Decision-Making of Transnational Supply Chain Considering Tariff and Third-Party Logistics Service

Abstract

Countries’ economic policies, such as tariff barriers, have a profound impact on the global economy and international trade. The imposition of tariffs seriously disturbs the global trade and supply chain operations. This paper studies a supply chain composed of an overseas manufacturer, a domestic supplier and a third-party integrated international logistics service provider. A three-level decentralized leader-follower decision-making model and its variant--leader-follower alliance decision-making models are established, and the influences of revenue sharing and cost sharing on the three-level decentralized decision-making are analyzed. The results show that it is difficult for the supply chain to achieve coordination when the transportation and insurance costs are considered in the tariff cost. The increase of tariff rates will reduce the profits of all parties and the overall profit of the supply chain, and weaken the dominant position of the supplier in the supply chain. Revenue sharing can improve the supply chain performance; the performance of the whole supply chain cannot be improved or may even deteriorate by sharing the transportation cost alone. The study can provide practitioners with implications for how to carry effective cooperation and coordination in the supply chain and how to effectively reduce the influence of tariffs in the global trade system.

1. Introduction

At present, various uncertainties such as the COVID-19 epidemic are seriously disrupting world economic growth and exacerbating the instability of the global economy [1]. The escalation of economic and trade frictions in the global scope has an important impact on global supply chain systems at different levels, which not only leads to supply interruption, but also results in serious inventory disorder. Tariffs are one of the main factors causing international trade barriers. The rise of tariff rates increases operation costs, reduces the efficiency of logistics, and seriously damages global supply chain systems. Therefore, tariff has become the key factor restricting the development of transnational supply chains.

The purpose of this paper is to investigate the decision-making and coordination of a transnational supply chain, analyze the impact of tariff and international logistics on supply chain decision-making, and provide implications for practitioners in global supply chain management operations. Although some literatures have studied the issue of the global supply chain modelling and the impact of tariffs on global trade, little attention has been paid to the decision-making and coordination mechanism of transnational supply chains with multiple participators, especially when it comes to third-party logistics service providers. In this paper, a transnational supply chain involves three parties, namely, an overseas manufacturer (buyer) purchasing materials from a domestic local supplier, and a third-party international logistics service provider responsible for the international logistics of the purchased goods. Compared with the traditional two-level supply chain, the decision-making of the multi-level transnational supply chain is more complex. Therefore, it is of great significance to study the decision and coordination mechanism of transnational supply chain with multiple agents’ participation. In particular, when tariff is considered as an impacting factor in the decision, new academic ideas and practical implications can be derived out.

Our research aims to answer the following questions:

• How does the increase of tariff rate affect the pricing decision in a three-level transnational supply chain?
• How to coordinate the decisions of participants in a transnational supply chain when considering tariffs?

This paper contributes to a new perspective of three parties’ participation game decision in the field of transnational supply chain management. It can clearly illustrate the influence of tariffs on the decision of the transnational supply chain, and more clearly reveal the intentions and performance of participators in the multi-agent supply chain. Based on the different roles of participants in the transnational supply chain, we first establish centralized and decentralized multi-agent decision models, extending previous two-level game decision to a three-level game decision. Then, we show the differences of the revenue sharing and cost sharing mechanisms. Eventually, based on numerical analysis, we provide important implications for practitioners.

The structure of this paper is as follows: Section 2 reviews the literature, providing shortcomings of current research. Section 3 describes the problem, model assumptions, and symbol definitions. Section 4 formulates and analyzes the theoretical models. Section 5 presents the numerical analysis. Section 6 summarizes the conclusions and further research directions.

2. Literature Review

Transnational supply chain is an extension of the regional and local supply chain. It drives production by global demand, integrates various advantageous resources in the world with the support of modern transportation, communication, and other technologies. Compared with the regional and local supply chain, a transnational supply chain should not only consider procurement, production, storage and transportation costs, but also involve the international political, trade and financial factors, such as export control, tariffs, exchange rates and other factors including the economic politics and infrastructure of different countries. In recent years, the impact of tariffs on the development of industrial chains and supply chains has attracted academic attention. Many authors have investigated issues related to the transnational supply chain and the effect of tariffs on trade and supply chain operations.

Nagarajan and Sharma [2] studied the changes in global equity valuations after the outbreak of the COVID-19 pandemic to infer market’s expectations regarding the possible long-term impact of the pandemic on global supply chains. Amiti et al. [3] found that the costs of tariffs imposed in the United States were mainly borne by American consumers. Empirical and realities show that all tariffs are passed on almost entirely to consumers and importers, and that the prices of intermediate and final products in the subject industries have risen sharply. Contrary to the effect of tariff increase, Fan et al. [4] pointed out that tariff reduction is beneficial to export enterprises through reduced marginal production costs. Niu et al. [5] showed that tariffs imposed by importing countries increase the procurement costs of domestic multinational corporations and reduce the procurement volumes of multinational corporations. Rong and Xu [6] assessed the impact of manufacturer altruistic preferences and government subsidies on the multinational green supply chain under dynamic tariffs. Cole et al. [7] showed that the price rise effect of retailers would affect the price transmission of tariffs to other goods along the supply chain. Cipollina et al. [8] studied the impact of EU agricultural tariff policy on agricultural product imports and found that the tariff reduction directly increased the import volume of products. Liu et al. [9] believed that the reduction of intermediate product tariffs reduced the usage costs of foreign high-quality intermediate products. Most of the above literatures are empirical studies or theoretical analyses of explaining the impact of tariff on the macro economy or industry. Few scholars have studied the impact of tariffs on the global supply chain through quantitative models. However, the transmission mechanism of tariffs in the supply chain has not been systematically studied. Therefore, investigating the effect of tariff issue from the perspective of supply chain operations and revealing the micro mechanism of tariff transmission along the supply chain will help us further understand the impact of tariff increase on the industrial supply chain.

When studying the operations of the transnational supply chain, transportation cost should not be ignored. Scholars have conducted extensive research on transportation cost factors. Swenseth and Godfrey [10] believed that it is necessary to consider transportation cost when replenishing inventory. Wang and Disney [11] established a transportation coordination control model based on continuous inspection strategy under stochastic demand. The third-party logistics service provider (TPL) has many advantages in the global supply chain. It can cooperate with supply chain members to achieve the rapid flow of products in the global market. With the diversification of products, TPL plays an increasingly important role in the supply chain structure. Therefore, the supply chain with the consideration of participation of TPL has become an important academic research area. Jayaram et al. [12] found that group companies integrating TPL have better benefits than those without integrating TPL. Meanwhile, the investment benefits of group companies integrating TPL are higher than those without integrating TPL. They found that TPL can effectively coordinate the supply chain. Abbasi et al. [13] considered product perishability and inventory costs in TPLs logistics network design; they revealed the effects of product perishability and disruption of the storing facilities on the TPLs network designing. Tavana et al. [14] proposed a game-theoretic approach to examine several possible coalition strategies in a four-echelon supply chain consisting of a supplier, a manufacturer, a wholesaler, and a retailer. Jiang et al. [15] studied the decision and coordination mechanism of a competing retail channel with consideration of the participation of a TPL provider. They provided a new insight that whether to introduce the TPL provider depends on the balance of the advantage and disadvantage of the TPL provider. Jiang et al. [16] discussed three types of sub-coordination in a competing supply chain comprising two manufacturers, a retailer, and a TPL provider. They found that sub-coordination is not always effective in improving the profit of the supply chain; in some cases it even does harm to supply chain members or the whole supply chain. The performance of sub-coordination critically depends on the degree of product substitutability. Huang et al. [17] put forward the supply chain coordination conditions when the TPL firm offers financing service. They found that under TPL financing service, the profit of the supply chain can achieve Pareto improvement.

