5. Model Analysis
Given the above model, we solve the logistics-service level and pledge rate when the 3PL enterprise provides ‘logistics + finance’ service and expects profit maximization. We also analyze their relationship with tariffs, the default rate of the cross-border e-commerce enterprise, the capability coefficient of the 3PL enterprise, and the logistics coefficient of service sensitivity. Conclusions are then derived from the results.
Theorem 1. When the cross-border e-commerce enterprise has capital constraints, is a joint concave function of the pledge rate and logistics-service level .
Proof. As shown in Equation (3), the supply quantity of the cross-border e-commerce enterprise can be regarded as a function of the logistics-service level . The first-order partial derivatives of the pledge rate and logistics-service level for Equation (9) are obtained as follows:
For
, the second-order partial derivatives for
and
, respectively, are
The second-order partial derivatives are obviously less than 0. Therefore, to prove the joint concavity
concerning
and
, we establish the following equation:
where the mixed partial derivatives are
Substituting Equations (12), (13) and (15) into Equation (14) and simplifying, we obtain
As , Equation (14) is established whilst is the joint concave function of the pledge rate and logistics-service level . Theorem 1 is thus proved. □
Theorem 2. The optimal pledge rate and level of logistics services provided by the 3PL enterprise respectively exist as and , where and are determined by Equation (16):where Proof. From Theorem 1, we know that is a joint concave function with respect to ; thus, there exists a maximal value. Let Equations (10) and (11) equal 0 and solve the system of cubic equations to obtain the extreme value point .
Equation (10) is set to 0 and simplified as . As , the solution is , where .
Letting Equation (11) be 0 and simplifying it yields
The above equation is a quadratic equation with respect to . It is solved using the root formula.
Let , ,
.
We can easily ascertain that
and that the positive or negative value of
depends on
; letting it be
gives
.
monotonically increases relative to
. In addition, because
,
H(0) = 0; thus,
,
. Then,
, and the equation has two different solutions:
and
. Discarding the negative values yields
In sum, the extreme value point of
is
where
.
As , ; therefore, the optimal strategy for the logistics enterprise is
, . Theorem 2 is proved. □
Theorems 1 and 2 prove that under the assumptions of this study, when the cross-border e-commerce enterprise has capital constraints and chooses inventory pledge loans, the existence and uniqueness of the ‘logistics + finance’ service strategy for the 3PL enterprise, the optimal pledge rate for loan issuance, and the optimal level of logistics service should be selected.
Theorem 3. The optimal pledge rate of the 3PL enterprise and the level of logistics services are positively correlated with tariff rate .
Proof. Let
. The first-order derivative of
from Equation (16) yields
where
.
Equations (18) and (19) are less than 0. , are decreasing functions of . decreases relative to . The optimal rate of the 3PL enterprise and the level of logistics services are positively correlated with the tariff rate . Theorem 3 is thus proved. □
Theorem 3 illustrates the impact of the offshore tariff policy on the ‘logistics + finance’ service strategy of the 3PL enterprise. With the increase in offshore market tariffs, the level of logistics service and pledge rate provided by the 3PL enterprise increases. Specifically, the rise in tariffs increases the barriers to entry into offshore markets and raises the cost of the cross-border e-commerce enterprise, causing it to reduce the number of supplies it sends to offshore markets. This condition also leads to a loss of profit and market share for the 3PL enterprise. Therefore, the 3PL enterprise increases market demand by improving the quality of its services, that is, by providing a higher pledge rate and logistics-service level to increase market demand and to stimulate the cross-border e-commerce enterprise and thereby increase its supply to offshore markets. In this way, the impact of the tariff rate increase is mitigated.
Theorem 4. The optimal pledge rate of the 3PL enterprise and the level of logistics services are negatively correlated with the default rate of the cross-border e-commerce enterprise .
