On the computational complexity of the patrol boat scheduling problem with complete coverage
Our study is primarily concerned with analyzing the computational complexity of the patrol boat scheduling problem with complete coverage (PBSPCC). This combinatorial optimization problem has important implications for maritime border protection and surveillance operations. The objective of the PBSP...
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Published in | Naval research logistics Vol. 67; no. 4; pp. 289 - 299 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Hoboken, USA
John Wiley & Sons, Inc
01.06.2020
Wiley Subscription Services, Inc |
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Online Access | Get full text |
ISSN | 0894-069X 1520-6750 |
DOI | 10.1002/nav.21900 |
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Abstract | Our study is primarily concerned with analyzing the computational complexity of the patrol boat scheduling problem with complete coverage (PBSPCC). This combinatorial optimization problem has important implications for maritime border protection and surveillance operations. The objective of the PBSPCC is to find a minimum size patrol boat fleet to provide ongoing continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. This requirement is complicated by the necessity for patrol vessels to be replenished on a regular basis in order to carry out patrol operations indefinitely. We introduce the PBSPCC via an example, discuss its relationship to related but dissimilar problems in the literature and proffer a mathematical description of the problem. We then show that the PBSPCC is NP‐hard by a transformation of the Hamiltonian graph decision problem into the problem of finding a minimum cyclic covering of a patrol network. We conclude that the associated decision problem of whether a patrol network has a continuous cover is NP‐complete, subject to the requirement that patrol covering solutions are cyclic of a bounded polynomial order. |
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AbstractList | Our study is primarily concerned with analyzing the computational complexity of the patrol boat scheduling problem with complete coverage (PBSPCC). This combinatorial optimization problem has important implications for maritime border protection and surveillance operations. The objective of the PBSPCC is to find a minimum size patrol boat fleet to provide ongoing continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. This requirement is complicated by the necessity for patrol vessels to be replenished on a regular basis in order to carry out patrol operations indefinitely. We introduce the PBSPCC via an example, discuss its relationship to related but dissimilar problems in the literature and proffer a mathematical description of the problem. We then show that the PBSPCC is
‐hard by a transformation of the Hamiltonian graph decision problem into the problem of finding a minimum cyclic covering of a patrol network. We conclude that the associated decision problem of whether a patrol network has a continuous cover is
‐complete, subject to the requirement that patrol covering solutions are cyclic of a bounded polynomial order. Our study is primarily concerned with analyzing the computational complexity of the patrol boat scheduling problem with complete coverage (PBSPCC). This combinatorial optimization problem has important implications for maritime border protection and surveillance operations. The objective of the PBSPCC is to find a minimum size patrol boat fleet to provide ongoing continuous coverage at a set of maritime patrol regions, ensuring that there is at least one vessel on station in each patrol region at any given time. This requirement is complicated by the necessity for patrol vessels to be replenished on a regular basis in order to carry out patrol operations indefinitely. We introduce the PBSPCC via an example, discuss its relationship to related but dissimilar problems in the literature and proffer a mathematical description of the problem. We then show that the PBSPCC is NP‐hard by a transformation of the Hamiltonian graph decision problem into the problem of finding a minimum cyclic covering of a patrol network. We conclude that the associated decision problem of whether a patrol network has a continuous cover is NP‐complete, subject to the requirement that patrol covering solutions are cyclic of a bounded polynomial order. |
Author | Chircop, Paul A. Surendonk, Timothy J. |
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Cites_doi | 10.1016/j.ocecoaman.2012.01.001 10.1007/978-1-4684-2001-2_9 10.1016/j.tre.2011.07.005 10.1177/1548512919883955 10.1007/s10846-013-9958-8 10.1007/s10846-012-9727-0 10.1016/j.cor.2014.12.002 10.1007/s10846-013-9970-z 10.1016/j.ejor.2015.05.067 10.1057/jors.2013.116 |
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Copyright | 2020 Commonwealth of Australia. Naval Research Logistics © 2020 Wiley Periodicals, Inc. 2020 Wiley Periodicals, Inc. |
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References | 2012; 60 2015; 59 2012 2015; 247 2019 2017 2013; 70 1972 2013 2012; 48 2014; 74 1979 2014; 65 e_1_2_8_13_1 e_1_2_8_14_1 e_1_2_8_15_1 e_1_2_8_3_1 e_1_2_8_2_1 e_1_2_8_4_1 e_1_2_8_6_1 e_1_2_8_9_1 e_1_2_8_8_1 e_1_2_8_10_1 e_1_2_8_11_1 Chircop P. A. (e_1_2_8_5_1) 2013 e_1_2_8_12_1 Garey M. R. (e_1_2_8_7_1) 1979 |
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SubjectTerms | Boats Combinatorial analysis Completeness Complexity computational complexity continuous coverage problem Defence craft Optimization patrol operations Polynomials routing Scheduling |
Title | On the computational complexity of the patrol boat scheduling problem with complete coverage |
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