Lagrangian relaxation for airport gate assignment problem

Abstract

In this study 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 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 our Lagrangian relaxation based method returns strong lower bounds and good quality upper bounds that are comparable to the state-of-the art results from the literature.