# Analyzing the Impact of Vaccine Availability on Alternative Supplier Selection Amid the COVID-19 Pandemic: A cFGM-FTOPSIS-FWI Approach

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Impact of the COVID-19 Pandemic on Suppliers

#### 2.2. Alternative Supplier Selection amid the COVID-19 Pandemic

#### 2.3. Decision-Making amid the COVID-19 Pandemic

## 3. The Fuzzy Collaborative Intelligence Approach

- Step 1.
- (Each expert) Determine the priorities of criteria using cFGM.
- Step 2.
- (Each expert) If the critical ratio is less than 0.1, go to Step 3; otherwise, modify the comparison matrix and return to Step 1.
- Step 3.
- (Each expert) Apply FTOPSIS to compare the overall performances of alternative suppliers.
- Step 4.
- If experts’ authority levels are specified, go to Step 5; otherwise, derive the authority level of each expert based on the consistency of his/her judgment.
- Step 5.
- Apply FWI to aggregate the comparison results by all experts.

#### 3.1. Calibrated FGM Method for Determining the Priorities of Criteria

**Theorem 1**

**[43].**

**Theorem**

**2**

**[43].**

**Theorem**

**3**

**[43].**

#### 3.2. FTOPSIS for Comparing Alternatives

**Theorem**

**4**

**[22].**

#### 3.3. FWI for the Aggregation of the Comparison Results by All Experts

- (1)
- ${\tilde{C}}_{q}(all)={\tilde{C}}_{q}(l)$ if ${\omega}_{l}=1$ and ${\omega}_{k}=0$ ∀ k ≠ l
- (2)
- ${\tilde{C}}_{q}(all)=\tilde{FI}(\{{\tilde{C}}_{q}(k)\})$ if ${\omega}_{k}=\frac{1}{K}$ ∀ k; $\tilde{FI}$ is the fuzzy intersection operator.
- (3)
- $\underset{k}{\mathrm{min}}{\mu}_{{\tilde{C}}_{q}(k)}(x)\le {\mu}_{{\tilde{C}}_{q}(all)}(x)\le \underset{k}{\mathrm{max}}{\mu}_{{\tilde{C}}_{q}(k)}(x)$
- (4)
- $\frac{\partial {\mu}_{{\tilde{C}}_{q}(all)}(x)}{\partial {\mu}_{{\tilde{C}}_{q}(k)}(x)}\propto {\omega}_{q}$

