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Open Physics

formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina


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Volume 15, Issue 1

Issues

Volume 13 (2015)

A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy

Xueying Li / Ying Peng / Jing Zhang
Published Online: 2017-03-22 | DOI: https://doi.org/10.1515/phys-2017-0011

Abstract

Under the background of a low carbon economy, this paper examines the impact of carbon tax policy on supply chain network emission reduction. The integer linear programming method is used to establish a supply chain network emission reduction such a model considers the cost of CO2 emissions, and analyses the impact of different carbon price on cost and carbon emissions in supply chains. The results show that the implementation of a carbon tax policy can reduce CO2 emissions in building supply chain, but the increase in carbon price does not produce a reduction effect, and may bring financial burden to the enterprise. This paper presents a reasonable carbon price range and provides decision makers with strategies towards realizing a low carbon building supply chain in an economical manner.

Keywords: low carbon economy; building supply chain; carbon tax policy; cost

PACS: 02.; 02.10.-v; 02.10.Ud

1 Introduction

With the development of the global economy and the improvement in people’s living standards, the building industry has become one of the largest contributors to China’s economic growth and its effectiveness is very important. At the moment, the building supply chain has a kind of management approach for advocating cooperation and win-win solutions. This gradually attracting more and more attention. Many countries have introduced the supply chain concept and promoted its operation, so that their building industries have had a great change, and management methods and means have also seen a significant improvement. Therefore, under the trend of economic globalization, the building supply chain provides a new and suitable construction management mode that can efficiently deal with intense competition in the market.

While the building industry makes a big contribution in improving the GDP, but at the same time, it consumes a lot of resources and energy and is a huge burden to the environment. According to statistics, the average annual growth rate of CO2 emissions was 6.9% in China’s building industry, from 1994 to 2012 [1]. In 2012, the building industry produced CO2 115 million tonnes, which accounted for 3.4% of the whole nation’s carbon emissions [1]. Faced with the ultra high carbon emissions in the building field, implementation of building energy conservation and emissions reduction has become an effective way to reduce the pressure on China’s carbon emissions. In addition, problems such as global warming and the deterioration of the ecological environment further accelerate the process of sustainable development between the economy and environment in China, and also takes the concept of the low carbon building to new heights. Therefore, on the basis of guiding construction enterprises to optimize management modes and improve economic benefits, the Chinese government also promotes the well being of the environment and society, and seeks multiple paths to realize sustainable development. At the moment, the low carbon supply chain, as a new operation mode that can improve the environment, is becoming more and more popular. The combination of a low carbon economy and the building supply chain not only enhances an enterprise’s core competitiveness, but also complies with the global trend of energy saving and emissions reduction, and has great significance in realizing win-win solutions in the economy, environment and society.

There have been many studies on low carbon supply in China and other countries. In the aspect of network design, Pin [2, 3] established a supply chain network design model which considered the cost of carbon emissions and optimized the location, distribution of demand and route selection parameters. Chaabane et al. [4] used life cycle assessment method to design a sustainable supply chain under a carbon emissions trading system, specifying the laws that could help the building industry achieve long-term sustainable development. Considering the difference among node enterprises’ investment marginal benefits, Zhao et al. [5] set up a double-objective model, including environmental and economic performance. Here, they designed and optimized the low carbon supply chain by optimal allocation of investment node and transportation options. Tseng et al. [6] put forward a supply chain emissions reduction strategic decision model considering an enterprise’s operating cost and carbon emissions cost, laying a solid foundation for enterprises realizing sustainable management. Ghayebloo et al. [7] set up a double-objective model, including product disassembly and the selection of suppliers in a closed-loop supply chain, to realize a green supply chain through technical reform. Xie et al. [8] used a classical economics method and game theory to analyze emissions reduction and profits in three different cooperation cases. They further discussed the impact of the interaction between enterprises and the price of carbon trading on emissions reduction. Li et al. [9] set up a game model on government subsidies for the cooperation of manufacturers and retailers, and defined an enterprise’s optimal cost and the government’s optimal subsidy rate to help it use emissions reduction subsidy strategies effectively. In the aspect of members’ behavior, Zhang et al. [10] studied multiple phase equilibrium problems, including manufacturers, retailers, recyclers and customers, and analyzed the effect of carbon emissions constraints on the equilibrium results, thus determining each member’s optimal behavior under the supply chain network equilibrium. Yang et al. [11] analyzed the main factors influencing the closed-loop supply chain members’ low carbon behavior, and designed an index system of the supply chain members and established a low carbon behavior evaluation model, providing a theoretical basis and practical guidance for the implementation of low carbon behavior. Xu [12] designed a low carbon supply chain system framework including responsibility division and cost allocation. It not only defined the responsibility of supply chain members, but also showed that members take an active until the cost and profits are shared together.

