Blockchain-Driven Supply Chain’s Financing and Coordination Strategy under Nash Bargaining Scheme

the


Introduction
Supply chain fnance (SCF) is a series of technology-based business and fnancing procedures that connect multiple parties (suppliers, manufacturers, retailers, and fnancial institutions) to reduce fnancing costs and improve business efciency.SCF provides short-term credit to supply chain members, which optimizes their working capital (https://www.investopedia.com/terms/s/supply-chain-fnance.asp).Traditional SCF modes include bank credit fnance (BCF) and trade credit fnance (TCF) [1].Under TCF, core enterprises provide short-term credit to capital-constrained small and mediumsized enterprises (SMEs) in the upstream and downstream of the supply chain [2].Under BCF, it is difcult for SMEs to obtain loans due to their own credit or fnancial factors [3], so TCF is a more common fnancing choice for SMEs, and is also more conducive to supply chain coordination [4].
Blockchain technology is a peer-to-peer distributed database of assets that can be shared across multiple sites, geographic locations, or institutional networks [5].In recent years, with the development of blockchain technology, the blockchain-driven SCF mode has become increasingly popular.Te supply chain players can link to each other through the blockchain platform, optimize the overall credit environment, transfer the core corporate credit, simplify the fnancing transaction process, and efectively deal with the various drawbacks of traditional SCF [3].Blockchain-driven supply chain platform has become a development trend and upsurge in the industry, which the industry refers to as "digital supply chain transformation" (https://www.forbes.com/sites/stevebanker/2019/09/18/20-things-to-knowabout-digital-supply-chain-transformations/ #7011e0bb45b1).More and more companies and fnancial institutions are participating in this innovative mode of blockchain-driven SCF, such as ant fnancial's "Shuangliantong" blockchain platform.Based on the real transaction background between supply chain players, the credit of core enterprises can be transferred and split on the blockchain platform, which enables more SMEs in the supply chain to obtain equal and efcient inclusive fnancial services (https://www.lianmenhu.com/blockchain-15483-1).Another example is the accounts receivable chain platform of Zheshang bank.Till the end of June 2019, the platform has helped more than 8,000 companies to fnance more than 170 billion yuan (https://www.lianmenhu.com/blockchain-15483-1).
Te blockchain-driven SCF is an emerging fnancing mode that combines disruptive innovative technology and traditional SCF.It is the key to breaking through the existing barriers of traditional SCF and promoting the development of SCF to the next stage.Terefore, studies analyzing the characteristics and development issues of the emerging blockchain-driven SCF based on the traditional SCF theory and the realistic background of fnancial technology have sufcient practical operational signifcance to help the supply chain in reality and can help deepening the development of SCF theory.
Tis paper aims to solve the fnancing mode selection problem of a capital-constrained supply chain under the three most common supply chain contracts (including but not limited to revenue-sharing contract, proft-sharing contract, and two-part tarif contract) and explores it by comparing the traditional BCF with blockchain-driven SCF mode.Trough comparing supply chain output decisions and supply chain performance under the above-given two modes, we analyze the impact of production costs, fnancing costs, and initial capital on the supply chain performance of the above-given modes, respectively.Our research results provide a decision-making basis for the selection of SCF modes and provide ideas for the research on blockchaindriven SCF.
Te rest of this paper is organized as follows.Section 2 reviews the relevant literature.Section 3 frst introduces the basic framework and assumptions of our model and then analyzes the supply chain coordination of the two fnancing modes (BCF and blockchain-driven SCF) under the three supply chain contracts.Section 4 compares the equilibrium between the two fnancing modes.Section 5 conducts numerical tests to examine and illustrate the infuencing factors, values, and advantages of the blockchain-driven SCF mode.Section 6 summarizes our fndings.

Literature Review
Our article is related to the following two streams of literature: traditional SCF modes considering supply chain contracts and blockchain-driven SCF solutions.

