Closed-loop supply chain for recycling of waste clothing: A comparison of two different modes

Huaqing Cao; Cai Liling; Xiaofen Ji

doi:10.1515/aut-2025-0031

Article Open Access

Closed-loop supply chain for recycling of waste clothing: A comparison of two different modes

Huaqing Cao , Cai Liling and Xiaofen Ji

Published/Copyright: April 17, 2025

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From the journal AUTEX Research Journal Volume 25 Issue 1

Abstract

Waste clothing, as a renewable resource, has received increasing attention. Due to high production costs, establishing an efficient supply chain for the recycling of waste clothing is a problem that brand owners need to solve. This study uses mathematical modeling methods to study the closed-loop supply chain models of original equipment manufacturers and cutting making trimming (CMT) in the recycling of waste clothing. By using the Stackelberg game method to analyze the model, the optimal decisions and profits of supply chain members under these two modes were obtained. Based on this, further comparative analysis was conducted between the two modes. Our research finds that brand owners choose to produce and sell recycled clothing not for profit maximization, but based on enhancing brand image or corporate social responsibility considerations. For the brand owner, adopting the CMT model is more advantageous, but this mode requires higher production technology for the recycled fabric supplier.

Keywords: Waste clothing; closed loop supply chain; supply chain mode

1 Introduction

With the development of recycled fiber production technology, clothing recycling has gradually attracted attention worldwide. International retail giants such as Uniqlo have been carrying out recycling activities since 2006, and Adidas has also announced that it will use 100% recyclable polyester fiber by 2024 [1]. Compared to using traditional fabrics to produce clothing, recycling and reusing waste clothing through the chemical method can reduce the consumption of raw materials such as oil, thereby reducing the use of water, energy, and chemicals in the production chain [2,3]. With the advancement of the global fashion industry’s goal of replacing traditional materials with recycled materials by 2030, the demand for recycled fiber raw materials will rapidly increase in the future [4]. This urgently requires improving the recycling rate of waste clothing and the production of recycled fibers, and building a closed-loop supply chain system for waste clothing [5,6,7,8].

The closed-loop supply chain for the chemical recycling of waste clothing is a combination of forward and reverse supply chains. Forward supply chain is the process in which manufacturers use traditional fabrics for clothing production and consumers purchase and consume. Reverse supply chain is a series of activities in which supply chain members recycle waste clothing products from consumers and reprocess them (classification, testing, remanufacturing, and recycling). As an early researcher on closed-loop supply chain, Savaskan et al. compared three closed-loop supply chain recycling models: manufacturer recycling, retailer recycling, and third-party recycling [9]. Furthermore, Savaskan and Van Wassenhove investigated two competing retailer recycling channels in a closed-loop supply chain [10]. Choi et al. studied the supply chain performance under different channel leaders in a fashion closed-loop supply chain consisting of retailers, collectors, and manufacturers [11]. Gao et al. established a closed-loop supply chain set consisting of a manufacturer and a retailer to study the optimal decisions of collection efforts, sales efforts, and pricing under different channel power structures [12]. Ranjbar et al. studied the optimal pricing and recycling decisions under two competitive recycling channels (including retailer recycling and third-party recycling) in a three-layer closed-loop supply chain consisting of manufacturers, retailers, and third-party suppliers [13]. Wu et al. studied the performance of three recycling channels in a closed-loop supply chain consisting of a single manufacturer and a single retailer: manufacturer recycling, retailer recycling, and third-party recycling under different channel leadership and recycling channel combinations [14]. Some scholars studied the pricing problem of remanufactured products [15,16,17,18]. Other scholars studied the competition between remanufactured products and new products [19,20,21,22,23,24,25].

Through a review of existing research in the field of closed-loop supply chain, we find that research on supply chain channel design, pricing, and competition is relatively complete. However, current research in this field mainly focuses on the OEM model, in which brand owners have designs but do not have their own factories. Therefore, they find another manufacturer to produce the products or accessories for them, and the manufacturer is responsible for purchasing raw materials. In the clothing industry, there is another common supply chain model called CMT, where brand owners purchase and provide manufacturers with certain raw materials, semi-finished products, components, and equipment. Sometimes, relevant equipment and technology are also provided, and manufacturers produce according to brand requirements. The finished products are sold by brand owners, and manufacturers are paid processing fees, as shown in Figure 1. It is still unclear how this model differs from the OEM model, and how brand owners should choose these two models when recycling waste clothing. The purpose of this study is to investigate the changes in decision-making and profits of supply chain agents under different models.

Figure 1

Original equipment manufacturer (OEM) mode and cutting making trimming (CMT) mode.

