This article presents an exact algorithm that is combined with a heuristic method to find the optimal solution for an airplane landing problem. For a given set of airplanes and runways, the objective is to minimize the accumulated deviations from the target landing time of the airplanes. A cost associated with landing either earlier or later than the target landing time is incurred for each airplane within its predetermined time window. In order to manage this type of large-scale optimization problem, a set partitioning formulation that results in a mixed integer linear program is proposed. One key contribution of this article is the development of a branch-and-price methodology, in which the column generation method is integrated with the branch-and-bound method in order to find the optimal integer solution. In addition to the exact algorithm, a simple heuristic method is also presented to tighten the solution space. Numerical experiments are undertaken for the proposed algorithm in order to confirm its effectiveness using public data from the OR-Library. As an application in the real-world situation of airplane landing, air traffic data from Incheon International Airport is employed to assure the efficiency of the proposed algorithm.