© 2021 Elsevier LtdIn this study, we consider an airport gate assignment problem that assigns a set of aircraft to a set of gates. The aircraft that cannot be assigned to any gate are directed to an apron. We aim to make aircraft-gate assignments so as to minimize the number of aircraft assigned to apron and among the apron usage minimizing solutions, we aim to minimize total walking distance travelled by all passengers. The problem is formulated as a mixed-integer nonlinear programming model and then it is linearized. A branch and bound algorithm, beam search and filtered beam search algorithms that employ powerful lower and upper bounding mechanisms are developed. The results of the computational experiment have shown the satisfactory performance of the algorithms.