If all numbers in the transnational supply chain are concerned only with their own interests, then the whole supply chain may be inefficient. In order to maximize the benefits to the members and the whole transnational supply chain, supply chain members should not only consider their own optimal profits, but also consider the interaction and coordination between the upstream and the downstream of the supply chain. Many literatures have studied the supply chain coordination. Karaenke et al. [18] found that the lack of coordination between operators would also lead to low logistics efficiency. Supply chain contracts can promote the cooperation among supply chain members in strategy, skills, management process, and innovation; achieve the balance of multi-party capabilities; and give full play to the maximum performance of the whole supply chain. Yang et al. [19] developed option contracts in a supplier-retailer agricultural supply chain where the market demand depends on sales effort. Liu et al. [20] designed a coordination mechanism based on value-added profit distribution to coordinate the supply chain composed of a dominant retailer, a socially responsible supplier, and a non-socially responsible supplier. Per and Peter [21] used agency theory to examine the role of information asymmetry in coordinating supply chains. Krishnan and Winter [22] demonstrated that the revenue-sharing contract can coordinate and optimize the supply chain. Lack of coordination among transportation companies leads to low logistics efficiency. Sainathan and Groenevelt [23] provided a general mathematical framework for analyzing contracts under both RMI (retailer managed inventory) and VMI (vendor managed inventory). Palsule-Desai [24], Heydari and Ghasemi [25], and Li et al. [26] adopted a revenue-sharing contract to coordinate the supply chain. Lu et al. [27] systematically reviewed the profit allocation, decision sequence, and compliance aspects of these contracts. Some authors also studied the supply chain coordination issue through mechanism design considering information asymmetry. Vosooghidizaji et al. [28] systematically reviewed the research progress of supply chain coordination under information asymmetry, and put forward some suggestions on the application strategies of coordination mechanisms considering information asymmetry. Pishchulov and Richter [29] investigated the optimal contract design of joint lot size for a single-supplier-single-buyer supply chain considering multi-dimensional asymmetric information. They formulated the problem as a principal-agent decision model and proved the KKT condition of solving the problem. Zissis et al. [30] designed a contract based on quantity discount mechanisms to coordinate the inventory lot size decision of a supply chain composed of a manufacturer and a distributor under bilateral information asymmetry.

Unlike previous studies, this paper integrates a transportation service provider into the game decision of a transnational supply chain, with consideration of the transportation cost and insurance cost when calculating tariff cost. The above two factors are the important originality of this paper. Considering the impact of tariff on the supply chain, this paper constructs a supply chain system composed of an oversea manufacturer, a third-party integrated international logistics service provider (TPIILSP), and a domestic supplier (offshore outsourcing factory). We apply game theory to formulate Stackelberg game models based on the different roles of the members in the supply chain, analyze the impacts of tariff on the supplier’s pricing, the TPIILSP’s transportation pricing, and the manufacturer’s ordering; as well as the profits of supply chain members, discuss the coordination mechanism based on revenue sharing and cost sharing for three-level decentralized game decision of the transnational supply chain; and provide implications for transnational supply chain operations.

3. Problem Description and Symbol Definitions

The transnational supply chain studied in this paper consists of a manufacturer (overseas product manufacturer), a TPIILSP, and a domestic part supplier (offshore outsourcing factory). The manufacturer produces a type of oil production machinery and outsources the rough machining business to the supplier. The TPILSP undertakes the international logistics and related services.

The market demand faced by the manufacturer is uncertain, usually, it can be assumed as different stochastic functions, e.g., normal distribution, Gamma distribution, uniform distribution, etc. In order to better formulate the problem and simplify the calculation results of the model, and obtain closed-form solution during the game process, this paper refers to Erlebacher [31], Horjo [32], Abdel-Malek [33], Chernonog and Goldberg, [34] and Patra and Jha [35]. We assume that the demand faced by the manufacturer is a continuous and non-negative random variable and follows a uniform distribution. The density function of market demand is $\{\begin{array}{l}\frac{1}{b},0\le x\le b\\ 0,others\end{array}$, the distribution function is $\{\begin{array}{l}0,x<0\\ \frac{x}{b},0\le x\le b\\ 1,x\ge b\end{array}$. In the independent or decentralized decision-making, the three members of the transnational supply chain form a three-level game, that is, the supplier first decides the Free On Board (FOB) price $\omega$, then the TPIILSP decides the unit transportation price $\delta$, and finally the manufacturer decides the order quantity $Q$.

Tariffs play a special role during the decision-making process. A tariff is a kind of tax levied by a country’s customs on the imported goods according to the laws of that country. The tariff rate is the ratio of the charged tax to the goods price. For example, if a commodity is imported from country A to country B, county B will charge a certain ratio of tax to the imported goods, which is a percentage number of the price of the commodity, e.g., 10%. Tariff increases the import cost of the company in country B, so if the tariff is too high, then some companies at country B will give up the import business from country A and turn to other counties, this leads to the supply chain disruption between country A and country B. In this paper, we assume that tariff rate is $\theta$.

The other parameters used in this paper are as follows:

• $p$—The manufacturer’s unit selling price;
• $\vartheta$—Salvage value of unsold products;
• $R$—Revenue sharing rate of the manufacturer;
• $\tau$—Transportation cost sharing rate of the manufacturer;
• $\lambda$—Tariff sharing rate of the manufacturer;
• $c_1$—Manufacturer’s manufacturing cost per unit product;
• $c_2$—Transportation cost per unit product of the TPIILSP;
• $c_3$—Supplier’s manufacturing cost per unit product; and
• $f$—Unit product insurance cost.

4. Theoretical Model Construction

Based on the above assumptions, we first formulate the profit functions of the manufacturer, the TPIILSP, and the supplier respectively.

The profit function of the manufacturer is as follows:

$${\Pi }_m(Q)=p\min (D,Q)-\omega Q-c_{1}Q-fQ-\delta Q-\theta (\omega +\delta +f)Q+\vartheta {(Q-D)}^{+}$$

(1)

In Equation (1), the first item is the sales revenue of the manufacturer, the second item is the international procurement cost, the third item is the manufacturer’s production cost, the fourth item is insurance cost, the fifth item is transportation cost paid to the TIILSP, and the sixth item is the tariff cost, the seven item is the residual value of unsold products. From $E\min (D,Q)=Q-{\displaystyle {\int }_0^{Q}F(x)}dx=Q-Q^2/2b$, $E{(Q-D)}^{+}={\displaystyle {\int }_0^{Q}F(x)}dx=Q^2/2b$, by solving the mathematical expectation of Equation (1), we can get the manufacturer’s expected profit function as follows:

$${\pi }_m(Q)=[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]Q-0.5(p-\vartheta )Q^2/b$$

(2)

The profit function of the TPIILSP is

$${\pi }_t(\delta )=\delta Q-c_{2}Q$$

(3)

In Equation (3), the first item is transportation service income, and the second item is transportation cost.

The supplier’s profit function is as follows:

$${\pi }_s(\omega )=\omega Q-c_{3}Q$$

(4)

In Equation (4), the first item is sales revenue of the supplier, and the second item is the manufacturing cost of the supplier.

4.1. Decision Making of Transnational Supply Chain When Tariff Is Zero

In order to analyze the impact of tariffs on the transnational supply chain, we first analyze the situation when the tariff is zero, taking it as the basis for analysis and comparison of the following sections. Three decision models are formulated when the tariff is zero, i.e., centralized decision, decentralized decision, and alliance decision.

Under the centralized decision, the manufacturer, the TPIILSP, and the supplier constitute a virtual entity to make the decision. In this case, the order quantity of the manufacturer is $Q_c^{\ast }=b(p-c_1-c_2-c_3-f)/(p-\vartheta )$, the profit of the whole supply chain can be maximized under the centralized decision.

Under the decentralized decision, the manufacturer, the TIILSP and the supplier independently make their own decisions, this is a non-alliance three-level game decision process. Applying the inverse induction method to solve the game problem, one can obtain the FOB price of the supplier ${\omega }_d^{\ast }=0.5(p-c_1-f-c_2+c_3)$, the transportation price of the TPIILSP ${\delta }_d^{\ast }=0.25(p-c_1-f-c_3+3c_2)$, and the order quantity of the manufacturer $Q_d^{\ast }=0.25b(p-c_1-f-c_2-c_3)/(p-\vartheta )$. It is seen that the order quantity under the decentralized decision is 0.25 times of that under the centralized decision. Therefore, from the above results, we can know that the decentralized decision with three game agents obviously reduces the order quantity compared with the centralized decision with only one decision agent.

Under the alliance decision, the manufacturer and the TPIILSP form an alliance to play a game with the supplier. Thus, this decision has only two agents. Then under this alliance decision, the optimal FOB price of the supplier ${\omega }_d^{\ast \ast }=0.5(p-c_1-c_2+c_3-f)$, and the optimal order quantity of the manufacturer $Q_d^{\ast \ast }=0.5b(p-c_1-c_2-c_3-f)/(p-\vartheta )$ can be obtained by using the reverse induction method. It is seen that the FOB price ${\varpi }_d^{\ast \ast }$ under the alliance decision is the same as the FOB price ${\varpi }_d^{\ast }$ under the decentralized decision without an alliance, but the order quantity $Q_d^{\ast \ast }$ under the alliance decision is twice as much as the order quantity $Q_d^{\ast }$ under the decentralized decision (i.e., without alliance).