Te Traditional SCF Modes and Supply Chain Contracts.
Supply chain contracts are the basic form to promote supply chain coordination [6].Academic studies on traditional SCF and supply chain contracts have achieved fruitful results.Most of the early studies mainly explored the efect of diferent supply chain contracts on supply chain coordination [7].For example, Dada and Hu [8] considered the capital-constrained retailer and devised a mechanism for partial coordination of the supply chain with wholesale price contracts under the BCF mode.Caldentey and Haugh [9] designed supply chain contracts for a supply chain consisting of a manufacturer and a capital-constrained retailer.Kouvelis and Zhao [10] considered the bankruptcy risk and cost when borrowing from bank-insolvent suppliers and studied the contract design and supply chain coordination problems.Jing et al. [11] discussed the impact of production costs, initial capital, and changes in market demand on the fnancing efciency of both the BCF and TCF modes.Chen [12] compared the supply chain equilibrium under BCF and TCF based on revenue-sharing contract and wholesale price contract.
As another important channel of supply chain fnancing, TCF has also attracted widespread attention.For example, Hwan Lee and Rhee [13] studied supply chain coordination mechanisms (including quantity discount contract, buyback contract, two-part tarif contract, and revenue sharing contract) by considering active inventory fnancing costs, and found that all these contracts can be combined with TCF to coordinate the supply chain, but which is not working when combined with BCF.Under similar circumstances, Lee and Rhee [4] further discussed the coordination efect of price-cut subsidies and reached a similar conclusion that the supply chain cannot be fully coordinated in terms of BCF, but the supply chain can be coordinated under TCF.Zhang et al. [14] also explored supply chain coordination issues by considering trade credit and default risks.Tey proposed a modifed quantity discount contract based on quantity and advance payment and found that when the retailer's risk of default is higher and the supply chain is more likely to achieve coordination.Li et al. [15] compared partial credit guarantees and TCF and found that there was a region where TCF outperforms partial credit guarantees.
Some studies also highlight the role of blockchain technology to improve SCF.Te current literature has primarily focused on comparing the blockchain-driven SCF with traditional SCF to explore the value of blockchain technology to SCF, which is also mostly related to our research.For example, Wang et al. [32]  Giovanni [34] compared a traditional supply chain online platform and a blockchain platform, highlighting the smart contracts which make blockchain applications more appealing from the point of supply chain management.Tere are also a few studies that explored the innovative application of the blockchain-driven supply chain model.Tang and Zhuang [1] considered the credit transfer mechanism of the blockchain, applied the traditional newsboy model to study the decision-making problem of a multiperiod supply chain, and verifed the improvement impact of the blockchain-driven SCF platform on the supply chain fnancing performance.Choi and Ouyang [35] compared the SCF performance with and without digital currency as an incentive mechanism and found that a supply chain that adopts both blockchain technology and digital currency can achieve a win-win situation.Natanelov et al. [36] identifed examples of how fnancial risks can be mitigated or reduced with blockchain and smart contracts, where the credit fnancing itself could be fundamentally transformed.An overview of the most related studies to ours in Table 1 reveals that most of the available literature still focuses on the role of blockchain technology in supply chain management, and few studies have considered this emerging SCF model from the perspective of both supply chain contracts and fnancing efciency.Terefore, on the basis of Choi [3]; we further consider the situation that the supply chain is capitalconstrained, compare the blockchain-driven SCF and traditional BCF, analyzes the similarities and diferences of these two fnancing modes in supply chain output decisions and supply chain performance, and discusses the ordering strategies as well as the performance of the supply chain in diferent modes under the most common supply chain contracts.

Contribution Statement.
Blockchain-driven SCF is an important topic.With the rapid development of blockchaindriven SCF in practical applications, the decision-making of supply chain and screening of fnancing channels is an urgent problem that enterprises and academia are concern.At the same time, a supply chain contract is an important way to increase supply chain cash fow efciency and promote supply chain coordination.Terefore, this paper considers the most commonly used supply chain contracts (revenue-sharing contract, proft-sharing contract, and two-part tarif contract), and based on which compares and analyzes the blockchain-driven SCF and traditional BCF modes, which can provide valuable guidance to supply chain on the selection of fnancing channel.