2 Problem description and model analysis

2.1 Problem description

We consider a closed-loop supply chain for waste clothing recycling consisting of a brand owner, a clothing manufacturer, a traditional fabric supplier, a recycled fabric supplier, and a collector. The clothing brand is the Stackelberg leader in the supply chain, and the manufacturer, fabric supplier, and recycler are followers. The brand owner can choose OEM mode, as shown in Figure 2, or CMT mode, as shown in Figure 3. The collector is responsible for collecting clothing used by consumers, downgrading it, exporting it overseas, or reselling it to the recycled fabric supplier. The recycled fabric supplier uses waste clothing to produce recycled fabrics, while the traditional fabric manufacturer uses chemical raw materials to produce traditional fabrics. The manufacturer is responsible for producing traditional or recycled clothing and selling it to the brand. The brand owner sells both traditional and recycled clothing to consumers simultaneously, and consumers maximize their own utility to decide whether to purchase traditional or recycled clothing.

Figure 2

OEM mode closed-loop supply chain for waste clothing.

Figure 3

CMT mode closed-loop supply chain for waste clothing.

Before analyzing, we propose the following assumptions:

Assuming that clothing produced from waste clothing has the same quality as clothing produced from traditional fabrics, but consumers are concerned about factors such as quality and hygiene, they still hold biases toward recycled products that come into contact with the skin, and are more inclined to purchase traditional clothing products. Based on common assumptions in supply chain research [26,27,28], we assume that the willingness of consumers to purchase clothing produced from traditional fabrics v is uniformly distributed in ( 0 , 1 ) , and the willingness to purchase clothing produced from recycled fabrics is θ v , θ ∈ [ 0,1 ] . When consumers purchase traditional clothing, their net utility is U n = v − p n and when they purchase recycled clothing, their net utility is U r = θ v − p r , where p n and p r are the prices of traditional and recycled clothing, respectively. Consumers will decide whether to purchase and which products (traditional clothing or recycled clothing) to maximize their net utility. For the given product prices p n and p r , when U n > U r and U n > 0 , consumers purchase traditional clothing, and their purchase intention v ∈ p n − p r 1 − θ , 1 . When U r > U n and U r > 0 , consumers purchase recycled clothing, and their purchase intention v ∈ p r θ , p n − p r 1 − θ . In other cases, consumers do not purchase the product. Assuming that the highest price consumers are willing to pay for clothing is Q , the inverse demand functions for traditional clothing and recycled clothing are p n = Q − q n − θ q r and p r = θ ( Q − q n − q r ) , where q n and q r are the production quantities of traditional clothing and recycled clothing, respectively.
The brand owner sells traditional clothing and recycled clothing at prices of p n and p r , with unit profits of r n and r r , respectively. The manufacturer produces traditional and recycled clothing at a cost of c m , with selling prices of w n and w r , and unit profits of m n and m r , respectively. The traditional fabric supplier’s unit cost for producing traditional fabrics is c n , the selling price is s n , and the unit profit is l n . The recycled fabric supplier’s unit cost for producing recycled fabrics is c r , the selling price is s r , and the unit profit is l r .
In reverse channels, the collector determines the quantity of waste clothing to be collected. Due to the extremely low collection cost of waste clothing [29], we assume that the collector does not need to pay for each collected waste clothing, but rather needs to invest in logistics and labor costs, including the cost of setting up recycling bins in residential areas and campuses, as well as corresponding transportation and manual sorting costs. According to research in the field of closed-loop supply chain [30,31,32], we express the collection cost as a quadratic function of the collection quantity, with a coefficient c ; therefore, the collection cost is c q c 2 . The collector sells the collected waste clothing to the recycled fabric supplier at a price f , and downgrades or exports the remaining waste clothing overseas to obtain unit income P . The symbols used in this research are explained in Table 1.

Table 1

Symbols and definition

Notation	Definition
θ	Consumer preference coefficient for recycled clothing
c n / c r	The unit production cost of traditional/recycled fabrics
c m	The manufacturer’s unit production cost
c	The cost coefficient for collecting waste clothing
P	The collector’s unit income from downgrading and utilization of waste clothing
i	i = { E , C } , representing OEM mode and CMT mode, respectively
p n i / p r i	The retail price of traditional/recycled clothing
r n i / r r i	The brand owner’s unit profit from selling traditional/recycled clothing
w n E / w r E	The wholesale price of traditional/recycled clothing in OEM mode
w m C	The wholesale price of traditional/recycled clothing in CMT mode
m n E / m r E	The unit profit of the manufacturer selling traditional/recycled clothing in OEM mode
m m C	The unit profit of the manufacturer selling traditional/recycled clothing in CMT mode
s n i / s r i	The sales price of traditional/recycled fabrics
l n i / l r i	The unit profit of the traditional fabric supplier selling traditional fabrics/the unit profit of the recycled fabric supplier selling recycled fabrics
f i	The unit transfer price of waste clothing
q n i / q r i	The production quantity of traditional/recycled clothing
q c i	The collection quantity of waste clothing
Π j i	The profit of each supply chain member, j = { R , M , S 1 , S 1 , C } , representing the brand owner, manufacturer, traditional fabric supplier, recycled fabric supplier, and collector, respectively