Although studies of the low carbon supply chain have gradually matured in many industries, in the building industry, a few researchers have explored such issues. For example, Ofori [13] expounded the influenced of construction activities on the environment, and taking Singapore as a typical example for exploring its green building model. The research confirmed that green building supply chain can not only achieve a long-term cooperation between enterprises, but can also promote the coordinated development of the economy and environment. Based on the analysis of the green building supply chain structure and policy, Zhou et al. [14] used system dynamics to establish a supply chain model of energy conservation and emissions reduction, and used Dalian, China as a example to confirm the feasibility of the model. Zou et al. [15] applied the green supply chain risk management to the building industry, determining the factors which influence vulnerability of the building supply chain, and put forward decisions to optimize the green supply chain system. Cheng [16] came up with a web services framework for measuring and monitoring the carbon footprint in the building supply chain, providing a green performance management system for the building industry. Seo et al. [17] established a system for measuring CO2 emissions of building materials through an assessment of building material carbon emissions in the supply chain, and provided a reliable and effective calculation method for carbon emissions for decision makers.

In recent years, the low carbon policy, as a effective means to reduce CO2, has become a hot topic among scholars. Based on carbon tax policy, Fahimnia et al. [18] set up a closed-loop supply chain optimization model that considered the cost of carbon emissions, and confirmed that the carbon tax policy and closed-loop supply chain can help reduce carbon emissions. Based on carbon tax and carbon trading policies, Zakeri et al. [19] established an emissions reduction model in the supply chain to provide reference by selecting a reasonable carbon policy. Under carbon taxes, carbon caps and carbon trading policies, Choudhary et al. [20] built a forward and reverse logistics optimization model in supply chain and compared the pros and cons of three policies. Considering the impact of transportation on carbon emissions, Jin et al. [21] established a supply chain network design and logistics optimization model and used sensitivity analysis on the impact of policy parameters on carbon emissions and logistics cost. Li et al. [22] studied supply chain coordination problem, based on buy-back contract, and indicated that buy-back contract can achieve supply chain coordination. However, the manufacturers’ optimal order quantity and suppliers’ repurchase price are not same under different low carbon policies. Gupta [23] took Indian road passenger transport as a example, and set up a passengers’ “willingness to pay for carbon tax policy” model and analyzed the factors that influence the WTP. Considering the influence of an enterprise’s appetite on carbon tax policy, Liu et al. [24, 25] established an enterprise’s willingness to pay model and analyzed the relationship between policy parameters and the enterprise’s appetite. However, compared with many other low carbon policies, carbon tax is considered as one of the most common market-based approaches from the aspect of economic incentives in carbon emission regulation [26], it is transparent, visible and hard to evade or avoid. Therefore, the research on carbon tax has great practical significance.

In summary, the building supply chain covers a wide range, so it not only consumes a lot of energy and resources, but also has a big influence on the environment. Hence, under the global trend of energy saving and emissions reduction, governments and construction enterprises in China have moved their attention from profit performance into sustainable development of economies, environment and society. They seek realization of low carbon construction and reduction of stress which the building industry brings to the environment. At the moment, there is great impetus to explore building supply chain carbon emission reduction strategies under a low carbon economy. Studies of the low carbon supply chain have gradually been mature in many industries, but researches about low carbon building supply chain are still at a preliminary stage, and mainly focus on operation models and risk management of low carbon supply chain and monitoring and measurement of the carbon footprint. While research regarding carbon policy mainly exists in developed countries, only a few scholars have explored its theoretical framework in China. Most of the research is based on the overall development of the country, but not on a specific industry [2729].

This paper studies the impact of carbon pricing on building supply chain cost and carbon emissions reduction, establishes a mixed integer linear programming model targeting cost minimization and suggests a reasonable range of carbon pricing. It aims to realize a low carbon building supply chain in an economical manner.

