Abstract
The design of a household waste collection system must integrate decisions related to planning and control of all related operations, which may generate significant economic impacts to the organization responsible of addressing the problem as well as social impacts to involved communities. This study proposed a mixed integer linear programming model with multiple periods, which aims at designing a household waste collection system for a set of rural islands according to a set of visit patterns with a single barge for a multiple period planning horizon. The proposed model simultaneously optimizes the selection of collection sites or ports for each island and a mainland transfer port to unload the collected household waste along with a set of daily visit sequences associated with the selected ports, while minimizing total waste transportation costs. The proposed model is applied to a particular rural archipelago in southern Chile. The model solution provides an efficient waste collection system design that addresses a current ecological and health problems in the studied area.
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Appendix
Appendix
Matrix Distance Between Nodes (Ports).
Ports | Dalcahue | Dal puerto | Quemchi | Quellón | Coldita | Añihué | Tac | Llingua | Meulín | Quenac | Caguache | Apiao | Chaulinec |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Dalcahue | 0 | 0 | 0 | 0 | 82 | 20 | 23 | 13 | 16 | 17 | 23 | 27 | 25 |
Dal puerto | 0 | 0 | 0 | 0 | 82 | 20 | 23 | 13 | 16 | 17 | 23 | 27 | 25 |
Quemchi | 0 | 0 | 0 | 154 | 166 | 33 | 40 | 62 | 59 | 59 | 68.4 | 53 | 56 |
Quellón | 0 | 0 | 154 | 0 | 14 | 164 | 153 | 150 | 146 | 139 | 138 | 129 | 119 |
Coldita | 82 | 82 | 166 | 14 | 0 | 69 | 65 | 62 | 66 | 64 | 57.3 | 52 | 53 |
Añihué | 20 | 20 | 33 | 164 | 69 | 0 | 5.1 | 14 | 6.7 | 9.5 | 12.9 | 17 | 20 |
Tac | 23 | 23 | 40 | 153 | 65 | 5.1 | 0 | 19 | 11 | 17 | 11.3 | 14 | 18 |
Llingua | 13 | 13 | 62 | 150 | 62 | 14 | 19 | 0 | 9.3 | 5.6 | 11.3 | 16 | 20 |
Meulín | 16 | 16 | 59 | 146 | 66 | 6.7 | 11 | 9.3 | 0 | 4.6 | 9.3 | 14 | 18 |
Quenac | 17 | 17 | 59 | 139 | 64 | 9.5 | 17 | 5.6 | 4.6 | 0 | 5.9 | 11 | 14 |
Caguache | 23 | 23 | 68 | 138 | 57 | 13 | 11 | 11 | 9.3 | 5.9 | 0 | 5.4 | 8.9 |
Apiao | 27 | 27 | 53 | 129 | 52 | 17 | 14 | 16 | 14 | 11 | 5.4 | 0 | 4.1 |
Chaulinec | 25 | 25 | 56 | 119 | 53 | 20 | 18 | 20 | 18 | 14 | 8.9 | 4.1 | 0 |
Alao | 24 | 24 | 52 | 121 | 53 | 21 | 19 | 20 | 18 | 15 | 9.4 | 5.1 | 1.6 |
Aulén | 63 | 63 | 189 | 252 | 101 | 44 | 41 | 57 | 57 | 55 | 54.8 | 61 | 59 |
Chelín 1 | 15 | 15 | 45 | 137 | 69 | 30 | 34 | 20 | 25 | 22 | 16.2 | 15 | 11 |
