The Optimal Strategy in Remanufacturing Green

Supply Chains

Xiaohang Ren*, Qian Liu and Yumeng Zhang

Academy of Chinese Energy Strategy, University of Petroleum -Beijing, Beijing, China

domrxh@outlook.com

Abstract. Due to the environmental protection problem attaching more and

more attentions of countries and regions of the world, our country launched a

series of related policy measures, in order to reduce environmental pollution. At

the same time, the subsidy policy based on green manufacture is playing a

important role in control of producing green products. This paper is to explore

that in order to maximize the social welfare what effective strategy should the

government take and corresponding to different strategy, what decision should

the enterprises make, and establish a green supply chain game model to analyze

the optimal equilibrium results in different situations. Then through numerical

simulation analysis, the paper analyses the impact of various parameters

change, and the results indicate that the government and the manufacturers are

affected by the whole society attentions to the environmental pollution degree.

The results provide insights into the decision-making of governments and

companies.

Keywords: green supply chains; game model; subsidy; social welfare

1 Introduction

The importance of green supply chain is being recognized due to high demand in

many raw material markets and greater awareness of the environmental impacts of

disposal. In the past decade, much attention has focused on design, planning, and

modeling for closed-loop (forward and reverse) supply chain systems. Government

regulation has an important role in managing and recycling e-scrap.

A literature review reveals some examples of policies concerning green supply

chain in common use throughout the world. Some researchers discussed manufacture

management problems in single enterprise in their paper (Ferguson and Toktay, 2006;

Vlachos et al., 2007; Oraiopoulos et al., 2012). Ji and Huang (2012) put forward the

pattern that manufacturers process by its own will maximize the social welfare. Also

there are some researches about the role of fund subsidies and tax in reverse logistics

(Bansal and Gangopadhyay, 2003; Palmer, 1997; Wojanowski, 2007). Mitra et al.

(2008) demonstrate that besides subsidies for recycling reproduction enterprises,

government should also give certain subsidy to production enterprises.

In this paper, we consider the purpose of government to maximize social welfare,

as well as factors such as government subsidies, product green degree, product

Advanced Science and Technology Letters Vol.121 (AST 2016), pp.157-162

http://dx.doi.org/10.14257/astl.2016.121.29

ISSN: 2287-1233 ASTL Copyright © 2016 SERSC

competition and consumer preferences. Then through numerical simulation analysis,

the paper analyses the impact of various parameters change, and the results indicate

that the government and the manufacturers are affected by the whole society

attentions to the environmental pollution degree. The results provide insights into the

decision-making of governments and companies．

2 Model Assumption

We use g (0<g<1) denote the green degree, here suppose that the bigger g is, the

higher green degree will be, and the products selling on the market need to meet the

lowest green degree level of government regulations. Suppose that there are two kinds

of manufactures, manufacture B passively take green supply chain management

strategy, and A actively take green supply chain management strategy. A

continuously takes research and development of green products, so their marginal cost

of production (c1) is lower than B (c2). So, we call the productions of A as green

products and B as normal products. In this paper, the government prefers to high

green degree products, and gives the manufacturer of the degree higher than some

subsidy r, , t is the coefficient of unit production subsidies.

Assumption 1. Both A and B exceed the government regulation of the minimum

requirements of the product green degree level, and , .

Assumption 2. The unit production costs of manufacturer is negatively related to

the green degree, , c is the coefficient. The sales of A

is , and B is , a>b>0. Also the

consumers prefer to buy green products, that is .

Assumption 3. Manufacturers, recyclers and government in green supply chain are

risk neutral and information completely.

Assumption 4. The unit advertising costs of manufacturer is negatively related to

the green degree , is advertising fees coefficient, and the

total advertising cost is .

