A minimum cost network flow model for the maximum covering and patrol routing problem

Dewil, Reginald; Vansteenwegen, Pieter; Cattrysse, Dirk; Oudheusden, Dirk Van

doi:10.1016/j.ejor.2015.05.067

Cited by 27 publications

(19 citation statements)

References 22 publications

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“…As outlined in Section 3.3, the study of the MCPRP conducted by Dewil et al (2015) demonstrated that the problem is not  -hard as claimed by Keskin et al (2012), where the MCPRP was formulated as an extensive MIP. This highlights a valuable lesson in addressing the computational complexity of a combinatorial optimization problem which can be correctly formulated via different modeling approaches.…”

Section: Mathematical Description Of the Pbspccmentioning

confidence: 97%

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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Section: Mathematical Description Of the Pbspccmentioning

confidence: 97%

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

Surendonk

Chircop

2020

Naval Research Logistics

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“…Models and algorithms for optimal dynamic allocation of patrol tugs to oil tankers along the northern Norwegian coast General models on resource allocation and patrol routing problems in the literature include p-median problems (p-MP) (Campbell, 1996;Church and ReVelle, 1976;Church et al, 2004;Ishfaq and Sox, 2010), p-center problems (p-CP) (Davidović et al, 2011;Drezner, 1984;Espejo et al, 2015;Suzuki and Drezner, 1996), covering problems that are categorized into maximal covering location problems (MCLP) (Balcik and Beamon, 2008;Church and ReVelle, 1974;Davari et al, 2011), set covering problems (SCP) (Badri et al, 1998;Beasley and Jørnsten, 1992;Caprara et al, 2000), maximum coverage patrol routing problems (MCPRP) (Capar et al, 2015;Dewil et al, 2015;Keskin et al, 2012;Li and Keskin, 2013) and police districting problems (PDP) D'Amico et al, 2002).…”

Section: Related Literaturementioning

confidence: 99%

Preventing environmental disasters from grounding accidents: A case study of tugboat positioning along the Norwegian coast

Assimizele

Røyset

Bye

et al. 2018

Journal of the Operational Research Society

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An important task of operators in Norwegian vessel traffic services (VTS) centers is to cleverly position tugboats before potential vessel distress calls. Here, we formulate a nonlinear binary-integer program, integrated in a receding horizon control algorithm, that minimizes the expected cost of grounding accidents by positioning tugboats optimally under uncertainty about vessel incidents and environmental conditions. Linearizations of the model lead to easy-to-compute bounds on the optimal value. Numerical experiments with real-world data demonstrate significant reduction in the expected cost, suggesting that the model can be used as a decision-support tool at VTS centers.

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“…Thus, the problem is finding the cheapest way of sending the city bus from o to d through the network [61,62] while imposing that all the PoI and the pickup/dropout links are visited at least once.…”

Section: Mathematical Model and Solution Methodsmentioning

confidence: 99%

A multi-user decision support system for online city bus tour planning

et al. 2017

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Tourism is rapidly becoming a sustainable pathway toward economic prosperity for host countries and communities. Recent advances in information and communications technology, the smartphone, the Internet and Wi-Fi have given a boost to the tourism industry. The city bus tour (CBT) service is one of the most successful businesses in the tourism industry. However, there exists no smart decision support system determining the most efficient way to plan the itinerary of a CBT. In this research, we report on the ongoing development of a mobile application (app) and a website for tourists, hoteliers and travel agents to connect with city bus operators and book/purchase the best CBT both in terms of cost and time. Firstly, the CBT problem is formulated as an asymmetric sequential three-stage arc routing problem. All places of interest (PoI) and pickup/dropout points are identified with arcs of the network (instead of nodes), each of which can be visited at least once (instead of exactly once). Secondly, the resulting pure integer programming (IP) problem is solved using a leading optimization software known as General Algebraic Modeling System (GAMS). The GAMS code developed for this project returns: (1) the exact optimal solution identifying the footprints of the city bus relative to all the arcs forming the minimal cost network; (2) the augmenting paths corresponding to the pickup stage, the PoI visiting stage and the drop-off stage. Finally, we demonstrate the applicability of the mobile app/website via a pilot study in the city of Melbourne (Australia). All the computations relative to the initial tests show that the ability of the app to answer users' inquiries in a fraction of a minute.

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A minimum cost network flow model for the maximum covering and patrol routing problem

Cited by 27 publications

References 22 publications

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

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

Preventing environmental disasters from grounding accidents: A case study of tugboat positioning along the Norwegian coast

A multi-user decision support system for online city bus tour planning

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