2 Problem description

In order to make our research generalised, we assume that the operation process of the building supply chain is as shown in Fig 1. Raw material suppliers provide raw materials for manufacturers, then manufacturers convert the raw materials into products and ship them to distribution centers. Finally, the building suppliers sell the products to contractors. In the whole supply chain, the flow of fund only circulates from downstream enterprises to upstream enterprises, and the flow of information circulates mutually between upstream enterprises and downstream enterprises. The government is regarded as a macroscopic regulator and a decision maker, formulating carbon tax policy during the whole operation of supply chain. Specifically, the government formulates the carbon price which is unit price of carbon emissions and levies tax in order to restrain the carbon emissions in the building industry.

Building supply chain process
Figure 1

Building supply chain process

3 Model assumption

Under the carbon tax policy, the primary modeling assumptions include the following:

  1. The carbon price in the carbon tax policy is set by government, combined with various elements;

  2. Types of raw materials and products are known;

  3. Capacity of manufacturers are known;

  4. Number and location of raw material suppliers, manufacturers, building suppliers and contractors are known;

  5. Inventory levels and initial inventory levels of manufacturers and building suppliers are known; the inventory capacity of the raw material suppliers and contractors are neglected;

  6. In each study period, the demand for raw materials by the manufacturers and products for contractors are known;

  7. The cost and CO2 emissions caused by inventory are neglected;

  8. Raw material suppliers fully meet the needs of manufacturers in regard to raw materials;

  9. During each study period, the contractors’ demands may not be satisfied, but before the total study period is finished, the contractors’ total demand must be satisfied.

4 Mathematical model

Under the carbon tax policy, a mixed integer linear programming model of building supply chain network is established which considers construction enterprises’ operating cost, transportation cost and carbon emissions cost. The model, with the target of cost minimization, provides some reference to realize low carbon building supply chain economically for decision makers. The network structure is shown in Fig 2.

Building supply chain network
Figure 2

Building supply chain network

Symbol definitions include the following:

  1. Sets

    s: Set of potential raw material suppliers(raw material supply factories) location; s ∈ {1, 2,…,S};

    i: Set of potential manufacturers(manufacturing plants) location; i ∈ {1, 2, …, I};

    j: Set of potential building suppliers(distribution centers) location; j ∈ {1, 2, …, J};

    c: Set of potential contractors location; c ∈ {1, 2, …, C};

    m: Types of raw materials; m ∈ {1, 2, …, M};

    n: Types of products; n ∈ {1, 2, …, N};

    t: One study period; tT(T is total study period).

  2. Parameters

    dimt: Demand for raw materials m in manufacturing plants i at t period;

    dcnt: Demand for products n in contractors c at t period;

    fst: Fixed cost for raw material supply factories s to operate at t period;

    fit: Fixed cost for manufacturing plants i to operate at t period;

    fjt: Fixed cost for distribution centers j to operate at t period;

    wint: Holding capacity in manufacturing plants i for products n at t period;

    wjnt: Holding capacity in distribution centers j for products n at t period;

    βin: initial inventory level in manufacturing plants i for products n;

    βjn: initial inventory level in distribution centers j for products n;

    pinmt: Consumption of raw materials m for producing a unit of products n in manufacturing plants i at t period;

    aint: cost for producing a unit of products n in manufacturing plants i at t period;

    usimt: Unit transportation cost of raw materials m from raw material supply factories s to manufacturing plants i at t period;

    uijnt: Unit transportation cost of products n from manufacturing plants i to distribution centers j at t period;

    ujcnt: Unit transportation cost of products n from distribution centers j to contractors c at t period;

    bcnt: Unit shortage cost for products n in contractors c at t period;

    hsimt: Maximum transportation capacity for a truck of raw materials m from raw material supply factories s to manufacturing plants i at t period;

    hijnt: Maximum transportation capacity for a truck of products n from manufacturing plants i to distribution centers j at t period;

    hjcnt: Maximum transportation capacity for a truck of products n from distribution centers j to contractors c at t period;

    ksimt: Number of trucks available for shipping raw materials m from raw material supply factories s to manufacturing plants i at t period;

    kijnt: Number of trucks available for shipping products n from manufacturing plants i to distribution centers j at t period;

    kjcnt: Number of trucks available for shipping products n from distribution centers j to contractors c at t period;

    est: Estimated carbon emissions for the operation of raw material supply factories s at t period;

    eit: Estimated carbon emissions for the operation of manufacturing plants i at t period;

    ejt: Estimated carbon emissions for the operation of distribution centers j at t period;

    eint: Estimated carbon emissions to produce a unit of products n in manufacturing plants i at t period;

    esimt: Estimated carbon emissions for the shipment of raw materials m from raw material supply factories s to manufacturing plants i at t period;

    eijnt: Estimated carbon emissions for the shipment of products n from manufacturing plants i to distribution centers j at t period;

    ejcnt: Estimated carbon emissions for the shipment of products n from distribution centers j to contractors c at t period;

    g: Price of carbon emissions per ton;

    M: A very large positive integer.