Chelín 2 | 19 | 19 | 51 | 138 | 62 | 28 | 32 | 19 | 24 | 20 | 13.8 | 14 | 10 |
Quehui 1 | 21 | 21 | 52 | 139 | 61 | 27 | 33 | 19 | 24 | 21 | 14.6 | 15 | 11 |
Quehui 2 | 20 | 20 | 53 | 139 | 60 | 27 | 32 | 18 | 23 | 20 | 13.7 | 14 | 10 |
Cailín 1 | 70 | 70 | 151 | 2.8 | 8.4 | 70 | 74 | 61 | 66 | 62 | 57.7 | 56 | 52 |
Cailín 2 | 71 | 71 | 156 | 7.4 | 9.8 | 72 | 76 | 62 | 67 | 64 | 59.1 | 57 | 54 |
Laitec 1 | 83 | 83 | 172 | 20 | 3.7 | 73 | 69 | 70 | 69 | 65 | 59.9 | 53 | 53 |
Laitec 2 | 77 | 77 | 163 | 6.4 | 2.8 | 67 | 63 | 68 | 66 | 64 | 55.2 | 47 | 48 |
Caucahué 1 | 30 | 30 | 3.1 | 194 | 92 | 21 | 22 | 25 | 20 | 22 | 27.6 | 31 | 35 |
Caucahué 2 | 25 | 25 | 7 | 190 | 87 | 16 | 17 | 20 | 15 | 17 | 22.9 | 26 | 30 |
Mechuque 1 | 22 | 22 | 27 | 170 | 70 | 3.6 | 7.7 | 16 | 11 | 14 | 17.6 | 21 | 25 |
Mechuque 2 | 20 | 20 | 33 | 170 | 71 | 3.5 | 7.9 | 13 | 9.3 | 12 | 16.7 | 20 | 24 |
Lin Lin 1 | 10 | 10 | 55 | 152 | 65 | 9.7 | 13 | 8.8 | 6.8 | 7 | 13.7 | 19 | 22 |
Lin Lin 2 | 11 | 11 | 49 | 149 | 63 | 11 | 14 | 4.5 | 5.5 | 5.7 | 11.3 | 16 | 20 |
Ayacara Buill 1 | 39 | 39 | 63 | 194 | 74 | 21 | 18 | 35 | 33 | 29 | 29.2 | 35 | 36 |
Ayacara Buill 2 | 43 | 43 | 76 | 189 | 74 | 29 | 23 | 34 | 32 | 27 | 28.2 | 31 | 30 |
Tranqui 1 | 43 | 43 | 99 | 62 | 42 | 47 | 52 | 33 | 38 | 36 | 29.8 | 29 | 25 |
Tranqui 2 | 54 | 54 | 116 | 45 | 28 | 57 | 63 | 44 | 49 | 47 | 40.5 | 39 | 35 |
Tranqui 3 | 57 | 57 | 123 | 38 | 24 | 60 | 67 | 47 | 52 | 50 | 43.5 | 42 | 38 |
Butachauques 1 | 29 | 29 | 32 | 170 | 73 | 10 | 9.8 | 24 | 18 | 22 | 18.2 | 22 | 26 |
Butachauques 2 | 31 | 31 | 35 | 173 | 74 | 12 | 12 | 27 | 19 | 24 | 23.5 | 27 | 31 |
Butachauques 3 | 32 | 32 | 35 | 176 | 75 | 12 | 12 | 28 | 22 | 25 | 23.7 | 28 | 32 |
Ports | Alao | Aulén | Chelín 1 | Chelín 2 | Quehui 1 | Quehui 2 | Cailín 1 | Cailín 2 | Laitec 1 | Laitec 2 | Caucahué 1 | Caucahué 2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Dalcahue | 24 | 63.4 | 15 | 19 | 21 | 20 | 70 | 71 | 83 | 77 | 30 | 25 |
Dal puerto | 24 | 63.4 | 15 | 19 | 21 | 20 | 70 | 71 | 83 | 77 | 30 | 25 |
Quemchi | 52 | 189 | 45 | 51 | 52 | 53 | 151 | 156 | 172 | 163 | 3.1 | 7 |
Quellón | 121 | 252 | 137 | 138 | 139 | 139 | 2.8 | 7.4 | 20 | 6.4 | 194 | 190 |
Coldita | 53 | 101 | 69 | 62 | 61 | 60 | 8.4 | 9.8 | 3.7 | 2.8 | 92 | 87 |
Añihué | 21 | 43.5 | 30 | 28 | 27 | 27 | 70 | 72 | 73 | 67 | 21 | 16 |
Tac | 19 | 41.4 | 34 | 32 | 33 | 32 | 74 | 76 | 69 | 63 | 22 | 17 |
Llingua | 20 | 56.5 | 20 | 19 | 19 | 18 | 61 | 62 | 70 | 68 | 25 | 20 |
Meulín | 18 | 57.4 | 25 | 24 | 24 | 23 | 66 | 67 | 69 | 66 | 20 | 15 |
Quenac | 15 | 55.1 | 22 | 20 | 21 | 20 | 62 | 64 | 65 | 64 | 22 | 17 |
