# Developing a Decision-Making Framework to Improve Healthcare Service Quality during a Pandemic
## 3 Method
### Best-Worst Method (BWM)  
Step 1: Identifying Criteria and Strategies.  
The appropriate criteria \([CR_{1},\,CR_{2},\,CR_{3},\,\ldots,\,CR_{m}]\) for improving quality of service in the ICU were identified based on the literature. Table 1 lists and describes the selected criteria along with their corresponding references. The appropriate alternatives or strategies \(\{A_{1},\,A_{2},A_{3},\,\ldots,\,A_{m}\}\) for improving service quality in the ICU are listed in Table 2.  
Step 2: Identifying Key Stakeholders.  
Five potential key stakeholders were identified: physicians, patients, medical staff, insurance providers, and policymakers. To demonstrate the applicability of the proposed framework, all of these stakeholders were considered.  
Step 3: Determining the Best and Worst Criteria.  
All stakeholders were asked to select the best (\(B\)) and worst criteria (\(W\)) from the general list of identified criteria. This process was naturally dependent on each stakeholder's background and preference to achieve the common goal.  
Step 4: Rating the Best Criterion over the Other Criteria.  
Figure 2: BWM–MAMCA–MOLP framework for improving service quality in an ICU during the COVID-19 pandemic.  
In this step, the stakeholders were asked to rate the degree to which they preferred their best criteria over the other criteria on a 9-point scale, where 1 indicates equal preference and 9 indicates the highest preference. This process can be written as:  
\[A_{B}=(a_{B1},\,a_{B2},\,a_{B3},\,a_{B4},\,\ldots,\,a_{Bn}) \tag{1}\]  
where \(A_{B}\) represents the pairwise comparison of best criteria, \(a_{Bj}\) represents the preference of best criterion over the other criterion \(j\), and \(a_{BB}=1\).  
Step 5: Rating the Other Criteria over the Worst Criterion.  
In this step, each stakeholder was asked to rate all of the other criteria compared to their selected worst criterion using the same 9-point scale as step 4. This can be represented as:  
\[A_{W}=(a_{1W},\,a_{2W},\,a_{3W},\,a_{4W},\,\ldots,\,a_{nW}) \tag{2}\]  
where \(A_{W}\) indicates the pairwise comparison of worst criteria, \(a_{jW}\) represents the preference of j criteria over the worst criterion, and \(a_{WW}=1\).  
Step 6: Determining the Optimal Weights of the Selected Criteria.  
The optimal weights of the criteria \((k_{1}^{\ast},\,k_{2}^{\ast},\,k_{3}^{\ast},\,\ldots,\,k_{n}\")\) must be determined to satisfy the following requirements. Each pair of \(k_{B}/k_{j}\) and \(k_{j}/k_{w}\) has a possible solution of \(k_{B}/k_{j}=aB_{j}\) and \(k_{j}/k_{w}=a_{jW}\). To achieve a better solution, the maximum among the set, \(\{\,|\,k_{B}-aB_{j}\,\,|\,k_{j}\,\,-\,a_{jW}\,\,k_{W}\,|\,\}\), is minimized, and the problem is formulated as:  
\[\begin{array}{c}\min max_{j}\,\left\{\left|k_{B}-a_{Bj}k_{j}\right|,\,\left| k_{j}-a_{jw}k_{w}\right|\right\}\\ \sum_{j}k_{j}=1,\,k_{j}\geq\,\,0,\,\,\text{for all }j\end{array} \tag{3}\]  
Equation (3) can then be transformed into a linear program:  
\[min\,\,\eta^{L}\]  
subject to,  
\[\begin{array}{c}\left|k_{B}-a_{Bj}k_{j}\right|\,\leq\,\eta^{L}\,\,\text{for all }j\\ \left|k_{j}-a_{jw}k_{w}\right|\,\,\leq\,\eta^{L}\,\,\text{for all }j,\,\,\sum_{j}k_{j}=1,\,\,k_{j}\geq 0,\,\, \text{for all }j\end{array} \tag{4}\]  
After finding the weights \((k_{1}^{\ast},\,k_{2}^{\ast},\,k_{3}^{\ast},\,\ldots,\,k_{n}\")\), the \(\eta^{L}\) can be determined. Note that the reliability and consistency of the results increase as the \(\eta^{L}\) value nears zero.