  3. Decision variables

    Qsimt: Quantity of raw materials m shipped from raw material supply factories s to manufacturing plants i during t period;

    Qijnt: Quantity of products n shipped from manufacturing plants i to distribution centers j during t period;

    Qjcnt: Quantity of products n shipped from distribution centers j to contractors c during t period;

    Rint: Quantity of products n produced in manufacturing plants i at t period;

    Vcnt: Quantity of products n shortage in contractors c at the end of t period;

    Oint: Inventory amount of products n in manufacturing plants i at the end of t period;

    Ojnt: Inventory amount of products n in distribution centers j at the end of t period;

Xst=1,if raw material supply factoriess operates intperiod0,otherwiseYit=1,if manufacturing plantsioperates intperiod0,otherwiseZjt=1,if distribution centersjoperates int period0,otherwise

The model aims at cost minimization, and the objective function R is defined as following: minR=stfst×Xst+itfit×Yit+jtfjt×Zjt+intaint×Rint+simtQsimt×usimt+ijntQijnt×uijnt+jcntQjcnt×ujcnt+[stest×Xst+iteit×Yit+jtejt×Zjt+inteint×Rint+simtQsimt×esimt+ijntQijnt×eijnt+jcntQjcnt×ejcnt]×g+cntbcnt×Vcnt(1)

In this objective function, the first three items mean the fixed cost of operating raw material supply factories, manufacturing plants and distribution centers respectively. The fourth item indicates the cost of producing products in the manufacturing plants; the fifth item means the transportation cost of raw materials from the raw material supply factories to the manufacturing plants; the sixth item is the transportation cost of products from the manufacturing plants to the distribution centers; the seventh item denotes the transportation cost of products from distribution centers to contractors; the eighth to the tenth terms respectively mean the cost of carbon emissions for operating raw material supply factories, manufacturing plants and distribution centers; the eleventh item is the cost of carbon emissions for manufacturing products; the twelfth to the fourteenth items respectively denotes the cost of carbon emissions for transportation from the raw material supply factories to the manufacturing plants, then to distribution centers and finally to contractors; the last item is the cost of product shortages.

Specific variables constraints are shown as follows: sQsimtdimt,i,m,t(2) dimt=npinmt×Rint,i,m,t(3) Qsimthsimt×ksimt,s,i,m,(4) Qijnthijnt×kijnt,i,j,n,t(5) Qjcnthjcnt×kjcnt,j,c,n,t(6) Ointwint,i,n,t(7) Ojntwjnt,j,n,t(8) OintOin(t1)=RintjQijnt,i,n,t(9) OjntOjn(t1)=iQijntcQjcnt,j,n,t(10) jQjcnt=dcntVcnt+Vcn(t1),c,n,t(11) itRintjctQjcnt,c,n,t(12) jtQjcnttdcnt,n(13) imQsimtM×Xst,s,t(14) jnQijntM×Yit,i,t(15) cnQjcntM×Zjt,j,t(16) Xst,Yit,Zjt0,1,s,i,j,t(17) Qsimt,Qijnt,Qjcnt,Rint,Vcnt,Oint,Ojnt0,s,i,j,c,m,n,t(18)

Formula (2) is a constraint regarding the satisfaction of manufacturers’ demand; formula (3) is a constraint on the proportion between raw materials and products; formulas (4), (5) and (6) are constraints about transportation capacity among raw material supply factories, manufacturing plants, distribution centers and contractors; formulas (7) and (8) are constraints about the largest inventory capacity of manufacturing plants and distribution centers; formula (9) means inventory quantity of manufacturing plants is equal to the number of manufacturing product minus the number of products shipped to distribution centers in a study period; formula (10) means inventory quantity of distribution centers is equal to the number of products shipped from manufacturing plants minus the number of products shipped to contractors in a study period; formula (11) means the number of products shipped from distribution centers to contractors is equal to the demand of contractors minus the increasing number of shortage products compared with last period in a study period; formulas (12) and (13) simultaneously mean the demand of contractors are satisfied before the end of total period; formulas (14) to (16) are binomial constraints; formula (17) is a 0-1 variable constraint; formula (18) is variables nonnegative constraint.