Proof. Let
. Finding the first-order derivative of R gives
< 0.
decreases monotonically with
. The first-order derivatives of
and
with respect to
are respectively obtained from Equation (16) as
As shown in Equation (17), is a decreasing function of . Therefore, Equations (20) and (21) are less than 0, that is, and , respectively. Thus, and are monotonically decreasing functions of . Theorem 4 is thus proved. □
Theorem 4 shows that the pledge rate and logistics-service level decisions of the 3PL enterprise are affected by the default rate of the cross-border e-commerce enterprise and that both decrease as the default rate increases. The higher the default rate of the cross-border e-commerce enterprise, the greater the risk faced by the 3PL enterprise, which consequently requires a significant number of pledges to control the business risk when granting the same amount of loan; hence, it provides a lower pledge rate. The reason the logistics-service level decision of the 3PL enterprise is affected by the default rate of the cross-border e-commerce enterprise is illustrated in Corollary 1.
Corollary 1. Other things being equal, we compare the optimal levels of logistics services provided by the 3PL enterprise when the cross-border e-commerce enterprise applies for inventory pledge loans. When the default rate of the cross-border e-commerce enterprise applying for loans is , the 3PL enterprise provides it with better logistics services; here, is determined by .
Proof. The expected profit function when the 3PL enterprise does not provide financial services to the cross-border e-commerce enterprise is as follows:
. The solution method is the same as that for Theorem 2 and is not repeated here. The solution is
Comparing with reveals that they differ by only one term, ; thus, . The equality sign holds when and only when , . Corollary 1 is thus proved. □
Corollary 1 suggests that for the cross-border e-commerce enterprise with a default rate within a specific range, the 3PL enterprise provides pledged loans for a higher level of logistics services. As the difference term between and is a decreasing function of and , the stronger the capability of the 3PL enterprise to provide services and the better the credit level of the cross-border e-commerce enterprise, the more significant the difference in the logistics services provided by the 3PL enterprise. In this case, the cross-border e-commerce enterprise is less likely to default. Consequently, the 3PL enterprise becomes increasingly willing to improve its logistics services to encourage the cross-border e-commerce enterprise to increase its supply to offshore markets. This increased supply boosts the 3PL enterprise’s logistics revenue. This result explains why the default rate affects the logistics-service decisions of the 3PL enterprise, as in Theorem 4.
Theorem 5. The optimal pledge rate of the 3PL enterprise and level of logistics services are negatively correlated with the 3PL enterprise’s capability coefficient .
Proof. Let ; thus, .
The first-order derivative of
from Equation (16) yields
Equations (22) and (23) are less than 0. Theorem 5 is thus proved. □
Theorem 5 shows that the larger the capability coefficient of the 3PL enterprise, the lower the pledge rate and logistics services provided to the cross-border e-commerce enterprise. Specifically, the higher the value of , the lesser the capability of the 3PL enterprise, the greater the logistics cost, and the smaller the profit from providing the same level of logistics services. Thus, the less capable 3PL enterprise will be more inclined to provide a lower level of logistics services to control costs. Meanwhile, a low level of logistics services reduces the market demand of the cross-border e-commerce enterprise, and the financial service risk faced by the 3PL enterprise increases. Thus, risk must be controlled by lowering the pledge rate.
Theorem 6. The optimal pledge rate of the 3PL enterprise and the level of logistics services are positively correlated with the logistics sensitivity coefficient of the offshore market .
Proof. The first-order derivative of
according to Equation (16) is obtained separately as
As , the above two equations are obviously greater than 0; thus, and are positively related to the logistics sensitivity coefficient .