## 4. Application

#### 4.1. Application of the Proposed Methodology

#### 4.2. Discussion

- (1)
- When vaccines for the COVID-19 pandemic were expected to emerge, experts believed that “delivery speed” and “level of buyer–supplier cooperation” were more important criteria than the others. In contrast, without COVID-19 vaccines, “pandemic containment performance” and “delivery speed” were considered to be the first two important criteria.
- (2)
- As expected, the pairwise comparison results by experts in different scenarios varied greatly.
- (3)
- The overall performances of alternative suppliers, in terms of their closenesses, evaluated by different experts were quite similar
- (4)
- The difference between the two scenarios did affect the decisions of experts. For example, Expert #1 thought that Alternative Supplier #2 was better than Alternative Supplier #1 in Scenario I, but preferred Alternative Supplier #1 to Alternative Supplier #2 in Scenario II.
- (5)
- The comparison results also showed that no matter which scenario was considered, Alternative Supplier #3 was always the best choice. Therefore, this choice was quite robust.
- (6)
- For comparison, two existing methods were also applied to this case. The first method was the FGM-FGM-fuzzy weighted average (FWA) method, in which FGM was applied to aggregate experts’ fuzzy judgment matrixes and to derive the priorities of criteria from the aggregation result. Subsequently, FWA was applied to evaluate the overall performance of each alternative supplier. The second method was the FGM-FEA-FWA method, in which FEA was applied to derive the priorities of criteria instead. The ranking results using various methods are compared in Table 9.
- (7)
- It is interesting to know whether the consideration of different criteria changes the comparison result. In order to investigate this issue, an experiment was conducted by dropping one of the five criteria at a time and alternative suppliers were compared based on the remaining criteria. The experimental results are summarized in Table 10. Alternative Supplier #3 was always the best choice. In addition, the ranking results in the two scenarios differed when “pandemic containment performance” or “pandemic severity” was removed.
- (8)
- One contribution of this research is that issues related to the COVID-19 pandemic were considered in the selection of alternative suppliers, which has not yet been fully resolved. On the contrary, past studies have reported the disruption of supply chains by the COVID-19 pandemic [34,35,46], identified and assessed the risks faced by organizations [34], identified factors or barriers to the sustainability of an organization amid the COVID-19 pandemic [36,43,61], or discussed treatments (including contract management [35], workforce management [35], and demand management [46]) that could be taken to mitigate the impact. Biswas et al. [68] also applied a FAHP method for a similar purpose amid the COVID-19 pandemic. However, their FAHP method was based on the compromise among all experts, while the cFGM-FTOPSIS-FWI approach proposed in this study sought the consensus among all experts.
- (9)
- In the view of Chen et al. [43], pandemic containment performance, pandemic severity, vaccine acquisition speed, demand shrinkage, supplier impact, and infection risk affect the robustness of a factory to the COVID-19 pandemic. A supplier faces the same risks and can take similar measures (e.g., wearing masks, physical distancing, moving raw material inventory to places free from quarantine and easy to ship, securing future transportation services, negotiating with customers on possible delays or cancellation, etc.) to mitigate the impact [4,6,43]. In addition, compared with downstream assemblers, upstream raw material suppliers have a lower degree of automation, so they may be more susceptible to these risks. However, due to the COVID-19 pandemic, some suppliers have shut down, which is an opportunity for other suppliers because they can increase their prices.
- (10)
- If the results of the two scenarios were different, the wafer foundry could choose the best alternative suppliers of the two scenarios and allocate the required quantity of raw materials between the two alternative suppliers.

## 5. Conclusions

- (1)
- In the absence of a COVID-19 vaccine, “pandemic containment performance” was considered the most important criterion. On the contrary, if vaccines will be available, “delivery speed” was the highest priority.
- (2)
- Experts have made different decisions in different scenarios.
- (3)
- However, after aggregation, Alternative Supplier #3 was always the best choice regardless of the considered scenario.
- (4)
- The result of alternative supplier selection using the proposed methodology was the same as those using two existing methods, showing the robustness of the proposed methodology.
- (5)
- If more experts are involved, or if more alternative suppliers are considered, the selection result will be different.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Factors critical to the selection of an alternative supplier amid the coronavirus disease 2019 (COVID-19) pandemic.

**Figure 6.**An example of the fuzzy weighted intersection (FWI) aggregator ({${\omega}_{k}$} = (0.6, 0.3, 0.1)).

Method | Expert Inputs | Expert’s Authority Levels | How Authority Levels Are Derived | Method for Deriving Priorities | Aggregation Method |
---|---|---|---|---|---|

Zheng et al. [12] | - Relative priorities of criteria
| Equal | - | FGM | Discussion |

Chen [20] | - Relative priorities of criteria
| Equal | - | FGM | FGM |

Chen et al. [26] | - Forecast
| Unequal | Subjectively assigned | - | FWI |

Gao et al. [27] | - Relative priorities of criteria
| Equal | - | FGM | FGM |

Wang et al. [28] | - Relative priorities of criteria
| Equal | - | FEA | FGM |

Lin et al. [29] | - Relative priorities of criteria
| Equal | - | FI | FGM |

The proposed methodology | - Relative priorities of criteria
- Expert’s sensitivity
| Unequal | Automatically assigned | cFGM | FWI |

