Integrated aircraft routing and cargo routing problem for combination airlines

The combination airlines operate both passenger aircraft and freighter aircraft to meet passenger and cargo demand. At present, combination airlines employ a sequential approach to allocating their capacity for passenger and cargo demand. Nevertheless, implementing an integrated resource allocation procedure has the potential to improve overall resource allocation efficiency. In this paper, we introduce an integrated model to help combination airlines integrate their aircraft routing and cargo routing decisions to maximize the expected overall profits derived from both passenger and cargo demand. We considered the stochastic nature of passenger baggage and proposed a set of individual chance constraints to ensure the robustness of the integrated solution. We reformulate the chance constraints using piecewise linear approximation to ensure solution efficiency. In addition, we proposed a column-and-row generation based solution approach that removes the through-connection related constraints at the beginning of the solution process and then adds the columns and rows during the iterations as needed. We proved that the proposed column-and-row generation approach can obtain an optimal solution for the LP relaxation problem. The model and the solution approach were tested in a number of scenarios obtained from a major Chinese combination airline. The computational results show that the combination airline can improve their expected profits by integrating capacity allocation. The results also demonstrated that the proposed column-and-row generation solution approach can decrease the solution time of the integrated model. These findings indicate that the model and the solution method are useful and efficient tools for combination airlines when planning their aircraft and cargo routes.