Theorem 6 is thus proved. It shows that the larger the foreign consumer’s logistics sensitivity coefficient is, the higher the pledge rate and logistics service provided by the 3PL enterprise. Specifically, with other things being equal, when the 3PL enterprise improves the level of equivalent logistics services, the more sensitive the logistics services become, the more significant the increase in demand in offshore markets, and the more the cross-border e-commerce enterprise improves its supply to offshore markets. The 3PL enterprise also gains significant benefits from the logistics services. Meanwhile, a substantial increase in demand in offshore markets reduces the risk of pledge liquidation, prompting the 3PL enterprise to increase the pledge rate of financial services. □
6. Numerical Analysis and Discussion
As described in this section, we conduct a numerical analysis to examine the impact of several key parameters on the ‘logistics + finance’ service decisions of the 3PL enterprise and its overall expected profitability. These key parameters include tariff rate, the cross-border e-commerce enterprise’s default rate, the 3PL enterprise’s capability coefficient, the offshore market price and logistics sensitivity coefficient, and the size of exchange rate fluctuations. In this study, we assume that the logistics-service price
of the 3PL enterprise and the sales price
of the cross-border e-commerce enterprise are exogenous and are determined by market supply and demand. Taking cross-border e-commerce in China and Mongolia as an example, this study uses the historical exchange rate values of RMB and the Mongolian tugrik for 2019–2020 published by China UnionPay as a sample of exchange rate
(as shown in
Table A2 in the
Appendix A). For the sample of primary demand
(as shown in
Table A4 in the
Appendix A), we used 1/50,000th of the monthly import value of machinery, tape recorders, TV sets, and parts imported into Mongolia from February 2020 to January 2021 according to the CEIC database. The normality of the two datasets was verified using SPSS 22.0 (see
Appendix A Table A1 and
Table A3), yielding a mean value of 394.65 and a standard deviation of 16.09 for the exchange rate
and a mean value of 1747 and a standard deviation of 284.36 for the basic demand
. Mongolia’s import duty rate for general goods under the Customs Law is 15%. In addition, the annual interest rate of 3.85% announced by China Merchants Bank in 2021 for best-pledged customers is taken as the cost of capital for the 3PL enterprise. The sales and pledging cycle
of the cross-border e-commerce enterprise is assumed to be 3 months. The other parameters are set as listed in
Table 1. The following data are processed and estimated based on actual transaction data of an SME cross-border e-commerce platform in China through research.
From Equations (1) and (2), we obtain the pledge rate interval as [0, 0.909] and the logistics-service level interval as [0, 2]. According to the basic parameters, the optimal logistics-service level provided by the 3PL enterprise is
. The optimal supply quantity of the cross-border e-commerce enterprise to offshore markets is
. The supply quantity that its own capital can satisfy is
. Therefore, the cross-border e-commerce enterprise needs to make inventory pledge loans so that the pledged amount,
, can obtain the best-quality pledge rate,
, from the 3PL enterprise.
Figure 2,
Figure 3 and
Figure 4 show the changes in the values of tariff rate
, default rate
, 3PL enterprise’s capability coefficient
, offshore market price
, and logistics sensitivity coefficient
whilst keeping the other parameters in
Table 1 unchanged.
Figure 2,
Figure 3 and
Figure 4 also present the trends of the optimal logistics-service level and optimal quality charge rate of the 3PL enterprise with tariff rate
, default rate
, 3PL enterprise’s capability coefficient
, price sensitivity coefficient
, and logistics sensitivity coefficient
. From
Figure 2, we find that the optimal logistics-service level and pledge rate of the 3PL enterprise increase with an increase in the tariff rate; this result is the same as the conclusion of Theorem 3. However, relative to other factors, due to the fact that tariff rates do not have a direct impact on the logistics-service revenue and financial service revenue of 3PL enterprises, the tariff rate does not exert much influence on the 3PL enterprise’s decision. From
Figure 3, as stated in Theorems 4 and 5, the optimal logistics-service level and pledge rate of the 3PL enterprise decrease with an increase in the cross-border e-commerce enterprise’s default rate and the 3PL enterprise’s capability coefficient. The higher the default rate of cross-border e-commerce enterprises, the lower the logistics-service level provided by 3PL enterprises, and the lower the pledge rate to provide lower loans. The higher the 3PL enterprises’ capability coefficient, the lower the 3PL enterprises’ capability; thus, 3PL enterprises provide lower logistics-service levels and can only provide lower loans. As shown in
Figure 4, the type of offshore market is one of the factors influencing the decision of the 3PL enterprise. The optimal logistics-service level and pledge rate of the 3PL enterprise decrease with an increase in the price sensitivity coefficient
in offshore markets. The price sensitivity coefficient has less influence on the logistics-service level decision and more influence on the pledge rate decision. Consistent with Theorem 6, the price sensitivity coefficient increases with the logistics sensitivity factor
in the offshore market.
