Globally Optimal Facility Locations for Continuous-Space Facility Location Problems
The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is cons...
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| Format: | Article |
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MDPI AG
2021-08-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/16/7321 |
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| author | Xuehong Gao Chanseok Park Xiaopeng Chen En Xie Guozhong Huang Dingli Zhang |
| author_facet | Xuehong Gao Chanseok Park Xiaopeng Chen En Xie Guozhong Huang Dingli Zhang |
| author_sort | Xuehong Gao |
| collection | DOAJ |
| description | The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems. |
| first_indexed | 2024-03-10T09:02:28Z |
| format | Article |
| id | doaj.art-7cc80e020b1b4cfd8016eb81023c3d14 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T09:02:28Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-7cc80e020b1b4cfd8016eb81023c3d142023-11-22T06:39:49ZengMDPI AGApplied Sciences2076-34172021-08-011116732110.3390/app11167321Globally Optimal Facility Locations for Continuous-Space Facility Location ProblemsXuehong Gao0Chanseok Park1Xiaopeng Chen2En Xie3Guozhong Huang4Dingli Zhang5Research Institute of Macro-Safety Science, School of Civil & Resources Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaDepartment of Industrial Engineering, Pusan National University, Busan 609-735, KoreaDepartment of Industrial Engineering, Pusan National University, Busan 609-735, KoreaSchool of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, ChinaResearch Institute of Macro-Safety Science, School of Civil & Resources Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaResearch Institute of Macro-Safety Science, School of Civil & Resources Engineering, University of Science and Technology Beijing, Beijing 100083, ChinaThe continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems.https://www.mdpi.com/2076-3417/11/16/7321facility location problemmathematical programmingglobal optimization |
| spellingShingle | Xuehong Gao Chanseok Park Xiaopeng Chen En Xie Guozhong Huang Dingli Zhang Globally Optimal Facility Locations for Continuous-Space Facility Location Problems Applied Sciences facility location problem mathematical programming global optimization |
| title | Globally Optimal Facility Locations for Continuous-Space Facility Location Problems |
| title_full | Globally Optimal Facility Locations for Continuous-Space Facility Location Problems |
| title_fullStr | Globally Optimal Facility Locations for Continuous-Space Facility Location Problems |
| title_full_unstemmed | Globally Optimal Facility Locations for Continuous-Space Facility Location Problems |
| title_short | Globally Optimal Facility Locations for Continuous-Space Facility Location Problems |
| title_sort | globally optimal facility locations for continuous space facility location problems |
| topic | facility location problem mathematical programming global optimization |
| url | https://www.mdpi.com/2076-3417/11/16/7321 |
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