From the above analysis we know that the order quantities of the manufacturer under three decision models have the relationship: $Q_c^{\ast }=2Q_d^{\ast \ast }=4Q_d^{\ast }$. This shows that compared with the decentralized decision with three decision agents (three-level game decision), the alliance decision with two decision agents (two-level game decision) has better performance, while the centralized decision with only one decision agent has the highest performance. This means that reducing the level of the game process can increase the order quantity of the manufacturer, which can then increase the profit of the transnational supply chain. Therefore, we can say that reducing the decision level of the game process can achieve Pareto improvement of the transnational supply chain. Pareto improvement means that in a multi-agent decision environment, one decision improvement does not impact others’ decisions, or at least does not weaken others’ decisions. This means that reducing the level of the game process (i.e., from three game agents to two game agents, or even to a single agent) can obtain performance improvement of the entire transnational supply chain.

4.2. Three-Level Decentralized Decision-Making of Transnational Supply Chain When Tariff Is Not Zero

When the tariff is not zero, the decentralized decision-making is also a three-level Stackelberg game process with three decision agents. The supplier first decides the FOB price $\omega$, then the TPIILSP decides the transportation price $\delta$, and finally the manufacturer decides the order quantity $Q$.

Proposition 1.

When the tariff is not zero, with decentralized decision-making mechanism, the decisions of the manufacturer, the TPIILSP and the supplier in the transnational supply chain have the following results:

1. 

The optimal order quantity of the manufacturer, the optimal transportation price of the TPIILSP, and the optimal FOB price of the supplier are$Q^{\ast }=\frac{b\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}{4(p-\vartheta )}$,${\delta }^{\ast }=\frac{p-c_1-(f+c_3-3c_2)(1+\theta )}{4(1+\theta )}$,${\omega }^{\ast }=\frac{p-c_1-(c_2+f-c_3)(1+\theta )}{2(1+\theta )}$.

2. 

The optimal profits of the manufacturer, the TPIILSP and the supplier are${\pi }_m(Q^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{32(p-\vartheta )}$,${\pi }_t({\delta }^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{16(p-\vartheta )(1+\theta )}$,${\pi }_s({\omega }^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{8(p-\vartheta )(1+\theta )}$.

Proof of Proposition 1.

By using the method of reverse recursion, the first derivative with respect to Q for Equation (2) is $\frac{\partial {\pi }_m(Q)}{\partial Q}=[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]-(p-\vartheta )Q/b$, $\frac{{\partial }^2{\pi }_m(Q)}{\partial Q^2}=-\frac{p-\vartheta }{b}<0$, ${\pi }_m\left(Q\right)$ is a strictly concave function of $Q$.

Set $\frac{\partial {\pi }_m(Q)}{\partial Q}=0$, $Q=\frac{b[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]}{(p-\vartheta )}$ is available, then putting it into Equation (3), we can get ${\pi }_t(\delta )=(\delta -c_2)\frac{b[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]}{(p-\vartheta )}$.

The first derivative with respect to $\delta$ for ${\pi }_t\left(\delta \right)$ is $\frac{\partial {\pi }_t(\delta )}{\partial \delta }=\frac{b[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]-b(1+\theta )(\delta -c_2)}{(p-\vartheta )}$, and the second order derivate with respect to $\delta$ for ${\pi }_t\left(\delta \right)$ has $\frac{{\partial }^2{\pi }_t(\delta )}{\partial {\delta }^2}=-\frac{2b(1+\theta )}{(p-\vartheta )}<0$.

Set $\frac{\partial {\pi }_t(\delta )}{\partial \delta }=0$, $\delta =\frac{p-\omega -c_1-f-\theta (\omega +f)+(1+\theta )c_2}{2(1+\theta )}$ is available, then put $\delta =\frac{p-\omega -c_1-f-\theta (\omega +f)+(1+\theta )c_2}{2(1+\theta )}$, $Q=\frac{b[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]}{(p-\vartheta )}$ into Equation (4). Set $\frac{\partial {\pi }_s(\omega )}{\partial \omega }=0$, we can get

$${\omega }^{\ast }=\frac{p-c_1-(c_2+f-c_3)(1+\theta )}{2(1+\theta )}$$

(5)

Then by putting ${\omega }^{\ast }$ into $\delta =\frac{p-\omega -c_1-f-\theta (\omega +f)+(1+\theta )c_2}{2(1+\theta )}$, we can get

$${\delta }^{\ast }=\frac{p-c_1-(f+c_3-3c_2)(1+\theta )}{4(1+\theta )}$$

(6)

Then by putting ${\omega }^{\ast }$, ${\delta }^{\ast }$ into $Q=\frac{b[p-\omega -c_1-f-\delta -\theta (\omega +\delta +f)]}{(p-\vartheta )}$, we can get

$$Q^{\ast }=\frac{b\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}{4(p-\vartheta )}$$

(7)

By substituting Equations (5)–(7) into (2)–(4), respectively, the optimal profits of the manufacturer, the TPIILSP, and the supplier can be obtained.

$${\pi }_m(Q^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{32(p-\vartheta )}$$

(8)

$${\pi }_t({\delta }^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{16(p-\vartheta )(1+\theta )}$$

(9)

$${\pi }_s({\omega }^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{8(p-\vartheta )(1+\theta )}$$

(10)

This completes the proof of Proposition 1. □

Compared with the situation of a tariff of zero, it is obvious that the increase of tariff rate leads to a decrease of $\frac{b\theta (c_2+c_3+f)}{4(p-\vartheta )}$ in the order quantity of the manufacturer, while the TPIILLSP transportation service price is reduced by $\frac{\theta (p-c_1)}{4(1+\theta )}$, and the FOB price of the supplier is reduced by $\frac{\theta (p-c_1)}{2(1+\theta )}$.

Meanwhile, the increase of tariff rate also leads to the decrease in the profits of the manufacturer, the TPIILSP, and the supplier, respectively, which are:

$L=\frac{b\theta (c_2+c_3+f)\left[2(p-c_1-c_2-c_3-f)-\theta (c_2+c_3+f)\right]}{32(p-\vartheta )}$, $M=\frac{b\theta \left[{(p-c_1)}^2-(1+\theta ){(c_2+c_3+f)}^2\right]}{16(p-\vartheta )(1+\theta )}$, $N=\frac{b\theta \left[{(p-c_1)}^2-(1+\theta ){(c_2+c_3+f)}^2\right]}{8(p-\vartheta )(1+\theta )}$.

From above results, we can see that the increase of the tariff rate significantly affects the decision-making of the transnational supply chain, resulting in the decrease of the logistics service price of the TPIILSP, the FOB price of the supplier, and the order quantity of the manufacturer. The reduction of the manufacturer order quantity means the decrease in the market demand; ultimately, it will lead to the decrease of profits of all parties in the transnational supply chain.

Proposition 2.

(1)${\pi }_s({\omega }^{\ast })=2{\pi }_t({\delta }^{\ast })$, (2)$(1+\theta ){\pi }_s({\omega }^{\ast })=4{\pi }_m(Q^{\ast })$.

Proof of Proposition 2.

 

(1) ${\pi }_s({\omega }^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{8(p-\vartheta )(1+\theta )}=2\times \frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{16(p-\vartheta )(1+\theta )}=2{\pi }_t({\delta }^{\ast }).$ (2) $(1+\theta ){\pi }_s({\omega }^{\ast })=\frac{b{\left[p-c_1-(c_2+c_3+f)(1+\theta )\right]}^2}{8(p-\vartheta )}=4{\pi }_m(Q^{\ast })$.

This completes the proof of Proposition 2. □

Based on Proposition 2, it can be seen from ${\pi }_s({\omega }^{\ast })=2{\pi }_t({\delta }^{\ast })$ that the supplier’s profit is twice that of the TPIILSP. Meanwhile, the profits of the supplier and the manufacturer have the relationship $\eta =\frac{{\pi }_s({\omega }^{\ast })}{{\pi }_m(Q^{\ast })}=\frac{4}{1+\theta }$. From these two relationships, we can see that the transnational supply chain is dominated by the supplier; that is to say, the supplier grasps the initiative of Stackelberg game.

Proposition 3.

In the transnational supply chain, any increase in the manufacturing costs of the manufacturer and the supplier, the transportation cost of the TPIILSP, and the insurance cost of the manufacturer, will lead to the decrease of the manufacturer’s order quantity.

Proof of Proposition 3.