2.2 OEM mode analysis

In this model, each member makes decisions based on their own profit maximization, and the decision-making order of supply chain members is as follows: as a Stackelberg leader the brand owner decides the production quantity of traditional clothing q n and the production quantity of recycled clothing q r based on market conditions first. Then, the manufacturer decides the wholesale price of traditional clothing w n and the wholesale price of recycled clothing w r . Afterward, the fabric supplier decides the sales price of traditional fabrics s n and recycled fabrics s r , respectively. Finally, the collector decides the collection quantity q c and the transfer price f of the waste clothing. The profit functions of the brand owner, manufacturer, traditional fabric supplier, recycled fabric supplier, and collector are as follows:

(1) Π R E q n , q r = ( p n − w n ) q n + ( p r − w r ) q r ,

(2) Π M E w n , w r = ( w n − s n − c m ) q n + ( w r − s r − c m ) q r ,

(3) Π S 1 E s n = ( s n − c n ) q n ,

(4) Π S 2 E s r = ( s r − c r − f ) q r ,

(5) Π C E f , q c = f q r + P ( q c − q r ) − c q c 2 .

Table 2

Optimal decision of supply chain members in OEM mode

Optimal decision
l n E	4 ( 1 − θ ) Q − ( 4 − 3 θ ) c n + c r + P − 3 ( 1 − θ ) c m 4 ( 8 − 5 θ )
l r E	2 θ ( 1 − θ ) Q + θ A c n − ( 4 − 3 θ ) ( c r + P ) − B c m 4 ( 8 − 5 θ )
m n E	Q − c n − c m 4
m r E	θ Q − c r − P − c m 4
r n E	Q − c n − c m 2
r r E	θ Q − c r − P − c m 2
s n E	4 ( 1 − θ ) Q + ( 28 − 17 θ ) c n + c r + P − 3 ( 1 − θ ) c m 4 ( 8 − 5 θ )
s r E	6 θ ( 1 − θ ) Q + 3 θ A c n + ( 52 − 31 θ ) ( c r + P ) − 3 B c m 8 ( 8 − 5 θ )
w n E	( 12 − 9 θ ) Q + ( 20 − 12 θ ) c n + c r + P + ( 21 − 12 θ ) c m 4 ( 8 − 5 θ )
w r E	( 22 θ − 16 θ 2 ) Q + 3 θ A c n + ( 36 − 21 θ ) ( c r + P ) + 3 ( 12 − 5 θ − θ 2 ) c m 8 ( 8 − 5 θ )
p n E	( 28 − 19 θ ) Q + 2 A c n + c r + P + ( 5 − 2 θ ) c m 4 ( 8 − 5 θ )
p r E	( 54 θ − 36 θ 2 ) + 3 θ A c n + ( 4 − θ ) ( c r + P ) + ( 4 + 5 θ − 3 θ 2 ) c m 8 ( 8 − 5 θ )
f E	2 θ ( 1 − θ ) Q + θ A c n − ( 4 − 3 θ ) c r + ( 60 − 37 θ ) P − B c m 8 ( 8 − 5 θ )
q n E	4 A ( 1 − θ ) Q − ( 4 − 3 θ ) A c n + A ( c r + P ) − 3 A ( 1 − θ ) c m 8 ( 8 − 5 θ ) ( 1 − θ )
q r E	( 2 θ − 2 θ 2 ) Q + θ A c n − ( 4 − 3 θ ) ( c r + P ) − B c m 8 ( 8 − 5 θ ) ( 1 − θ )
q c C	P 2 c

Proposition 1

The optimal decisions of each supply chain member are displayed in Table 2.

Here A = ( 2 − θ ) , B = 4 − 5 θ + θ 2 .

Proof: See Appendix 1.

Proposition 2

The brand owner will only decide to produce and sell recycled clothing when the production cost of recycled fabrics c r < c 0 , where c 0 = 2 θ ( 1 − θ ) Q + θ A c n − ( 4 − 3 θ ) P − B c m 4 − 3 θ .

Proposition 2 indicates that there is a production cost threshold for recycled fabrics entering the market. The higher the threshold c 0 , the greater the likelihood of recycled fabrics entering the market. In addition, through the analysis of the expression of the threshold c 0 , it can be found that when the production cost of traditional fabrics is low, c o > c n . However, when the production cost of traditional fabrics is high, c 0 < c n , which means the production cost of recycled fabrics must be lower than that of traditional fabrics. In the clothing industry, the production cost of recycled fabrics is higher than that of traditional fabrics. Therefore, most of the recycled clothing brands in the market are European and American clothing brands, such as Decathlon, Uniqlo, Nike, and Adidas. They sell recycled clothing not for profit maximization, but for their own corporate social responsibility or to achieve the carbon emission reduction goals set by the EU.

