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# Channel structures of transnational supply chains

• *Corresponding author: Hui Yu

The study is supported in part by the National Natural Science Foundation of China (Project No. 72172019, 71872021) and the Fundamental Research Funds for the Central Universities (Project No. 2021CDJSKJC11)

• There are two fundamental and important problems for enterprises with an existing domestic supply chain: whether to build a new transnational supply chain and which channel should be chosen to build the new transnational supply chain. In this paper, we assume that the enterprise's existing domestic supply chain structure and the transnational supply chain structure to be considered are likely to be distributor channels and direct sales channels. By considering different channel scenarios at home and abroad, we establish a robust newsvendor model with profit maximization motivation to study the above-mentioned problems. We find that exchange rate risk and foreign price are key factors that determine whether an enterprise chooses to build a new transnational supply chain. However, the channel preference of enterprises when constructing transnational supply chains depends not only on exchange rate risk and foreign price, but also on the drive of foreign demand attributes (demand scale and demand uncertainty). We also find that enterprises have a humanitarian "principle of equality" when considering the construction of transnational supply chains $-$ the operational characteristics and channel structure of domestic supply chains will not affect whether and how enterprises build a new transnational supply chain.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

• Figure 1.  The enterprise's local supply chain representation under distributor channels and direct sales channels

Figure 2.  The enterprise's transnational supply chain representation in four different domestic and foreign channels

Figure 3.  The supply quantity and profit of the enterprise as a function of $w_{1 }$ (Note. $c = 28, s = 20, p_{1 } = 50, \mu_{1 } = 800$, and $\sigma_{1 } = 500$)

Figure 4.  Comparison of supply strategies in home markets at different selling pric (Note. $w_{1 } = 35, c = 28, s = 20, \mu_{1} = 1000$, and $\sigma_{1} = 300$)

Figure 5.  Comparison of supply quantity in host markets at different exchange rates (Note. $p_{2 } = 40, w_{2 } = 30, c = 28, s = 20, \mu_{2 } = 800$, and $\sigma_{2 } = 200$)

Figure 6.  Channel choice under different trade-offs

Figure 7.  The two functions $g(x)$ and $\pi_{d1}^{D}(q_{1}^{D}, x)$ will have two touch points at most (a total of two cases)

