Service Operations

3.1. SOs in E-Commerce Industry

Selling products in web-based retail platforms has been the mainstream in e-commerce industry. In this subsection, we focus on reviewing the work of Choi et al. which investigates the optimal SOs in web-based retail platform Taobao.com, the hottest online shopping platforms in China. Choi et al. examine the customer service of online shopping platforms (OSP). First, they conduct a case-based empirical study regarding Taobao.com and find that the online customer loyalty $l$ is significantly related to the "fulfillment and responsiveness" function $\lambda$. Second, driven by the empirical result, they build up the analytical model in which the customer loyalty $l$ is increasing in the "fulfillment and responsiveness" function $\lambda$ as follows:

$l=a+b \lambda, \quad \text { where } a, b>0.$

Afterwards they consider that the revenue function of web-based retailer platform is stochastic. Specifically, a higher level of customer loyalty $l$ leads to a higher platform's revenue $R(l)$; namely, they have the following equation:

$R(l)=G(l)+\varepsilon,$

where (i) $G(l)$ is concave and is an increasing function of $l$ and (ii) $\varepsilon$ is a random variable and follows a symmetric distribution such as normal distribution with a zero mean and constant variance $\sigma^{2}$. Moreover, they consider that the cost function $C(\lambda)$ is convex function and an inereasing in $\lambda$.

They denote the profit of OSP as $\pi(\lambda)$, the corresponding expected profit as $E[\pi(\lambda)]$, and the corresponding variance of profit as $V[\pi(\lambda)]$. The functions above are as follows:

They consider that the OSP is risk averse. They examine the OSP's performance associated with risk by using the mean-variance safety first measure $(\operatorname{SFM}(\lambda))$ as the objective function for the OSP:

$\operatorname{SFM}(\lambda)=\frac{(E[\pi(\lambda)]-\beta)}{\sqrt{V[\pi(\lambda)]}},$

where $\beta$ is the expected profit target that the OSP expects to achieve. The mean-variance safety first measure is innovative in SOs, which could trace back to the prestigious meanvariance approach and safety-first principle in portfolio selection model. The mean-variance safety first measure is a risk management technique and could provide the optimal control strategy when considering payoff and risk.

Choi et al.'s work is a multimethodological study. They first investigate the service quality in OSP empirically, and then, based on the empirical results, they further examine the optimal service quality analytically. They find that $\lambda_{\mathrm{SFM}}^{*}$ and $\lambda_{\mathrm{EP}}^{*}$ uniquely exist and $\lambda_{\mathrm{SFM}}^{*}=\lambda_{\mathrm{EP}}^{*}$. Their results imply that the optimal level of "fulfillment and responsiveness" for risk averse OSP is equivalent to the one for risk neutral. In other words, the optimal service level does not depend on the risk preference of the OSP.

3.2. SOs in Consumer Service Industry

Service time is significantly important in consumer service industry. In this subsection, we focus on reviewing Park and Hong's work in. Park and Hong consider the case where the market demand is influenced by not only the retail price and service level, but also service time. They consider that the retailer sells a product to customers at retail price $p$, and the supplier sets the service level $s$ and the guaranteed service time $l$. The customer demand arrives according to a Poisson process with a mean rate $\lambda$. They consider that the demand function is

$\lambda(p, l, s)=a-b p-c l+g s$

where $a$ is the potential market size and $b$, $c$, and $g$ represent the degree of sensitivity of price, the service time, and the service level to the mean demand rate.

They also consider that the investment costs are $\mu A$, the unit variable cost is $m$, and the unit wholesale price is $w_{S}$. The expected profit functions of retailer and supplier are as follows:

$\begin{gathered}\pi_{R}(p)=\left(p-w_{S}\right) \lambda(p, l, s) \\\pi_{S}(l, s, \mu)=\left(w_{S}-m\right) \lambda(p, l, s)-A \mu\end{gathered}$

The supplier's optimization problem is expressed as follows:

$\begin{aligned}&\max _{l, s, \mu}\left(w_{S}-m\right) \lambda(p, l, s)-A \mu \\&\text { subject to } \quad \lambda(p, l, s) \leq \mu \\&1-e^{-(\mu-\lambda) l} \geq s \\&l>0, \quad \mu>0 \\&1>s \geq s_{C}\end{aligned}$

Constraint implies system stability in that the supplier's mean service rate exceeds the mean demand rate. Constraint is the actual service level which is larger than the proposed service. Constraint represents the guaranteed service time and the capacity for the service/product is positive. Constraint restricts the proposed service level which is greater than the industry standard service level $s_{C}$ and less than 1.

The retailer's optimization objective is expressed as follows:

$\max _{p}\left(p-w_{S}\right) \lambda(p, l, s)$

The profit function of retailer $\pi_{R}(p)$ is the concave function of $p$. Thus the optimal retail price, $p^{*}$, is able to be obtained by taking the first-or der derivative of the retailer's profit function. The profit function of supplier is jointly concave with respect to $s$ and $l$; thus the optimal service level $s^{*}$ and the optimal guaranteed service time $l^{*}$ can be derived.

Park and Hong find that it is more desirable to simultaneously rmine the optimal price, the optimal guaranteed service time, and the optimal service level, instead of sequentially in consumer service industry. This finding implies that the central planner can help maximize the supply chain profit. The service supply chain with service time and service level is better to determine the service time and service level simultaneously by the central planner.