Using column generation for gate planning at Amsterdam Airport Schiphol

Assigning a set of flights to a set of gates at an airport used to be very easy. Due to the increased number of flights and the increased number of constraints that have to be satisfied, the assignment of flights to gates has become very complex nowadays. In this paper we look at the gate assignment problem as it appears at Schiphol Airport Amsterdam. Given the expected arrivals and departures for the next 24 hours, we aim at finding a robust solution, such that the amount of replanning due to deviations from the expected arrival and departure times is minimum. We solve this problem by a two-phase procedure. In the first phase, we solve the problem in which we include the single-gate constraints; in the second phase, we consider the constraints in which multiple gates are involved. We solve the first-phase problem by formulating it as an integer linear program (ILP) using a completely new formulation. We find an approximately optimal solution for it by solving the ILP for a restricted set of variables. We find this restricted set by first solving the LP-relaxation problem by means of column generation. In every iteration of the column generation a small number of additional columns are also generated and put into a column pool. After the LP-relaxation problem has been solved to optimality, the generated columns and all additional columns from the column pool are used to solve the ILP problem. This part of the solution is then handed to the planners at Schiphol as an input for the second phase. To test the performance of the algorithm we have implemented it, and we have tested this implementation with real life data provided by Amsterdam Airport Schiphol. The results are promising and the algorithm is able to solve real-life instances within acceptable running