**Coordination mechanism of wooden furniture supply chains with consideration of carbon footprint**,"

*BioResources*17(4), 6203-6221.

#### Abstract

This study emphasizes a three-level wooden furniture supply chain, which involves one supplier, one manufacturer, and one retailer. Focusing on maximizing the profit of the supply chain while adhering to low-carbon principles, the Three-level Leader-follower Game (TLG) model, Stackelberg Game Model I (SGI model), Stackelberg Game Model II (SGlI model), and Cooperative Decision-making (CD) model were established by using game theory. The carbon emission reduction cost and benefit sharing contract was introduced into the model with the maximum profit, and the ranges of sharing coefficients for a solid wood bed supply chain and the optimal decision-making process for each supply chain member were discussed. Results showed that the profit for the solid wood bed supply chain reached maximum under the CD model, followed by the SGII model, and then the SGI model, and the TLG model showed the lowest profit. A higher preference for low-carbon products can lead to lower demand for products and higher retail prices. Through introducing the cost and benefit-sharing contract into the CD model, the profit of the supply chain can be guaranteed with different sharing coefficients, and the profit of each member was improved compared to the TLG model.

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#### Full Article

**Coordination Mechanism of ****Wooden Furniture Supply Chains with**** Consideration of Carbon Footprint**

Hui Wang, Jinzhuo Wu,* Bing Han, and Yilin Fang

This study emphasizes a three-level wooden furniture supply chain, which involves one supplier, one manufacturer, and one retailer. Focusing on maximizing the profit of the supply chain while adhering to low-carbon principles, the Three-level Leader-follower Game (TLG) model, Stackelberg Game Model I (SGI model), Stackelberg Game Model II (SGlI model), and Cooperative Decision-making (CD) model were established by using game theory. The carbon emission reduction cost and benefit sharing contract was introduced into the model with the maximum profit, and the ranges of sharing coefficients for a solid wood bed supply chain and the optimal decision-making process for each supply chain member were discussed. Results showed that the profit for the solid wood bed supply chain reached maximum under the CD model, followed by the SGII model, and then the SGI model, and the TLG model showed the lowest profit. A higher preference for low-carbon products can lead to lower demand for products and higher retail prices. Through introducing the cost and benefit-sharing contract into the CD model, the profit of the supply chain can be guaranteed with different sharing coefficients, and the profit of each member was improved compared to the TLG model.

*DOI: 10.15376/biores.17.4.6203-6221*

*Keywords: Wooden furniture; Carbon footprint; Supply chain; Game theory; Revenue sharing contract*

*Contact information: College of Engineering and Technology, Northeast Forestry University, Harbin 150040 China; *Corresponding author: wjz@nefu.edu.cn*

**INTRODUCTION**

Mitigating climate change by decreasing global greenhouse gas emissions is currently one of the major challenges faced by human beings (Vicente-Vicente and Piorr 2021). To control carbon emissions and achieve carbon reduction targets, a series of carbon reduction policies have been introduced by governments, and green supply chain management in all sectors have gained increased attention (Zhu and Côté 2004; Dragomir 2012; Zhou *et al.* 2014). According to a report by the Intergovernmental Panel on Climate Change (IPCC), the forestry industry is the third-largest source of greenhouse gas emissions after the energy industry and manufacturing industry (Bai 2013). Currently, China has become the world’s largest emitter of carbon dioxide. Both the total carbon footprints and carbon footprint intensity of the wooden furniture industry in China are rather large; therefore, it is critically important to reduce the carbon footprints of the wooden furniture supply chain (Gu *et al.* 2014). To promote the low-carbon development of the forestry industry, the core enterprises of the supply chains must expand their internal greening activities through vertical and horizontal integration with their upstream and downstream stakeholders (Noh and Kim 2019). The biggest challenge to the supply chain is to manage disparate but dependent members of the supply chain. For an efﬁcient supply chain, it is required that all supply chain members behave coherently to achieve supply chain coordination (Whang 1995). This can be realized by making joint decisions on all processes of the supply chain, including procurement, production, distribution, as well as the allocations of resources and economic benefits (Kim* et al*. 2005). Therefore, it is necessary to introduce the coordination mechanism into the wooden furniture supply chain, which is of great significance to low-carbon development and green supply chain management for the wooden furniture industry.

