Column generation based solution for bi-objective gate assignment problems

In this paper, we present a column generation-based algorithm for the bi-objective gate assignment problem (GAP) to generate gate schedules that minimize squared slack time at the gates while satisfying passenger expectations by minimizing their walking distance. While most of the literature focuses on heuristic or metaheuristic solutions for the bi-objective GAP, we propose flow-based and column-based models that lead to exact or near optimal solution approaches. The developed algorithm calculates a set of solutions to approximate the Pareto front. The algorithm is applied to the over-constrained GAP where gates are a limited resource and it is not possible to serve every flight using a gate. Our test cases are based on real data from an international airport and include various instances with flight-to-gate ratios between 23.9 and 34.7. Numerical results reveal that a set of solutions representing a compromise between the passenger-oriented and robustness-oriented objectives may be obtained with a tight optimality gap and within reasonable computational time even for these difficult problems.