Table 1.  Parameters and decisions variables

 Notation Description $\theta$ The current exchange rate of the enterprise's country at the time of signing the wholesale price contract, i.e., one unit of the home currency is equal to $\theta$ units of the host country currency $\Delta\theta$ The exchange rate variation, $\Delta\theta \in (-\theta, \infty)$ $q_{1 }^{D}$, $q_{1 }^{S}$ The home market supply quantity for Models D and S, respectively, decision variables $q_{1 }^{DD}$, $q_{1 }^{DS}$, $q_{1 }^{SD}$, $q_{1 }^{SS}$ Home country supply quantity for Models DD, DS, SD, and SS respectively, decision variables $q_{2 }^{DD}$, $q_{2 }^{DS}$, $q_{2 }^{SD}$, $q_{2 }^{SS}$ Host country supply quantity for Models DD, DS, SD, and SS respectively, decision variables $p_{1 }$, $p_{2 }$ The retail prices per unit of product, expressed in the currency of the country in which the enterprise is located $w_{1 }$, $w_{2 }$ The enterprise's wholesale prices per unit of product, expressed in the currency of the country in which the enterprise is located, $p_{i}>w_{i}$ ($i=1, 2$) $c$ The enterprise's production cost per unit of product, expressed in the currency of the country in which the enterprise is located, $w_{i}\geq c$ ($i=1, 2$) $s$ The residual value per unit of product, expressed in the currency of the country in which the enterprise is located, $s Table 2. Optimal supply strategy for home market and host market  Model Home market supply quantity Home market supply conditions Host market supply quantity Host market supply conditions D$ \mu_{1 }+\frac{\sigma_{1 }}{2}\left(\sqrt{\frac{p_{1 }-w_{1 }}{w_{1 }-s}}-\sqrt{\frac{w_{1 }-s}{p_{1 }-w_{1 }}}\right)  (\frac{\sigma_{1}}{\mu_{1}})^{2}<\frac{p_{1}-w_{1}}{w_{1}-s}  -  - $S$ \mu_{1 }+\frac{\sigma_{1 }}{2}\left(\sqrt{\frac{p_{1 }-c}{c-s}}-\sqrt{\frac{c-s}{p_{1 }-c}}\right)  (\frac{\sigma_{1}}{\mu_{1}})^{2}<\frac{p_{1}-c}{c-s}  -  - $DD$ \mu_{1 }+\frac{\sigma_{1 }}{2}\left(\sqrt{\frac{p_{1 }-w_{1 }}{w_{1 }-s}}-\sqrt{\frac{w_{1 }-s}{p_{1 }-w_{1 }}}\right)  (\frac{\sigma_{1}}{\mu_{1}})^{2}<\frac{p_{1}-w_{1}}{w_{1}-s}  \mu_{2 }+\frac{\sigma_{2 }}{2}\left(\sqrt{\frac{p_{2 }-w_{2 }}{w_{2 }-s}}-\sqrt{\frac{w_{2 }-s}{p_{2 }-w_{2 }}}\right)  (\frac{\sigma_{2}}{\mu_{2}})^{2}<\frac{p_{2}-w_{2}}{w_{2}-s} $DS$ \mu_{1 }+\frac{\sigma_{1 }}{2}\left(\sqrt{\frac{p_{1 }-w_{1 }}{w_{1 }-s}}-\sqrt{\frac{w_{1 }-s}{p_{1 }-w_{1 }}}\right)  (\frac{\sigma_{1}}{\mu_{1}})^{2}<\frac{p_{1}-w_{1}}{w_{1}-s}  \mu_{2 }+\frac{\sigma_{2 }}{2}\left(\sqrt{\frac{p_{2 }\theta-c(\theta + \Delta \theta)}{(c-s)(\theta + \Delta \theta)}}-\sqrt{\frac{(c-s)(\theta + \Delta \theta)}{p_{2 }\theta-c(\theta + \Delta \theta)}}\right)  (\frac{\sigma_{2}}{\mu_{2}})^{2}<\frac{p_{2}\theta-c(\theta+\Delta \theta)}{(c-s)(\theta+\Delta \theta)} $SD$ \mu_{1 }+\frac{\sigma_{1 }}{2}\left(\sqrt{\frac{p_{1 }-c}{c-s}}-\sqrt{\frac{c-s}{p_{1 }-c}}\right)  (\frac{\sigma_{1}}{\mu_{1}})^{2}<\frac{p_{1}-c}{c-s}  \mu_{2 }+\frac{\sigma_{2 }}{2}\left(\sqrt{\frac{p_{2 }-w_{2 }}{w_{2 }-s}}-\sqrt{\frac{w_{2 }-s}{p_{2 }-w_{2 }}}\right)  (\frac{\sigma_{2}}{\mu_{2}})^{2}<\frac{p_{2}-w_{2}}{w_{2}-s} $SS$ \mu_{1 }+\frac{\sigma_{1 }}{2}\left(\sqrt{\frac{p_{1 }-c}{c-s}}-\sqrt{\frac{c-s}{p_{1 }-c}}\right)  (\frac{\sigma_{1}}{\mu_{1}})^{2}<\frac{p_{1}-c}{c-s}  \mu_{2 }+\frac{\sigma_{2 }}{2}\left(\sqrt{\frac{p_{2 }\theta-c(\theta + \Delta \theta)}{(c-s)(\theta + \Delta \theta)}}-\sqrt{\frac{(c-s)(\theta + \Delta \theta)}{p_{2 }\theta-c(\theta + \Delta \theta)}}\right)  (\frac{\sigma_{2}}{\mu_{2}})^{2}<\frac{p_{2}\theta-c(\theta+\Delta \theta)}{(c-s)(\theta+\Delta \theta)} $Table 3. Factors that enterprises weigh when deciding whether to build transnational supply chains  Decide Exchange rate risk ($ \Delta \theta $) Foreign market prices ($ p_{2} $) Build Low High/Moderate Not build High Low Table 4. Factors that enterprises weigh when deciding the channel choice of transnational supply chain  Channel choice Exchange rate risk ($ \Delta \theta $) Foreign market prices ($ p_{2} $) Foreign demand scale ($ \mu_{2} $) Foreign demand uncertainty ($ \sigma_{2} $) DD (or SD) Low Moderate Large High DS (or SS) Low High Small Low Note. We divide foreign market prices into high, moderate, and low levels, divide exchange rate risk and foreign demand uncertainty into high and low levels, and divide foreign demand scale into large and small levels. The division of these levels is only convenient for understanding and elaboration, so it lacks accuracy. Table 5. The influence of domestic and foreign markets on different decisions of enterprises  Model choice Operational characteristics of domestic supply chain Channel structure of domestic supply chain Operational characteristics of foreign supply chain Exchange rate risk D (or S)$ \times  \times $√ √ DD (or SD)$ \times  \times $√ √ DS (or SS)$ \times  \times $√ √ Note. The symbol "$\times$" means no impact, and the symbol "$√\$" means yes.

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