Lagrangian Relaxation for Airport Gate Assignment Problem

In this paper we focus on the Airport Gate Assignment Problem that minimizes the total walking distance of passengers while ensuring that the number of aircraft assigned to apron is at its minimum. We utilize an alternative formulation for the problem compared to the ones in the literature and propose approaches based on Lagrangian relaxation so as to obtain tight lower bounds. The method also harnesses the power of a good initial upper bound and provides good quality solutions. To the best of our knowledge, the current studies in the literature rely only on upper bounds or the linear relaxation lower bounds, which are hard to obtain when the problem size is large, to assess the quality of heuristic solutions. We propose using the tighter Lagrangian relaxation-based bounds as a better reference to assess solution quality. Our computational experiments demonstrate that the new formulation we propose yields tighter lower bounds compared to previous formulations in the literature. Moreover, our Lagrangian relaxation-based method returns even stronger lower bounds than those obtained by solving mixed integer programming formulations or their linear relaxations by an off-the-shelf solver.