2.3 CMT mode analysis

In this model, the decision-making order of supply chain members is as follows: as a Stackelberg leader, the brand owner decides the production quantity of traditional clothing q n C and the production quantity of recycled clothing q r C based on market conditions first. Then, the manufacturer decides the wholesale price w m C . Afterward, the fabric supplier decides the sales price of traditional fabrics s n C and recycled fabrics s r C , respectively. Finally, the collector decides the collection quantity q c C and the transfer price f C of the waste clothing. The profit functions of the brand owner, manufacturer, traditional fabric supplier, recycled fabric supplier, and collector are as follows:

(6) Π R C q n C , q r C = ( p n C − w m C − s n C ) q n C + ( p r C − w m C − s r C ) q r C ,

(7) Π M C w n C , w r C = ( w m C − c m ) ( q n C + q r C ) ,

(8) Π S 1 C s n C = ( s n C − c n ) q n C ,

(9) Π S 2 C s r C = ( s r C − c r − f C ) q r C ,

(10) Π C C f C , q c C = f C q r C + P ( q c C − q r C ) − c q c C 2 .

Table 3

Optimal decision of supply chain members in CMT mode

Optimal decision
l n C	2 E ( 1 − θ ) Q − ( 32 − 2 θ − 27 θ 2 + 9 θ 3 ) c n + D ( c r + P ) − 3 C ( 1 − θ ) c m 4 C ( 8 − 5 θ )
l r C	2 ( 1 − θ ) F Q + θ D ( 2 − θ ) c n − ( 16 + 40 θ − 63 θ 2 + 19 θ 3 ) ( c r + P ) − B C c m 4 C ( 8 − 5 θ )
m m C	2 θ ( 5 − 2 θ ) Q − 3 θ ( 2 − θ ) c n − ( 4 − θ ) ( c r + P ) − C c m 4 C
r n C	Q − c n − c m 2
r r C	θ Q − c r − P − c m 2
s n C	2 E ( 1 − θ ) Q + ( 96 + 82 θ − 169 θ 2 + 51 θ 3 ) c n + D ( c r + P ) − 3 C ( 1 − θ ) c m 4 C ( 8 − 5 θ )
s r C	6 ( 1 − θ ) F Q + 3 D θ ( 2 − θ ) c n + ( 208 + 40 θ − 203 θ 2 + 63 θ 3 ) ( c r + P ) − 3 B C c m 8 C ( 8 − 5 θ )
w m C	2 θ ( 5 − 2 θ ) Q − 3 θ ( 2 − θ ) c n − ( 4 − θ ) ( c r + P ) + 3 C c m 4 C
p n C	2 ( 48 + 49 θ − 101 θ 2 + 31 θ 3 ) Q + E ( 2 − θ ) c n + F ( c r + P ) + ( 5 − 2 θ ) C c m 4 C ( 8 − 5 θ )
p r C	18 θ ( 3 − 2 θ ) Q + 3 θ ( 2 − θ ) c n + ( 4 − θ ) ( c r + P ) + C c m 8 ( 8 − 5 θ )
f C	2 ( 1 − θ ) F Q + θ D ( 2 − θ ) c n − ( 16 + 40 θ − 63 θ 2 + 19 θ 3 ) c r − B C c m + ( 240 + 120 θ − 329 θ 2 + 101 θ 3 ) P 8 C
q n C	2 E ( 1 − θ ) Q − ( 32 − 2 θ − 27 θ 2 + 9 θ 3 ) c n + D ( c r + P ) − 3 ( 1 − θ ) C c m 8 C ( 1 − θ ) ( 8 − 5 θ )
q r C	2 θ ( 1 − θ ) F Q + θ D ( 2 − θ ) c n − ( 16 + 40 θ − 63 θ 2 + 19 θ 3 ) ( c r + P ) − B C c m 8 C θ ( 1 − θ ) ( 8 − 5 θ )
q c C	P 2 c

Proposition 3

The optimal decisions of each supply chain member are displayed in Table 3.

Here A = ( 2 − θ ) , B = 4 − 5 θ + θ 2 , C = 4 + 5 θ − 3 θ 2 , D = 20 − 5 θ − 3 θ 2 , E = 16 + 5 θ − 6 θ 2 , F = 23 θ − 8 θ 2 − 12 .

Proof: See Appendix 1.

2.4 Comparison of two modes

Proposition 4

The comparison of decision-making of supply chain members under two modes is as follows:

(1) l n E < l n C , l r E > l r C , m r E < m m C < m n E , r n E = r n C , r r E = r r C ;

(2) s n E < s n C , s r E > s r C , w n E > w m C , w r E > w m C , p n E > p n C , p r E = p r C , f E > f C ;

(3) q n E < q n C , q r E > q r C , q c E = q c C .

