ 1, k 0. 

At this time, the expected profits of manufacturers and 
retailers are : 

*

* *

* *(1 )

CN CI
M S

CI CI
R S
CN

S

T T

T T

 

   

   


      
Proposition 9: In the case of supply chain coordination, if 

the financial support meets the following conditions, the 
expected profits of manufacturers and retailers will be 
improved by Pareto. 

2 2 2
2 2

2

(1 )( ) (37 85 5

3

)(2 )

7 8 (7 8 )

r a c u r r a c u
T

r r

+ - + + + - +
£ £

+ +  

Certificate 
(1) That is,∅ 1, 𝑘 1is substituted into 𝑒3

∗and 𝑞3
∗, it 

can be found that 𝑒3
∗ 𝑒3

∗, 𝑞3
∗ 𝑞3

∗, so the supply chain 
is coordinated 

(2) The constraint conditions for manufacturers and 
retailers to participate in combined contracts are 𝜋 ∗

𝜋 ∗, 𝜋 ∗ 𝜋 ∗ respectively, and the result of proposition 
6 can be obtained by combining the expected profits of 
manufacturers and retailers under decentralized decision-
making. 

6. Conclusion 
This paper studies the coordination problem of the two-

level supply chain consisting of a single manufacturer and a 
single retailer. By using the game theory method, the paper 
analyzes the decentralized decision-making and centralized 
decision-making under the three models of no financing, bank 
loan and internal financing, and obtains the relevant optimal 
solutions. Through comparison, it is found that the optimal 
green input level and the optimal production input volume 
under the decentralized decision-making cannot reach the 
optimal level under the centralized decision-making, so the 
decentralized decision-making cannot coordinate the supply 
chain. Therefore, this paper designs a combined contract of 
"revenue sharing + two-part costs + green cost sharing", that 
is, the manufacturer will give part of its revenue to the retailer, 
and the retailer will bear part of the manufacturer's green 
processing costs and production equipment improvement 
costs, so as to encourage the manufacturer to improve the 
level of green input and increase the production input, so as 
to realize the global optimization of the supply chain. It can 
benefit both manufacturers and retailers, which shows that the 
combined contract designed is very effective for the financing 
of small, medium and micro manufacturing enterprises with 
financial constraints. 

Acknowledgment 
This work was supported by the Social Science Planning 

Project of Chongqing(2023NDQN34). 

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