This is easy to prove. Taking the first derivative of $Q^{\ast }$ with respect to $c_1$, $c_2$, $c_3$, $f$ respectively, we have $\partial Q^{\ast }/\partial c_1=-0.25b/(p-\vartheta )<0$, $\partial Q^{\ast }/\partial c_2=-0.25b(1+\theta )/(p-\vartheta )<0$, $\partial Q^{\ast }/\partial c_3=-0.25b(1+\theta )/(p-\vartheta )<0$, $\partial Q^{\ast }/\partial f=-0.25b(1+\theta )/(p-\vartheta )<0$. This means that $Q^{\ast }$ is a concave function of $c_1$, $c_2$, $c_3$, $f$ respectively.

This completes the proof of Proposition 3. □

The implication of Proposition 3 means that the increase of any link cost in the transnational supply chain will lead to internal friction in the supply chain, which weakens the profitability of all stakeholders in the transnational supply chain. Ultimately, it increases the risk of profit loss. In this situation, the supplier who is in the leading position of the supply chain will transfer the risk to the TPIILSP; in turn, the TPIILSP will transfer the risk to the manufacturer. Finally, the manufacturer will reduce the order quantity for the purpose of reducing the risk, thus, the profit of the whole transnational supply chain is reduced.

Proposition 4.

(1) The higher the tariff rate of the importing country, the lower the FOB price set by the supplier; (2) the higher the manufacturing cost of the supplier, the higher the FOB price set by the supplier; (3) the higher the transportation cost of the TPIILSP, the lower the FOB price set by the supplier; (4) the higher the manufacturing cost of the manufacturer, the lower the FOB price set by the supplier.

Proof of Proposition 4.

Taking the first derivative of ${\omega }^{\ast }$ with respect to $\theta$, $c_3$, $c_2$, $c_1$, we have (1) $\partial {\omega }^{\ast }/\partial \theta =-0.5(p-c_1)/{(1+\theta )}^2<0$, (2) $\partial {\omega }^{\ast }/\partial c_3=0.5>0$, (3) $\partial {\omega }^{\ast }/\partial c_2=-1<0$, (4) $\partial {\omega }^{\ast }/\partial c_1=-0.5/(1+\theta )<0$.

This completes the proof of Proposition 4. □

The management significance of Proposition 4 can be explained as follows. First, if the tariff rate of the importing country is increased, then, the importer (i.e., the manufacturer in the transnational supply chain) will reduce the order quantity for the purpose of reducing the cost; in turn, the exporter (i.e., the supplier in the transnational supply chain) will lower the FOB price for the purpose of promoting the export. Second, the increasing manufacturing cost of the supplier requires a higher price to maintain a profit, so the supplier will raise the FOB price. Third, the increase of transportation cost will make up for the loss by increasing the freight rate to the manufacturer, which will lead to the manufacturer reducing the order quantity. In order to promote the increase of the order quantity of the manufacturer, the supplier has to reduce the FOB price. Fourth, the higher the manufacturer’s cost, the more the profit loss to the manufacturer; thus, the manufacturer will reduce the production of products, then reduce the order quantity from the supplier; in turn, the supplier has to reduce the FOB price to induce the manufacturer to increase the order quantity. Therefore, raising the tariff rate in the importing country is an unfavorable policy for both exporters and importers in the international trade. This is a barrier to the transnational supply chain. And then we have Proposition 5.

Proposition 5.

The increase of tariff rate damages the profits of the manufacturer, the TPIILSP, the supplier and the whole transnational supply chain.

Proof of Proposition 5.

It is necessary to find the first derivative of ${\pi }_s({\omega }^{\ast })$, ${\pi }_t({\delta }^{\ast })$, ${\pi }_m(Q^{\ast })$ with respect to $\theta$, it has

$\frac{\partial {\pi }_m(Q^{\ast })}{\partial \theta }=-\frac{b[(f+c_2)+c_3]\left[p-c_1-(f+c_2+c_3)(1+\theta )\right]}{16(p-\vartheta )}<0$,

$\frac{\partial {\pi }_t({\delta }^{\ast })}{\partial \theta }=-\frac{b[(f+c_2)+c_3]\left[p-c_1-(f+c_2+c_3)(1+\theta )\right]}{8(p-\vartheta )(1+\theta )}-\frac{b{\left[p-c_1-(f+c_2+c_3)(1+\theta )\right]}^2}{16(p-\vartheta ){(1+\theta )}^2}<0$,

$\frac{\partial {\pi }_s({\omega }^{\ast })}{\partial \theta }=-\frac{b[(f+c_2)+c_3]\left[p-c_1-(f+c_2+c_3)(1+\theta )\right]}{4(p-\vartheta )(1+\theta )}-\frac{b{\left[p-c_1-(f+c_2+c_3)(1+\theta )\right]}^2}{8(p-\vartheta ){(1+\theta )}^2}<0$.

This completes the proof of Proposition 5. □

This proposition means that when the tariff rate increases, the profits of all members of the transnational supply chain decrease. However, the effects of tariff rate on the decisions of the supplier and the manufacturer are different. Therefore, we have Corollary 1.

Corollary 1.

(1)$\left|\frac{\partial {\omega }^{\ast }}{\partial \theta }\right|>\left|\frac{\partial {\delta }^{\ast }}{\partial \theta }\right|$. (2) $\left|\frac{\partial {\pi }_s({\omega }^{\ast })}{\partial \theta }\right|>\left|\frac{\partial {\pi }_t({\delta }^{\ast })}{\partial \theta }\right|>\left|\frac{\partial {\pi }_m(Q^{\ast })}{\partial \theta }\right|$.

Proof of Corollary 1.

(1) $\left|\frac{\partial {\omega }^{\ast }}{\partial \theta }\right|=\frac{p-c_1}{2{(1+\theta )}^2}>\frac{\partial {\delta }^{\ast }}{\partial \theta }=\frac{p-c_1}{4{(1+\theta )}^2}$. (2) From the proof process of Proposition 5, it is easy to obtain $\left|\frac{\partial {\pi }_s({\omega }^{\ast })}{\partial \theta }\right|>\left|\frac{\partial {\pi }_t({\delta }^{\ast })}{\partial \theta }\right|>\left|\frac{\partial {\pi }_m(Q^{\ast })}{\partial \theta }\right|$.

This completes the proof of Corollary 1. □

The meanings of the Corollary 1 are that the impact of tariff increases on the supplier FOB price is higher than its effect on the TPIILSP logistics service price; on the other hand, the imposition of tariff has the greatest impact on the profit of the supplier, the least impact on manufacturers’ profits, and an intermediate effect on the profit of the TPIILSP.

Having analyzed the impact of tariff on the transnational supply chain under the decentralized decision with three-level game process when the tariff is not zero, in the next section, we further analyze the impact of tariff on the transnational supply chain under alliance decision with two-level game process when the tariff is not zero, then show the effect of reducing the decision level of the game process.

4.3. Two-Level Leader-Follower Game Alliance Decision-Making of Transnational Supply Chain When Tariff Is Not Zero

In Section 4.1, we have already shown that reducing the decision level of supply chain during game decision can improve the supply chain performance. In this part, we further investigate the game decision-making after reducing the game level of the transnational supply chain. Under this situation, when the manufacturer, the TPIILSP, and the supplier construct the transnational supply chain, if reducing the game level of the transnational supply chain, there are two cases. The first is that the manufacturer and the TPIILSP form an alliance (MT alliance); the second is that the supplier and the TPIILSP form an alliance (ST alliance). Below, we formulate these two cases.

• Case I: The manufacturer and the TPIILSP form an alliance (MT alliance)

When the manufacturer and the TPIILSP form an alliance to play a game with the supplier, the unit transportation cost is taken as an exogenous variable to ensure that the profit of the TPIILSP in forming alliance with the manufacturer is not lower than when they do not form an alliance with the manufacturer. Therefore, the profit of the alliance of the manufacture and the TPILLSP is:

$${\pi }_{mt}(Q)=\left[p-c_1-c_2-f(1+\theta )-\theta \delta -\omega (1+\theta )\right]Q-0.5(p-\vartheta )Q^2/b$$

(11)

Proposition 6.

The optimal decision of the supplier and the manufacturer on FOB and order quantity under MT alliance is$({\omega }_{mt}^{\ast \ast },Q_{mt}^{\ast \ast })$.

Proof of Proposition 6.

