Table 5 Key performance indicators... | Emerald Publishing

Table 5

Key performance indicators

Symbol	Metric	Interpretation
Evaluating the peak prediction using ModSIR
ρ_pModSIR	Closeness to the actual peak using ModSIR (days)	How close the predicted peak of ModSIR is from the actual peak
*ρ_pSIR*	Closeness to the actual peak using SIR (days)	How close the predicted peak of SIR is from the actual peak
*ρ_pSIRS*	Closeness to the actual peak using SIRS (days)	How close is the predicted peak of SIRS to the actual peak
*ρ_pSIRV*	Closeness to the actual peak using SIRV (days)	How close the predicted peak of SIRV is from the actual peak
ρI%_SIR	Percentage improvement in the peak closeness of ModSIR over SIR	How improved peak of ModSIR is from the SIR peak
ρI%_SIRS	Percentage improvement in the peak closeness of ModSIR over SIRS	How improved peak of ModSIR is from the SIRS peak
ρI%_SIRV	Percentage improvement in the peak closeness of ModSIR over SIRV	How improved peak of ModSIR is from the SIRV peak
Evaluating the network models
ϑ_DC	Variance in degree centrality	The lower the value, the more impartial the importance of the hubs
*ϑ_V*	Variance in vulnerability-weighted degree centrality	The lower the value, the more impartiality in vulnerability coverage by the hubs
*ϑ_P*	Variance in population-weighted degree centrality	The lower the value, the more impartiality in population coverage by the hubs
*ϑ_CC*	Variance in closeness centrality	The lower the value, the more impartially the closeness of the cities distributed from the hubs
**d_avg_vul_≥_thrs**	Average distance of the most vulnerable region (among nodes ≥ threshold) from its nearest facility	The lower the value, the lesser the distance of the vulnerable region (among ≥ threshold) from the nearest facility
$d_{a v g}^{} = \frac{\sum_{j} \sum_{i} d_{i j}}{\| N \| - \| O P \|}$	Average distance	The average distance of all the hubs from the assigned locations
*d_max = max{dij}*	Maximum distance from facility centers	The region is located furthest from the assigned hub
$C_{i j} = d_{i j}^{r} . c_t r a n s_{r} . y_{i j}^{r}$	Cost of transportation	The cost of the selected mode of transportation from \|R\| type of vehicles from location i to j
$P C % = \frac{C_{i j}^{1} - C_{i j}^{k}}{C_{i j}^{1}} \times 100$	Percentage of cost compensated for addressing vulnerability	Where k ∈ K\|r ∈ R\| (i, j) ∈ A_pn and K is the set of MIQCPs with vulnerability in the objective function

Symbol	Metric	Interpretation
Evaluating the peak prediction using ModSIR
ρ_pModSIR	Closeness to the actual peak using ModSIR (days)	How close the predicted peak of ModSIR is from the actual peak
ρ_pSIR	Closeness to the actual peak using SIR (days)	How close the predicted peak of SIR is from the actual peak
ρ_pSIRS	Closeness to the actual peak using SIRS (days)	How close is the predicted peak of SIRS to the actual peak
ρ_pSIRV	Closeness to the actual peak using SIRV (days)	How close the predicted peak of SIRV is from the actual peak
ρI%_SIR	Percentage improvement in the peak closeness of ModSIR over SIR	How improved peak of ModSIR is from the SIR peak
ρI%_SIRS	Percentage improvement in the peak closeness of ModSIR over SIRS	How improved peak of ModSIR is from the SIRS peak
ρI%_SIRV	Percentage improvement in the peak closeness of ModSIR over SIRV	How improved peak of ModSIR is from the SIRV peak
Evaluating the network models
ϑ_DC	Variance in degree centrality	The lower the value, the more impartial the importance of the hubs
ϑ_V	Variance in vulnerability-weighted degree centrality	The lower the value, the more impartiality in vulnerability coverage by the hubs
ϑ_P	Variance in population-weighted degree centrality	The lower the value, the more impartiality in population coverage by the hubs
ϑ_CC	Variance in closeness centrality	The lower the value, the more impartially the closeness of the cities distributed from the hubs
d_avg_vul_≥_thrs	Average distance of the most vulnerable region (among nodes ≥ threshold) from its nearest facility	The lower the value, the lesser the distance of the vulnerable region (among ≥ threshold) from the nearest facility
$d_{a v g}^{} = \frac{\sum_{j} \sum_{i} d_{i j}}{\| N \| - \| O P \|}$	Average distance	The average distance of all the hubs from the assigned locations
d_max = max{dij}	Maximum distance from facility centers	The region is located furthest from the assigned hub
$C_{i j} = d_{i j}^{r} . c_t r a n s_{r} . y_{i j}^{r}$	Cost of transportation	The cost of the selected mode of transportation from \|R\| type of vehicles from location i to j
$P C % = \frac{C_{i j}^{1} - C_{i j}^{k}}{C_{i j}^{1}} \times 100$	Percentage of cost compensated for addressing vulnerability	Where k ∈ K\|r ∈ R\| (i, j) ∈ A_pn and K is the set of MIQCPs with vulnerability in the objective function

Source: Authors’ own work