The total cost and carbon emissions in this building supply chain are calculated, finally obtaining a reasonable carbon price range.

5 Model implementation: a case study

The authors show a simulation example of a building supply chain to verify the following questions: (1) the impact of carbon tax policy on building supply chain; (2) the impact of different carbon prices on the supply chain cost and carbon emissions reduction.

Assume that there are three raw materials suppliers, two manufacturers, three building suppliers and a contractor. Raw material suppliers provide three types of raw materials, cement, sand and steel. The manufacturers produce precast box girders with A and B specifications, and each raw material suppliers or manufacturers provide a single variety of raw materials or products. The largest inventory of the two manufacturing plants are 500 and 400; the largest inventory of the three distribution centers are 400, 500 and 600; and their initial inventory amounts are all 0. The largest production capacity of the two manufacturing plants are 800 and 600. The total study period T is equal to 2.

The model with an interval of 15RMB/t, chooses carbon price from 0RMB/t to 120RMB/t in turn, and calculates the total cost and carbon emissions of building supply chain for these different carbon prices. The calculation results are shown in Table 1. In the table, the total carbon emissions include operation carbon emissions(OCE), production carbon emissions (PCE) and transportation carbon emissions (TCE); the total cost includes operation cost (OC), production cost (PC), transportation cost (TC), shortage cost (SC) and carbon emissions cost (CEC). Table 1 indicates that when the carbon price increases from 0RMB/t to 120RMB/t, total CO2 emissions are reduced by 13399kg and the total cost increases by 21631RMB in building supply chain.

Table 1

Calculation results of cost and carbon emissions

Supply chain network with carbon prices of 15 RMB/t and 30 RMB/t are shown in Fig 34. The figure indicates that in the first period, the network structure and the transportation path of the building supply chain are significantly different. This is because the carbon price increase causes a total cost increase, and it makes the supply chain network non-optimal when the carbon price change from 15RMB/t to 30RMB/t. Therefore, the node enterprises are promoted to take the initiative to adjust the supply chain structure and change the transportation path, so that the total carbon emissions and the cost of carbon emissions can all be reduced. Finally, the new optimal network with minimum total cost is established. In the second period, the network structure and the transportation path of building supply chain are quite similar under these two carbon prices. This shows the supply chain network is most optimal with a carbon price range of 15RMB/t to 30RMB/t.

Supply chain network with carbon price as15 RMB/t
Figure 3

Supply chain network with carbon price as15 RMB/t

Supply chain network with carbon price as 30 RMB/t
Figure 4

Supply chain network with carbon price as 30 RMB/t

The cost of each aspect under different carbon prices is shown in Fig 5. It indicates that in the total cost of supply chain, operation and production account for the largest, transportation cost ranks the third, shortage cost, only less than 3%, carbon emissions cost is gradually increased from 0% to 7.43% and eventually exceed the shortage cost. The carbon emissions cost is caused by the carbon price directly, so they increase with the carbon price increase, and they change faster and have a great range. In the process of the carbon price rise, production and shortage cost remains the same, operation cost increases by 5.49% because of the change of the supply chain structure, transportation cost decreases by 6.47% because of the optimization of the transportation path. However, the percentage of operation cost is larger than the transportation cost, and the percentage of carbon emissions cost gradually increase, so the total cost shows an increasing trend.

The consumption of each cost under different carbon price
Figure 5

The consumption of each cost under different carbon price

Each carbon emission under different carbon prices are shown in Fig 6. It indicates that the total carbon emissions of supply chain, transportation emissions account for the largest, operation and production emissions are roughly similar and less. In the process of carbon price rising, production emissions remain the same, operation emissions increase by 17.54% because of the change of supply chain structure, and transportation emissions decrease by 9.17% because of the optimization of the transportation path. However, the percentage of transportation emissions are much larger than operation emissions, so the total carbon emissions show a decreasing trend. It is worth noting that transportation is not the only main process which produce carbon emissions in the building supply chain, but is also the largest contributor to reduce CO2 under the carbon tax policy. Therefore, decision makers should regard transportation as a key objective, and can further consider other strategies, such as technological reformation to reduce emissions based on the carbon tax policy.