The alliance of the manufacturing and the TPIILSP plays a Stackelberg game decision with the supplier, which can be solved by backward recursion, and ${\omega }_{mt}^{\ast \ast }$, $Q_{mt}^{\ast \ast }$ can be expressed as

${\omega }_{mt}^{\ast \ast }=\frac{p-c_1-c_2-f(1+\theta )-\theta \delta +c_3(1+\theta )}{2(1+\theta )}$, $Q_{mt}^{\ast \ast }=\frac{b\left[p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )\right]}{2(p-\vartheta )}$.

Bringing ${\omega }_{mt}^{\ast \ast }$, $Q_{mt}^{\ast \ast }$ into Equations (8)–(10), respectively, the following profit functions are available:

$${\pi }_m(Q_{mt}^{\ast \ast })=\frac{b{\left[p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )\right]}^2}{8(p-\vartheta )}+\frac{b{c}_2\left[p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )\right]}{2(p-\vartheta )},$$

(12)

$${\pi }_t(\delta )=\frac{b(\delta -c_2)\left[p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )\right]}{2(p-\vartheta )}$$

(13)

$${\pi }_s({\omega }_{mt}^{\ast \ast })=\frac{b{\left[p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )\right]}^2}{4(1+\theta )(p-\vartheta )}$$

(14)

This completes the proof of Proposition 6. □

Proposition 7.

Under the case of the leader-follower game alliance (case I), i.e., the manufacturer and the TPIILSP form an alliance; the higher the tariff rate of the importing country, the lower the supplier’s FOB price and the lower the order quantity.

Proof of Proposition 7.

It is necessary to find the first derivative of $Q_{mt}^{\ast \ast }$ and ${\omega }_{mt}^{\ast \ast }$ with respect to $\theta$, as follows:

(1) $\partial {\omega }_{mt}^{\ast \ast }/\partial \theta =-0.5\{(f+\delta )(1+\theta )+\left[p-c_1-c_2-f(1+\theta )-\theta \delta \right]\}/{(1+\theta )}^2<0$; and (2) $\partial Q_{mt}^{\ast \ast }/\partial \theta =-0.5b(f+\delta +c_3)/(p-\vartheta )<0$.

This completes the proof of Proposition 7. □

Property 1.

(1) Under the case of the leader-follower game alliance (case I), the FOB price is lower than that under the three-level decentralized decision; (2) the order quantity is greater than that under the three-level decentralized decision.

Proof of Property 1.

 

(1) $\delta >c_2$$\Rightarrow$$-\delta <-c_2\Rightarrow -c_2-\theta \delta$$<-c_2(1+\theta )\Rightarrow$$p-c_1-f(1+\theta )-c_2-\theta \delta <$

$p-c_1-f(1+\theta )-c_2(1+\theta )\Rightarrow {\omega }_{mt}^{\ast \ast }<{\omega }^{\ast }$;

(2) $p-c_1-c_2-f(1+\theta )-\theta \delta -c_3-c_3\theta -\theta \delta +\theta c_2>0$$\Rightarrow$

$p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )-\theta (\delta -c_2)>0$$\Rightarrow$

$(p-c_1-c_2-f(1+\theta )-\theta \delta )-c_3(1+\theta )-\theta (\delta -c_2)>0$$\Rightarrow$$Q_{mt}^{\ast \ast }>Q^{\ast }$.

This completes the proof of Property 1. □

Property 1, as shown above, means that when the manufacturer and the TPIILSP form an alliance to make game decision with the supplier, it reduces the level of the game process, reduces the supplier’s FOB price, increases the order quantity of the manufacturer, and improves the interests of the whole transnational supply chain system.

2.

Case II: The supplier and the TPIILSP form an alliance (ST alliance)

In this case, the supplier and the TPIILSP form an alliance to make a game decision with the manufacturer. In this case, the unit transportation cost is taken as an exogenous variable to ensure that the profit of the TPIILSP in forming alliance with the supplier is not lower than that without forming alliance with the supplier. The profit of the alliance is as follows:

$${\pi }_t(\delta )=\frac{b(\delta -c_2)\left[p-c_1-c_2-f(1+\theta )-\theta \delta -c_3(1+\theta )\right]}{2(p-\vartheta )}$$

(15)

Proposition 8.

The optimal decision of the supplier and the manufacturer on FOB and order quantity under the case of ST alliance is$({\omega }_{st}^{\ast \ast },Q_{st}^{\ast \ast })$.

Proof of Proposition 8.

The alliance of the supplier and the TPIILSP plays a Stackelberg game decision with the manufacturer, which can be solved by reverse recursion:

${\omega }_{st}^{\ast \ast }=\frac{p-c_1-(1+\theta )(2\delta +f-c_2-c_3)}{2(1+\theta )}$, $Q_{st}^{\ast \ast }=\frac{b\left[p-c_1-(1+\theta )(f+c_2+c_3)\right]}{2(p-\vartheta )}$.

By bringing ${\omega }_{st}^{\ast \ast }$ and $Q_{st}^{\ast \ast }$ into Equations (8)–(10), respectively, the following profit functions are available.

$${\pi }_m(Q_{st}^{\ast \ast })=\frac{b{\left[p-c_1-(1+\theta )(f+c_2+c_3)\right]}^2}{8(p-\vartheta )}$$

(16)

$${\pi }_m(Q_{st}^{\ast \ast })=\frac{b{\left[p-c_1-(1+\theta )(f+c_2+c_3)\right]}^2}{8(p-\vartheta )}$$

(17)

$${\pi }_s({\omega }_{st}^{\ast \ast })=\frac{b\left[p-c_1-(1+\theta )(2\delta +f-c_2+c_3)\right]\left[p-c_1-(1+\theta )(f+c_2+c_3)\right]}{4(1+\theta )(p-\vartheta )}$$

(18)

This completes the proof of Proposition 8. □

Property 2.

(1) The supplier’s FOB price under MT alliance is higher than that under ST alliance; (2) the order quantity under MT alliance is less than that under ST alliance.

Proof of Property 2.

(1) ${\omega }_{mt}^{\ast \ast }-{\omega }_{st}^{\ast \ast }=\frac{(2+\theta )(\delta -c_2)}{2(1+\theta )}>0$; (2) $Q_{mt}^{\ast \ast }-Q_{st}^{\ast \ast }=-\frac{b\theta (\delta -c_2)}{2(p-\vartheta )}<0$.

This completes the proof of Property 2. □

Corollary 2.

(1)${\omega }_{st}^{\ast \ast }<{\omega }_{mt}^{\ast \ast }<{\omega }^{\ast }$. (2)$Q^{\ast }<Q_{mt}^{\ast \ast }<Q_{st}^{\ast \ast }$.

Proof of Corollary 2.

(1) Because of the following relationships ${\omega }_{mt}^{\ast \ast }>{\omega }_{st}^{\ast \ast }$, ${\omega }_{mt}^{\ast \ast }<{\omega }^{\ast }$, the inequality ${\omega }_{st}^{\ast \ast }<{\omega }_{mt}^{\ast \ast }<{\omega }^{\ast }$ is available; (2) as $Q_{mt}^{\ast \ast }<Q_{st}^{\ast \ast }$, $Q^{\ast }<Q_{mt}^{\ast \ast }$, we have that $Q^{\ast }<Q_{mt}^{\ast \ast }<Q_{st}^{\ast \ast }$.

This completes the proof of Corollary 2. □

Corollary 3.

(1)${\pi }_m(Q_{st}^{\ast \ast })>{\pi }_m(Q^{\ast })$. (2)${\pi }_s({\omega }_{mt}^{\ast \ast })>{\pi }_s({\omega }_{st}^{\ast \ast })$.

Proof of Corollary 3.

(1) Since ${\pi }_m(Q_{st}^{\ast \ast })-{\pi }_m(Q^{\ast })=\frac{3b{\left[p-c_1-(1+\theta )(f+c_2+c_3)\right]}^2}{32(p-\vartheta )}>0$, then ${\pi }_m(Q_{st}^{\ast \ast })>{\pi }_m(Q^{\ast })$; (2) Put ${\delta }^{\ast }=\frac{p-c_1+(1+\theta )(3c_2-f-c_3)}{4(1+\theta )}$ into ${\pi }_s({\omega }_{mt}^{\ast \ast })$, we can get ${\pi }_s({\omega }_{mt}^{\ast \ast })=\frac{b{\left[(p-c_1)-(1+\theta )(f+c_2+c_3)\right]}^2}{8(1+\theta )(p-\vartheta )}\frac{{(\sqrt{16}+\sqrt{9}\theta )}^2}{{(\sqrt{8}+\sqrt{8}\theta )}^2}>\frac{b{\left[p-c_1-(1+\theta )(f+c_2+c_3)\right]}^2}{8(1+\theta )(p-\vartheta )}$, then ${\pi }_s({\omega }_{mt}^{\ast \ast })>{\pi }_s({\omega }_{st}^{\ast \ast })={\pi }_s({\omega }^{\ast })$.