Proof

See Appendix 1.□

The unit profit of clothing sold by brand owners in both modes is the same, and the retail price depends on the changes in purchasing costs of the brand owner. In CMT mode, the manufacturer only needs to produce clothing without purchasing fabrics, so the wholesale price of clothing is lower than that of OEM mode. In the CMT model, for the brand owner, the magnitude of the wholesale price reduction of recycled clothing is equal to the sales price of recycled fabrics ( w r E − w m C = s r C ). That is to say, in the CMT model, the total cost for the brand owner to purchase recycled fabrics from the supplier and commission the manufacturer for processing is equal to the cost for the brand owner to directly purchase recycled clothing from the manufacturer in the OEM model ( w m C + s r C = w r E ). Therefore, the retail prices of recycled clothing are the same in both modes. In CMT mode, the selling price of traditional fabrics is higher, but the wholesale price of the manufacturer is lower ( w n E − w m C > s n C ), which means that the total cost for the brand owner to purchase traditional fabrics from the traditional fabric supplier and commission the manufacturer for processing in the CMT model is lower than the cost of directly purchasing traditional clothing from the manufacturer in the OEM model ( w m C + s n C < w n E )， so the retail price of traditional clothing in CMT model is lower. Therefore, compared to the OEM model, the CMT model has a higher production quantity of traditional clothing and a lower production quantity of recycled clothing. It is worth mentioning that from the proof process, it can be found that since our research assumes that the production cost of recycled fabrics is higher than that of traditional fabrics based on actual production conditions, the CMT model is more advantageous for traditional clothing. When the production cost of recycled fabrics decreases sufficiently low ( c r < c n − ( 1 − θ ) Q − P ), the CMT model will be beneficial for expanding the production of recycled clothing.

3 Numerical analysis

In order to provide a more intuitive comparison of the decisions and profits of each member of the supply chain in the two modes, this section uses numerical analysis to present the previous research conclusions. According to relevant research in the field of supply chain [33], the parameter settings of our research are as follows: c n = 5 , c r = ( 5,6 ) , c m = 1 , Q = 100 , p = 1 , θ = 0.9 .

According to the previous analysis, there are thresholds for the entry of recycled clothing into the market. In order to ensure the rationality of the analysis, that is, the production quantity of recycled clothing is not negative, we first discuss the production quantity of traditional clothing and recycled clothing in two supply chain modes, as shown in Figure 4. The horizontal axis represents the production cost of recycled fabric, the vertical axis represents the production quantity of clothing, the blue represents the OEM mode, and the red represents the CMT mode.

Figure 4

Production quantities of traditional and recycled clothing in two modes.

From Figure 4, it can be seen that the CMT mode has a higher production quantity of traditional clothing and a lower production quantity of recycled clothing compared to the OEM mode. In the CMT mode, when the production cost of recycled fabrics exceeds the threshold 5.86, the brand owner decides not to produce recycled clothing due to the high production cost of recycled fabrics, which is consistent with Proposition 2. Under this production cost, the brand owner in the OEM mode will still produce recycled clothing, indicating that in OEM mode, brand owner can accept higher production costs for recycled fabrics and has lower requirements for recycled fabric production technology. Therefore, in the following analysis, in order to ensure the existence of recycled clothing in the market, we set the production cost of recycled fabrics c r ∈ ( 5,5.5 ) .

From Figures 5 and 6, it can be seen that the traditional fabric supplier with lower production costs has higher unit profit and selling price in the CMT mode, while the recycled fabric supplier has the opposite, higher unit profit and selling price in the OEM mode. Therefore, in the CMT mode, compared to the OEM mode, the traditional fabric supplier has higher profits and the recycled fabric supplier has lower profits, indicating that the CMT mode is beneficial for the fabric supplier with lower production costs.

Figure 5

(a) Unit profit, (b) sales price, and (c) profit of the traditional fabric supplier.

Figure 6

(a) Unit profit, (b) sales price, and (c) profit of the recycled fabric supplier.

In the CMT mode, the manufacturer does not need to purchase raw materials and only needs to manufacture clothing, so the sales prices and unit profit of the two types of clothing in the mode are the same (Figure 7). In the CMT mode, the manufacturer’s unit profit in manufacturing clothing is higher than the profit in manufacturing recycled clothing in the OEM mode, and lower than the profit in manufacturing traditional clothing in the OEM mode. The selling price of both types of clothing in the OEM mode is higher than that in the CMT mode. This is because in the CMT mode, the brand owner needs to purchase raw materials, which increases the total procurement cost. As a channel leader, for the sake of maximizing their own profits, they will compress the price of clothing purchased from the manufacturer. Therefore, in this mode, the manufacturer’s unit profit and selling price are lower. As a result, the manufacturer’s profit is lower in the CMT mode.

Figure 7

(a) Unit profit, (b) sales price, and (c) profit of the manufacturer.

It can be seen from Figure 8 that in the two modes, the brand owner has the same unit profit in selling traditional clothing and recycled clothing, the retail price of traditional clothing is higher in the OEM mode, and the retail price of recycled clothing is the same. From Figure 8(c), it can be seen that in the CMT mode, the brand owner has higher profits compared to the OEM mode. Based on the previous analysis, it can be seen that in this mode, the brand owner will lower the wholesale prices of the manufacturer, compress the profits of the manufacturer and the supplier with higher production costs (recycled fabric supplier) to increase their own profit.

Figure 8

(a) Unit profit, (b) sales price, and (c) profit of the brand owner.

Figure 9

Collector’s profit.

