Soumen Atta1
1Faculty of Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FI-40014, Finland
☆Corresponding author: soumen.s.atta@jyu.fi
The instances for the Tool Indexing Problem (TIP) mentioned in this page are adapted from the Single Row Facility Layout Problem (SRFLP) [1, 2], and the original instances of SRFLP can be found from http://www.miguelanjos.com/flplib. In the table shown below, the symbol '0' in the 'Solution' column represents an empty slot.
Cite this article as follows:
Soumen Atta. Linear Formulations and a Hybrid Large Neighborhood Search Algorithm for the Tool Indexing Problem. Computers and Operations Research, Elsevier, Vol. 186, Article 107321, 2026. https://doi.org/10.1016/j.cor.2025.107321.
Click here to download all the instances as single zip file
| Instance | No. of Tools | No. of Slots | Solution | Cost |
|
60 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 34, 48, 27, 11, 40, 56, 21, 12, 13, 24, 6, 54, 25, 3, 16, 7, 9, 15, 36, 8, 32, 51, 33, 46, 4, 44, 35, 57, 47, 26, 17, 2, 49, 38, 5, 31, 37, 59, 53, 22, 43, 42, 30, 10, 14, 45, 55, 52, 23, 60, 19, 20, 41, 39, 58, 18, 29, 1, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
54053 |
|
|
60 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 10, 28, 19, 44, 29, 40, 46, 41, 50, 34, 15, 30, 24, 14, 9, 21, 32, 5, 33, 36, 37, 56, 25, 18, 45, 17, 52, 22, 31, 2, 4, 42, 8, 47, 49, 48, 38, 58, 16, 23, 57, 39, 51, 59, 54, 43, 6, 27, 55, 7, 1, 13, 12, 3, 35, 26, 11, 20, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
31274 |
|
|
60 |
100 |
0, 0, 0, 0, 0, 40, 6, 26, 13, 27, 1, 47, 34, 53, 36, 49, 15, 22, 43, 54, 23, 52, 30, 60, 51, 56, 10, 32, 39, 28, 45, 58, 46, 33, 55, 18, 25, 31, 8, 35, 14, 21, 2, 41, 9, 17, 7, 44, 20, 37, 11, 48, 12, 57, 16, 24, 42, 50, 59, 3, 19, 29, 38, 5, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
23510 |
|
|
60 |
100 |
0, 0, 0, 0, 0, 0, 12, 43, 51, 46, 9, 41, 32, 25, 8, 38, 54, 49, 34, 1, 28, 47, 18, 52, 16, 26, 30, 29, 60, 42, 11, 35, 2, 37, 58, 15, 21, 17, 14, 3, 48, 59, 45, 27, 53, 5, 40, 6, 4, 44, 56, 33, 23, 24, 50, 7, 55, 10, 39, 36, 57, 22, 31, 19, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
11592 |
|
|
60 |
100 |
0, 0, 0, 0, 0, 38, 33, 49, 44, 11, 12, 57, 5, 34, 51, 43, 15, 23, 3, 52, 1, 45, 32, 22, 14, 18, 29, 31, 26, 58, 42, 27, 21, 56, 24, 28, 6, 2, 46, 48, 17, 54, 60, 20, 8, 50, 59, 36, 16, 41, 25, 19, 35, 13, 47, 37, 10, 7, 4, 9, 40, 30, 55, 53, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
15168 |
|
|
70 |
100 |
0, 0, 0, 0, 53, 47, 31, 28, 62, 32, 63, 37, 69, 2, 65, 1, 15, 41, 19, 51, 5, 9, 68, 27, 49, 43, 4, 16, 48, 13, 10, 67, 56, 33, 45, 42, 34, 18, 36, 52, 60, 6, 54, 7, 23, 21, 58, 14, 3, 66, 44, 70, 24, 12, 64, 46, 59, 20, 25, 55, 26, 61, 38, 17, 11, 57, 30, 29, 35, 39, 8, 50, 22, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
