Using Submodularity within Column Generation to Solve the Flight-to-Gate Assignment Problem

TL;DR

This paper introduces a novel column generation approach utilizing submodularity and dynamic programming to efficiently solve the airport flight-to-gate assignment problem, minimizing delays and handling large instances effectively.

Contribution

It is the first to leverage submodularity in the pricing problem within column generation for this application, enhancing computational efficiency and solution quality.

Findings

The approach reduces total delay times significantly.

Dynamic programming is pseudo-polynomial with integer inputs.

The method scales well to large problem instances.

Abstract

In this paper, we provide a column generation-based approach for solving the airport flight-to-gate assignment problem, where the goal is to minimize the on-ground portion of arrival delays by optimally assigning each scheduled flight to a compatible gate. Specifically, we use a set covering formulation for the master problem and decompose the pricing problem such that each gate is the basis for an independent pricing problem to be solved for assignment patterns with negative reduced costs. We use a combination of an approximation algorithm based on the submodularity of the underlying set and dynamic programming algorithms to solve the independent pricing problems. To the best of our knowledge, this is the first use of submodularity property to efficiently solve pricing problems and improve the performance of column generation algorithm. We show that the dynamic programming algorithm is pseudo-polynomial when there are integer inputs. We also design and employ a rolling horizon method and block decomposition algorithm to solve large-sized instances. Finally, we perform extensive computational experiments to validate the performance of our approach.