From Figure 9 it can be seen that the profit of the collector in the OEM mode is higher than that in the CMT mode. This is because the supply chain in this mode is longer, and the production costs of the recycled fabric supplier can be transmitted to the brand owner through the supply chain. Therefore, the price of the collector selling waste clothing is higher and the collector’s profit is higher.

4 Conclusion

Our research uses mathematical modeling methods to establish two closed-loop supply chains for the recycling of waste clothing, considering two typical clothing supply chain modes: OEM and CMT. The main research conclusions of this study are as follows.

In the CMT mode, compared to the OEM mode, the profit of the brand owner and traditional fabric supplier is higher, while the profit of the recycled fabric supplier and manufacturer is lower. In addition, the CMT mode requires higher production technology for recycled fabrics. Under this mode, the recycled fabric suppliers need to reduce production costs to lower levels than the OEM model in order for brand owners to be willing to produce and sell recycled clothing.

In practice, the brand owner often chooses the CMT model to increase their own profits. As carbon emissions become increasingly stringent, we suggest that the brand owner provide a certain subsidy to the production of the recycled fabric supplier under this model to reduce the production cost of the recycled fabric and help its development. Otherwise, the recycled fabric supplier will withdraw from the market due to high production costs.

Although our research has explored the OEM and CMT modes in the recycling of waste clothing, there are also limitations. Our research only considers the situation where the collector collects waste clothing, and in the future, it can consider the situation where the brand owner or fabric supplier collect it.

Acknowledgments

This research was supported by Philosophy and Social Science Planning Projects of Zhejiang Province (24NDJC170YB), Fundamental Research Funds of Zhejiang Sci-Tech University (23196023-Y).

Funding information: This research was financially supported by Philosophy and Social Science Planning Projects of Zhejiang Province (24NDJC170YB), Fundamental Research Funds of Zhejiang Sci-Tech University (23196023-Y).
Author contributions: Huaqing Cao wrote the manuscript; Cai Liling revised the manuscript; Xiaofen Ji provides technical guidance.
Conflict of interest: Authors state no conflict of interest.
Ethical approval: The conducted research is not related to either human or animals use.
Data availability statement: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Appendix 1

Proof of Proposition 1:

Combining assumptions 1 and 2, we can obtain the following equation: p n = Q − q n − θ q r = w n + r n = s n + m n + c m + r n = c n + l n + m n + c m + r n , p r = θ ( Q − q n − q r ) = w r + r r = s r + m r + c m + r r = c r + l r + f + m r + c m + r r , we can obtain q n = Q − p n − p r 1 − θ = ( 1 − θ ) Q − c n − l n − m n − r n + c r + l r + f + m r + r r 1 − θ , q r = θ ( c n + l n + m n + r n + c m ) − c r − l r − f − m r − r r − c m θ ( 1 − θ ) . According to the Stackelberg game sequence, using the reverse solving method to solve the profit models of each member, and substituting q r in the collector′s profit function ∏ C f , q c = f q r + P ( q c − q r ) − c q c 2 , we can get the Hesse matrix of ∏ C regarding transfer price and the collection quantity H = − 2 θ ( 1 − θ ) 0 0 − 2 c = 4 c θ ( 1 − θ ) > 0 . Therefore, there exists a unique optimal solution for ∏ C . Using simultaneous equations ∂ ∏ C ∂ q c = 0 and ∂ ∏ C ∂ f = 0 , we can obtain f = θ ( c n + l n + m n + r n + c m ) − c r − l r − m r − r r − c m + P 2 , q c = P 2 c . Substituting f in q n and q r , we can obtain q n = 2 ( 1 − θ ) Q − ( 2 − θ ) ( c n + l n + m n + c m + r n ) + c r + l r + m r + c m + r r + P 2 ( 1 − θ ) , q r = θ ( c n + l n + m n + r n + c m ) − c r − l r − m r − r r − c m − P 2 θ ( 1 − θ ) . Since ∏ S 1 s n = ( s n − c n ) q n = l n q n , ∏ S 2 s r = ( s r − c r − f ) q r = l r q r , substituting q n , q r in ∏ S 1 , ∏ S 2 and solving ∂ ∏ S 1 ∂ l n = 0 and ∂ ∏ S 2 ∂ l r = 0 , we can obtain l n = 4 ( 1 − θ ) Q − ( 4 − 3 θ ) ( c n + m n + c m + r n ) + c r + m r + r r + c m + P 8 − 5 θ and l r = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) ( c n + m n + r n + c m ) − ( 4 − 3 θ ) ( c r + m r + c m + r r + P ) 8 − 5 θ . Substituting l n and l r in q n and q r , we can obtain q n = 4 ( 1 − θ ) ( 2 − θ ) Q − ( 2 − θ ) ( c n + m n + r n + c m ) + ( 2 − θ ) ( c r + m r + r r + + c m P ) 2 ( 1 − θ ) ( 8 − 5 θ ) , q r = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) ( c n + m n + r n + c m ) − ( 4 − 3 θ ) ( c r + m r + r r + c m + P ) 2 θ ( 1 − θ ) ( 8 − 5 θ ) . Since ∏ M w n , w r = ( w n − s n − c m ) q n + ( w r − s r − c m ) q r = m n q n + m r q r , substituting q n , q r in ∏ M and solving ∂ ∏ M ∂ m n = 0 and ∂ ∏ M ∂ m r = 0 , we can obtain m n = Q − r n − c n − c m 2 and m r = θ Q − r r − c r − c m − P 2 . Substituting m n , m r in q n , q r , we can obtain q n = 4 ( 1 − θ ) ( 2 − θ ) Q − ( 2 − θ ) ( 4 − 3 θ ) ( c n + c m + r n ) + ( 2 − θ ) ( c r + c m + r r + P ) 2 ( 1 − θ ) ( 8 − 5 θ ) , q r = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) ( c n + c m + r n ) − ( 4 − 3 θ ) ( c r + c m + r r + P ) 2 θ ( 1 − θ ) ( 8 − 5 θ ) . Since ∏ R q n , q r = ( p n − w n ) q n + ( p r − w r ) q r = r n q n + r r q r , substituting q n , q r in ∏ R , and solving ∂ ∏ R ∂ r n = 0 and ∂ ∏ R ∂ r r = 0 , we can obtain r n = Q − c n − c m 2 and r r = θ Q − c r − c m − P 2 . Substituting r n , r r in m n and m r , we can obtain m n = Q − c n − c m 4 and m r = θ Q − c r − P − c m 4 . Substituting r n , r r , m n , m r into l n , l r , f , we can obtain l n = 4 ( 1 − θ ) Q − ( 4 − 3 θ ) c n + c r + P − 3 ( 1 − θ ) c m 4 ( 8 − 5 θ ) , l r = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) c n − ( 4 − 3 θ ) ( c r + P ) − ( 4 − 5 θ + θ 2 ) c m 4 ( 8 − 5 θ ) , f = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) c n − ( 4 − 3 θ ) c r + ( 60 − 37 θ ) P − ( 4 − 5 θ + θ 2 ) c m 8 ( 8 − 5 θ ) .