Expert # | Scenario I | Scenario II |
---|---|---|

1 | $\left[\begin{array}{ccccc}1& -& -& (1,1,3)& -\\ (5,7,9)& 1& (3,5,7)& (2,4,6)& -\\ (1,3,5)& -& 1& (1,3,5)& -\\ -& -& -& 1& -\\ (1,3,5)& (1,1,3)& (1,1,3)& (1,1,3)& 1\end{array}\right]$ | $\left[\begin{array}{ccccc}1& -& -& -& -\\ (5,7,9)& 1& (3,5,7)& -& -\\ (1,3,5)& -& 1& -& -\\ (3,5,7)& (1,3,5)& (3,5,7)& 1& (2,4,6)\\ (1,3,5)& (1,1,3)& (1,1,3)& -& 1\end{array}\right]$ |

2 | $\left[\begin{array}{ccccc}1& -& (1,3,5)& (3,5,7)& (2,4,6)\\ (3,5,7)& 1& (2,4,6)& (1,3,5)& (3,5,7)\\ -& -& 1& (1,3,5)& -\\ -& -& -& 1& -\\ -& -& (1,2,4)& (1,1,3)& 1\end{array}\right]$ | $\left[\begin{array}{ccccc}1& -& (1,3,5)& -& (1,3,5)\\ (3,5,7)& 1& (2,4,6)& (1,1,3)& (2,4,6)\\ -& -& 1& -& -\\ (3,5,7)& -& (3,5,7)& 1& -\\ -& -& (1,2,4)& (1,1,3)& 1\end{array}\right]$ |

3 | $\left[\begin{array}{ccccc}1& (1,3,5)& (1,3,5)& (1,3,5)& (2,4,6)\\ -& 1& (1,3,5)& (2,4,6)& (1,3,5)\\ -& -& 1& (1,3,5)& (1,3,5)\\ -& -& -& 1& (1,3,5)\\ -& -& -& -& 1\end{array}\right]$ | $\left[\begin{array}{ccccc}1& (1,3,5)& (1,3,5)& -& -\\ -& 1& (1,3,5)& (1,1,3)& -\\ -& -& 1& -& -\\ (1,3,5)& -& (1,3,5)& 1& (1,3,5)\\ (1,3,5)& (1,1,3)& (1,3,5)& -& 1\end{array}\right]$ |

k | Scenario #1 | Scenario #2 |
---|---|---|

1 | $(0.00,0.10,6.99)$ | $(0.00,0.09,6.42)$ |

2 | $(0.00,0.17,8.70)$ | $(0.00,0.15,7.30)$ |

3 | $(0.00,0.12,14.17)$ | $(0.00,0.16,13.25)$ |

Criterion | Rule |
---|---|

Level of buyer–supplier cooperation | ${\tilde{p}}_{q1}({x}_{q})=\{\begin{array}{ccc}(0,0,1)& \mathrm{if}& {x}_{q}=\mathrm{very}\text{}\mathrm{low}\\ (0,1,2)& \mathrm{if}& {x}_{q}=\mathrm{low}\\ (1.5,2.5,3.5)& \mathrm{if}& {x}_{q}=\mathrm{moderate}\\ (3,4,5)& \mathrm{if}& {x}_{q}=\mathrm{high}\\ (4,5,5)& \mathrm{if}& {x}_{q}=\mathrm{very}\text{}\mathrm{high}\end{array}$ where ${x}_{q}$ is the level of buyer–supplier cooperation. |

Delivery speed | ${\tilde{p}}_{q2}({x}_{q})=\{\begin{array}{ccc}(0,0,1)& \mathrm{if}& {x}_{q}\le 0.9\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.1\cdot \underset{r}{\mathrm{max}}{x}_{r}\text{}\mathrm{or}\text{}\mathrm{data}\text{}\mathrm{not}\text{}\mathrm{available}\\ (0,1,2)& \mathrm{if}& 0.9\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.1\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.65\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.35\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (1.5,2.5,3.5)& \mathrm{if}& 0.65\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.35\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.35\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.65\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (3,4,5)& \mathrm{if}& 0.35\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.65\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.1\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.9\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (4,5,5)& \mathrm{if}& 0.1\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.9\cdot \underset{r}{\mathrm{max}}{x}_{r}{x}_{q}\end{array}$ where ${x}_{q}$ is the average delivery time. |

