Slot Allocation by Column Generation

A slot allocation policy assigns a time slot for departure to each of a number of flights in order to avoid overload in control sectors and on runways. We present a new solution method for a basic version of the European slot allocation problem. The approach is based on an integer linear programming model, where for each flight there is a set of 0-1 variables each associated with one of its possible departure slots. First, column generation is used to solve the LP-relaxation. This results in the construction of a reasonable set of departure slots for each of the flights. Then, the resulting integer linear program is solved. We also present a rounding heuristic to derive feasible integral solutions from fractional solutions after each iteration of the column generation algorithm. Computational results for real-world problems are encouraging, because they indicate that compared to existing exact optimisation algorithms our method generates solutions of approximately the same quality but requires only a fraction of the computation time. Moreover, they indicate that the rounding heuristic performs well.