BUS606: Operations and Supply Chain Management

4.1. SOs of Advertising

One stream of the literature has investigated the advertising investment issue in $\mathrm{SOs}$ management. In this subsection, we focus on reviewing Xu et al. investigate the advertising competition in three advertising game models: Cooperative game, Boxed Pig game, and Prisoner's game. These three models comprehensively represent the SOs of advertising. They consider two different sizes of service providers in one service market. One is the dominant service provider (D) who occupies major market share $w_{D}$. The other is $M$ small service providers $(S)$ who share the remaining market share $1-w_{D}$ equally, where $w_{D} \gg w_{i}$ and $w_{D}+\sum_{i=1}^{M} w_{i}=1$.

They consider that the service provider $D$ (or $S$) can decide whether or not to invest in advertising. They summarize four cases.

Case 1. Both service providers $D$ and $S$ choose to invest in advertising. They denote the total investment on advertising as $I$. The service provider $D$ has $a I$ and the service provider $S$ has $b I$, where $a+b=1$. They also denote $l(l>1)$ as the resource coefficient, where $a I=l b I$, and $k(k>1)$ as the effect of cooperative advertising, where $R_{D 1}=k b l I$ and $R_{S 1}=k b I$. The payoff functions are as follows:

$\begin{gathered}\pi_{D 1}=(1-\theta) k b l I-b l I+\lambda k b l I \\\pi_{S 1}=(1-\theta) k b I-b I+\lambda k b I\end{gathered}$

Case 2. Service provider $D$ advertises but service provider $S$ waits. The effect of advertising coefficient is $k_{D}$ and the service provider $D$ 's advertising investment is $R_{D 2}=b l k_{D} I$. The payoff functions are as follows:

$\begin{gathered}\pi_{D 2}=(1-\theta) k_{D} b l I-b l I+\lambda k_{D} b l I, \\\pi_{S 2}=\frac{\theta}{M} k_{D} b l I .\end{gathered}$

Case 3. Service provider $S$ advertises, but service provider $D$ waits. Similarly, the effects of advertising coefficient are $k_{S}$, where $k>k_{D}>k_{S}$. The payoff functions are as follows:

$\begin{gathered}\pi_{D 3}=\frac{\theta}{M} \beta k_{S} b l I, \\\pi_{S 3}=(1-\theta) k_{S} b I-b I+\lambda k_{D} b I,\end{gathered}$

where $\beta(\beta>1)$ is the spillover effect of service provider $D$.

Case 4. Noncooperative advertising, namely, no service provider, chooses to offer advertising. The payoff functions are $\pi_{D 4}=\pi_{S 4}=0$.

Xu et al. derive the various conditions and identify the optimal decisions for different advertising games. They find that the advertising spillover and the number of the small service providers $S$ would significantly influence the optimal strategies in advertising mode selection. Comparing the results of the above four cases they find that the service providers can achieve the advertising synergy effects through Case 1. Therefore, they conclude that service providers should collaborate with each other in order to optimize their payoff and gain the most revenue instead of taking free ride.

4.2. Channel Coordination in Service Supply Chain

Channel coordination is the key competitive dimension in supply chain. In this subsection, we focus on reviewing the work of He et al. study the coordination issues in a two-period supply chain in which there are a single manufacturer and a single retailer. They consider two cases: (1) manufacturer and retailer make decisions within a cooperative advertising program and (2) the retailer is vertically integrated with a manufacturer. They denote the manufacturer's quality effort as $x$. Moreover, they denote the retailer's advertising efforts as $e_{1}$ and $e_{2}$ and the market demand as $D_{1}$ and $D_{2}$. They consider that the market demand in the first period is a linear function of manufacturer's quality effort $x$ and first-period retailer's advertising efforts $e_{1}$ as follows:

$D_{1}=\alpha_{1}+\beta x+\lambda e_{1}$

where $\beta$ and $\lambda$ are both positive and $\alpha_{1}\left(\alpha_{1} \gg 0\right)$ is the potential intrinsic demand. In the second period the market demand is increasing in second-period retailer's advertising efforts $e_{2}$ as follows:

$D_{2}=\alpha_{2}+\theta \lambda e_{2}$

where $\theta$ is constant and $\alpha_{2}\left(\alpha_{2} \gg 0\right)$ is the potential intrinsic demand in the second period. They consider that the cost functions of quality $(C(x))$ and advertising $\left(C\left(e_{i}\right)\right)$ are quadratic with respect to quality effort $x$ and advertising effort $e_{i}$, respectively:

$\begin{gathered}C(x)=x^{2} \\C\left(e_{i}\right)=\frac{1}{2} e_{i}^{2}, \quad i \in\{1,2\} .\end{gathered}$

They consider that the manufacturer's profit margin for each unit in the period $i$ is $\rho_{m i}$ and the retailer's profit marginal in the period $i$ is $\rho_{r i}$. The profit functions of manufacturer and retailer are expressed as follows:

$\begin{gathered}\pi_{m}=\rho_{m 1} D_{1}+\rho_{m 2} D_{2}-x^{2} \\\pi_{r}=\rho_{r 1} D_{1}+\rho_{r 2} D_{2}-\frac{1}{2} e_{1}^{2}-\frac{1}{2} e_{2}^{2}\end{gathered}$

They first examine the situation where the manufacturer provides two different subsidy rates $\left(\phi_{1}\right.$ and $\left.\phi_{2}\right)$ to the retailer during the two periods. The profit functions of manufacturer and retailer are expressed as follows:

$\pi_{m}=\rho_{m 1} D_{1}+\rho_{m 2} D_{2}-x^{2}-\phi_{1} \frac{1}{2} e_{1}^{2}-\frac{1}{2} \phi_{2} e_{2}^{2}$

$\pi_{r}=\rho_{r 1} D_{1}+\rho_{r 2} D_{2}-\frac{1}{2}\left(1-\phi_{1}\right) e_{1}^{2}-\frac{1}{2}\left(1-\phi_{2}\right) e_{2}^{2}$

Second, they study the situation where the manufacturer provides the same subsidy rate ( $\phi$ ) to the retailer during the two periods. The profit functions of manufacturer and retailer are expressed as follows:

$\begin{gathered}\pi_{m}=\rho_{m 1} D_{1}+\rho_{m 2} D_{2}-x^{2}-\phi \frac{1}{2} e_{1}^{2}-\frac{1}{2} \phi e_{2}^{2}, \\\pi_{r}=\rho_{r 1} D_{1}+\rho_{r 2} D_{2}-\frac{1}{2}(1-\phi) e_{1}^{2}-\frac{1}{2}(1-\phi) e_{2}^{2} .\end{gathered}$

He et al. examine the impacts of different subsidy policies on supply chain. They find that both the manufacturer's optimal quality effort and the retailer's first-period advertising effort are influenced by the centralized first-period profit margin. Therefore, the quality effort and advertising effort are the determinant factors for the entralized supply chain profit in the first period. Furthermore, He et al. find the optimal advertising efforts for the retailer during the two periods. They also derive the optimal quality effort and subsidy policies for the manufacturer during the two periods. Moreover, they find that the two-way subsidy contract can coordinate both the oneperiod and two-period advertising models. This study implies that the integration between supply chain and advertising program is beneficial to supply chain coordination.