Company reputation | ${\tilde{p}}_{q3}({x}_{q})=\{\begin{array}{ccc}(0,0,1)& \mathrm{if}& {x}_{q}=\mathrm{very}\text{}\mathrm{poor}\\ (0,1,2)& \mathrm{if}& {x}_{q}=\mathrm{poor}\\ (1.5,2.5,3.5)& \mathrm{if}& {x}_{q}=\mathrm{moderate}\\ (3,4,5)& \mathrm{if}& {x}_{q}=\mathrm{good}\\ (4,5,5)& \mathrm{if}& {x}_{q}=\mathrm{very}\text{}\mathrm{good}\end{array}$ where ${x}_{q}$ is the company reputation of the alternative supplier. |

Pandemic containment performance | ${\tilde{p}}_{q4}({x}_{q})=\{\begin{array}{ccc}(0,0,1)& \mathrm{if}& {x}_{q}<0.9\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.1\cdot \underset{r}{\mathrm{max}}{x}_{r}\mathrm{or}\text{}\mathrm{data}\text{}\mathrm{not}\text{}\mathrm{available}\\ (0,1,2)& \mathrm{if}& 0.9\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.1\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.65\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.35\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (1.5,2.5,3.5)& \mathrm{if}& 0.65\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.35\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.35\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.65\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (3,4,5)& \mathrm{if}& 0.35\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.65\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.1\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.9\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (4,5,5)& \mathrm{if}& 0.1\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.9\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}\end{array}$ where ${x}_{q}$ is the recovery index of the region [64]. |

Pandemic severity | ${\tilde{p}}_{q5}({x}_{k})=\{\begin{array}{ccc}(0,0,1)& \mathrm{if}& 0.1\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.9\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}\text{}\mathrm{or}\text{}\mathrm{data}\text{}\mathrm{not}\text{}\mathrm{available}\\ (0,1,2)& \mathrm{if}& 0.35\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.65\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.1\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.9\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (1.5,2.5,3.5)& \mathrm{if}& 0.65\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.35\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.35\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.65\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (3,4,5)& \mathrm{if}& 0.9\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.1\cdot \underset{r}{\mathrm{max}}{x}_{r}\le {x}_{q}0.65\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.35\cdot \underset{r}{\mathrm{max}}{x}_{r}\\ (4,5,5)& \mathrm{if}& {x}_{q}0.9\cdot \underset{r}{\mathrm{min}}{x}_{r}+0.1\cdot \underset{r}{\mathrm{max}}{x}_{r}\end{array}$ where ${x}_{q}$ is the current number of active cases in the region [67]. |

q | 1 | 2 | 3 |
---|---|---|---|

${\tilde{p}}_{q1}$ | (3, 4, 5) | (4, 5, 5) | (1.5, 2.5, 3.5) |

${\tilde{p}}_{q2}$ | (1.5, 2.5, 3.5) | (0, 0, 1) | (4, 5, 5) |

${\tilde{p}}_{q3}$ | (3, 4, 5) | (4, 5, 5) | (1.5, 2.5, 3.5) |

${\tilde{p}}_{q4}$ | (0, 0, 1) | (0, 0, 1) | (4, 5, 5) |

${\tilde{p}}_{q5}$ | (0, 0, 1) | (0, 0, 1) | (4, 5, 5) |

Scenario I | Scenario II | |||||||
---|---|---|---|---|---|---|---|---|

Expert #1 | q | ${\tilde{C}}_{q}$ | $COG({\tilde{C}}_{q})$ | Rank | q | ${\tilde{C}}_{q}$ | $COG({\tilde{C}}_{q})$ | Rank |

1 | (0.081, 0.385, 1.000) | 0.489 | 3 | 1 | (0.071, 0.385, 0.916) | 0.457 | 2 | |

2 | (0.087, 0.381, 1.000) | 0.489 | 2 | 2 | (0.078, 0.381, 0.911) | 0.457 | 3 | |

3 | (0.350, 0.773, 1.000) | 0.801 | 1 | 3 | (0.376, 0.773, 1.000) | 0.716 | 1 | |