Model Description and Assumptions
Tis study considers a supply chain consisting of a capitalconstrained manufacturer M with limited initial capital m and a newsvendor-like retailer R. Te manufacturer M provides the retailer R with a production cost of c and a quantity of Q products at a wholesale price w.Retailer R sells the product at a unit retail price p. Te salvage value of the product is s.Te market demand is D, which follows a probability density function f(x) and cumulative distribution function F(x).
Assume that the supply chain can choose from traditional BCF mode (B) and blockchain-driven SCF mode (BCT).Te supply chain considers the expected proft  i j (i � R, M; j � B, BCT), the optimal output Q SC * j (j � B, BCT) the operation fee θ of the blockchaindriven supply chain platform, and the supply chain fnancing cost r B to determine its fnancing model (notation details are provided in Table 2).To analytically show how supply chain contracts coordinate both types of the supply chain, and how do they infuence the supply chain's selection of fnancing channels, we compare the optimal performances between the two models.
To further analyze the infuence of supply chain power structure on the above-given decisions, suppose that the manufacturer and the retailer possess bargaining powers.Te retailer's bargaining power is α, and the manufacturer's bargaining power is 1 − α.We consider the Nash bargaining solution, which is often used when two players decide how to share the surplus [37,38].Many studies [39][40][41] apply the Nash bargaining solution to analyze the game and decisionmaking between upstream and downstream enterprises in the supply chain.
In this study, the manufacturer and the retailer frst negotiate the main indicators under supply chain contracts (revenue-sharing contract, proft-sharing contract, and twopart tarif contract).Ten, the retailer determines its optimal order quantity.To satisfy the order quantity, the capitalconstrained manufacturer needs to determine the fnancing method and loan amount based on the order quantity and its initial capital.

Revenue-Sharing Contract.
Under the revenue-sharing contract, the retailer shares a certain percentage (η, 0 < η < 1) of sales revenue to the manufacturer to obtain lower wholesale prices and improve the performance of supply chain operations.

Te Bank Credit Finance (Model B
).Under this model, the capital-constrained manufacturer M applies for fnancing from the bank to satisfy the order quantity from the newsvendor-like retailer R. 4 Complexity manufacturer M and retailer R seek to maximize their profts.Terefore, the retailer R's proft function is From equation ( 1), the retailer R's expected proft is written as follows: it is easy to fnd the optimal ordering quantity of retailer R as follows: Similarly, the proft and expected proft functions of manufacturer M are derived as follows: Te respective proft and expected proft functions of the supply chain are Te optimal product quantity of the supply chain under the blockchain-driven SCF model Complexity It is also easy to derive the optimal product quantity of the supply chain by solving the frst-order condition of equation ( 7): decreases in c and r B .
Lemma 1 indicates that, under model B, both the production cost and the manufacturer M's fnancing cost have a great impact on the optimal output of the supply chain.
Following the Nash bargaining framework [3,6], the supply chain needs to solve the following problem (B): To coordinate the supply chain, the optimal ordering quantity of the retailer R should be equaled to the optimal output quantity of the supply chain, which means For problem (B), the optimal whole price of manufacturer M and the optimal revenue sharing rate can both be derived.
Proposition 1.With the Nash bargaining scheme, the supply chain under the bank credit fnance model can be coordinated by setting the parameters as follows (see Appendix): Proposition 1 shows that, under the bank credit fnancing model, supply chain coordination can be achieved through a revenue-sharing contract, and under the Nash bargaining strategy, the parameters of this supply chain contract are unique and optimal.

Te Blockchain-Driven Supply Chain Financing (Model BCT
).Under this model, the supply chain-related transaction information is automatically recorded on the blockchain-driven SCF platform, and every transaction on the platform will incur a certain operating fee θ [3], which means both the retailer and the manufacturer will pay the operating fee.Since there is no loan involved and the manufacturer M does not need to pay fnancing interest, the retailer R's proft and expected proft functions are Terefore, solving the frst-order equation of ( 13), we can derive the optimal order quantity of retailer R as follows: Assuming that, after the order information is recorded on the blockchain-driven SCF platform, the manufacturer M 6 Complexity can use the account receivable corresponding to the order to purchase raw materials on the platform.Terefore, under the BCT model, the manufacturer M does not need to raise funds or pay fnancing interest, only a certain platform usage fee (fee rate θ) is required.Similar to model B, we can derive the proft and expected proft functions of the manufacturer M and the supply chain as follows: Based on equations ( 15)-( 17), the optimal product quantity of the supply chain can be derived as follows: Lemma .Q SC * BCT decreases in c and θ.
Similarly, following the Nash bargaining framework, the supply chain needs to solve the following problem (BCT): To coordinate the supply chain, the optimal ordering quantity of the retailer R should be equaled to the optimal product quantity of the supply chain, which means For problem (BCT), the optimal whole price of manufacturer M and the optimal revenue-sharing rate can both be derived in the following.
Proposition .With the Nash bargaining scheme, the supply chain under the blockchain-driven SCF model can be coordinated by setting the parameters as follows (see Appendix): Proposition 2 shows that, under the blockchain-driven SCF model, the supply chain coordination is also achievable by using the revenue-sharing contract, and under the Nash bargaining scheme, the optimal contract parameters are also unique.

