A near-linear time algorithm and a min-cost flow approach for determining the optimal landing times of a fixed sequence of planes

The aircraft landing problem (ALP) is an important issue of assigning an airport’s runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts in practice. A large number of the extant studies have tried to address such a practical problem with using various algorithm...

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Published in:	Annals of operations research Vol. 344; no. 1; pp. 479 - 498
Main Authors:	Cao, Bin, Xu, Chao
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.01.2025 Springer Nature B.V
Subjects:	Aircraft Aircraft landing Algorithms Business and Management Combinatorics Linear programming Minimum cost Operations Research/Decision Theory Original - OR Modeling/Case Study Runways Schedules Theory of Computation Min-cost flow static single-runway system Scheduling Polynomial-time algorithm Aircraft landing problem
ISSN:	0254-5330, 1572-9338
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Abstract	The aircraft landing problem (ALP) is an important issue of assigning an airport’s runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts in practice. A large number of the extant studies have tried to address such a practical problem with using various algorithms for one or more runways. For a static single-runway of the ALP, this paper proposes a new approach to develop an alternative powerful algorithm. For a given sequence of planes, we develop a faster algorithm for solving the ALP with the running time O ( n log n ) , where n is the number of aircrafts in the schedule. Alternatively, we reduce the proposed problem of minimizing the total cost by determining the landing times for a given landing sequence into a min-cost flow problem. We conduct a set of experimental studies to compare the performance of our near-linear time algorithm to the quadratic time algorithm whose time complexity is O ( n 2 ) , for computing the optimal landing times. The computational results show that the proposed heuristic based on our algorithm could be much faster than both such quadratic time algorithm and the one using linear programming.
AbstractList	The aircraft landing problem (ALP) is an important issue of assigning an airport’s runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts in practice. A large number of the extant studies have tried to address such a practical problem with using various algorithms for one or more runways. For a static single-runway of the ALP, this paper proposes a new approach to develop an alternative powerful algorithm. For a given sequence of planes, we develop a faster algorithm for solving the ALP with the running time O(nlogn), where n is the number of aircrafts in the schedule. Alternatively, we reduce the proposed problem of minimizing the total cost by determining the landing times for a given landing sequence into a min-cost flow problem. We conduct a set of experimental studies to compare the performance of our near-linear time algorithm to the quadratic time algorithm whose time complexity is O(n2), for computing the optimal landing times. The computational results show that the proposed heuristic based on our algorithm could be much faster than both such quadratic time algorithm and the one using linear programming. The aircraft landing problem (ALP) is an important issue of assigning an airport’s runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts in practice. A large number of the extant studies have tried to address such a practical problem with using various algorithms for one or more runways. For a static single-runway of the ALP, this paper proposes a new approach to develop an alternative powerful algorithm. For a given sequence of planes, we develop a faster algorithm for solving the ALP with the running time O ( n log n ) , where n is the number of aircrafts in the schedule. Alternatively, we reduce the proposed problem of minimizing the total cost by determining the landing times for a given landing sequence into a min-cost flow problem. We conduct a set of experimental studies to compare the performance of our near-linear time algorithm to the quadratic time algorithm whose time complexity is O ( n 2 ) , for computing the optimal landing times. The computational results show that the proposed heuristic based on our algorithm could be much faster than both such quadratic time algorithm and the one using linear programming.
Author	Xu, Chao Cao, Bin
Author_xml	– sequence: 1 givenname: Bin orcidid: 0000-0002-0368-9232 surname: Cao fullname: Cao, Bin email: bincscut@gmail.com organization: School of Management, Jinan University – sequence: 2 givenname: Chao surname: Xu fullname: Xu, Chao organization: School of Computer Science and Engineering, University of Electronic Science and Technology of China
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SubjectTerms	Aircraft Aircraft landing Algorithms Business and Management Combinatorics Linear programming Minimum cost Operations Research/Decision Theory Original - OR Modeling/Case Study Runways Schedules Theory of Computation
Title	A near-linear time algorithm and a min-cost flow approach for determining the optimal landing times of a fixed sequence of planes
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