Caguache | 9.4 | 54.8 | 16 | 14 | 15 | 14 | 58 | 59 | 60 | 55 | 28 | 23 |
Apiao | 5.1 | 61.2 | 15 | 14 | 15 | 14 | 56 | 57 | 53 | 47 | 31 | 26 |
Chaulinec | 1.6 | 59.2 | 11 | 10 | 11 | 10 | 52 | 54 | 53 | 48 | 35 | 30 |
Alao | 0 | 57.6 | 11 | 9.4 | 10 | 9.5 | 52 | 53 | 54 | 49 | 35 | 31 |
Aulén | 58 | 0 | 71 | 71 | 72 | 71 | 96 | 98 | 103 | 96 | 44 | 39 |
Chelín 1 | 11 | 71.4 | 0 | 5 | 5.9 | 5.3 | 58 | 60 | 72 | 63 | 41 | 37 |
Chelín 2 | 9.4 | 70.9 | 5 | 0 | 1.6 | 1 | 55 | 56 | 64 | 59 | 39 | 35 |
Quehui 1 | 10 | 72 | 5.9 | 1.6 | 0 | 0.9 | 54 | 56 | 64 | 59 | 38 | 34 |
Quehui 2 | 9.5 | 71.1 | 5.3 | 1 | 0.9 | 0 | 53 | 55 | 63 | 58 | 37 | 33 |
Cailín 1 | 52 | 96.2 | 58 | 55 | 54 | 53 | 0 | 1.9 | 11 | 5.7 | 82 | 78 |
Cailín 2 | 53 | 97.6 | 60 | 56 | 56 | 55 | 1.9 | 0 | 13 | 7.1 | 84 | 80 |
Laitec 1 | 54 | 103 | 72 | 64 | 64 | 63 | 11 | 13 | 0 | 6 | 87 | 84 |
Laitec 2 | 49 | 96.1 | 63 | 59 | 59 | 58 | 5.7 | 7.1 | 6 | 0 | 83 | 79 |
Caucahué 1 | 35 | 44 | 41 | 39 | 38 | 37 | 82 | 84 | 87 | 83 | 0 | 4.7 |
Caucahué 2 | 31 | 39.3 | 37 | 35 | 34 | 33 | 78 | 80 | 84 | 79 | 4.7 | 0 |
Mechuque 1 | 26 | 45.3 | 33 | 32 | 31 | 30 | 71 | 72 | 74 | 68 | 13 | 8.3 |
Mechuque 2 | 25 | 48.5 | 29 | 28 | 28 | 27 | 70 | 72 | 75 | 68 | 15 | 11 |
Lin Lin 1 | 23 | 52.9 | 24 | 23 | 23 | 22 | 65 | 67 | 73 | 72 | 20 | 15 |
Lin Lin 2 | 20 | 54.3 | 21 | 22 | 22 | 21 | 63 | 65 | 71 | 70 | 21 | 16 |
Ayacara Buill 1 | 35 | 36.4 | 46 | 44 | 46 | 45 | 73 | 74 | 76 | 70 | 35 | 31 |
Ayacara Buill 2 | 34 | 44.9 | 44 | 43 | 45 | 44 | 72 | 73 | 75 | 69 | 44 | 39 |
Tranqui 1 | 24 | 76 | 33 | 26 | 27 | 26 | 35 | 37 | 45 | 40 | 58 | 54 |
Tranqui 2 | 35 | 86.7 | 44 | 35 | 36 | 35 | 22 | 24 | 30 | 25 | 69 | 65 |
Tranqui 3 | 38 | 89.7 | 45 | 38 | 39 | 39 | 18 | 20 | 27 | 21 | 72 | 68 |
Butachauques 1 | 27 | 34.1 | 40 | 37 | 38 | 37 | 80 | 81 | 78 | 71 | 17 | 13 |
Butachauques 2 | 32 | 36.6 | 42 | 39 | 40 | 39 | 82 | 83 | 79 | 72 | 19 | 14 |
Butachauques 3 | 32 | 36.9 | 42 | 38 | 38 | 37 | 82 | 83 | 79 | 73 | 19 | 14 |
Ports | Mechuque 1 | Mechuque 2 | Lin Lin 1 | Lin Lin 2 | Ayacara Buill 1 | Ayacara Buill 2 | Tranqui 1 | Tranqui 2 | Tranqui 3 | Butachauques 1 | Butachauques 2 | Butachauques 3 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
Dalcahue | 22 | 20 | 9.8 | 11 | 39 | 43 | 43 | 54 | 57 | 29 | 31 | 32 |
Dal puerto | 22 | 20 | 9.8 | 11 | 39 | 43 | 43 | 54 | 57 | 29 | 31 | 32 |
Quemchi | 27 | 33 | 55 | 49 | 63 | 76 | 99 | 116 | 123 | 32 | 35 | 35 |
Quellón | 170 | 170 | 152 | 149 | 194 | 189 | 62 | 45 | 38 | 170 | 173 | 176 |
Coldita | 70 | 71 | 65 | 63 | 74 | 74 | 42 | 28 | 24 | 73 | 74 | 75 |
Añihué | 3.6 | 3.5 | 9.7 | 11 | 21 | 29 | 47 | 57 | 60 | 10 | 12 | 12 |