42296 |
|
|
70 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57, 41, 52, 47, 53, 10, 62, 38, 59, 69, 65, 16, 31, 48, 27, 61, 66, 37, 68, 12, 22, 15, 34, 35, 17, 54, 51, 24, 42, 32, 20, 40, 14, 5, 2, 55, 46, 70, 43, 60, 6, 44, 33, 11, 8, 29, 7, 23, 9, 30, 25, 18, 4, 1, 67, 26, 49, 3, 58, 13, 63, 19, 36, 50, 64, 45, 56, 28, 39, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
51723 |
|
|
70 |
100 |
0, 0, 0, 0, 22, 69, 16, 44, 34, 13, 62, 56, 57, 33, 31, 48, 12, 66, 43, 28, 15, 46, 38, 29, 53, 64, 3, 35, 45, 36, 60, 18, 24, 25, 58, 59, 39, 55, 40, 37, 41, 1, 5, 14, 23, 10, 42, 4, 6, 67, 68, 11, 9, 61, 70, 65, 21, 27, 7, 51, 49, 26, 20, 17, 2, 32, 19, 50, 47, 63, 54, 30, 52, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
43794 |
|
|
70 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 35, 8, 38, 13, 37, 4, 19, 3, 65, 45, 31, 39, 59, 47, 20, 32, 55, 1, 36, 23, 69, 44, 21, 40, 17, 27, 56, 28, 50, 48, 70, 57, 10, 53, 62, 2, 68, 11, 61, 42, 24, 33, 22, 64, 29, 58, 18, 5, 54, 52, 14, 34, 9, 60, 43, 15, 12, 26, 49, 67, 7, 6, 30, 51, 46, 63, 25, 16, 66, 0, 0, 0, 0 |
27701 |
|
|
70 |
100 |
0, 28, 67, 17, 64, 38, 19, 21, 26, 68, 9, 56, 55, 47, 65, 43, 69, 59, 15, 53, 7, 13, 60, 29, 49, 54, 52, 42, 4, 48, 46, 57, 61, 3, 66, 36, 11, 5, 63, 35, 70, 12, 16, 39, 50, 25, 34, 14, 45, 30, 10, 40, 8, 33, 18, 31, 41, 2, 37, 6, 1, 23, 51, 22, 58, 24, 32, 44, 62, 20, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
134238 |
|
|
75 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 67, 9, 58, 38, 69, 47, 29, 33, 59, 16, 63, 52, 5, 54, 39, 73, 51, 1, 10, 32, 45, 70, 4, 75, 43, 31, 68, 13, 21, 66, 53, 17, 34, 19, 3, 24, 12, 71, 37, 55, 62, 7, 22, 8, 74, 42, 26, 15, 27, 18, 35, 41, 56, 65, 30, 25, 44, 11, 57, 40, 28, 72, 50, 49, 23, 48, 61, 6, 14, 20, 36, 46, 60, 2, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
66630 |
|
|
75 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 26, 57, 32, 56, 61, 22, 72, 12, 3, 47, 28, 62, 60, 65, 1, 14, 6, 5, 75, 66, 39, 23, 7, 46, 34, 24, 18, 52, 71, 67, 33, 4, 10, 8, 11, 53, 19, 15, 27, 9, 17, 59, 68, 74, 35, 31, 48, 40, 45, 69, 38, 41, 30, 50, 36, 58, 63, 73, 70, 16, 20, 21, 29, 54, 37, 43, 64, 55, 42, 44, 13, 25, 2, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
111806 |
|
|
75 |
100 |
0, 0, 0, 0, 0, 10, 22, 68, 20, 17, 36, 33, 19, 23, 4, 54, 64, 41, 26, 5, 60, 35, 61, 40, 65, 74, 57, 21, 45, 55, 62, 38, 28, 56, 11, 7, 24, 30, 9, 75, 58, 67, 59, 12, 44, 37, 3, 48, 39, 34, 16, 31, 73, 27, 18, 2, 52, 49, 66, 72, 6, 8, 70, 25, 32, 29, 46, 1, 13, 53, 14, 51, 50, 71, 63, 43, 69, 47, 15, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
38151 |
|
|