Carbon emissions under different carbon prices
Figure 6

Carbon emissions under different carbon prices

The influence of carbon price on total cost is shown as Fig 7. The figure indicates that the total cost shows a trend of linear increase with rising carbon price. When the carbon price reaches 120RMB/t, the total cost increases 8.17% by 21631RMB. Carbon emissions cost caused by carbon price increase of 21276RMB, accounts for more than 95% of the total cost increase. Other cost increases which are caused by the change of supply chain structure and the optimization of transportation path account for less than 5% of the total cost increase. So the carbon price can bring up the total cost growth directly; if set too high, it will bring economic burden to the node enterprises when the carbon tax policy is implemented.

The influence of carbon price on total cost
Figure 7

The influence of carbon price on total cost

The influence of carbon price on total carbon emissions is shown in Fig 8. The Figure indicates that the total carbon emissions show a trend of periodic change with rising carbon price. When the carbon price changes from 0RMB/t to 15RMB/t, the carbon emissions are in a constant state, because the cost caused by carbon emissions are low and belong in an enterprises’ acceptable range, so enterprises do not take measures to reduce CO2. When the carbon price changes from 15RMB/t to 30RMB/t, the carbon emissions are significantly reduced from 190703 kg to 177304 kg, the total emissions decrease by 7.03%. This is because the node enterprises adjust the supply chain structure and change the transportation path to reduce the emission cost, so it results in the emission reduction effect. When the carbon price changes from 30RMB/t to 120RMB/t, the carbon emissions return to a constant state. If the node enterprises take measures to reduce CO2 again, this cost consumption will exceed the CO2 emissions cost, so enterprises prefer to accept the economic burden caused by the rising carbon price. If the carbon price is further improved, CO2 emissions will still have a trend of periodic reduction, but the decline is not obvious and it will bring a large economic burden to the node enterprises, the results are not shown here. In summary, if decision makers want to realize a low carbon building supply chain economically, the carbon price should be from 15RMB/t to 30RMB/t.

The influence of carbon price on total carbon emissions
Figure 8

The influence of carbon price on total carbon emissions

6 Conclusions and future research

The paper establishes a mixed integer linear programming model of a building supply chain network under carbon tax policy, and analyzes the impact of different carbon prices on supply chain cost and carbon emissions reduction. The target is to realize a low carbon building supply chain economically.The results show that:

  1. Carbon tax policy can decrease CO2 emissions of the building supply chain effectively and it reduces carbon emissions by adjusting the supply chain structure and changing the transportation path;

  2. Transportation is not the only process which produces carbon emissions in the building supply chain, but is also the largest contributor to reduce CO2 under a carbon tax policy, the decision makers should regard transportation as a key objective, and can further consider other strategies such as technological reformation to reduce emissions based on the carbon tax policy;

  3. Rising carbon price doesn’t always bring about a reduction effect, but may make carbon emissions to be constant within a certain range, so the research suggests that 15RMB/t to 30RMB/t is an economical and reasonable range for the carbon price;

  4. Carbon tax policy can reduce emissions effectively, but at the same time, it may bring financial burdens caused by carbon emissions cost. Therefore, the carbon price should be formulated with consideration of the dependence of the energy, the actual carbon emissions and the economic conditions in particular enterprises.

Future work may further consider the impact of other factors, such as contractors’ willingness to pay for low carbon effects and an enterprises’ risk appetite on carbon policy implementation. The impact of technology investment on building supply chain carbon emission reduction strategy should be considered in the future.

Acknowledgement

The authors thank the anonymous referees for their constructive suggestions. We appreciate the support provided for this paper by the National Natural Science Funds of China (Project Nos. 71471123 and 71071102); and the Sichuan province philosophy social sciences key research base (XHJJ-1507).

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About the article

Received: 2016-09-30

Accepted: 2016-10-27

Published Online: 2017-03-22


Citation Information: Open Physics, Volume 15, Issue 1, Pages 97–107, ISSN (Online) 2391-5471, DOI: https://doi.org/10.1515/phys-2017-0011.

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© 2017 Xueying Li et al.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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