Tac | 7.7 | 7.9 | 13 | 14 | 18 | 23 | 52 | 63 | 67 | 9.8 | 12 | 12 |
Llingua | 16 | 13 | 8.8 | 4.5 | 35 | 34 | 33 | 44 | 47 | 24 | 27 | 28 |
Meulín | 11 | 9.3 | 6.8 | 5.5 | 33 | 32 | 38 | 49 | 52 | 18 | 19 | 22 |
Quenac | 14 | 12 | 7 | 5.7 | 29 | 27 | 36 | 47 | 50 | 22 | 24 | 25 |
Caguache | 18 | 17 | 14 | 11 | 29 | 28 | 30 | 41 | 44 | 18 | 24 | 24 |
Apiao | 21 | 20 | 19 | 16 | 35 | 31 | 29 | 39 | 42 | 22 | 27 | 28 |
Chaulinec | 25 | 24 | 22 | 20 | 36 | 30 | 25 | 35 | 38 | 26 | 31 | 32 |
Alao | 26 | 25 | 23 | 20 | 35 | 34 | 24 | 35 | 38 | 27 | 32 | 32 |
Aulén | 45 | 49 | 53 | 54 | 36 | 45 | 76 | 87 | 90 | 34 | 37 | 37 |
Chelín 1 | 33 | 29 | 24 | 21 | 46 | 44 | 33 | 44 | 45 | 40 | 42 | 42 |
Chelín 2 | 32 | 28 | 23 | 22 | 44 | 43 | 26 | 35 | 38 | 37 | 39 | 38 |
Quehui 1 | 31 | 28 | 23 | 22 | 46 | 45 | 27 | 36 | 39 | 38 | 40 | 38 |
Quehui 2 | 30 | 27 | 22 | 21 | 45 | 44 | 26 | 35 | 39 | 37 | 39 | 37 |
Cailín 1 | 71 | 70 | 65 | 63 | 73 | 72 | 35 | 22 | 18 | 80 | 82 | 82 |
Cailín 2 | 72 | 72 | 67 | 65 | 74 | 73 | 37 | 24 | 20 | 81 | 83 | 83 |
Laitec 1 | 74 | 75 | 73 | 71 | 76 | 75 | 45 | 30 | 27 | 78 | 79 | 79 |
Laitec 2 | 68 | 68 | 72 | 70 | 70 | 69 | 40 | 25 | 21 | 71 | 72 | 73 |
Caucahué 1 | 13 | 15 | 20 | 21 | 35 | 44 | 58 | 69 | 72 | 17 | 19 | 19 |
Caucahué 2 | 8.3 | 11 | 15 | 16 | 31 | 39 | 54 | 65 | 68 | 13 | 14 | 14 |
Mechuque 1 | 0 | 3.6 | 12 | 13 | 23 | 32 | 50 | 60 | 63 | 11 | 12 | 12 |
Mechuque 2 | 3.6 | 0 | 9.1 | 10 | 26 | 35 | 46 | 57 | 60 | 11 | 12 | 12 |
Lin Lin 1 | 12 | 9.1 | 0 | 3.4 | 30 | 36 | 37 | 48 | 51 | 20 | 22 | 23 |
Lin Lin 2 | 13 | 10 | 3.4 | 0 | 31 | 36 | 35 | 46 | 49 | 21 | 23 | 24 |
Ayacara Buill 1 | 23 | 26 | 30 | 31 | 0 | 4 | 51 | 62 | 65 | 21 | 22 | 23 |
Ayacara Buill 2 | 32 | 35 | 36 | 36 | 4 | 0 | 51 | 62 | 65 | 25 | 27 | 27 |
Tranqui 1 | 50 | 46 | 37 | 35 | 51 | 51 | 0 | 10 | 13 | 55 | 57 | 57 |
Tranqui 2 | 60 | 57 | 48 | 46 | 62 | 62 | 10 | 0 | 4.7 | 66 | 68 | 68 |
Tranqui 3 | 63 | 60 | 51 | 49 | 65 | 65 | 13 | 4.7 | 0 | 69 | 71 | 71 |
Butachauques 1 | 11 | 11 | 20 | 21 | 21 | 25 | 55 | 66 | 69 | 0 | 1.6 | 2 |
Butachauques 2 | 12 | 12 | 22 | 23 | 22 | 27 | 57 | 68 | 71 | 1.6 | 0 | 1.8 |
Butachauques 3 | 12 | 12 | 23 | 24 | 23 | 27 | 57 | 68 | 71 | 2 | 1.8 | 0 |
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Zambra-Rivera, M., Miranda-González, P.A. & Blazquez, C.A. A multiperiod household waste collection system for a set of rural islands with dynamic transfer port selection. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09862-4
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DOI: https://doi.org/10.1007/s11081-023-09862-4