Frugal innovation in supply chain cooperation considering e-retailer’s platform value

Abstract

E-retailers have recently paid close attention to frugal innovation in their supply chains. However, there are few studies on frugal innovation considering the e-retailer’s platform value raised by the increase in the platform user scale. Motivated by industrial practice, we consider a supply chain consisting of an e-retailer and a manufacturer in the context of frugal innovation, where the platform value of the retailer is characterized by Metcalfe’s law. We use game models to investigate the frugal product price and optimal degree of frugality decisions for the centralized, decentralized, retailer-led revenue-sharing contract and bargaining revenue-sharing contract scenarios. Our results indicate that the bargaining revenue-sharing contract can improve the frugal degree of the development-intensive frugal product (DIFP), while the frugal degree of the marginal cost-intensive frugal product (MIFP) cannot be improved by cooperation in the supply chain. We then compare the supply chain profit, the platform value of the retailer and the profit of the manufacturer in different scenarios. The results show that the centralized scenario is the optimal scenario where the platform retailer implements vertical integration strategy. Otherwise, establishing strategic partnership through the bargaining revenue-sharing contract is suboptimal for both the platform retailer and the manufacturer.

Appendices

A Proof of Proposition 2

As for the DIFP, we first compare the optimal degree of frugality under revenue-sharing contract and centralized model. Note that the condition $a, \beta \ne 0, 4r(1-\lambda ^2)-\beta ^2\ne 0$ and $8r(1-\lambda ^2)-\beta ^2\ne 0$ implies that $a, \beta \ne 0, 4r-\frac{\beta ^2}{1-\lambda ^2}\ne 0$ and $8r-\frac{\beta ^2}{1-\lambda ^2}\ne 0$. Since $\frac{a\beta }{4r(1-\lambda ^2)-\beta ^2}>\frac{a\beta }{2[4r(1-\lambda ^2)-\beta ^2]}=\frac{a\beta }{8r(1-\lambda ^2)-2\beta ^2}>\frac{a\beta }{8r(1-\lambda ^2)-\beta ^2}$, we can obtain that $\alpha (B)>\alpha (RS)>\alpha (D)$.

Then, we should prove that $\alpha (B)>\alpha (BS)>\alpha (RS)$. Since $\frac{a\beta }{4r(1-\lambda ^2)-\beta ^2}>\frac{2}{3}\cdot \frac{a\beta }{4r(1-\lambda ^2)-\beta ^2}=\frac{2a\beta }{12r(1-\lambda ^2)-3\beta ^2}>\frac{1}{2}\cdot \frac{a\beta }{4r(1-\lambda ^2)-\beta ^2}= \frac{a\beta }{8r(1-\lambda ^2)-2\beta ^2}$, we know that $\alpha (B)>\alpha (BS)>\alpha (RS)$. Thus, $\alpha (B)>\alpha (BS)>\alpha (RS)>\alpha (D)$ when $a, \beta \ne 0, 4r-\frac{\beta ^2}{1-\lambda ^2}\ne 0$ and $8r-\frac{\beta ^2}{1-\lambda ^2}\ne 0$.

B Proof of Proposition 4

We first compare the total supply chain profit of the MIFP under different scenarios. From Table 2, it is easy to say that $\frac{(\beta ^2+4ak)^2}{64k^2(1-\lambda ^2)}>\frac{(\beta ^2+4ak)^2}{72k^2(1-\lambda ^2)}>\frac{3(\beta ^2+4ak)^2}{256k^2(1-\lambda ^2)}$. Since $\varPi _C^m(D)=\varPi _C^m(RS)$, it can be derived that $\varPi _C^m(B)>\varPi _C^m(BS)>\varPi _C^m(RS)=\varPi _C^m(D)$. Note that the condition is $k\ne 0$.

For the DIFP, we first compare the total supply chain profit under centralized model, bargaining revenue-sharing contract and revenue-sharing contract. Since $\frac{a^r}{4r(1-\lambda ^2)-\beta ^2}>\frac{8a^r}{9[4r(1-\lambda ^2)-\beta ^2]}=\frac{8a^2r}{36r(1-\lambda ^2)-9\beta ^2}>\frac{3a^2r}{4[4r(1-\lambda ^2)-\beta ^2]}=\frac{3a^2r}{16r(1-\lambda ^2)-4\beta ^2}$, it is easy to see that $\varPi _C^d(B)>\varPi _C^d(BS)>\varPi _C^d(RS)$. The conditions of establishment are $a, r, \beta \ne 0$ and $\frac{1}{1-\lambda ^2}\ne \frac{4r}{\beta ^2}$. Next, we compare the total supply chain profit between decentralized model and revenue-sharing contract. It can be obtained that $\scriptstyle {\frac{\varPi _C^d(D)}{\varPi _C^d(RS)}=\frac{192r^2(1-\lambda ^2)^2-48r(1-\lambda ^2)\beta ^2-16r(1-\lambda ^2)\beta ^2+4\beta ^4}{192r^2(1-\lambda ^2)^2-48r(1-\lambda ^2)\beta ^2+3\beta ^4}}$. When $\frac{1}{1-\lambda ^2}\le 16r$, $\varPi _C^d(B)>\varPi _C^d(BS)>\varPi _C^d(RS)\ge \varPi _C^d(D)$. When $\frac{1}{1-\lambda ^2}>16r$, $\varPi _C^d(RS)<\varPi _C^d(D)$. We continue to compare the total supply chain profit under the decentralized model and bargaining revenue-sharing contract. Similarly, we can obtain that when $16r<\frac{1}{1-\lambda ^2}\le \frac{20r}{\beta ^2}$, the order is $\varPi _C^d(B)>\varPi _C^d(BS)\ge \varPi _C^d(D)>\varPi _C^d(RS)$; when $\frac{1}{1-\lambda ^2}>\frac{20r}{\beta ^2}$, the order is $\varPi _C^d(B)>\varPi _C^d(D)>\varPi _C^d(BS)>\varPi _C^d(RS)$, while in practice $\lambda \in [0,0.5]\Leftrightarrow \frac{1}{1-\lambda ^2}<1.3$, $\frac{1}{1-\lambda ^2}$ will not be larger than 16r. In summary, $\varPi _C^d(B)>\varPi _C^d(BS)>\varPi _C^d(RS)\ge \varPi _C^d(D)$.