3 Model Analysis

Demand function for manufacturer A is:

(1)

The profit of A is:

(2)

Demand function for manufacturer B is:

(3)

The profit of B is:

Advanced Science and Technology Letters Vol.121 (AST 2016)

158 Copyright © 2016 SERSC

(4)

The purpose of government is to maximize social welfare. So consumer surplus is

. Manufacturer's profit is the producer surplus. The government subsidies

according to green degree is . E indicates the pollution costs per unit

product, , and e is the pollution cost coefficient. Therefore, the social

welfare is:

(5)

We use backward induction to solve the model. At the beginning, two producers

choose their own optimal price. We take the derivative of by

respectively, and then jointly solve the functions:

(6)

(7)

Proposition 1: From (6) and (7), we can have some conclusions. The higher the

production cost coefficient is, the greater price difference between ordinary products

and green products will be. Also, a higher minimum green degree level of subsidy

will increase the price of productions.

Proof: From (6) and (7), we can get

(8)

(9)

If the government raise , the result can only make the price of all products on

the market increase. So, the government should consider subsidies for green degree

level carefully.

Taking and into (1) and (2) :

(10)

(11)

Proposition 2: The quantity of common products will reduce, but the quantity of

green products will increase, as the government raise .

Proof: From (10) and (11), we can get:

(12)

Advanced Science and Technology Letters Vol.121 (AST 2016)

Copyright © 2016 SERSC 159

(13)

Furthermore, two producers will find their optimal levels of green degree. Taking

(6), (7), (10), (11) into (2), (4) :

(14)

(15)

Then taking the derivative of :

(16)

(17)

Solving (17) and (18) jointly:

(18)

(19)

Finally, the government determines the coefficient of unit production subsidies.

Convenient for calculating, we fix , and only seek the optimal value of t. So, we

maximize , then take the derivative of , getting t* satisfying:

(20)

4 Numerical Simulation

Due to the complexity of the functions, we use software to simulate the results.

Supposing a=2, b=1, c=3, , , , , t=1, ,

.

Figure 1 shows that the higher the production cost coefficient is, the greater price

difference between ordinary products and green products will be. Figure 2 indicates

that if the government raise , the result can only make the price of all products on

the market increase.

Advanced Science and Technology Letters Vol.121 (AST 2016)

160 Copyright © 2016 SERSC

Fig. 1. Production cost coefficient

Fig. 2. The lowest level of subsides changes

5 Conclusions

This paper describes a social welfare maximization model examining the impacts of

subsidies on green productions. We suggest that the government should improve

subsidies for green products, so as to maximize the social welfare, when society pay

more attention to environmental problems. For the producers, when the government

and society has attached great importance to environmental issues, they should take

green degree higher, make the same advertising effect is better, that is more advantage

for them.

References

1. Ferguson, M. E., Toktay, L. B.: The effect of competition on recovery strategies [J].

Production and Operations Management. 3, 15 (2006)

2. Vlachos, D., Georgiadis, P., Iakovou, E.: A system dynamics model for dynamic capacity

planning of remanufacturing in closed-loop supply chains [J]. Computers & Operations

Research. 2, 34, (2007)

3. Oraiopoulos, N., Ferguson, M. E., Toktay, L. B.: Relicensing as a secondary market

strategy [J]. Management Science. 5, 58 (2012)

Advanced Science and Technology Letters Vol.121 (AST 2016)

Copyright © 2016 SERSC 161

4. Ji, G., Huang, W. W.: Effective implementation of WEEE take-back directive [J]. Journal

of Management Science in China. 5, 15 (2012). (in Chinese)

5. Bansal, S., Gangopadhyay, S.: Tax/subsidy policies in the presence of environmentally

aware consumers [J]. Journal of Environmental Economics and Management. 2, 45 (2003).

6. Palmer, K., Walls, M.; Optimal policies for solid waste disposal: taxes, subsidies and

standards [J]. Journal of Public Economics. 2, 65 (1997)

7. Palmer, K., Sigman, H., Walls, M.: The cost of reducing municipal solid waste [J]. Journal

of Environmental Economics and Management. 2, 33 (1997)

8. Wojanowski, R., Verter, V., Boyaci, T.: Retail-collection network design under deposit-

refund [J]. Computers & Operations Research. 2, 34 (2007)

9. Mitra, S., Webster, S.: Competition in remanufacturing and the effects of government

subsidies [J]. International Journal of Production Economics. 2, 110 (2008)

Advanced Science and Technology Letters Vol.121 (AST 2016)

162 Copyright © 2016 SERSC