75 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 60, 56, 10, 14, 27, 15, 5, 7, 62, 37, 48, 70, 52, 50, 42, 57, 22, 41, 75, 47, 33, 16, 55, 3, 64, 65, 30, 31, 39, 29, 12, 40, 20, 46, 53, 35, 44, 28, 67, 34, 63, 19, 24, 13, 71, 58, 1, 4, 59, 54, 11, 18, 51, 25, 45, 32, 43, 74, 68, 2, 49, 73, 72, 38, 26, 17, 69, 23, 61, 6, 21, 66, 9, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
106341 |
|
|
75 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 17, 43, 52, 20, 37, 31, 9, 63, 75, 19, 50, 8, 2, 72, 38, 58, 64, 40, 6, 65, 51, 56, 41, 4, 30, 3, 55, 39, 23, 32, 49, 5, 73, 71, 44, 47, 28, 7, 25, 46, 35, 42, 68, 34, 74, 29, 1, 16, 53, 59, 48, 18, 15, 11, 69, 14, 70, 66, 10, 45, 21, 62, 61, 67, 36, 57, 33, 54, 60, 26, 12, 13, 24, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
47017 |
|
|
80 |
100 |
0, 0, 0, 0, 0, 0, 55, 60, 80, 16, 65, 34, 14, 29, 12, 67, 2, 21, 68, 46, 44, 49, 62, 19, 17, 27, 56, 40, 54, 61, 39, 63, 43, 20, 45, 41, 47, 51, 52, 75, 32, 10, 13, 58, 66, 48, 9, 23, 76, 24, 53, 6, 33, 5, 42, 15, 36, 73, 22, 35, 59, 8, 74, 37, 69, 26, 50, 38, 31, 3, 71, 1, 30, 64, 57, 7, 4, 11, 77, 28, 18, 79, 25, 72, 78, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
54463 |
|
|
80 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 11, 48, 66, 70, 42, 52, 68, 61, 43, 45, 28, 74, 69, 49, 13, 63, 75, 51, 2, 64, 73, 78, 60, 72, 80, 30, 54, 7, 32, 15, 20, 31, 19, 76, 16, 36, 65, 21, 8, 59, 71, 35, 3, 34, 67, 25, 39, 4, 1, 6, 38, 37, 79, 56, 9, 27, 47, 41, 62, 50, 14, 53, 44, 58, 12, 40, 23, 26, 5, 33, 29, 10, 55, 46, 77, 22, 17, 18, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
52851 |
|
|
80 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 57, 61, 54, 29, 34, 53, 21, 13, 36, 71, 70, 39, 69, 50, 35, 8, 52, 3, 22, 27, 32, 30, 48, 72, 56, 76, 64, 44, 17, 77, 25, 80, 23, 51, 78, 10, 14, 11, 7, 67, 55, 9, 19, 15, 41, 59, 1, 4, 12, 31, 73, 2, 79, 38, 28, 26, 60, 75, 62, 6, 5, 47, 45, 18, 42, 43, 37, 49, 16, 58, 20, 68, 33, 65, 46, 24, 40, 66, 63, 74, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
95091 |
|
|
80 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 69, 47, 60, 66, 29, 21, 38, 64, 71, 42, 7, 34, 80, 35, 28, 75, 30, 54, 43, 79, 67, 32, 78, 17, 31, 46, 76, 6, 4, 9, 14, 62, 18, 16, 12, 15, 2, 72, 27, 3, 74, 77, 70, 8, 25, 1, 53, 33, 23, 65, 11, 19, 73, 63, 45, 39, 68, 13, 20, 52, 26, 5, 10, 36, 55, 37, 51, 57, 22, 49, 58, 40, 48, 24, 50, 59, 61, 44, 56, 41, 0, 0, 0, 0, 0, 0, 0 |
100828 |
|
|
80 |
100 |
0, 0, 0, 0, 0, 0, 48, 25, 46, 11, 7, 41, 12, 40, 39, 59, 13, 69, 42, 35, 64, 29, 56, 5, 51, 78, 57, 23, 16, 63, 3, 77, 45, 50, 72, 14, 18, 8, 62, 20, 4, 43, 65, 80, 32, 19, 66, 44, 15, 67, 55, 24, 31, 36, 71, 22, 75, 9, 49, 37, 28, 30, 33, 70, 76, 1, 54, 79, 34, 47, 10, 61, 21, 27, 74, 73, 6, 38, 68, 52, 60, 58, 2, 17, 53, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
