# Dynamic Relief Items Distribution Model with Sliding Time Window in the Post-Disaster Environment
## 3 Dynamic RID Model with Sliding Time Window
### Priority Indexing  
During post-disaster humanitarian relief task, ensuring equity in distribution to all disaster regions in a comparable way is required to enhance the effectiveness of the distribution task [6]. In some RID models, a trade-off between distribution quantitative measures in terms of distribution time, operational cost, response time and reliability have been applied by implementing rational and optimised distribution [44; 57]. The study showed that response time and the number of victims, distribution time, operational cost, demand satisfaction and resource allocations are among the objectives for an effective distribution task [58]. However, with the variations in urgency levels, prioritisation of disaster areas is more important [59]. However, there has not been any unique single approach for prioritisation. Researchers have applied different approaches for defining disaster region priority, such as fuzzy clustering [43; 60], multi-attribute decision-making [61] and relative priority rules using time windows [62].  
The inclusion of priorities in generating distribution sequences reflects more realistic relief item distribution in disaster environments as it first delivers the relief items to the disaster regions with a higher priority. However, in doing so, the disaster regions with low priority have a long wait for relief items. With the long wait, the conditions in those regions may get worse. Therefore, a balanced distribution is required that addresses the long wait issues such that low-priority disaster regions' wait time is within a reasonable limit. Therefore, applying wait-time priority as one of the components of deciding the priority index makes the distribution highly effective, covering the distribution of relief items to all the disaster regions over time. In this paper, two priorities: causality level priority (based on the ratio of the affected population to the total population) and wait-time priority (based on the relief item last available at the disaster region) are implemented. These two priorities are calculated for each disaster region and, hence, the weighted priority is calculated by combining the two priorities at each time slot.  
Priority Index = w1 * casually factor (normalised) + w2 * wait-time (normalised)  
where w1 + w2 = 1.  
Adjusting the weights of these two priorities is another challenge as there is no unique weight adjustment approach defined. However, research has shown that there has been a temporary adjustment of resources to the disaster regions with higher casually [59; 60; 61; 62; 63; 64; 65], which shows casualty level has a higher impact on disaster management. Considering the higher importance of casualty, the weight for casualty is set with a value of 0.75 whereas the weight for wait-time is set at 0.25. Normalisation on each factor is applied in the range [0 1] where the maximum value is set to 1 and other values are divided by the corresponding maximum value. The casualty index is calculated as a ratio of the severe causality population to the total affected population in the demand regions. In general, victim conditions get worsen with time. To adjust this condition on priority, the exponential function is chosen to reflect the disaster victims' situations with wait-time. These two priorities are combined with weight factors to evaluate priorities regarding priority index as a single weighted priority scheduling model. The sum of the three weight factors is set as 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Type-1** & **Type-2** & **Type-3** & **Type-4** \\ \hline Cost/Hour (\(\ell\)) & 1000 & 1500 & 2200 & 3500 \\ \hline Capacity (kg) & 4000 & 3000 & 2500 & 2000 \\ \hline Speed (kmph) & 40 & 50 & 60 & 80 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Vehicle parameters of each type at supply points.