Figure 5 shows that when the parameters in
Table 1 are constant, the level of logistics services and the pledge rate provided by the 3PL enterprise gradually decrease as the standard deviation of the exchange rate increases. Hence, the stability of the exchange rate is also one of the critical factors affecting the decision of the 3PL enterprise. In addition,
Figure 5 shows that exchange rate fluctuations have less impact on the decision regarding the logistics-service level and more impact on the pledge rate. For example, in the
market environment, the standard deviation of the exchange rate increases from 10 to 22, the pledge rate decreases by 69%, and the logistics-service level decreases by only 6.5%. Specifically, the stability of the exchange rate mainly affects the financial service risk faced by the 3PL enterprise. Therefore, the 3PL enterprise needs to adjust its pledge rates actively for risk control.
Combining the results of the model analysis and numerical experiment, we can obtain the relationships between the decision variables of the 3PL enterprise, namely the logistics-service level
and pledge rate
; and the tariff rate
, default rate
of the cross-border e-commerce enterprise, capability coefficient
of the 3PL enterprise, price sensitivity coefficient
of offshore markets, logistics sensitivity coefficient
, and standard deviation
of the exchange rate (
Table 2).
According to
Table 2, the decision variables of logistics-service level
and pledge rate
of the 3PL enterprise decrease with an increase in the tariff rate
and the logistics sensitivity coefficient
of offshore markets. They also decrease with an increase in the cross-border e-commerce default rate
, capability coefficient
of the 3PL enterprise, price sensitivity coefficient
of offshore markets, and standard deviation of exchange rate
. We also conducted Sobol sensitivity analysis on these influencing factors. Based on the results, we obtained the ranking of the impact degree of the relevant factors on the decision variable of logistics-service level
of the 3PL enterprise, which is as follows:
>
>
>
>
>
. The ranking of the impact degree on the pledge rate
is as follows:
>
>
>
>
>
. Therefore, we have identified the main factors that influence the decision variables of the logistics-service level and pledge rate for 3PL enterprises, and these factors can be used by 3PL enterprises to determine the decision-making sequence based on their degree of impact. We have provided a theoretical basis for the decision making of 3PL enterprises, which is beneficial for their management and further development.
Figure 6 shows the impact of the 3PL enterprise’s capability coefficient
and the cross-border e-commerce enterprise’s default rate θ on the profits of the cross-border e-commerce enterprise, the 3PL enterprise, and 3PL as a whole. When other parameters are the same and constant, as in the primary example, the expected profits of the cross-border e-commerce enterprise are mainly influenced by the capability coefficients of the 3PL enterprise. Therefore, in the context of this study, SMEs with low creditworthiness should choose to cooperate with highly capable 3PL enterprises. For 3PL enterprises, the smaller the capability coefficient, the lower the default rate of cross-border e-commerce enterprises, and the greater the expected profit. Therefore, to increase their profits at a certain level of capacity, 3PL enterprises should choose SMEs with good credit to cooperate with and provide services for them. For 3PL as a whole, the total profit is less affected by the default rate of cross-border e-commerce enterprises and more affected by the capability coefficient of 3PL enterprises. The improvement of 3PL enterprises plays a crucial role in promoting the further development of cross-border e-commerce in China.
In summary, when the tariff rate and the degree of exchange rate fluctuation change and 3PL enterprises with different capabilities face different types of offshore markets and provide services to cross-border e-commerce enterprises with different credit levels, the ‘logistics + finance’ service decision model approach proposed in this study remains valid. Therefore, the proposed model approach has good generality and can be used in practical decision making for cross-border e-commerce. In addition, this service decision-making model approach can also help enterprises in cross-border service supply chains achieve their sustainability goals. Through this model and method, 3PL enterprises can increase their revenue and promote development by balancing logistics and financial service income. Furthermore, SMEs can alleviate financial pressure through this service, which is beneficial for their growth and expansion. Therefore, the ‘logistics + finance’ service decision-making model approach can promote the sustainable development of enterprises and contribute to the sustainable development of the cross-border e-commerce industry.