This completes the proof of Corollary 3. □

4.4. Pareto Improvement Based on Revenue Sharing and Cost Sharing for Three-Level Decentralized Game Decision of the Transnational Supply Chain

Because of the three-level decentralized game decision; i.e., the manufacturer, the supplier and the TPIILSP independently making their own decisions, actors cannot maximize the benefit of the transnational supply chain. Therefore, it is necessary to adopt appropriate strategies to coordinate the transnational supply chain and improve the supply chain. This is because Pareto improvement can improve the performance of the entire decision system without weakening any of all participators. This paper proposes a coordination mechanism—revenue sharing and cost sharing—to induce Pareto improvement for the transnational supply chain.

Revenue sharing means that the manufacturer in the supply chain shares her revenue with the supplier; that is, the supplier can share some of the revenue of the manufacturer. Cost sharing means that the manufacturer helps the supplier to bear part of the cost of the supplier.

Under the strategy of revenue sharing and cost sharing, we assume that the manufacturer shares R proportion of sales revenue and residual value revenue, bears $1-\tau$ proportion of transportation cost, and bears $\lambda$ proportion of tariff cost. The supplier shares $1-R$ proportion of sales income and residual value income, bears $\tau$ proportion of transportation cost, and bears $1-\lambda$ proportion of tariff cost. Under this strategy, the manufacturer’s profit is as follows:

$${\pi }_m(Q)=[Rp-\omega -c_1-f-(1-\tau )\delta -\lambda \theta (\omega +\delta +f)]Q-0.5R(p-\vartheta )Q^2/b$$

(19)

The supplier’s profit is:

$${\pi }_s(\omega )=[(1-R)p+\omega -c_3-\tau \delta -\theta (1-\lambda )(\omega +\delta +f)]Q-0.5(1-R)(p-\vartheta )Q^2/b$$

(20)

Set $E=Rp-c_1-f-\lambda \theta f$, $F=(1-\tau +\lambda \theta )$, $G=(1-R)p-c_3-(1-\lambda )\theta f$, $H=1-(1-\lambda )\theta$, $I=\tau +(1-\lambda )\theta$, $J=G-I\frac{E+c_{2}F}{2F}-\frac{(1-R)(E-c_{2}F)}{4R}$, $K=H+\frac{I(1+\lambda \theta )}{2F}+\frac{(1-R)(1+\lambda \theta )}{4R}$.

By using the method of reverse recursion, we can get the following results:

$$Q^{\ast \ast \ast }=\frac{bKE-c_{2}bKF+Jb(1+\lambda \theta )}{4R(p-\vartheta )K}$$

(21)

$${\delta }^{\ast \ast \ast }=\frac{KE+3c_{2}KF+J(1+\lambda \theta )}{4KF}$$

(22)

$${\omega }^{\ast \ast \ast }=\frac{KE-c_{2}KF-J(1+\lambda \theta )}{2K(1+\lambda \theta )}$$

(23)

By taking Equations (21)–(23) into Equations (3), (19), (20) respectively, we obtain the following results:

$${\pi }_s({\omega }^{\ast \ast \ast })=\frac{b{\left[KE-c_{2}KF+J(1+\lambda \theta )\right]}^2}{8KR(1+\lambda \theta )(p-\vartheta )}$$

(24)

$${\pi }_t({\delta }^{\ast \ast \ast })=\frac{b{\left[KE-c_{2}KF+J(1+\lambda \theta )\right]}^2}{16K^{2}FR(p-\vartheta )}$$

(25)

$${\pi }_m(Q^{\ast \ast \ast })=\frac{b{\left[KE-c_{2}KF+J(1+\lambda \theta )\right]}^2}{32K^{2}R(p-\vartheta )}$$

(26)

Due to the complexity of $Q^{\ast \ast \ast }$, ${\omega }^{\ast \ast \ast }$, ${\delta }^{\ast \ast \ast }$, the impacts of the tariff rate $\theta$, revenue sharing ratio $R$, transportation cost sharing ratio $\tau$, and tariff sharing ratio $\lambda$ on the $Q^{\ast \ast \ast }$, ${\omega }^{\ast \ast \ast }$, ${\delta }^{\ast \ast \ast }$, ${\pi }_s({\omega }^{\ast \ast \ast })$, ${\pi }_t({\delta }^{\ast \ast \ast })$ and ${\pi }_m(Q^{\ast \ast \ast })$ will be analyzed in the numerical analysis.

5. Numerical Analysis

When the tariff rate is zero, we set $p=70$, $c_1=7$, $c_2=5$, $c_3=8$, $f=2$, $\vartheta =10$, $b=480$. By applying the calculation formulas in Section 4.1, the following results are obtained. Under the centralized decision, the order quantity of the manufacturer is $Q_c^{\ast }=384$; the profit of the transnational supply chain is 9216. Under the three-level decentralized decision, ${\omega }_d^{\ast }=32$, ${\delta }_d^{\ast }=17$, $Q_d^{\ast }=96$, ${\pi }_s({\omega }_d^{\ast })=2304$, ${\pi }_t({\delta }_d^{\ast })=1152$, ${\pi }_m(Q_d^{\ast })=576$, the profit of the transnational supply chain is 4032. The results show that the profit of the transnational supply chain under the decentralized decision is much lower than that under the centralized decision. Under the alliance decision (i.e., the manufacturer and the TPIILSP form an alliance), ${\omega }_d^{\ast \ast }=32$, $Q_d^{\ast \ast }=192$. It is seen that ${\omega }_d^{\ast \ast }={\omega }_d^{\ast }$, $Q_c^{\ast }=2Q_d^{\ast \ast }=4Q_d^{\ast }$. This validates the conclusion in Section 4.1 that reducing the level of Stackelberg game can increase the order quantity and promote the Pareto improvement of the supply chain.

When the tariff rate is not zero, considering the tariff rates are different for different countries and different products, normally the tariff rate is less than 10%. When one country increases the tariff rate, the tariff rate can be 20% or even more; here, we set $\theta =0.25$ (25%), then by applying formulas in Section 4.2 to solve the three-level decentralized decision model, we obtain the following results ${\omega }^{\ast }=25.70$, ${\delta }^{\ast }=13.85$, $Q^{\ast }=89$. The profits of the supplier, the TPIILSP and the manufacturer are ${\pi }_s({\omega }^{\ast })=1566.45$, ${\pi }_t({\delta }^{\ast })=783.23$, ${\pi }_m(Q^{\ast })=489.52$. The profit of the transnational supply chain is 2839.19. Compared with the three-level decentralized decision when the tariff is zero, the existence of the tariff will reduce the FOB price of the supplier, the transportation price of the TPIILSP, and the order quantity of the manufacturer. The result data also shows that the increase of tariff rate leads to the decrease of the manufacturer’s profit by 86.48, the TPIILSP‘s profit by 368.78, and the supplier’s profit by 737.55. This shows that the existence of tariffs in the three-level decentralized decision weakens the interests of all parties and the whole transnational supply chain. This validates the conclusion in Section 4.2 that tariffs are an unfavorable factor for all parties in the transnational supply chain.

In the following section, we further illustrate, in detail, the impacts of some important parameters on decisions, and summarize some implications.

• Impacts of tariff rate on profits in three-level decentralized decision

Figure 1 shows how the profits of the supplier, the TPIILSP, and the manufacturer vary with the change of tariff rate under the three-level decentralized decision. It shows that with the increase of tariff rates, the profits of all parties in the transnational supply chain decrease, but the impacts of the tariff on the profits of all parties in the transnational supply chain are different. The impact on the supplier is the largest, the profit of the supplier declines rapidly with the increase of tariff rate, which also leads to the decrease of the proportion of the suppliers’ profit in the profit of the transnational supply chain. On the surface, the increase of the tariff rate weakens the role of the supplier in the transnational supply chain. The increase of the tariff rate has the least influence on the manufacturer. For all partners, with the increase of the tariff rate, the impacts of tariffs on the profits tend to slow down. The profit margins of all parties are also reduced with the increase in the tariff rate.

It can be seen from Figure 2 that the proportion of the profit of the TPIILSP in the profit of the transnational supply chain also decreases with the increase of the tariff rate, but the proportion of the profit of the manufacturer increases with the increase of the tariff rate, which means that the increase of the tariff rate will enhance the role position of the manufacturer in the transnational supply chain.

