# A Hybrid Brain Storm Optimization Algorithm to Solve the Emergency Relief Routing Model
## 3 The Emergency Relief Routing Problem
### Deprivation Cost  
This paper is based on the premise that commercial and humanitarian logistics have a fundamental difference. Commercial logistics prioritize delivery strategies based on efficiency and customer satisfaction in a supply-demand balanced or surplus environment. Conversely, humanitarian logistics operations aim to minimize the social cost of disasters in situations of severe shortage. This necessitates prioritizing assistance to those who need it the most within a given timeframe. When conducting emergency relief, speed and efficiency are considered as the priority. In previous studies, scholars mostly used the objective function values of total time and total travel distance. They used the total time to gauge the efficiency of relief operations \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter Symbols** & **Parameter Meaning** \\ \hline \(c_{ij}\) & The distance between patient \(i\) and patient \(j\) \\ \(v\) & Travel speed of the relief vehicle \\ \(s_{i}\) & Operation time for patient \(i\) \\ \(t_{ij}\) & Travel time from patient \(i\) to patient \(j\) \\ \(a_{i}\) & The left time window for patient \(i\) \\ \(b_{i}\) & The right time window for patient \(i\) \\ \(E\) & The left time window for the emergency logistics center \\ \(L\) & The right time window for the emergency logistics center \\ \(d_{i}\) & Distribution demand of patient \(i\) \\ \(P_{i}\) & Recovery demand of patient \(i\) \\ \(C\) & The maximum loading of the relief vehicle \\ \(M\) & A large enough positive number \\ \(\alpha\) & Coefficient of the penalty function for exceeding the capacity restriction \\ \(\beta\) & Coefficient of the penalty function for exceeding the time window \\  & restriction \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The parameters in the model for the ERRP. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variable Symbols** & **Variable Meaning** \\ \hline \(w_{ik}\) & Start time of the operation to patient \(i\) for vehicle \(k\) \\ \(L_{ok}\) & Current loading of the vehicle \(k\) when leaving the emergency logistics center \\ \(L_{i}\) & Current loading of the vehicle after operating on patient \(i\) \\ \(x_{ijk}\) & Whether vehicle \(k\) departs from patient \(i\) to patient \(j\) \\ \(DC_{i}\) & Deprivation cost of patient \(i\) when the vehicle arriving \\ \(q\) & The sum of the default costs associated with exceeding the vehicle capacity constraint for each relief route \\ \(w\) & The sum of the default costs associated with each relief route exceeding the time window restriction \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The variables in the model for the ERRP. and the total travel distance to gauge whether relief routes were cost-saving. Few scholars have considered the degree of patients' suffering. In emergency relief operations, the longer the waiting time, the higher the degree of patients' suffering, and the less likely they are to be successfully rescued. To ensure patients' safety, the patient should be reached before the degree of suffering reaches a dangerous level. From this perspective, the suffering of patients at the time of receiving rescue operations can also measure the effectiveness of relief operations. [PERSON] et al. defined the deprivation cost as an economic assessment of human suffering [12]. While logistics costs can be estimated using standard cost estimation techniques, the most appropriate approach to reflect the impact of a delivery strategy on a population is by formally estimating a deprivation cost function. This function represents the economic cost of human suffering as a function of the amount of time a person is without a particular good or service. Although this estimate is based on economic evaluation techniques, the authors suggest that it is superior and preferable to the use of the alternative measures suggested in the literature. Then, they determined the appropriate basis for deprivation cost estimation.