## 2 Literature Review
### Service Quality Evaluation Model
#### 2.3.4 Establishment of Service Quality Performance Matrix  
[PERSON] and [PERSON] [14] proposed the PEM as a reference for quality improvement, but this matrix lacks generalization and standardization and is limited to a 7-point Likert scale [33]. Many subsequent scholars, such as [PERSON] et al. [34] and [PERSON] [28], proposed a revised PEM and applied it to the management method of quality improvement in enterprises. Scholars have not implemented this model as a basis for quality improvement in the LTC industry. In light of the views of previous scholars, this study applied a revised PEM to the quality management strategy of the LTC industry (see Figure 7). To generalize and standardize this model, a 5-point Likert scale, which is considered to be the most reliable scaling tool in the literature and widely used by scholars, was adopted in this study [35].  
Figure 6: Revised performance evaluation matrix. Sources: [PERSON] and [PERSON] [13].  
Figure 7: The service quality performance matrix.  
Below, according to the theory of [PERSON] et al. [33], the random variable \(D\) denotes demand, and \(S\) denotes satisfaction. A 5-point scale was adopted to evaluate the demand and satisfaction of each item. The indices of demand and satisfaction are defined as follows:  
\[P_{D} = \frac{\mu_{D}-\min}{R} \tag{1}\]  
\[P_{S} = \frac{\mu_{S}-\min}{R} \tag{2}\]  
where \(P_{D}\) is the index of demand, \(P_{S}\) is index of satisfaction, \(\min\) is the minimum value of scale k, and \(R\) is the full range of scale k. Furthermore, \(\mu_{D}\) and \(\mu_{S}\) are the means of demand (\(D\)) and satisfaction (\(S\)), respectively, \(\min=1\) represents the minimum of scale k, and \(R=\text{k}-1\) is the full range of scale k.  
Based on the literature review, we know that PEM has been used extensively in recent years and can be applied to decision-making practices [32]. This method is mostly used in logistics and in the semiconductor, financial, and service industries, and its application in relevant studies of LTC is still rare. Hence, we chose PEM as one of the research methods. In this study, the resource allocation for the LTC concept was used as the basis to explore service satisfaction levels for older people who require care. The corresponding strategies of maintenance, improvement, and priority improvement of the revised PEM put forward by [PERSON] and [PERSON] [13] were re-proposed. This matrix is called the service quality performance matrix (SQPM). Zones 1, 2, and 4 are areas where older adults' cognitive satisfaction exceeds demand. Therefore, service resources should be maintained at their current status, and the strategy is to maintain service quality. Zones 3, 5, and 7 are areas where satisfaction is equal to demand, indicating that the service does not exceed user expectations; therefore, organizations must improve their existing service quality by investing in more resources, and the proposed strategy is to improve. Zones 6, 8, and 9 are areas where demand exceeds satisfaction, indicating that older adults are well aware of service projects, but they are not satisfied with the services provided. As a result, governments and organizations must actively make improvements to correct these issues, and the response strategy is to prioritize improvement. All factors that prioritize improvement are the response strategies that this study puts forward and are regarded as factors that should be prioritized.  
In the relevant literature, most PEM-related applications were in the machinery industry [34] and education [36], and few were applied in the service industry, and PEM was not formally applied to LTC service demand and resource allocation at all. In this study, the literature and relevant practical experience were used to identify the elements of LTC service demands, and the SQPM method was used to determine the priority of these demands to optimize resource allocation and implement care for older adults' retirement.