An integer programming approach to sectorization with compactness and equilibrium constraints

Valeria Romanciuc; Cristina Lopes; Aydin Teymourifar; Ana Maria Rodrigues; José Soeiro Ferreira; Cristina Oliveira; Elif Göksu Öztürk

doi:10.1007/978-3-030-78170-5_17

An integer programming approach to sectorization with compactness and equilibrium constraints

Valeria Romanciuc, Cristina Lopes^*, Aydin Teymourifar, Ana Maria Rodrigues, José Soeiro Ferreira, Cristina Oliveira, Elif Göksu Öztürk

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Citations (Scopus)

Abstract

The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.

Original language	English
Title of host publication	Innovations in industrial engineering
Editors	José Machado, Filomena Soares, Justyna Trojanowska, Vitalii Ivanov
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	185-196
Number of pages	12
ISBN (Print)	9783030781699
DOIs	https://doi.org/10.1007/978-3-030-78170-5_17
Publication status	Published - 2022
Externally published	Yes
Event	1st International Conference on Innovation in Engineering, ICIE 2021 - Guimarães, Portugal Duration: 28 Jun 2021 → 30 Jun 2021

Publication series

Name	Lecture Notes in Mechanical Engineering
ISSN (Print)	2195-4356
ISSN (Electronic)	2195-4364

Conference

Conference	1st International Conference on Innovation in Engineering, ICIE 2021
Country/Territory	Portugal
City	Guimarães
Period	28/06/21 → 30/06/21

Keywords

Integer programming
Multi-criteria
Sectorization

Access to Document

10.1007/978-3-030-78170-5_17

Cite this

Romanciuc, V., Lopes, C., Teymourifar, A., Rodrigues, A. M., Ferreira, J. S., Oliveira, C., & Öztürk, E. G. (2022). An integer programming approach to sectorization with compactness and equilibrium constraints. In J. Machado, F. Soares, J. Trojanowska, & V. Ivanov (Eds.), Innovations in industrial engineering (pp. 185-196). (Lecture Notes in Mechanical Engineering). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-78170-5_17

Romanciuc, Valeria ; Lopes, Cristina ; Teymourifar, Aydin et al. / An integer programming approach to sectorization with compactness and equilibrium constraints. Innovations in industrial engineering. editor / José Machado ; Filomena Soares ; Justyna Trojanowska ; Vitalii Ivanov. Springer Science and Business Media Deutschland GmbH, 2022. pp. 185-196 (Lecture Notes in Mechanical Engineering).

@inproceedings{0778ae9894004e4fbde1d20ecd73197b,

title = "An integer programming approach to sectorization with compactness and equilibrium constraints",

abstract = "The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.",

keywords = "Integer programming, Multi-criteria, Sectorization",

author = "Valeria Romanciuc and Cristina Lopes and Aydin Teymourifar and Rodrigues, {Ana Maria} and Ferreira, {Jos{\'e} Soeiro} and Cristina Oliveira and {\"O}zt{\"u}rk, {Elif G{\"o}ksu}",

note = "Funding Information: Acknowledgments. This work is financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Funda¸c{\~a}o para a Ci{\^e}ncia e a Tecnologia within project POCI-01-0145-FEDER-031671. Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 1st International Conference on Innovation in Engineering, ICIE 2021 ; Conference date: 28-06-2021 Through 30-06-2021",

year = "2022",

doi = "10.1007/978-3-030-78170-5_17",

language = "English",

isbn = "9783030781699",

series = "Lecture Notes in Mechanical Engineering",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "185--196",

editor = "Jos{\'e} Machado and Filomena Soares and Justyna Trojanowska and Vitalii Ivanov",

booktitle = "Innovations in industrial engineering",

address = "Germany",

}

Romanciuc, V, Lopes, C, Teymourifar, A, Rodrigues, AM, Ferreira, JS, Oliveira, C & Öztürk, EG 2022, An integer programming approach to sectorization with compactness and equilibrium constraints. in J Machado, F Soares, J Trojanowska & V Ivanov (eds), Innovations in industrial engineering. Lecture Notes in Mechanical Engineering, Springer Science and Business Media Deutschland GmbH, pp. 185-196, 1st International Conference on Innovation in Engineering, ICIE 2021, Guimarães, Portugal, 28/06/21. https://doi.org/10.1007/978-3-030-78170-5_17

An integer programming approach to sectorization with compactness and equilibrium constraints. / Romanciuc, Valeria; Lopes, Cristina; Teymourifar, Aydin et al.
Innovations in industrial engineering. ed. / José Machado; Filomena Soares; Justyna Trojanowska; Vitalii Ivanov. Springer Science and Business Media Deutschland GmbH, 2022. p. 185-196 (Lecture Notes in Mechanical Engineering).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - An integer programming approach to sectorization with compactness and equilibrium constraints

AU - Romanciuc, Valeria

AU - Lopes, Cristina

AU - Teymourifar, Aydin

AU - Rodrigues, Ana Maria

AU - Ferreira, José Soeiro

AU - Oliveira, Cristina

AU - Öztürk, Elif Göksu

N1 - Funding Information: Acknowledgments. This work is financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Funda¸cão para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-031671. Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2022

Y1 - 2022

N2 - The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.

AB - The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.

KW - Integer programming

KW - Multi-criteria

KW - Sectorization

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DO - 10.1007/978-3-030-78170-5_17

M3 - Conference contribution

AN - SCOPUS:85111448953

SN - 9783030781699

T3 - Lecture Notes in Mechanical Engineering

SP - 185

EP - 196

BT - Innovations in industrial engineering

A2 - Machado, José

A2 - Soares, Filomena

A2 - Trojanowska, Justyna

A2 - Ivanov, Vitalii

PB - Springer Science and Business Media Deutschland GmbH

T2 - 1st International Conference on Innovation in Engineering, ICIE 2021

Y2 - 28 June 2021 through 30 June 2021

ER -

Romanciuc V, Lopes C, Teymourifar A, Rodrigues AM, Ferreira JS, Oliveira C et al. An integer programming approach to sectorization with compactness and equilibrium constraints. In Machado J, Soares F, Trojanowska J, Ivanov V, editors, Innovations in industrial engineering. Springer Science and Business Media Deutschland GmbH. 2022. p. 185-196. (Lecture Notes in Mechanical Engineering). doi: 10.1007/978-3-030-78170-5_17

An integer programming approach to sectorization with compactness and equilibrium constraints

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