Currently, most studies on the carbon footprint of the wooden furniture supply chain have aimed to identify the links with higher carbon footprint in business operations and supply chain management. For example, González-García *et al*. (2011) completed a life cycle assessment on several indoor and outdoor wood products from a cradle-to-gate perspective. The results showed that metals, boards, and energy usage were the most important factors contributing to the environmental impact of the different products under assessment, with total contributions ranging from 40% to 90%. Bai (2013) compared the carbon footprint of the production and processing process for tea cabinets made of wood-based panels and coffee tables and cabinets made of solid wood. The results showed that the carbon footprints of wood panel-based tea cabinets, solid wood-based coffee tables, and solid wood-based cabinets were 160 kg CO_{2}-eq, 89.9 kg CO_{2}-eq, and 139 kg CO_{2}-eq, respectively, and the carbon footprints of different products were mainly sourced from the processing of raw materials and the finishing process of the products. Wang *et al*. (2021) applied the ILCD 2011 midpoint assessment method to calculate the life-cycle carbon footprint of a solid wood bed (1800 mm × 2000 mm) based on imported logs. The results show that the carbon footprint of the upstream process accounted for 74.56% to 80.69% of the total carbon footprint, which was the major contributor to the total carbon footprint, followed by the downstream and manufacturing process. In summary, most of the carbon footprint of wooden furniture supply chains is borne by the upstream members in the supply chain, which has become an important link in reducing the carbon footprint of the entire supply chain.

Similar to other supply chains, a wooden furniture supply chain is also composed of different decision-makers pursuing different goals, and there may be conflicts among these goals, which may lead to the problem of “Double Marginalization” for the contract supply chain (Pang* et al.* 2014). The number of business members in the supply chain and the efforts of members to reduce carbon emissions can greatly affect the market demand for the wood furniture supply chain (Yong* et al*. 2007). In fact, supply chain members need to bear a certain amount of cost for their efforts, and the conflict between green effort level and cost will affect the coordination of the supply chain (Zui* et al.* 2008). Revenue sharing coordination mechanism is a coordination and profit distribution mechanism on the profits generated in a supply chain, negotiating commercial rules among the parties in the supply chain (Cachon and Lariviere 2005). In recent years, some studies have been conducted on the coordination mechanism of furniture supply chains to improve the operational performance of the supply chain. For example, Kang (2013) proposed revenue sharing and franchise fee coordination between suppliers and retailers in a furniture supply chain system based on the Stackelberg game model and found that the channel profit and member profit after coordination were greater than those under decentralized independent decision-making. Wen (2020) developed a model for furniture sellers to share the environmental costs with furniture manufacturers and analyzed the game between manufacturers and sellers in the case of revenue sharing. The calculations demonstrated that increasing the share of the manufacturer’s environmental costs by a furniture seller under a revenue-sharing scheme had a positive effect on the manufacturer’s improvement of environmental protection. Zheng (2020) analyzed the benefit distribution of a four-level furniture manufacturing green supply chain composed of raw material suppliers, furniture manufacturers, furniture sellers, and third-party logistics. A comprehensive benefit distribution model was established to determine the sharing value of each member in the green supply chain under comprehensive evaluation of multiple factors.

Since the carbon footprint of wood furniture products contributes to the combined emissions of upstream and downstream enterprises in the supply chain, the carbon reduction behavior of a single enterprise cannot effectively reduce the carbon footprint of the entire supply chain. Previous studies seldom considered the carbon reduction efforts of corporations from the perspective of supply chain. In fact, the carbon reduction behavior of supply chain members through technical carbon emission reduction or trading in the carbon emission market will increase the marginal cost of product, and the cost increment will be passed on to the downstream, thus causing the variations of market demand (Zui* et al.* 2008). Currently, China has set up carbon emission caps for some key enterprises and is moving the regional carbon emissions trading market to the national carbon emissions trading market (Liu *et al.* 2015). The part that exceeds the carbon emission cap can be traded in the carbon emission market. It is believed that the existence of emission regulation can promote collaboration of supply chain members (Benjaafar *et al.* 2013). With regard to wood furniture supply chain, the implementation of carbon reduction measures also requires the members to jointly bear a certain amount of costs, which will affect the profitability of the supply chain. Because the coordinated strategy between carbon footprint and profit in the three-level wooden furniture supply chain is rarely reported, it is necessary to coordinate the wood furniture supply chain to maximize the profits of the supply chain and the members with consideration of the carbon footprint of the supply chain.