As a result, we have s n = l n + c n = 4 ( 1 − θ ) Q + ( 28 − 17 θ ) c n + c r + P − 3 ( 1 − θ ) c m 4 ( 8 − 5 θ ) ,

s r = l r + c r + f = 6 θ ( 1 − θ ) Q + 3 θ ( 2 − θ ) c n + ( 52 − 31 θ ) ( c r + P ) − 3 ( 4 − 5 θ + θ 2 ) c m 8 ( 8 − 5 θ ) ,

w n = s n + m n = ( 12 − 9 θ ) Q + ( 20 − 12 θ ) c n + c r + P + ( 21 − 12 θ ) c m 4 ( 8 − 5 θ ) ,

w r = s r + m r = ( 22 θ − 16 θ 2 ) Q + 3 θ ( 2 − θ ) c n + ( 36 − 21 θ ) ( c r + P ) + 3 ( 12 − 5 θ − θ 2 ) c m 8 ( 8 − 5 θ ) ,

p n = w n + r n = ( 28 − 19 θ ) Q + ( 4 − 2 θ ) c n + c r + P + ( 5 − 2 θ ) c m 4 ( 8 − 5 θ ) ,

p r = w r + r r = ( 54 θ − 36 θ 2 ) + 3 θ ( 2 − θ ) c n + ( 4 − θ ) ( c r + P ) + ( 4 + 5 θ − 3 θ 2 ) c m 8 ( 8 − 5 θ ) ,

q n = 1 − p n − p r 1 − θ = ( 8 − 12 θ + 4 θ 2 ) Q − ( 4 − 3 θ ) ( 2 − θ ) c n + ( 2 − θ ) ( c r + P ) − 3 ( 2 − 3 θ + θ 2 ) c m 8 ( 8 − 5 θ ) ( 1 − θ ) ,

q r = θ p n − p r θ ( 1 − θ ) = ( 2 θ − 2 θ 2 ) Q + θ ( 2 − θ ) c n − ( 4 − 3 θ ) ( c r + P ) − ( 4 − 5 θ + θ 2 ) c m 8 ( 8 − 5 θ ) ( 1 − θ ) .

