Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems
The robust Mixed-Integer Linear Programming (MILP) model is an approach to address uncertainty in linear optimization involving integer and continuous variables, which can be solved using the Benders Decomposition method. One of its applications is facility location problems, which often face demand...
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| Format: | Article |
| Language: | English |
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Mathematics Department UIN Maulana Malik Ibrahim Malang
2025-03-01
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| Series: | Cauchy: Jurnal Matematika Murni dan Aplikasi |
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| Online Access: | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/31539 |
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| author | Fadiah Hasna Nadiatul Haq Diah Chaerani Anita Triska |
| author_facet | Fadiah Hasna Nadiatul Haq Diah Chaerani Anita Triska |
| author_sort | Fadiah Hasna Nadiatul Haq |
| collection | DOAJ |
| description | The robust Mixed-Integer Linear Programming (MILP) model is an approach to address uncertainty in linear optimization involving integer and continuous variables, which can be solved using the Benders Decomposition method. One of its applications is facility location problems, which often face demand, costs, and capacity uncertainties. This article presents a systematic literature review (SLR) on solving robust MILP models using the Benders Decomposition method and its application to facility location problems. The objectives are to explore the state-of-the-art and research trends, identify issues modeled as robust MILP and solved using Benders Decomposition, and determine the most frequently used uncertainty sets. SLR was conducted using the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) method on the Scopus, Science Direct, and Dimensions databases for the last five years of publication, with bibliometric analysis using VOSviewer and RStudio. The results show that there are limited articles that discuss the solution of the robust MILP model on the problem of facility location with the ellipsoidal uncertainty set. In addition, the Benders Decomposition method is widely used to solve robust MILP problems in energy, logistics, supply chains, and scheduling, with interval uncertainty sets being the most common. This topic is an influential theme and has the potential to be explored further. |
| format | Article |
| id | doaj-art-d1b311d459e84df495615cc80a47e409 |
| institution | Kabale University |
| issn | 2086-0382 2477-3344 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Mathematics Department UIN Maulana Malik Ibrahim Malang |
| record_format | Article |
| series | Cauchy: Jurnal Matematika Murni dan Aplikasi |
| spelling | doaj-art-d1b311d459e84df495615cc80a47e4092025-08-20T03:48:30ZengMathematics Department UIN Maulana Malik Ibrahim MalangCauchy: Jurnal Matematika Murni dan Aplikasi2086-03822477-33442025-03-0110132634410.18860/cauchy.v10i1.315398663Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location ProblemsFadiah Hasna Nadiatul Haq0Diah ChaeraniAnita Triska1Master's Program of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, 45363 Jatinangor, Sumedang, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Padjadjaran, 45363 Jatinangor, Sumedang, IndonesiaThe robust Mixed-Integer Linear Programming (MILP) model is an approach to address uncertainty in linear optimization involving integer and continuous variables, which can be solved using the Benders Decomposition method. One of its applications is facility location problems, which often face demand, costs, and capacity uncertainties. This article presents a systematic literature review (SLR) on solving robust MILP models using the Benders Decomposition method and its application to facility location problems. The objectives are to explore the state-of-the-art and research trends, identify issues modeled as robust MILP and solved using Benders Decomposition, and determine the most frequently used uncertainty sets. SLR was conducted using the Preferred Reporting Items for Systematic Review and Meta-Analysis (PRISMA) method on the Scopus, Science Direct, and Dimensions databases for the last five years of publication, with bibliometric analysis using VOSviewer and RStudio. The results show that there are limited articles that discuss the solution of the robust MILP model on the problem of facility location with the ellipsoidal uncertainty set. In addition, the Benders Decomposition method is widely used to solve robust MILP problems in energy, logistics, supply chains, and scheduling, with interval uncertainty sets being the most common. This topic is an influential theme and has the potential to be explored further.https://ejournal.uin-malang.ac.id/index.php/Math/article/view/31539systematic literature reviewrobust optimizationmixed-integer linear programmingbenders decompositionfacility location problem |
| spellingShingle | Fadiah Hasna Nadiatul Haq Diah Chaerani Anita Triska Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems Cauchy: Jurnal Matematika Murni dan Aplikasi systematic literature review robust optimization mixed-integer linear programming benders decomposition facility location problem |
| title | Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems |
| title_full | Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems |
| title_fullStr | Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems |
| title_full_unstemmed | Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems |
| title_short | Systematic Literature Review for Robust Mixed-Integer Linear Programming Models Using Benders Decomposition in Facility Location Problems |
| title_sort | systematic literature review for robust mixed integer linear programming models using benders decomposition in facility location problems |
| topic | systematic literature review robust optimization mixed-integer linear programming benders decomposition facility location problem |
| url | https://ejournal.uin-malang.ac.id/index.php/Math/article/view/31539 |
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