C Proof of Proposition 5

When the centralized scenario cannot be realized, the bargaining revenue-sharing contract is the optimal contract to coordinate the supply chain. Both the manufacturer and the e-retailer have incentive to choose this contract. For the manufacturer of the MIFP, since $\frac{(\beta ^2+4ak)^2}{128k^2(1-\lambda ^2)}<\frac{(\beta ^2+4ak)^2}{96k^2(1-\lambda ^2)}$ ($k\ne 0$), $\varPi _M^m(BS)>\varPi _M^m(D)=\varPi _M^m(RS)$. The profit of the manufacturer under bargaining revenue-sharing contract is larger than other scenarios. For the e-retailer selling the MIFP on the platform, since $\frac{\lambda ^2(\beta ^2+4ak)^2}{64k^2(1-\lambda ^2)^2}>\frac{\lambda ^2(\beta ^2+4ak)^2}{144k^2(1-\lambda ^2)^2}>\frac{\lambda ^2(\beta ^2+4ak)^2}{256k^2(1-\lambda ^2)^2}$, the platform value added under centralized model is larger than other scenarios. Moreover, the platform value added under bargaining revenue-sharing contract is the second largest. Therefore, if the centralized model cannot be achieved, the bargaining revenue-sharing contract is the optimal contract both for the manufacturer and the e-retailer.

For the manufacturer of the DIFP, since $\frac{2a^2r}{12r(1-\lambda ^2)-3\beta ^2}>\frac{a^2r}{8r(1-\lambda ^2)-2\beta ^2}>\frac{a^2r}{8r(1-\lambda ^2)-\beta ^2}$ ($r\ne 0$), $\varPi _M^d(BS)>\varPi _M^d(RS)>\varPi _M^d(D)$. The profit of the manufacturer under bargaining revenue-sharing contract is larger than other scenarios. For the e-retailer selling the DIFP, since $\frac{4a^2r^2\lambda ^2}{(4r-4r\lambda ^2-\beta ^2)^2}>\frac{16a^2r^2\lambda ^2}{9(4r-4r\lambda ^2-\beta ^2)^2}>\frac{a^2r^2\lambda ^2}{(4r-4r\lambda ^2-\beta ^2)^2}$, $V^d(B)>V^d(BS)>V^d(RS)$, where we use V to denote the platform value added. The platform value added under bargaining revenue-sharing contract is larger than revenue-sharing contract. We then compare $V^d(D)$ and $V^d(RS)$ by using the equation $\frac{V^d(D)}{V^d(RS)}=\frac{64r^2(1-\lambda ^2)^2-32r(1-\lambda ^2)\beta ^2+4\beta ^4}{64r^2(1-\lambda ^2)^2-16r(1-\lambda ^2)\beta ^2+\beta ^4}$. It is easy to see that when $3\beta ^4-16r(1-\lambda ^2)\beta ^2>0$, $V^d(D)>V^d(RS)$. By algebra, we have $V^d(D)>V^d(RS)\Leftrightarrow 3\beta ^2>16r(1-\lambda ^2)\Leftrightarrow \frac{1}{1-\lambda ^2}>\frac{16r}{3\beta ^2}$, where $\beta \ne 0$. The parameter $\lambda$ represents the user conversion rate of the platform e-retailer, and $\lambda \in [0,0.5]$ in practice usually. Hence, $\frac{1}{1-\lambda ^2}<1.3$. The parameters r and $\beta$ reflect the fixed cost coefficient of the DIFP and the consumer sensitivity with respect to the frugal level $\alpha$, respectively. r is much larger than $\beta$ in practice. In summary, what is in line with the actual situation is that $\frac{1}{1-\lambda ^2}<\frac{16r}{3\beta ^2}$. Therefore, $\frac{1}{1-\lambda ^2}<\frac{16r}{3\beta ^2}\Leftrightarrow V^d(D)<V^d(RS)$. It can be obtained that $V^d(B)>V^d(BS)>V^d(RS)>V^d(D)$.