Proft-Sharing Contract.
Under a proft-sharing contract, the retailer shares a certain percentage (λ, 0 < λ < 1) of the proft from the sale of the product to the manufacturer to obtain a lower wholesale price.

Te Bank Credit Finance (Model B).
Under this model, the capital-constrained manufacturer M still needs to apply for fnancing from the bank to satisfy the order quantity from the newsvendor-like retailer R. Keeping other conditions unchanged, the retailer R's proft function (we denote a "− " to represent the proft-sharing contract) is From equation (24), the retailer R's expected proft is written as follows: Since it is easy to fnd the optimal ordering quantity of retailer R as follows: Complexity 7 Similarly, the proft and expected proft functions of manufacturer M are derived as follows: Keeping other settings of the model unchanged, the expected proft function of the supply chain and the optimal order quantity are the same as in Section 3.1.1(see equations ( 6) and ( 7)).
Following the Nash bargaining framework, the supply chain needs to solve the following problem (B): ( Similarly, to coordinate the supply chain, we equalize the optimal order quantities of the retailer and the supply chain: By solving problem (B), we can derive the optimal wholesale price and the optimal proft share rate for manufacturer M.

Proposition 3. With the Nash bargaining scheme, the supply chain under the BCF model can be coordinated by setting the parameters as follows (see Appendix):
Proposition 3 shows: (1) under the BCF model, the proft-sharing contract can also coordinate the supply chain, and there is only one optimal contract parameter; (2) the proft-sharing ratio of the supply chain depends on the overall proft of the supply chain and the bargaining power of supply chain members.

Te Blockchain-Driven Supply Chain Financing (Model BCT)
. Refer to Section 3.1.2.For the model setting and keeping other conditions unchanged, the retailer R's proft function (we denote a "− " to represent the proft-sharing contract) is Terefore, solving the frst-order equation of ( 31), we can derive the optimal order quantity of retailer R as follows: Similar to Section 3.1.2,we can obtain the proft and expected proft functions of the manufacturer M as follows: Terefore, the optimal product quantity of the supply chain can be derived as follows: Similarly, under the Nash bargaining scheme, the supply chain needs to solve the following problem (BCT): By equaling equations ( 34) with (32), and solving problem (BCT), we can derive the optimal whole price of manufacturer M and the optimal proft-sharing rate in the following.

Proposition 4. With the Nash bargaining scheme, the supply chain using proft sharing contract under the blockchaindriven SCF model can be coordinated by setting the parameters as follows (see Appendix
Proposition 4 shows that under the blockchain-driven SCF model, proft-sharing contracts can also coordinate the supply chain by setting unique parameters.Diferent from Proposition 2, the supply chain proft-sharing ratio is only afected by the bargaining power.

Te Two-Part
Tarif Contract.the two-part tarif contract, the retailer pays the manufacturer a fxed transfer fee L while ordering products from the manufacturer at the wholesale price w (we denote a "∼" to represent the two-part tarif contract).

Te Bank Credit Finance (Model 􏽥 B).
Similar to Sections 3.1.1and 3.2.1,we can obtain the retailer R's proft function as follows: From equation (37), the retailer R's expected proft is written as follows: it is easy to fnd the optimal ordering quantity of retailer R as follows: Similarly, the proft and expected proft functions of manufacturer M are derived as follows: Te respective proft and expected proft functions as well as the optimal product quantity of the supply chain are the same in Section 3.1.1.
Following the Nash bargaining framework, the supply chain needs to solve problem (  B): We equalize the optimal ordering quantity of the retailer R to the optimal product quantity of the supply chain: With Problem (  B), the optimal whole price of manufacturer M and the optimal transfer fee can both be derived.

Proposition 5. With the Nash bargaining scheme, the supply chain under the BCF model can be coordinated by setting the parameters as follows (see Appendix):
Proposition 5 shows the following: (1) in the BCF model, the two-part tarif contract can also promote supply chain coordination; (2) the Nash negotiation framework ensures the uniqueness of the contract parameter settings, and the transfer fee L * B depends on  SC B the proft of the entire supply chain and the bargaining power of the supply chain members.