The objectives of the study are to: (1) Establish four game models for the three-level (supplier-manufacturer-retailer) wooden furniture supply chain; (2) Compare the optimal decision-making under different models and conduct sensitivity analyses by considering different consumers’ preferences on products with low carbon footprint; (3) Introduce the sharing contract of carbon emission reduction cost and benefit into the model with maximum profit to obtain the ranges of the optimal sharing coefficient for the members of the wooden furniture supply chain.

**Model Description and Hypotheses**

A supply chain is usually comprised of suppliers, manufacturers, distributors, and consumers, involving supply, production, sales, transportation, consumption, recycling, and so on (Pang et al. 2014). In this study, the wooden furniture supply chain is composed of one supplier, one manufacturer, and one retailer, as shown in Fig. 1. It is assumed that the information among suppliers, manufacturers, and retailers is completely symmetrical. The supplier, the manufacturer, and the retailer are the main sources of carbon emissions in the wooden furniture supply chain, which can meet the demand for carbon emission rights for normal operations by reducing technological emissions and purchasing carbon credits from the trading market. In this study, profit maximization is assumed to be the highest priority of all actors with considerations of policy and/or other motivators such as consumer preferences, short-term priorities of compliance, and consumer satisfaction. The cost of carbon emissions reduction, as an environmental performance cost, may be considered as a corporate/capital investment. When suppliers and manufacturers invest in carbon emission reduction technologies or trade in the carbon market, part of the marginal cost of emission reduction is passed along to consumers at the per-unit price level. The explanations of the parameters in the study are shown in Table 1.

**Fig. 1.** Structure of the wooden furniture supply chain with consideration of carbon emissions

**Table 1. **Model Parameters for the Three-level Supply Chain

The hypotheses for the three-level supply chain are as follows:

- The supplier sells the raw materials to the manufacturer at price w
_{s}, the manufacturer sells the wooden furniture products to the retailer at price w_{m}, and the retailer sells the products at market price P. Assuming that the supply chain emission reduction level is a continuous variable, the carbon reduction cost of supply chain is expressed as: C = r∆e^{2}(r > 0), where r is the carbon emission reduction cost coefficient (Subramanian et al. 2007). - The carbon emissions cap for the entire supply chain and the carbon transaction price set by the carbon trading regulations are G and p
_{c}, respectively. The carbon transaction price is a linear function of the upper limit of carbon emissions set by the government, that is, the carbon transaction price p_{c }= a – bG, where a and b are constants (Luo et al. 2014). - The retail price P of a product depends on the carbon emissions E of the supply chain, that is P = v – kE (0 < k < 1), where v is a constant and k reflects the consumers’ preference for carbon footprint. A higher k value meant a greater appeal of low-carbon products to consumers; a smaller k meant consumers were less sensitive to the carbon emissions of the supply chain. The carbon footprint of the supply chain is: E=(e
_{s}+e_{m}+e_{r})q–∆e, where e_{s}is the carbon emissions from raw materials per unit of product, e_{m}is the carbon emissions from manufacturing per unit of product, e_{r}is carbon emissions from transporting per unit of product per kilometer, ∆e is the carbon emission reduction level of the supply chain, and q is the demand on products (Yang and Ji 2013).

