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The time it takes passengers to board an airplane is known to influence the turnaround time of the aircraft and thus bears a significant cost-saving potential for airlines. Although minimizing boarding time therefore is the most important goal from an economic perspective, previous efforts to design efficient boarding strategies apparently never tackled this task directly. In this paper, we first rigorously define the problem and prove its NP-hardness. Although this generally justifies the development of inexact solution methods, we show that all commonly discussed boarding strategies may in fact give solutions that are far from optimal. We complement these theoretical findings by a simple time-aware boarding strategy with guaranteed approximation quality (under reasonable assumptions) as well as a local improvement heuristic and an exact mixed-integer programming (MIP) formulation. Our numerical experiments with simulation data show that for several airplane cabin layouts, provably high-quality or even optimal solutions can be obtained within reasonable time in practice by means of our MIP approach. We also empirically assess the sensitivity of boarding strategies with respect to disruptions of the prescribed boarding sequences and identify robustness against such disruptions as a bottleneck for further improvements.

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