Expert #2 | 1 | (0.067, 0.370, 1.000) | 0.479 | 2 | 1 | (0.069, 0.370, 0.999) | 0.479 | 2 |

2 | (0.058, 0.334, 1.000) | 0.464 | 3 | 2 | (0.060, 0.334, 0.999) | 0.464 | 3 | |

3 | (0.295, 0.833, 1.000) | 0.709 | 1 | 3 | (0.341, 0.833, 1.000) | 0.725 | 1 | |

Expert #3 | 1 | (0.070, 0.380, 1.000) | 0.483 | 3 | 1 | (0.058, 0.380, 1.000) | 0.479 | 3 |

2 | (0.088, 0.396, 1.000) | 0.495 | 2 | 2 | (0.072, 0.396, 1.000) | 0.490 | 2 | |

3 | (0.234, 0.755, 1.000) | 0.663 | 1 | 3 | (0.298, 0.755, 1.000) | 0.684 | 1 |

Scenario I | Scenario II | |
---|---|---|

Expert #1 | 0.40 | 0.50 |

Expert #2 | 0.24 | 0.26 |

Expert #3 | 0.37 | 0.24 |

q | Scenario I | Scenario II | ||
---|---|---|---|---|

$\mathit{C}\mathit{O}\mathit{G}({\tilde{\mathit{C}}}_{\mathit{q}}(\mathit{a}\mathit{l}\mathit{l}))$ | Rank | $\mathit{C}\mathit{O}\mathit{G}({\tilde{\mathit{C}}}_{\mathit{q}}(\mathit{a}\mathit{l}\mathit{l}))$ | Rank | |

1 | 0.4868 | 3 | 0.4580 | 3 |

2 | 0.4894 | 2 | 0.4584 | 2 |

3 | 0.6981 | 1 | 0.7148 | 1 |

Method | Ranking Result |
---|---|

FGM-FGM-FWA | 3 → 1 → 2 |

FGM-FEA-FWA | 3 → 1 → 2 |

The proposed methodology | 3 → 2 → 1 |

Considered Criteria | Scenario I | Scenario II |
---|---|---|

Delivery speed, company reputation, pandemic containment performance, pandemic severity | 3 → 2 → 1 | 3 → 2 → 1 |

Level of buyer–supplier cooperation, company reputation, pandemic containment performance, pandemic severity | 3 → 1 → 2 | 3 → 1 → 2 |

Level of buyer–supplier cooperation, delivery speed, pandemic containment performance, pandemic severity | 3 → 2 → 1 | 3 → 2 → 1 |

Level of buyer–supplier cooperation, delivery speed, company reputation, pandemic severity | 3 → 2 → 1 | 3 → 1 → 2 |

Level of buyer–supplier cooperation, delivery speed, company reputation, pandemic containment performance | 3 → 2 → 1 | 3 → 1 → 2 |

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## Share and Cite

**MDPI and ACS Style**

Chen, T.; Wang, Y.-C.; Wu, H.-C.
Analyzing the Impact of Vaccine Availability on Alternative Supplier Selection Amid the COVID-19 Pandemic: A cFGM-FTOPSIS-FWI Approach. *Healthcare* **2021**, *9*, 71.
https://doi.org/10.3390/healthcare9010071

**AMA Style**

Chen T, Wang Y-C, Wu H-C.
Analyzing the Impact of Vaccine Availability on Alternative Supplier Selection Amid the COVID-19 Pandemic: A cFGM-FTOPSIS-FWI Approach. *Healthcare*. 2021; 9(1):71.
https://doi.org/10.3390/healthcare9010071

**Chicago/Turabian Style**

Chen, Toly, Yu-Cheng Wang, and Hsin-Chieh Wu.
2021. "Analyzing the Impact of Vaccine Availability on Alternative Supplier Selection Amid the COVID-19 Pandemic: A cFGM-FTOPSIS-FWI Approach" *Healthcare* 9, no. 1: 71.
https://doi.org/10.3390/healthcare9010071