• Impacts of tariff rate on the MT alliance and ST alliance decisions

Table 1. Effects of tariff rate on order quantity and FOB price in MT and ST alliance decisions.

${\mathit{\theta }}^{\ast }$	${\mathit{\delta }}^{\ast }$	${\mathit{Q}}^{\ast }$	${\mathit{Q}}_{\mathit{m}\mathit{t}}^{\ast \ast }$	${\mathit{Q}}_{\mathit{s}\mathit{t}}^{\ast \ast }$	${\mathit{\omega }}^{\ast }$	${\mathit{\omega }}_{\mathit{m}\mathit{t}}^{\ast \ast }$	${\mathit{\omega }}_{\mathit{s}\mathit{t}}^{\ast \ast }$
0.21	14.27	90	172	325	26.53	25.73	17.27
0.22	14.16	89	171	325	26.32	25.49	17.16
0.23	14.05	89	170	326	26.11	25.26	17.05
0.24	13.95	89	169	326	25.90	25.04	16.95
0.25	13.85	89	168	327	25.70	24.82	16.85
0.26	13.75	88	167	328	25.50	24.60	16.75
0.27	13.65	88	166	328	25.30	24.38	16.65
0.28	13.55	88	166	329	25.11	24.17	16.55
0.29	13.46	87	165	329	24.92	23.97	16.46

shows the effects of the tariff rate on the MI alliance and SI alliance decisions. From Table 1, it is obvious that the FOB price of the supplier in the case of the MT alliance decision is higher than that in the case of ST alliance decision. The manufacturer’s order quantity under ST alliance decision is higher than that under the MT alliance decision, i.e., $Q^{\ast }<Q_{mt}^{\ast \ast }<Q_{st}^{\ast \ast }$, ${\omega }_{st}^{\ast \ast }<{\omega }_{mt}^{\ast \ast }<{\omega }^{\ast }$. Under ST alliance decision, with the increase of tariff rate, the order quantity of the manufacturer increases, but it decreases under the MT alliance decision. With the increase of tariff rates, the FOB price of the supplier under two types of alliance decision-making cases decreases. However, under the ST alliance decision, i.e., the manufacturer and TPIILSP form an alliance, due to the reduction of the game level, the supplier slightly reduces the FOB price, but the manufacturer’s order quantity increases significantly, resulting in a significant increase in the profits of the supplier and the TPIILSP.

Table 2. Impacts of tariff rate on profits of MT alliance decision, ST alliance decision, and three-level decentralized decision.

	Three-Level Decentralized Decision			MT Alliance Decision			ST Alliance Decision
$\mathit{\theta }$	${\mathit{\pi }}_{\mathit{s}}({\mathit{\omega }}^{\ast })$	${\mathit{\pi }}_{\mathit{t}}({\mathit{\delta }}^{\ast })$	${\mathit{\pi }}_{\mathit{m}}({\mathit{Q}}^{\ast })$	${\mathit{\pi }}_{\mathit{s}}({\mathit{\omega }}_{\mathit{m}\mathit{t}}^{\ast \ast })$	${\mathit{\pi }}_{\mathit{t}}({\mathit{Q}}_{\mathit{m}\mathit{t}}^{\ast \ast })$	${\mathit{\pi }}_{\mathit{m}}({\mathit{Q}}_{\mathit{m}\mathit{t}}^{\ast \ast })$	${\mathit{\pi }}_{\mathit{s}}({\mathit{\omega }}_{\mathit{s}\mathit{t}}^{\ast \ast })$	${\mathit{\pi }}_{\mathit{t}}({\mathit{Q}}_{\mathit{s}\mathit{t}}^{\ast \ast })$	${\mathit{\pi }}_{\mathit{m}}({\mathit{Q}}_{\mathit{s}\mathit{t}}^{\ast \ast })$
0.21	1662.42	831.21	502.88	3042.57	1590.29	250.47	3007.92	3007.92	693.83
0.22	1637.78	818.89	499.52	2986.88	1563.94	258.05	2978.78	2978.78	658.53
0.23	1613.58	806.79	496.18	2932.48	1538.15	265.33	2950.08	2950.08	623.09
0.24	1589.81	794.90	492.84	2879.35	1512.88	272.32	2921.81	2921.81	587.52
0.25	1566.45	783.23	489.52	2827.44	1488.13	279.02	2893.95	2893.95	551.81
0.26	1543.50	771.75	486.20	2776.72	1463.88	285.46	2866.50	2866.50	515.97
0.27	1520.95	760.47	482.90	2727.14	1440.11	291.62	2839.45	2839.45	479.99
0.28	1498.78	749.39	479.61	2678.67	1416.82	297.53	2812.78	2812.78	443.88
0.29	1476.99	738.50	476.33	2631.28	1393.98	303.19	2786.49	2786.49	407.63

further illustrates the differences of the impacts of tariffs on profits among the MT alliance decision, TS alliance decisions, and three-level-decentralized decisions. In the case of the MT alliance decision, the manufacturer’s profit increases with the increase of tariff rates, but its profit is lower than that in the three-level decentralized decision. On the other hand, the profits of the supplier and the TPIILSP are higher than those in the three-level decentralized decision. The total profit of the MT alliance decision is higher than that in the three-level decentralized decision situation. In the case of the ST alliance decision, we can know that all profits of the partners in the supply chain decrease with the increase of tariff rate, and the supplier’s profit is the same as the TPIILSP’s profit. The supplier’s and the TPIILSP’s profits in the case of the ST alliance decision are higher than those in the three-level decentralized decision. The profit of the manufacturer is higher than that in the three-level decentralized decision when the tariff rate is at a relatively lower value; with the increase of the tariff rate, when tariff rate increases to certain value, the profit of the manufacturer in the case of the ST alliance decision is higher than that in the three-level decentralized decision. Meanwhile, we find that the ST alliance decision can obtain more total profit from the transnational supply chain than the MT alliance decision and three-level decentralized decision. This shows that in order to reduce the negative influence of tariffs on the transnational supply chain, as the tariff rate increases, the supplier and the TPIILSP form an alliance to make decisions with the manufacturer, which will be beneficial to all partners and the whole supply chain.

3.

Effect of tariff cost sharing

When there is only tariff cost sharing, i.e., $R=1$, $\tau =0$, $\lambda =0.7$, applying the calculation formulas of the three-level game decision model in Section 4.4, we can get $Q^{\ast \ast \ast }=84$, ${\omega }^{\ast \ast \ast }=28.65$, ${\delta }^{\ast \ast \ast }=13.99$, ${\pi }_s({\omega }^{\ast \ast \ast })=1461.11$, ${\pi }_t({\delta }^{\ast \ast \ast })=759.02$, ${\pi }_m(Q^{\ast \ast \ast })=445.92$. The profit of the transnational supply chain is 2666.05.

Figure 3 shows that the higher the tariff cost sharing proportion borne by the manufacturer, the lower the FOB price $\delta$ of the supplier, and the lower the unit transport price of the TPIILSP, but the unit transport price is less insensitive to the tariff cost sharing proportion than the FOB price.

Figure 4 shows the impact of the tariff cost sharing proportion of the manufacturer on the profits of partners and the total profit of the transnational supply chain. It can be seen that the higher the proportion of tariff cost sharing borne by the manufacturer, the higher the profits of all parties and the total profit of the transnational supply chain. This result indicates that in order to reduce the negative influence of tariffs on the transnational supply chain, the manufacturer’s bearing certain tariff cost will help improve the performance of the whole supply chain performance. Although tariff cost sharing has positive effects on both the supplier and the manufacturer, in the long run, tariff rates negatively affect the trade. Since the manufacturer ultimately transfers the tariff cost to final consumers, i.e., by raising the sales prices of the imported products in the market, then, the manufacturer will lose some consumers. Therefore, in the short run, tariff cost sharing can improve the supply chain, but in the long run, with the increase of tariff rates, the negative effect of tariffs will emerge for the supply chain.

4.

Effect of transportation cost sharing

Table 3. Influences of transportation cost sharing on decision variables and profits.

