# Relief Aircraft Dispatch Strategies Based on Different Levels of Information Sharing Systems
## 3 Model Establishment  
In this research, our main aim is to compare the efficiency of different information sharing levels in air relief activities. To facilitate the modeling, we analyze the efficiency of different dispatch strategies, based on the different information sharing levels. This is a sequential optimization problem, which includes demand inputs to inform aircraft dispatchment decisions based on received information in real-time. We take an iterative approach to optimization, incorporating new information to obtain the optimal result. In this section, the characteristics of our aims are analyzed and an overall model is proposed. Different transport strategies for iterative optimization are proposed based on different information sharing levels in Section 4. Section 5 introduces the simulation structure used in this research.  
Based on past relief activities ([PERSON] et al. [1]), the demand requests from affected areas are generally reported to local authorities or relief response centers. Then, the authorities or centers transfer these requests to aircraft dispatchment centers in the airport to arrange relief aircraft transportation of persons to hospitals or designated locations. In this research, we simplify this process as follows: demand requests (injuries or personnel) can be reported from the shelter sites to aircraft dispatchment centers in airports; then, aircraft dispatchers can send aircrafts to these shelter sites and transport the injured to the airport. Besides, in actual air relief activities, the demand is usually greater than the actual transportation capacity. Thus, prediction of future demand is not usually considered.  
Therefore, this study considers an aircraft fleet transporting the injured back to the airport based on the requests from rescue centers that are updated throughout a finite horizon. Moreover, aircraft dispatchers cannot determine or forecast future requests.  
Figure 3 shows an overview of the temporal nature of the problem. At the instance \"now,\" the fleet operator has complete information about past injury requests, and the dispatchment center could assign the aircraft based on the injury requests and available aircraft. However, they have no information about future injury requests.  
Figure 3: Overview of the temporal aspect of relief aircraft dispatch.  
Our model is a type of sequential optimization problem [13; 33]. Here, we use the Bellman equation to provide a solution approach:  
\[Min{\sum_{t}}\Bigg{\{}C(S_{t},x_{t})+\sum_{s^{*}\in S}V_{t+1}(s^{*})\Bigg{\}} \tag{1}\]  
where \(S_{t}\) is the state of the system at time \(t\), which contains the states of all the agents such as demand reports, aircraft, and dispatch centers, \(x_{t}\) is the decision variable, which denotes the assignment of the aircraft to the demand request, \(C(S_{t},\,x_{t})\) is the summary objective value of the system in state \(S\) at time \(t\), \(Vt(s)\) represents the objective value of the system in state \(S\) at time \(t\) and \(s^{*}\) is the state of a part of the system at time \(t+1\).  
Based on this, we can compare several policies that differ in their method used in solving the local optimization problem \(Min\{C(S_{t},x_{t})\}\). These different policies are implemented when the system finds unprocessed reported requests and available aircraft simultaneously:  
\[Min{\sum_{t}}\sum_{a\in A^{t}}\left(Dis(\sum_{i\in R^{t}}x_{i}^{a})\right) \tag{2}\]  
\[\sum x_{i}^{a}\geq 1\quad\forall\;\;a\in A^{t} \tag{3}\]  
\[\sum x_{i}^{a}\geq 1\quad\forall\;\;i\in R^{t} \tag{4}\]  
where \(x\) is the decision variable at time \(t\), \(A^{t}\) is the set of available aircraft at time \(t\) and \(R^{t}\) is the set of requests at time \(t\).  
Equation (2) minimizes the overall distance covered in transporting the injured, which is the objective whenever the policy is implemented. Equation (3) indicates that any chosen aircraft can be assigned to one shelter. Equation (4) indicates that any chosen shelter can be dispatched to one aircraft.