Te Blockchain-Driven Supply Chain Financing (Model 􏽧 BCT). Similarly, the retailer R's proft and expected proft functions are
Terefore, solving the frst-order equation of equation ( 46), we can derive the optimal order quantity of retailer R as follows: Similar to Sections 3.1.2and 3.2.2,we can easily obtain the proft and expected proft functions of the manufacturer M as follows: As the other conditions remain the same, the respective proft and expected proft functions as well as the optimal output quantity of the supply chain are unchanged (refer to equations ( 16) and ( 17)).
Similarly, following the Nash bargaining framework, the supply chain needs to solve the following (  BCT): (50) Seemingly, With problem (  BCT), the optimal whole price of manufacturer M and the optimal transfer fee can both be derived in the following.

Proposition 6. With the Nash bargaining scheme, the supply chain under the blockchain-driven supply chain fnancing model can be coordinated by setting the parameters as follows (see Appendix):
Proposition 6 shows that, under the blockchain-driven SCF model, the two-part tarif contract can also help supply chain coordination, and the Nash bargaining scheme also ensures the uniqueness of contract parameters.
Comparing Sections 3.1, 3.2, and 3.3, we fnd that the diference between the optimal solutions of the two models under the three supply chain contracts lies in the fnancing cost of each model.In other words, the diferent fnancing costs between the two models have a large impact on the fnancing and pricing decisions of the supply chain (discussed in Section 4), this fnding provides a theoretical basis of decision-making for manufacturer M when faced with two diferent fnancing channels.

Impact of Blockchain on SCF
Trough the above-given analysis, we have obtained the optimal ordering and pricing decisions under diferent models and supply chain contracts, as well as the maximum proft of each player in the supply chain.Next, we will compare the above three settings to explore the optimal fnancing options for the manufacturer and the whole supply chain.

Optimal Output
Proposition 7. Te relationship between the optimal outputs of the supply chain under the two fnancing models is (i To explore the advantage of blockchain-driven SCF, we compare the optimal outputs of the two fnancing models and fnd that the fnancing costs will afect the optimal output of the supply chain.Tere is one threshold for the blockchain platform usage fee rate, and when the blockchain platform fee rate is higher than the threshold, the blockchain-driven SCF mode no longer has an advantage in terms of output; and when the platform fee rate is lower than the threshold, the blockchain-driven SCF mode is the more conducive fnancing model to increasing production in the supply chain (See Appendix for proof of Proposition 7).

Proposition 8. Te relationship between the expected profts of the supply chain under the two fnancing models is
Proposition 8 is similar to Proposition 7. It shows that the profts of the supply chain change positively with the outputs.Te larger the output, the greater the supply chain profts.Like the optimal outputs of the supply chain, the expected profts of the supply chain are also afected by the fnancing cost.Te higher the fnancing cost is, the lower the optimal output and the expected profts, and vice versa (See Appendix for proof of Proposition 8).

Benefts of Blockchain on SCF.
To be specifc, the optimal settings of the above three supply chain contracts are summarized in Table 3.
BCT Proposition 9 clearly states the relationship between optimal wholesale prices and supply chain contract parameters.Clearly, retailers under the BCT model share a higher contract ratio or amount in the supply chain, showing this model can improve the working capital efciency of a retailer.

Proposition 10. Te supply chain power structure has no efect on the above-given equilibrium results.
Proposition 10 is also straightforward because both the optimal order quantities (Q SC * B , Q SC * BCT ) and the expected 10 Complexity of the supply chain under the two models are independent of the bargaining power α.Proposition 10 shows that the power structure of the supply chain only afects the proft distribution of the internal members of supply chain (manufacturer and retailer) and does not afect the expected proft of the entire supply chain.

Numerical Studies
To obtain more insights about the supply chain's fnancing strategy preference, we present some concrete numerical studies in this section to illustrate and verify the above-given conclusions.In light of the parameters set by Buzacott and Zhang (2004), the exponential distribution (0.01) is used to isolate the efect of the market demand volatility.Te base values of the other parameters are p � 10, s � 2, c � 4, r B � 0.12, m � 50, θ � 0.1, and α � 0.2.

Impact of Production Cost on the Comparation.
To examine the impact of production cost (which is an exogenous factor) on the efciencies of diferent fnancing models, we keep other parameters at the basic value and vary the 12 Complexity production cost c.Te corresponding optimal production quantity, the proft of the supply chain, and the profts of the retailer and manufacturer are compared as follows.
Figure 1 shows that the BCT fnancing model is better than the other fnancing models on the above three aspects.Tis is reasonable because the BCT fnancing benefts from the technical characteristics of blockchain technology such as trustless and decentralization, which can eliminate the cumbersome loan review process in the traditional SCF mode, save time and reduce the cost of loan review, which in turn improves fnancing efciency and supply chain production efciency.BCT >  SC * B .Tis fnding suggests that if the production costs and the fnancing costs of the two models meet certain conditions, then model BCT is more efcient than model B; otherwise, model B is better.Model B is less efcient when the production cost increases.Tis is because under model B, the capital cost of the manufacturer r B as the interest rate set by the bank is usually high due to the complicated loan process and high handling fees, Complexity especially for the SMEs (such as the manufacturer M discussed in this paper).
Besides, Figure 1(c) illustrates the changes in the expected revenue of retailers and manufacturer with production costs.It is obvious that as production costs increase, the blockchaindriven SCF mode is also a better choice the supply chain.In Figure 2(b), we investigate how the fnancing cost of model B r B infuence the efciencies of the two fnancing models.When we vary r B and set the other parameters as the basic value (c � 4, α � 0.2, θ � 0.1), it is easy to fnd that θ < cr B /2 and BCT model is always the more efcient fnancing model however the capital cost of the manufacturer varies (Proposition 7 and 8).

Impact of Financing Costs on the
In Figure 2(c), we keep the other parameters unchanged and vary the blockchain-driven SCF platform usage fee rate θ, to illustrate the impact of which on the preference of the BCT model.As shown in Figure 2(c), there is one threshold values cr B /2 for the blockchain-driven SCF platform usage fee rate θ.When the platform rate is higher than the threshold cr B /2 � 0.24, the proft of the supply chain under the BCT model is lower than the traditional BCF model, which means the BCT model no longer has the advantage; otherwise, the BCT model is the more efcient fnancing model for the supply chain, that is, the supply chain performance is the higher under this model.Figure 2(c) further verifes Propositions 7 and 8.In reality, the blockchaindriven SCF mode is still in its infancy, to attract customers, its fnancing cost (platform usage fee rate) is usually low, which further shows that this emerging supply chain fnancing solution has advantages in improving supply chain performance.

Impact of Initial
Capital on the Comparation.Tis set of numerical studies illustrates how the degree of capital constraints of the manufacturer afects the performance of model BCT and model B. We defne the initial capital of the manufacturer m � 0 as the highly constrained situation, m � 50 as the moderate-constrained situation, and m � 100 as the less-constrained situation.In this section, we introduce a ROC (Receiver Operating Characteristic) curve analysis to compare the performance of the above-given two fnancing models.ROC curve is an important and common statistical analysis method which sorts the samples according to the prediction results of the learner and predicts the samples one  14 Complexity by one as positive examples in this order.Each time two important values (TPR, FPR) are calculated, and they are plotted as the horizontal and vertical coordinates.Te AUC value (which is between 0.1 and 1) is the area under the ROC curve.As a value, you can intuitively the quality of the classifer.Te larger the value, the better (see [42,43], for more information).
In this article, we compared the performance of model B and BCT.We frst divided the capital cost of the retailer r B (0.06 ≤ r B ≤ 0.2) into 29 sample groups, then kept the other parameters as the basic value, calculated the corresponding profts of the supply chain under the two fnancing models, and at last repeated the experiment as the platform usage fee rate θ (0 ≤ θ ≤ 0.2), and the degree of the capital constraint of the manufacturer changes.Similarly, when the total expected proft of the supply chain under the BCT model is greater than that of the B model, it is recorded as a positive sample (TP); otherwise, it is a negative sample (NP).Te results of the data processing are shown in Table 4.
According to Table 4, we have obtained the ROC curve comparing model BCT and B under three diferent degrees of capital constraints situations as shown in Figure 3. From Figure 3, the blockchain-driven SCF (model BCT) is always more efective than the bank credit fnance (model B), as the platform usage fee rate θ varies, and the less θ is, the more efective model BCT is.Terefore, the degree of capital constraints of the manufacturer has no impact on the performance of the two fnancing models.Because of the characteristics of blockchain technology, this mode efectively addresses the disadvantages of traditional SCF such as high cost and cumbersome review procedures.At present, this "digital supply chain transformation" has become a development trend.Terefore, it is very urgent and practical to study the similarities and diferences between the blockchain-driven SCF mode and the traditional SCF mode from diferent perspectives.Tis study thoroughly explored the performance of the blockchain-driven SCF and the traditional BCF mode under the most common supply chain contracts in terms of supply chain fnancing, pricing and production decision-making, and supply chain performance and analyzed the relationship between the fnancing costs of the above-given three models and the changes in the supply chain performance of each fnancing model under diferent fnancing costs.Te results are as follows:

Conclusion
(1) Te fnancing costs of diferent fnancing models have a great impact on the optimal output and the expected proft of the supply chain.(2) Tere is one threshold for the blockchain-driven SCF platform fee rate.When the blockchain-driven SCF platform fee rate is higher than the threshold, the BCT model no longer has an advantage in terms of supply chain performance; when the platform rate is lower than the threshold, the BCT model is the more conducive fnancing model to increasing production in the supply chain.(3) If the supply chain contracts can coordinate the supply chain in terms of the optimal order quantity decision, the above-given results hold.(4) Whatever the degree of capital constraint is, the blockchain-driven SCF mode is always better than the BCF mode.
6.2.Future Research.Tis research considers a fnancing channel selection problem for a capital-constrained manufacturer under supply chain contracts.Te results of the study provide a decision-making basis for the selection of the manufacturer's fnancing channel, that is, the blockchain-driven SCF.What needs to be further explored is whether the blockchain-driven SCF mode still has advantages when all supply chain players are subject to capital constraints.In addition, under other types of supply chain contracts, such as quantity discounts and wholesale prices, the performance of the blockchaindriven SCF mode is also an issue that can be further studied.

θθFigure 1 :
Figure 1: Te impact of production cost on the efciency of diferent fnancing models.

Figures 1 (
Figures 1(a) and 1(b) are examples of Propositions 7 and 8. we keep the other parameters the basic value, which means α � 0.2, r B � 0.12, θ � 0.1, it is easy to fnd that if the production costc > 2θ/r B � 1.67, then Q SC * BCT > Q SC * B and  SC * BCT >  SC * B .Tis fnding suggests that if the production costs and the fnancing costs of the two models meet certain conditions, then model BCT is more efcient than model B; otherwise, model B is better.Model B is less efcient when the production cost increases.Tis is because under model B, the capital cost of the manufacturer r B as the interest rate set by the bank is usually high due to the complicated loan process and high handling fees,

Figure 2 :
Figure 2: Te impact of fnancing costs on the efciency of diferent fnancing models.
Comparation.To investigate the impact of the fnancing cost of each model on the efciencies of model BCT and B, we vary the fnancing cost of each model and keep the other parameters at the basic value.For the BCT model, we see the platform usage fee rate θ as the fnancing cost; For model B, the capital cost r B is the corresponding fnancing cost.In light of Zhen et al.,[6];We defne ∆π SC BCT− B � π SC BCT − π SC B .If ∆π SC BCT− B > 0, then model BCT is more efcient than model B; Otherwise, model BCT is less efcient than model B.

Figure 2 (
a) is an extension experiment of Figure1, we fnd that when we keep other parameters unchanged as the basic value, only if the production cost c > 1.67, the BCT model is more efcient than model B, which means ∆π SC BCT− B > 0; otherwise, B model is better.

Figure 3 :
Figure 3: Te ROC curve comparing model BCT and B.

6. 1 .
Results.Blockchain-driven SCF is a new technological innovation supply chain fnancing mode in recent years.

Table 1 :
Summary of related literatures.
Te loan interest rate is r B .Both Complexity

Table 2 :
Notation/abbreviation and the respective meanings.
BTe optimal product quantity of the supply chain under the bank credit fnance modelπ R BCT , π M BCT ,π SC BCT Te proft of retailer, manufacturer, and supply chain under the blockchain-driven SCF model  R BCT ,  M BCT ,  SC BCT Te expected proft of retailer, manufacturer, and supply chain under the blockchain-driven SCF model

Table 3 :
Summary of supply chain contract settings.

Table 4 :
Dataset of the ROC curve comparing model BCT and B. is the usage fee rate of blockchain-driven supply chain, and is also the independent variable of the data in the table. θ