Proof of Proposition 3:

Combining assumptions 1 and 2, we can obtain the following equations: p n = Q − q n − θ q r = w m + r n + s n = m m + c m + c n + l n + r n , p r = θ ( Q − q n − q r ) = w m + r r + s r = m m + c m + c r + l r + f + r r , 可以得到 q n = Q − p n − p r 1 − θ = ( 1 − θ ) Q − c n − l n − r n + c r + l r + f + r r 1 − θ , q r = θ p n − p r θ ( 1 − θ ) = θ ( m m + c m + c n + l n + r n ) − ( m m + c m + c r + l r + f + r r ) θ ( 1 − θ ) . According to the Stackelberg game sequence, use the reverse solving method to solve the profit models of each member. Substitute q r into the collector′s profit function ∏ C f , q c = f q r + P ( q c − q r ) − c q c 2 , we can get the Hesse matrix of ∏ C regarding transfer price and the collection quantity H = − 2 θ ( 1 − θ ) 0 0 − 2 c = 4 c θ ( 1 − θ ) > 0 , Therefore, there exists a unique optimal solution for ∏ C . Simultaneous equations ∂ ∏ C ∂ q c = 0 and ∂ ∏ C ∂ f = 0 , we can obtain f = θ ( m m + c m + c n + l n + r n ) − ( m m + c m + c r + l r + r r ) + P 2 , q c = P 2 c . Substituting f in q n and q r , we can obtain q n = 2 ( 1 − θ ) Q − ( 2 − θ ) ( c n + l n + r n ) + c r + l r + r r − ( 1 − θ ) ( m m + c m ) + P 2 ( 1 − θ ) , q r = θ ( m m + c m + c n + l n + r n ) − ( m m + c m + c r + l r + r r ) − P 2 θ ( 1 − θ ) . Since ∏ S 1 s n = ( s n − c n ) q n = l n q n , ∏ S 2 s r = ( s r − c r − f ) q r = l r q r , substituting q n , q r in ∏ S 1 , ∏ S 2 , solving ∂ ∏ S 1 ∂ l n = 0 and ∂ ∏ S 2 ∂ l r = 0 , we can obtain l n = 4 ( 1 − θ ) Q − ( 4 − 3 θ ) ( c n + r n ) + c r + r r − 3 ( 1 − θ ) ( m m + c m ) + P 8 − 5 θ , l r = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) ( c n + r n ) − ( 4 − 3 θ ) ( c r + r r + P ) − ( 4 − 5 θ + θ 2 ) ( m m + c m ) 8 − 5 θ . Substituting l n , l r in q n , q r , we can obtain q n = ( 2 − θ ) 4 ( 1 − θ ) Q − ( c n + r n ) + c r + r r + P − 3 ( 1 − θ ) ( m m + c m ) 2 ( 1 − θ ) ( 8 − 5 θ ) , q r = 2 θ ( 1 − θ ) Q + θ ( 2 − θ ) ( c n + r n ) − ( 4 − 3 θ ) ( c r + r r + P ) − ( 4 − 5 θ + θ 2 ) ( m m + c m ) 2 θ ( 1 − θ ) ( 8 − 5 θ ) . Since ∏ M w m = ( w m − c m ) ( q n + q r ) = m m ( q n + q r ) , substituting q n , q r in ∏ M , and solving ∂ ∏ M ∂ m m = 0 , we can obtain m m = 2 θ ( 5 − 2 θ ) Q − 3 θ ( 2 − θ ) ( c n + r n ) − ( 4 − θ ) ( c r + r r + P ) − ( 4 + 5 θ − 3 θ 2 ) c m 2 ( 4 + 5 θ − 3 θ 2 ) . Substituting m m in q n , q r , we can obtain

q n = ( 2 − θ ) 2 ( 1 − θ ) ( 16 + 5 θ − 6 θ 2 ) Q − ( 32 − 2 θ − 27 θ 2 + 9 θ 3 ) ( c n + r n ) + ( 20 − 5 θ − 3 θ 2 ) ( c r + r r + P ) − 3 ( 1 − θ ) ( 4 + 5 θ − 3 θ 2 ) c m 4 ( 1 − θ ) ( 8 − 5 θ ) ( 4 + 5 θ − 3 θ 2 ) ,

q r = 2 θ ( 1 − θ ) ( 23 θ − 8 θ 2 − 12 ) Q + θ ( 2 − θ ) ( 20 − 5 θ − 3 θ 2 ) ( c n + r n ) − ( 16 + 40 θ − 63 θ 2 + 19 θ 3 ) ( c r + r r + P ) − ( 1 − θ ) ( 4 − θ ) ( 4 + 5 θ − 3 θ 2 ) c m 8 θ ( 1 − θ ) ( 8 − 5 θ ) ( 4 + 5 θ − 3 θ 2 ) . Since ∏ R q n , q r = ( p n − w n − s n ) q n + ( p r − w r − s r ) q r = r n q n + r r q r , substituting q n , q r in ∏ R and solving ∂ ∏ R ∂ r n = 0 , ∂ ∏ R ∂ r r = 0 , we can obtain r n = Q − c n − c m 2 and r r = θ Q − c r − P − c m 2 . Substituting r n , r r in m n , m r , we can obtain m n = Q − c n − c m 4 and m r = θ Q − c r − P − c m 4 and. Substituting r n , r r , m n , m r in l n , l r , f , we can get Proposition 3.

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Received: 2024-06-07

Revised: 2024-07-17

Accepted: 2025-02-17

Published Online: 2025-04-17

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/aut-2025-0031

Keywords for this article

Waste clothing; closed loop supply chain; supply chain mode

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