*Three-level leader–follower game model (TLG model)*

The Three-level leader-follower game model is a non-cooperative three-level Stackelberg game between the members of the supply chain in an attempt to maximize their own interests (Pakseresht *et al*. 2020). Under the TLG model, the supplier, manufacturer and retailer, as different decision-making subjects, have not reached a binding agreement, and they make decisions with the goal of maximizing their own profits. The game sequence is as follows: ﬁrstly, according to the cost of raw materials *c*_{s}, the supplier determines the optimal supply price of raw materials ; then, according to the supply price provided by the supplier and the carbon emission cap* G* stipulated by the government, the manufacturer invests in technology emission reduction and determines the optimal wholesale price of the retailed product and the optimal carbon reduction level ∆e^{TLG}; finally, according to the wholesale price of the manufacturer, the retailer determines the optimal demand on products *q*^{TLG }to maximize its profit. Therefore, the TLG model composed of one supplier, one manufacturer, and one retailer can be expressed as follows:

(1)

Under the TLG model, the above optimization problem can be solved by reverse induction. Take the partial derivative of the retailer’s profit with respect to the product demand under the TLG model, and set the result equal to 0 to obtain the retailer’s optimal product demand *q*^{TLG} (Eq. 2).

(2)

The manufacturer maximizes its own profit through decision Substitute Eq. 2 into Eq. 1 to calculate the partial derivative of the manufacturer’s profit with respect to the wholesale price and carbon emission reduction level under the TLG model, and then make the result equal to 0, and solve the simultaneous equations to obtain the manufacturer’s optimal wholesale price (Eq. 3) and the optimal carbon reduction level ∆*e*^{TLG} (Eq. 4):

The supplier maximizes its own profit through decision . Substitute Eqs. 2 through 4 into Eq. 1 to calculate the partial derivative of the supplier’s profit with respect to the supply price under the TLG model, and make the result equal to 0, then the optimal supply price of raw materials per unit of product (Eq. 5) can be obtained according to the first-order optimal condition:

According to hypothesis 3, equilibrium solutions can be obtained from Eqs. 2 through 5, When the condition 0 < *k < *8(*e*_{s }+ *e*_{m }+ *e*_{r})*r* is met, the manufacturer’s optimal wholesale price (Eq. 6), the optimal carbon reduction level ∆*e*^{TLG*} (Eq. 7), and the retailer’s optimal demand on products *q*^{TLG*} (Eq. 8) can be obtained, respectively:

Based on the above analysis, the optimal carbon emissions of the supply chain *E*^{TLG* }(Eq. 9), the optimal retail price of the product (Eq. 10), the optimal profit of the supplier (Eq. 11), the optimal profit of the manufacturer (Eq. 12), the optimal profit of the retailer (Eq. 13), and the profit of the whole supply chain (Eq. 14) can be obtained, respectively:

*Stackelberg game model I*

The Stackelberg game model I (SG model I) takes the cooperation between the supplier and the manufacturer into consideration, which is a non-cooperative two-level Stackelberg game between the small alliance I that is formed by the supplier and the manufacturer and the retailer and dominated by the alliance I (Zhang and Liu 2013). Under the SG model I, the alliance I is the major sources of carbon emissions in the wooden furniture supply chain. The game sequence is as follows: ﬁrstly, according to the cost of raw materials *c*_{s}, manufacturing cost *c*_{m}, and the carbon emission cap *G *stipulated by the government, the alliance I invests in technology emission reduction and determines the optimal wholesale price of the retailed product and the optimal carbon reduction level ∆*e*^{SGI} of the supply chain; then, according to the wholesale prices provided by the alliance I, the retailer determines the optimal demand on products *q*^{SGI} to maximize its profit. Therefore, the SG model I can be expressed as follows:

Under the SG mode I, the above optimization problem can be solved by reverse induction. According to the first-order optimal condition, the optimal product demand *q*^{SGI} is obtained *via* Eq. 16;

The alliance I maximizes its own profit through decision Substitute Eq. 16 into Eq. 15 to calculate the partial derivative of the alliance I ‘s profit with respect to the wholesale price and carbon emission reduction level under the SG model I, make the result equal to 0, and solve the simultaneous equations to obtain the optimal carbon reduction level ∆*e*^{SGI*} (Eq. 17) and the manufacturer’s optimal wholesale price (Eq. 18):