$\mathit{\tau }$	${\mathit{Q}}^{\ast \ast \ast }$	${\mathit{\delta }}^{\ast \ast \ast }$	${\mathit{\omega }}^{\ast \ast \ast }$	${\mathit{\pi }}_{\mathit{s}}({\mathit{\omega }}^{\ast \ast \ast })$	${\mathit{\pi }}_{\mathit{t}}({\mathit{\delta }}^{\ast \ast \ast })$	${\mathit{\pi }}_{\mathit{m}}({\mathit{Q}}^{\ast \ast \ast })$	Supply Chain
0.05	86	13.97	26.37	1522.38	772.78	463.67	2758.84
0.10	84	14.10	27.06	1477.32	761.51	437.87	2676.70
0.15	81	14.23	27.76	1431.22	749.33	412.13	2592.69
0.20	79	14.36	28.47	1384.03	736.19	386.50	2506.72
0.25	76	14.50	29.20	1335.70	722.00	361.00	2418.70
0.30	73	14.64	29.94	1286.16	706.68	335.67	2328.52
0.35	70	14.79	30.70	1235.37	690.15	310.57	2236.08
0.40	68	14.94	31.48	1183.24	672.29	285.73	2141.26
0.45	65	15.10	32.27	1129.71	653.01	261.21	2043.93
0.50	62	15.26	33.08	1074.71	632.19	237.07	1943.97
0.55	58	15.43	33.91	1018.16	609.68	213.39	1841.23

shows the impact of transportation sharing on the decision variables and profits. When $R=1$, $\tau =0.35$, $\lambda =1$, we can get $Q^{\ast \ast \ast }=70$, ${\delta }^{\ast \ast \ast }=14.79$, ${\omega }^{\ast \ast \ast }=30.70$, ${\pi }_s({\omega }^{\ast \ast \ast })=1235.37$, ${\pi }_t({\delta }^{\ast \ast \ast })=690.15$, ${\pi }_m(Q^{\ast \ast \ast })=310.57$. The total profit of the supply chain is 2236.08. It can be seen from Table 3 that the higher the transportation cost borne by the supplier, the higher the FOB price of the supplier and the transportation service price of the TPIILSP, the lower the order quantity of the manufacturer, and the lower all profits. This is because with the increase of the transportation cost shared by the supplier, in order to reduce the loss caused by transportation costs, the supplier will increase the FOB price, which leads to the reduction of the manufacturers’ orders and the reduction of the profits of all stakeholders and the transnational supply chain. The above results show that transportation cost sharing alone cannot improve the transnational supply chain but rather worsens it. The more transportation cost shared by the supplier, the more unfavorable to the improvement of the profits of all parties and the whole transnational supply chain.

5.

Effect of revenue sharing

Table 4. Impacts of revenue sharing on decision variables and profits.

$\mathit{R}$	${\mathit{Q}}^{\ast \ast \ast }$	${\mathit{\delta }}^{\ast \ast \ast }$	${\mathit{\omega }}^{\ast \ast \ast }$	${\mathit{\pi }}_{\mathit{s}}({\mathit{\omega }}^{\ast \ast \ast })$	${\mathit{\pi }}_{\mathit{t}}({\mathit{\delta }}^{\ast \ast \ast })$	${\mathit{\pi }}_{\mathit{m}}({\mathit{Q}}^{\ast \ast \ast })$	Supply Chain
0.35	201	12.04	−7.08	4475.14	1415.86	884.91	6775.92
0.40	186	12.46	−5.11	4081.79	1389.54	868.47	6339.80
0.45	173	12.80	−2.99	3733.89	1350.95	844.35	5929.19
0.50	162	13.08	−0.75	3424.30	1304.50	815.31	5544.11
0.5	151	13.30	1.60	3147.31	1253.23	783.27	5183.81
0.60	141	13.48	4.03	2898.28	1199.29	749.55	4847.12
0.65	133	13.62	6.55	2673.40	1144.17	715.11	4532.68
0.70	125	13.73	9.14	2469.54	1088.93	680.58	4239.06
0.75	117	13.81	11.78	2284.09	1034.31	646.44	3964.84
0.80	111	13.86	14.48	2114.84	980.80	613.00	3708.63
0.85	105	13.89	17.23	1959.93	928.75	580.47	3469.14
0.90	99	13.89	20.02	1817.77	878.39	548.99	3245.15
0.95	93	13.88	22.84	1687.00	829.85	518.66	3035.51
0.98	90	13.86	24.55	1613.51	801.64	501.03	2916.19

shows the effects of revenue sharing on decision variables and profits.

When $R=0.65$, $\tau =0$, $\lambda =1$, we can get $Q^{\ast \ast \ast }=133$, ${\omega }^{\ast \ast \ast }=6.55$, ${\delta }^{\ast \ast \ast }=13.62$, ${\pi }_s({\omega }^{\ast \ast \ast })=2673.4$, ${\pi }_t({\delta }^{\ast \ast \ast })=1144.17$, ${\pi }_m(Q^{\ast \ast \ast })=715.11$. The total profit of the supply chain is 4532.68. The results show that with the increase of the revenue sharing proportion of the supplier, i.e., the decrease of the manufacturer’s sharing rate (R), all partners’ profits increase. The results reveal that the manufacturer gives more benefits to the supplier in the supply chain; the supplier will lower the FOB price, the TPIILSP will reduce the unit freight rate, and the manufacturer will increase the order quantity. Therefore, we can conclude that revenue sharing can improve the performance of the whole transnational supply chain. This is because the more revenue the supplier obtains from the manufacturer, the more incentive the supplier has to reduce the FOB price. Although the FOB price is reduced, the lower price will promote the manufacturer to order a greater quantity, thus increasing the total demand. Therefore, revenue sharing can improve the supply chain performance.

It is worth noting that in Table 4, when R <= 0.5, the FOB price of the supplier is negative, which has no practical significance. This means that the revenue sharing rate of the manufacturer cannot be too low, that is, the supplier cannot share too much revenue from the manufacturer.

6. Conclusions

Globalization makes the operations of transnational supply chains more complex, and facing higher risks. During the last decade, different countries’ trade policies, especially the tariff policy, have seriously affected the operations of transnational supply chains. This paper analyzes the impact of tariffs on the partners in a transnational supply chain composed of a supplier, a TPIILSP, and a manufacturer. Three types of decision models are established; namely, the decision-making model when the tariff is zero, the three-level decentralized decision model when the tariff is not zero, and the two-level leader-follower alliance (MT and ST alliances) decision models when the tariff is not zero. The results show that the alliance game can reduce the level of the game and improve the performance of the transnational supply chain. The increasing tariff rate will reduce the order quantity of the manufacturer, the profits of all parties, and the overall profit of the transnational supply chain. In order to improve the transnational supply chain performance, we investigate the effects of revenue sharing and cost sharing strategies. The results show that sharing tariff costs between the supplier and the manufacturer can improve the performance of the supply chain, but sharing transportation costs alone cannot improve the performance of the whole transnational supply chain, and can even worsen the performance of the transnational supply chain. Revenue sharing can improve the performance of transnational supply chains more than tariff cost sharing or transportation cost sharing.

Our study has following important implications for theoretical research and practitioners.

6.1. Implications for Theoretical Implications

Theoretically, a transnational supply chain is one kind special global supply chain. Many theoretical studies on supply chain decision and coordination have been focused on the local supply chains inside one country, the complexity of global supply chain environment, and other global environment factors seriously impact the operations of supply chains, while the theoretical development of supply chain coordination mechanisms is not enough for the global supply chain. This paper can provide some new perspectives in developing transnational supply chain decisions and coordination, and there is important reference value for other researchers studying transnational supply chains.

6.2. Implications for Practitioners

• Tariffs have a negative impact on all members of the transnational supply chain, which will change their role positions in the supply chain. In order to reduce the adverse impact of tariffs, cooperation between the members of transnational supply chains should be strengthened and multi-level game behaviors should be reduced.
• Our study shows that the alliance formed by the supplier and the TPIILSP is superior to the alliance formed by the manufacturer and the TPIILSP MT in improving the performance of the whole supply chain. Therefore, from the perspective of the whole supply chain, we suggest the supplier and the TPIILSP strengthen their cooperation.
• In order to reduce the negative influence of tariffs, the manufacturer should take more actions to cooperate with the supplier, such as helping the supplier undertake some proportion of tariff cost and sharing the benefits with the supplier. These actions will be helpful for improving the whole supply chain.
• Our conclusions have important practical senses for SMEs (small-medium sized enterprises), since SMEs have more vulnerability in international trade friction of tariff barriers, reducing the impact of tariff risk and improving the supply chain coordination is important for SMEs. Therefore, our research conclusions have important value for SMEs.

This paper has some limitations. For example, this study considers only the impact of tariffs in the supply chain. In fact, many countries often use subsidies to weaken the negative impact of tariffs. In this case, the decision of the transnational supply chain is different. Therefore, the future research can consider the impact of tariffs and subsidies with the participation of third-party international logistics service providers, which will yield more interesting results.