Generic model for capacity allocation on transportation terminals

Transportation terminals play an important role in the functioning of the transportation system. Therefore, the efficient use of the capacity of transportation terminals is considered a major determinant of the performance of transportation networks. An important decision related to the efficient functioning of congested terminals relates to the optimum allocation of the available capacity to different operators (users). The capacity allocation problem in transportation terminals, such as airports, railroad stations, ports, involves the optimum apportion of the available capacity to different users, such as airlines, rail, and shipping companies, while satisfying operational, and regulatory constraints and requirements. Motivated by the similarities across capacity allocation problems in terminals of different transportation modes and the lack of a unifying framework, this study introduces a generic mixed integer linear programming (MILP) formulation and demonstrates its applicability through a detailed application of the proposed model for rail networks. The generic mathematical model is a generalization of models highly utilized in airport slot allocation. We explicitly present how the model applies to the train timetabling problem and conduct computational experiments using publicly available data. Our computational experiments show that the model consistently achieves optimal solutions across almost all tested cases, including instances where published solutions are suboptimal. The analysis of the results for a specific instance indicates that incorporating station capacity constraints yields the same set of scheduled requests but alters the deviations from the desired arrival and departure times. In contrast, increase in the flexibility of the requested times significantly affect the solution, leading to increase in the number of scheduled trains, deviations, and the overall length of the journey.