Analysis of an integrated maximum covering and patrol routing problem

Keskin, Burcu B.; Li, Shirley Xin; Steil, Dana; Spiller, Sarah

doi:10.1016/j.tre.2011.07.005

Cited by 39 publications

(53 citation statements)

References 32 publications

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“…The first area is related to defining hot spots via clustering analysis of historical crash and citation data [2][3][4]6,[11][12][13][14]. The second area in data-driven law enforcement, to which this paper contributes, is concerned with the use of predetermined hot spot information in setting effective operational plans that enhance public safety [9,10].…”

Section: Introductionmentioning

confidence: 99%

“…We present here an improved formulation to the maximum covering and patrol routing problem (MCPRP) that was first defined by Keskin et al [9]. In the MCPRP, certain locations on the highways are "hot" at certain times.…”

Section: Introductionmentioning

confidence: 99%

“…The objective of the MCPRP is to maximize coverage of hot spots with a fixed set of state troopers, belonging to a single trooper post. Keskin et al [9] formulate a mixed integer linear model to solve MCPRP. By demonstrating similarities to the team orienteering problem with time windows [5,16,17], Keskin et al [9] show that MCPRP is NP-Hard and resort to local-and tabusearch based heuristics.…”

Section: Introductionmentioning

confidence: 99%

“…Our improved formulation retains the original assumptions of the MCPRP formulation [9], including (i) that deterrence is not increased by the simultaneous presence of multiple state trooper vehicles, and (ii) that distinct hot spots at the same physical location (but different times) may be patrolled by different vehicles. In this paper, we first investigate the structural properties of the optimal solution of the MCPRP and prove that an optimal solution must exist in which no hot spot is patrolled by more than one state trooper.…”

Section: Introductionmentioning

confidence: 99%

“…Reformulating a problem and improving bounds are common techniques to solve "hard" optimization problems in the literature [1,8,15]. With the improved formulation, we solve real life test instances and large randomly generated test instances to optimality within a short time, where Keskin et al [9] fail to solve those instances to optimality. Moreover, we improve the coverage of the hot spots as much as 46.19% and 13.6% respectively for randomly generated and real life instances.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An improved formulation for the maximum coverage patrol routing problem

Çapar

Keskin

Rubin

2015

Computers & Operations Research

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An improved formulation for the maximum coverage patrol routing problem

Çapar

Keskin

Rubin

2015

Computers & Operations Research

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On the computational complexity of the patrol boat scheduling problem with complete coverage

Surendonk

Chircop

2020

Naval Research Logistics

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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.

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