# Airline Network Planning Considering Climate Impact: Assessing New Operational Improvements
## 2 Materials and Methods
### Integrated Network Planning Model
#### 2.3.2 Fleet Allocation Agents  
The fleet allocation agents define the best weekly flight schedule and aircraft routes per aircraft type in the fleet. A number of agents, equal to the number of fleet types, solve the partial fleet assignment problem. All the agents receive the same input but solve the fleet assignment problem partially, which is only associated with the available fleet from their own aircraft type. The problem that fleet allocation agents address has a similar approach to the framework in [43; 44]. At the same time, it was improved to incorporate the OIs-related considerations and multi-objective formulation. The idea is to break down the optimisation problem into smaller sub-problems for each aircraft type. Each fleet allocation agent determines their aircraft type's best route and schedule. They solve the problem independently and define the optimal allocation according to the considered route, _passenger flow_ per time step, associated airfare, and operating costs. Under standard circumstances, the optimal aircraft assignment is solely determined by profit (i.e., the difference between the potential revenue from passenger transportation and the operating costs of the flights on the schedule). However, if the climate impact is taken into account as an additional planning objective, the objective function formulation needs to be adjusted. To achieve this, we used a modified profitability metric [45], which factors in profit per climate impact unit (ATR20). The goal then becomes to identify the network planning decisions that maximise the ratio of profit to ATR20 values. We introduced ATR20 into the objective function using the formulation presented in Equation (1). Using ATR20 as the climate impact unit in this equation was due to focusing on the climate impact in the near future. Therefore, using any other unit in this regard, including ATR100, is possible and only depends on the research goal. \[ \begin{split} T_{i}^{t}&=\frac{Profit_{i}^{t}}{ATR20 _{i}}&& ifProfit_{i}^{t}\geq 0\\ T_{i}^{t}&=\frac{Profit_{i}^{t}}{ATR20_{max}+ ATR20_{min}-ATR20_{i}}&& ifProfit_{i}^{t}<0\end{split}  \tag{1}\]  
Figure 2: Weekly passenger demand distributions for KLM in 2018 (each time step equals 20 min): (**a**) initial demand; and (**b**) updated demand after assigning a flight. The multi-objective approach utilises the \(T_{i}^{t}\) formulation, which stands for _transformed profit_, where \(i\) is the route index and \(t\) is the time step. Different formulations are used to distinguish the positive and negative profit values to keep this metric monotonically increasing with the increase in profit and decrease in ATR20. Increasing a positive profit in the numerator or decreasing ATR20 in the denominator results in a higher value for _transformed profit_. In the case of negative profits, a lower ATR20 results in a higher absolute value of the _transformed profit_. Nevertheless, it is worse when maximising the objective function due to the negative sign. The time-space network represents the possible movements of aircraft over time (as can be seen in Figure 3). The arrows indicate the aircraft flights in time \(t\) (vertical axis) and space \(i\) (horizontal axis, representing airports). The edges represent the possibility of flying between airports at a specific departure time or the decision to ground the aircraft at the airport. The problem of determining which flight arcs the aircraft should be allocated is solved using a dynamic programming algorithm. According to this algorithm, the potential profits per flight are mapped, and the optimal aircraft route and flight schedule are obtained following the shortest path algorithm (i.e., profit maximisation). The profit per flight is calculated by multiplying the estimated _passenger flow_ by the average airfare on that route deducted by the associated DOC. The agents sequentially follow this process to allocate a set of aircraft of the same type to the network.