*Stackelberg game model II*

The Stackelberg game model II (SG model II) takes the cooperation between the manufacturer and the retailer into consideration, which is a two-level Stackelberg game between the small alliance II that is formed by the manufacturer and the retailer and the supplier. Different from the SG model I, the SG model II is dominated by the supplier (Chen *et al*. 2020). Under the SG model II, the alliance II has a preference for low-carbon products in the wooden furniture supply chain. The game sequence is as follows: ﬁrstly, according to the cost of raw materials *c*_{s}, the supplier determines the optimal supply price of the raw materials; then, according to supply price of the raw materials provided by the supplier, the alliance II invests in technology emission reduction and determines the optimal demand on products *q*^{SGII} and the optimal carbon reduction level ∆e^{SGII} to maximize its profit. Therefore, the SG model IIcan be expressed as follows:

Under the SG model II, the above optimization problem can be solved by reverse induction. The alliance II maximizes its own profit through decision (*q*^{SGII}, ∆e^{SGII}), the optimal carbon reduction level ∆*e*^{SGII} (Eq. 26), and the optimal demand on products* q*^{SGII} (Eq. 27) can be obtained:

Substituting Eqs. 26 and 27 into Eq. 25, the optimal supply price of raw materials per unit of product (Eq. 26) can be obtained according to the first-order optimal condition. Take the partial derivative of the supplier’s profit with respect to the supply price under the SG model II, and make the result equal to 0, the optimal supply price of raw materials per unit of product (Eq. 28) can be obtained according to the first-order optimal condition:

*Cooperative decision-making model*

The cooperative decision-making model (CD model) is a cooperative three-level Stackelberg game under centralized decision-making among the members of the supply chain in an attempt to maximize the profits of the supply chain (Landgren *et al*. 2021). Under the CD model, the supplier, the manufacturer, and the retailer determine the optimal demand on products *q*^{CD} and the optimal carbon reduction level ∆*e*^{CD} of the supply chain to maximize its profit. The expected profit function of the supply chain can be expressed as follows:

Under the CD model, the above optimization problem can be solved by reverse induction. According to the first-order optimal condition, the supplier, the manufacturer, and the retailer maximize the profit of the supply chain through decision (*q*^{CD}, ∆*e*^{CD}), the optimal carbon reduction level ∆*e*^{CD*} (Eq. 37), and the optimal demand on products *q*^{ CD*}Eq. 38) can be obtained. When the condition 0 < *k < *4(*e*_{s }+ *e*_{m }+ *e*_{r})*r* is met, the optimal carbon emissions of the supply chain *E*^{CD*} (Eq. 39), the optimal retail price of the product *P*^{CD*} (Eq. 40), and the profit of the whole supply chain (Eq. 41) can be obtained, respectively:

**Coordination Mechanism with the Contract of Sharing Carbon Emission Reduction Cost and Benefit**

Centralized decision-making is better than decentralized decision-making, but centralized decision-making will harm the interests of one participant. The carbon emission reduction cost-sharing and benefit-sharing coordination mechanism is a method to solve the problem of benefit distribution among supply chain enterprises and improve supply chain efficiency (Song and Gao 2018). In the present study, a carbon emission reduction cost-sharing and benefit-sharing coordination mechanism was introduced into the CD model under centralized decision-making introduces in order to improve the supply chain’s efficiency. The explanations of the variables in the mechanism are shown in Table 2.

**Table 2. **Model Variables for the Coordination Mechanism

Proposition: Under the coordination of the supply chain, the revenue sharing coefficient is the same as the carbon reduction cost coefficient for each supply chain member.

Prove: To make the profit function of the supply chain system under the carbon emission reduction cost-sharing and revenue sharing contract the same as the supply chain system profit in the CD model under centralized decision-making, it only needs to satisfy the following: q^{RS* }= q^{CD*}; ∆e^{RS* }= ∆e^{CD*}.

Take the partial derivatives of Eq. 42 with respect to q^{RS} and respectively and set them equal to 0, and solve the equations simultaneously. When the condition 0<k<4(e_{s}+e_{m}+e_{r})r/is met, then the optimal carbon reduction level ∆e^{RS*} (Eq. 45), the optimal demand on products q^{RS*} (Eq. 46), and the optimal supply price of the raw materials required for each product (Eq. 47) can be obtained: