Supply chain financing using blockchain: impacts on supply chains selling fashionable products

Abstract

Today, supply chain finance is a very important topic. Traditional supply chains rely on banks to support the related financing activities and services. With the emergence of blockchain technology, more and more companies in different industries have considered using it to support supply chain finance. In this paper, we study supply chain financing problems in supply chains selling fashionable products. Modeling under the standard newsvendor problem setting with a single manufacturer and a single retailer employing a revenue sharing contract, we develop analytical models for both the traditional and blockchain-supported supply chains. We derive the optimal contracting and quantity decisions in each supply chain with Nash bargaining between the manufacturer and retailer. We analytically show how the revenue sharing contract can coordinate both types of supply chains. We then compare the optimal systems performances between the two supply chains. We prove that the blockchain-supported supply chain incurs a lower level of operational risk than the traditional supply chain. We have shown that if the service fees by banks are sufficiently high, adopting blockchain technology is a mean-risk dominating policy which brings a higher expected profit and a lower risk for the supply chain and its members. For robustness checking, we examine other commonly seen supply chain contracts and alternative risk measures, and analytically reveal that the results remain valid.

Appendices

Appendix 1: Notation table

See Table 2.

Table 2 Notation/abbreviation and the respective meanings

Appendix 2: All proofs

Proof of Proposition 3.1 First, we have to identify the optimal “Nash bargaining solution”, which is found by solving Problem (TSC):

$$ \begin{aligned} & Problem\;\left( {TSC} \right)\;{\text{Max}}\;NBP = \left( {\Pi_{R} } \right)^{1 - \lambda } \left( {\Pi_{M} } \right)^{\lambda } \\ & {\text{Subject}}\;{\text{to}}\;\Pi_{R} + \Pi_{M} \le \Pi_{SC}^{*} . \\ \end{aligned} $$

Our approach follows the standard treatment for Nash bargaining in the literature (e.g., Shi et al. 2020; Choi and Guo 2020). First of all, in order to maximize $NBP$, the supply chain members should maximize the supply chain’s expected profit as far as possible. Under the revenue sharing contract, it is possible and hence the inequity constraint $\Pi_{R} + \Pi_{M} \le \Pi_{SC}^{*}$ becomes an equality constraint $\Pi_{R} + \Pi_{M} = \Pi_{SC}^{*}$.

Putting $\Pi_{M} = \Pi_{SC}^{*} - \Pi_{R}$,

$$ \begin{aligned} \frac{\partial NBP}{{\partial \Pi_{R} }} & = \frac{{\partial \left[ {\left( {\Pi_{R} } \right)^{1 - \lambda } \left( {\Pi_{SC}^{*} - \Pi_{R} } \right)^{\lambda } } \right]}}{{\partial \Pi_{R} }} \\ & = - \left( {\Pi_{R} } \right)^{1 - \lambda } \left[ {\lambda \left( {\Pi_{SC}^{*} - \Pi_{R} } \right)^{\lambda - 1} } \right] + (1 - \lambda )\left( {\Pi_{R} } \right)^{ - \lambda } \left( {\Pi_{SC}^{*} - \Pi_{R} } \right)^{\lambda } \\ & = \left( {\Pi_{SC}^{*} - \Pi_{R} } \right)^{\lambda - 1} \left( {\Pi_{R} } \right)^{ - \lambda } \left\{ { - \lambda \Pi_{R} + (1 - \lambda )\left( {\Pi_{SC}^{*} - \Pi_{R} } \right)} \right\} \\ & = \left( {\Pi_{SC}^{*} - \Pi_{R} } \right)^{\lambda - 1} \left( {\Pi_{R} } \right)^{ - \lambda } \left\{ {((1 - \lambda )\Pi_{SC}^{*} - \Pi_{R} } \right\}. \\ \end{aligned} $$

$\frac{\partial NBP}{{\partial \Pi_{R} }}$ = 0 implies

$$ \Pi_{R}^{*} = (1 - \lambda )\Pi_{SC}^{*} . $$

(A1)

Similarly, putting $\Pi_{R} = \Pi_{SC}^{*} - \Pi_{M}$, we can compute and solve $\frac{\partial NBP}{{\partial \Pi_{M} }} = 0$, which yields:

$$ \Pi_{M}^{*} = \lambda \Pi_{SC}^{*} . $$

(A2)

Second, to achieve supply chain coordination under the traditional supply chain system, we need to make $q_{R}^{*} = q_{SC}^{*}$, which implies:

$$ F^{ - 1} \left[ {\left( {(1 - \alpha )r - w} \right)/\left( {(1 - \alpha )r - v} \right)} \right] = F^{ - 1} [s]. $$

(A3)

Rearranging terms, (A3) becomes:

$$ w = (1 - \alpha )(1 - s)r + vs. $$

(A4)

From (3.2), we have: $\Pi_{R} (q)$ = $((1 - \alpha )r - w)q - ((1 - \alpha )r - v)\int_{\;0}^{\;q} {(q - x)f(x)dx} - T_{R}$. When (A4) holds, we have:

$$ \begin{aligned} \Pi_{R} \left( {q_{SC}^{*} } \right) & = \left( {(1 - \alpha )r - w} \right)q_{SC}^{*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{*} }} {\left( {q_{SC}^{*} - x} \right)f(x)dx} - T_{R} \\ & = \left( {(1 - \alpha )r - w} \right)q_{SC}^{*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{*} }} {F(x)dx} - T_{R}. \\ \end{aligned} $$

(A5)

Combining (A5) and (A1), we have:

$$ \left( {(1 - \alpha )r - w} \right)q_{SC}^{*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{*} }} {F(x)dx} - T_{R} = \left( {1 - \lambda } \right)\Pi_{SC}^{*} . $$

(A6)

Putting (A4) into (A6) gives:

$$ \left( {(1 - \alpha )r - \left[ {(1 - \alpha )(1 - s)r + vs} \right]} \right)q_{SC}^{*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{*} }} {F(x)dx} - T_{R} = (1 - \lambda )\Pi_{SC}^{*} . $$

(A6)

Solving (A6) gives:

$$ \alpha = \left\{ {\alpha^{*} \equiv 1 - H\left( {q_{SC}^{*} } \right)} \right\}, $$

(A7)

where $H(q_{SC}^{*} ) = \frac{{(1 - \lambda )\Pi_{SC}^{*} + T_{R} + v(sq_{SC}^{*} - \int_{0}^{{q_{SC}^{*} }} {F(x)dx} )}}{{r(sq_{SC}^{*} - \int_{0}^{{q_{SC}^{*} }} {F(x)dx} )}}$.

Then, putting (A7) into (A4) yields:

$$ w = \left\{ {w^{*} \equiv vs + (1 - s)rH\left( {q_{SC}^{*} } \right)} \right\}. $$

(Q.E.D.)

Proof of Proposition 4.1 Similar to Proposition 3.1, first, we have to find the optimal “Nash bargaining solution”, which is found by solving Problem (BSC):

$$ \begin{aligned} & Problem\;\left( {BSC} \right)\;{\text{Max}}\;NBP^{B} = \left( {\Pi_{R}^{B} } \right)^{1 - \lambda } \left( {\Pi_{M}^{B} } \right)^{\lambda } \\ & {\text{Subject}}\;{\text{to}}\;\Pi_{R}^{B} + \Pi_{M}^{B} \le \Pi_{SC}^{B*} . \\ \end{aligned} $$

The solution can be found using the same approach as in the proof of Proposition 3.1:

$$ \Pi_{R}^{B*} = (1 - \lambda )\Pi_{SC}^{B*} , $$

(A8)

$$ \Pi_{M}^{B*} = \lambda \Pi_{SC}^{B*} . $$

(A9)

Second, to achieve supply chain coordination under the blockchain-supported supply chain system, we need to make $q_{R}^{B*} = q_{SC}^{B*}$, which implies:

$$ F^{ - 1} \left[ {\left( {(1 - \alpha )r - w - b} \right)/\left( {(1 - \alpha )r - v} \right)} \right] = F^{ - 1} \left[ {s^{B} } \right]. $$

(A10)

From (A10), we have the following:

$$ w = (1 - \alpha )\left( {1 - s^{B} } \right)r - b + vs^{B} . $$

(A11)

From (4.2), we have: $\Pi_{R}^{B} (q)$ = $((1 - \alpha )r - b - w)q - ((1 - \alpha )r - v)\int_{0}^{q} {(q - x)f(x)dx}$. Thus, at the coordinated supply chain, we have:

$$ \begin{aligned} \Pi_{R}^{B} \left( {q_{SC}^{B*} } \right) & = \left( {(1 - \alpha )r - b - w} \right)q_{SC}^{B*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{B*} }} {\left( {q_{SC}^{B*} - x} \right)f(x)dx} \\ & = \left( {(1 - \alpha )r - b - w} \right)q_{SC}^{B*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{B*} }} {F(x)dx} . \\ \end{aligned} $$

(A12)

Putting (A12) into (A8), we have:

$$ \left( {(1 - \alpha )r - b - w} \right)q_{SC}^{B*} - \left( {(1 - \alpha )r - v} \right)\int_{0}^{{q_{SC}^{B*} }} {F(x)dx} = \left( {1 - \lambda } \right)\Pi_{SC}^{B*} . $$

(A13)

Substituting (A11) into (A13) and solving for $\alpha$ gives:

$$ \alpha^{B} = \left\{ {\alpha^{B*} \equiv 1 - H^{B} \left( {q_{SC}^{B*} } \right)} \right\}, $$

(A14)

$$ {\text{where}}\;H^{B} \left( {q_{SC}^{B*} } \right) = \frac{{(1 - \lambda )\Pi_{SC}^{B*} + v\left( {s^{B} q_{SC}^{B*} - \int_{0}^{{q_{SC}^{B*} }} {F(x)dx} } \right)}}{{r\left( {s^{B} q_{SC}^{B*} - \int_{0}^{{q_{SC}^{B*} }} {F(x)dx} } \right)}}. $$

(A15)

Putting (A15) into (A11) gives:

$$ w^{B} = \left\{ {w^{B*} \equiv vs^{B} + \left( {1 - s^{B} } \right)rH^{B} \left( {q_{SC}^{B*} } \right)} \right\}. $$

(Q.E.D.)

Proof of Proposition 5.1

We first prove part (b) and then part (a).

(b) Inventory service levels:

By definition, we have: $s^{B} = (r - m - 2b)/(r - v)$ and $s = (r - m)/(r - v)$. Since b is the unit operational cost for blockchain technology and it is positive, it is obvious that: $s^{B} < s$.

(a) Product quantities:

From Sect. 3 and Sect. 4, we have:

$$ q_{SC}^{*} = F^{ - 1} \left[ {(r - m)/(r - v)} \right] = F^{ - 1} [s], $$

$$ q_{SC}^{B*} = F^{ - 1} \left[ {(r - m - 2b)/(r - v)} \right] = F^{ - 1} \left[ {s^{B} } \right]. $$

$$ {\text{Since}}\;F^{ - 1} [.]\;{\text{is}}\;{\text{increasing}}\;{\text{in}}\;{\text{its}}\;{\text{argument,}}s^{B} < s\;{\text{implies}}\;q_{SC}^{B*} < q_{SC}^{*} . $$

(Q.E.D.)

Proof of Proposition 5.2

By definition, we have the following:

$$ q_{SC}^{*} = q_{SC}^{B*} + \delta , $$

(A16)

where $\delta > 0$,

$$ \begin{aligned} \Pi_{SC}^{*} & = \left( {r - m} \right)q_{SC}^{*} - (r - v)\int_{0}^{{q_{SC}^{*} }} {\left( {q_{SC}^{*} - x} \right)f(x)dx} - T_{R} - T_{M} \\ & = \left( {r - m} \right)q_{SC}^{*} - (r - v)\int_{0}^{{q_{SC}^{*} }} {F(x)dx} - T_{R} - T_{M} , \\ \end{aligned} $$

(A17)

$$ \begin{aligned} \Pi_{SC}^{B*} & = \left( {r - m - 2b} \right)q_{SC}^{B*} - (r - v)\int_{0}^{{q_{SC}^{B*} }} {\left( {q_{SC}^{B*} - x} \right)f(x)dx} \\ & = \left( {r - m - 2b} \right)q_{SC}^{B*} - (r - v)\int_{0}^{{q_{SC}^{B*} }} {F(x)dx} . \\ \end{aligned} $$

(A18)

Putting (A16) into (A17) gives:

$$ \Pi_{SC}^{*} = (r - m)\left( {q_{SC}^{B*} + \delta } \right) - (r - v)\int_{0}^{{q_{SC}^{B*} + \delta }} {F(x)dx} - T_{R} - T_{M} . $$

(A19)

Putting (A19) and (A18) into $EBB_{SC} = \Pi_{SC}^{B*} - \Pi_{SC}^{*}$ and simplifying, we have the following:

$$ \begin{aligned} EBB_{SC} & = T_{R} + T_{M} + (r - m)\delta - (r - v)\int_{0}^{\delta } {F(x)dx} - 2bq_{SC}^{B*} \\ & = T_{SC} + (r - m)\delta - (r - v)\int_{0}^{\delta } {F(x)dx} - 2bq_{SC}^{B*} . \\ \end{aligned} $$

(A20)

It is hence easy to find that:

$$ EBB_{SC} \left( {\begin{array}{*{20}c} > \\ = \\ < \\ \end{array} } \right)0\;{\text{if}}\;{\text{and}}\;{\text{only}}\;{\text{if}}\;T_{SC} \left( {\begin{array}{*{20}c} > \\ = \\ < \\ \end{array} } \right)(r - m)\delta + 2bq_{SC}^{B*} - (r - v)\int_{0}^{\delta } {F(x)dx} . $$

(Q.E.D.)

Proof of Proposition 5.3

The proof is straightforward. First, note that from Proposition 5.1, we have: $q_{SC}^{B*} < q_{SC}^{*}$. Second, observe that the variance of profit functions are all increasing in quantity q. Directly substituting the optimal product quantities into the respective variance of profit functions generates the result:

$$ V\left[ {\tilde{\Pi }_{i}^{B} \left( {q_{SC}^{B*} } \right)} \right] < V\left[ {\tilde{\Pi }_{i} \left( {q_{SC}^{*} } \right)} \right],\quad \forall i \in \left( {R,M,SC} \right). $$

(Q.E.D.)

Proof of Theorem 5.1

Observe that $\hat{T}_{SC} = (r - m)\delta + 2bq_{SC}^{B*} - (r - v)\int_{0}^{\delta } {F(x)dx}$. From Proposition 5.2, we have:

$EBB_{SC} \left( {\begin{array}{*{20}c} > \\ = \\ < \\ \end{array} } \right)0$ if and only if $T_{SC} \left( {\begin{array}{*{20}c} > \\ = \\ < \\ \end{array} } \right)\hat{T}_{SC}$. Thus, we have the following two cases:

When $T_{SC} > \hat{T}_{SC}$, we have $EBB_{SC} > 0$, which means using blockchain technology benefits the supply chain and also its members in terms of expected profit. As using blockchain technology always reduces the operational risk (Proposition 5.3), we have “using blockchain technology is a mean-risk dominating solution for the supply chain and its members if and only if $T_{SC} > \hat{T}_{SC}$”.

When $T_{SC} \le \hat{T}_{SC}$, we have $EBB_{SC} \le 0$, which means using blockchain technology hurts the supply chain and also its members in terms of expected profit. As using blockchain technology always reduces the operational risk (Proposition 5.3), we know that using blockchain technology is a mean-risk non-inferior solution for the supply chain and its members for this case. (Q.E.D.)

Proof of Theorem 6.1

For (1): Directly from the discussions that if the supply chain contract is changed to be the two-part-tariff contract, returns contract, or profit sharing contract, we can still achieve the coordinated optimal supply chain in the same way as the revenue sharing contract. As a result, the corresponding results also hold.

For (2): Note that the semi-deviation of profit (a downside risk measure) exhibits the same monotonic increasing property as the variance of profit. As such, we have the following:

$$ \begin{aligned} & SDV\left[ {\tilde{\Pi }_{i}^{B} \left( {q_{SC}^{B*} } \right)} \right] < SDV\left[ {\tilde{\Pi }_{i} \left( {q_{SC}^{*} } \right)} \right],\quad \forall i \in \left( {R,M,SC} \right),\end{aligned} $$

which completes the proofs. (Q.E.D.)

Appendix 3: Other contracts

3.1 The profit sharing contract

Under the profit sharing contract, the manufacturer supplies the product to the retailer at a wholesale price w and also shares a proportion $0 \le \theta \le 1$ of the retailer’s profit. It is easy to find that the following arrangement can achieve coordination of the supply chain:

Proposition A3.1

Using the profit sharing contract: (a) Under the traditional supply chain model, supply chain coordination under Nash bargaining can be achieved by setting the following: $w = m$ and $\theta = \lambda$. (b) Under the blockchain-supported supply chain model, supply chain coordination under Nash bargaining can be achieved by setting the following: $w = m + 2b$ and $\theta = \lambda$.

Once the supply chain can be coordinated by using the profit sharing contract, all remaining analyses can be conducted and we can see that the results would remain valid.

3.2 The two-part-tariff contract

Under the two-part-tariff contract, the manufacturer supplies the product to the retailer at a wholesale price w and also gets a side-payment of G from the retailer. It is direct to find that the following arrangement can achieve coordination of the supply chain:

Proposition A3.2

Using the two-part-tariff contract: (a) Under the traditional supply chain model, supply chain coordination under Nash bargaining can be achieved by setting the following: $w = m$ and $G = \lambda \Pi_{SC}^{*}$. (b) Under the blockchain-supported supply chain model, supply chain coordination under Nash bargaining can be achieved by setting the following: $w = m + 2b$ and $G = \lambda \Pi_{SC}^{B*}$.

Once the supply chain can be coordinated, all the remaining analyses for the supply chain systems can be conducted and we can see that the results would remain valid (except for the manufacturer, there is no risk under both the traditional and blockchain-supported supply chains, and hence using blockchain technology does not reduce the operational risk for the manufacturer).