36214 |
|
|
36 |
60 |
7, 1, 4, 5, 13, 12, 11, 6, 20, 14, 27, 23, 28, 19, 29, 30, 32, 34, 33, 31, 21, 22, 26, 25, 24, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 17, 2, 18, 3, 15, 9, 8, 10 |
10289 |
|
|
42 |
60 |
0, 0, 0, 0, 0, 6, 8, 16, 23, 36, 3, 22, 24, 1, 37, 38, 28, 21, 33, 39, 30, 2, 4, 40, 14, 15, 9, 35, 32, 18, 26, 19, 31, 13, 10, 20, 27, 12, 42, 17, 34, 5, 7, 11, 29, 25, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
24406 |
|
|
49 |
60 |
0, 0, 0, 0, 0, 0, 28, 46, 20, 18, 42, 47, 13, 14, 41, 35, 1, 29, 15, 9, 10, 34, 38, 27, 45, 12, 3, 43, 37, 2, 6, 31, 23, 48, 39, 8, 44, 5, 16, 40, 11, 22, 49, 33, 30, 21, 24, 32, 17, 4, 26, 36, 25, 19, 7, 0, 0, 0, 0, 0 |
36517 |
|
|
56 |
60 |
5, 44, 29, 7, 52, 36, 51, 32, 14, 28, 23, 49, 11, 30, 3, 42, 9, 33, 50, 56, 8, 24, 55, 38, 22, 53, 54, 25, 16, 21, 6, 19, 2, 0, 0, 0, 0, 26, 43, 45, 46, 4, 15, 31, 12, 27, 17, 20, 39, 34, 37, 48, 1, 47, 18, 35, 10, 40, 13, 41, |
52703 |
|
|
64 |
100 |
0, 0, 0, 57, 31, 53, 10, 9, 42, 25, 19, 8, 2, 63, 58, 26, 50, 37, 35, 17, 44, 1, 56, 33, 45, 64, 13, 49, 21, 59, 7, 16, 4, 22, 24, 62, 23, 52, 14, 29, 20, 55, 38, 51, 47, 6, 18, 39, 5, 48, 40, 60, 30, 43, 28, 46, 32, 11, 54, 34, 12, 36, 27, 41, 3, 61, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
95191 |
|
|
72 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 11, 34, 24, 45, 5, 3, 43, 62, 72, 4, 25, 69, 66, 20, 58, 19, 15, 41, 40, 48, 42, 68, 51, 36, 57, 55, 44, 71, 6, 9, 37, 63, 50, 33, 13, 46, 38, 49, 59, 39, 16, 61, 7, 32, 1, 23, 52, 30, 65, 47, 22, 14, 28, 70, 17, 26, 21, 2, 10, 67, 35, 64, 60, 27, 8, 18, 31, 56, 53, 29, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
132579 |
|
|
81 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 65, 33, 74, 19, 23, 67, 69, 14, 66, 9, 50, 81, 3, 21, 61, 17, 15, 48, 4, 6, 41, 38, 49, 70, 39, 56, 31, 7, 35, 36, 55, 11, 42, 52, 44, 78, 45, 22, 57, 62, 68, 13, 32, 1, 5, 43, 58, 77, 24, 73, 59, 53, 75, 71, 72, 10, 28, 47, 76, 16, 37, 79, 18, 64, 63, 29, 46, 27, 51, 8, 20, 2, 12, 54, 80, 60, 40, 34, 26, 25, 0, 0, 0, 0, 0, 0, 0, 0 |
183835 |
|
|
100 |
100 |
37, 63, 71, 75, 11, 95, 13, 34, 54, 55, 74, 6, 15, 77, 33, 22, 31, 43, 14, 1, 94, 82, 4, 19, 56, 81, 44, 8, 68, 98, 86, 59, 99, 67, 46, 3, 36, 38, 45, 90, 47, 70, 100, 66, 72, 51, 20, 69, 92, 48, 35, 26, 40, 7, 87, 41, 53, 17, 29, 76, 61, 50, 21, 64, 73, 12, 23, 60, 58, 10, 42, 24, 93, 85, 30, 96, 84, 28, 2, 18, 97, 88, 65, 91, 49, 39, 62, 32, 16, 9, 83, 52, 57, 79, 25, 5, 27, 80, 89, 78 |
288783 |
|
|
5 |
5 |
4, 5, 1, 3, 2 |
124 |
|
|
5 |
10 |
0, 2, 3, 5, 1, 4, 0, 0, 0, 0 |
150 |
|
|
6 |
10 |
5, 6, 1, 0, 0, 0, 0, 2, 3, 4 |
292 |
|
|
7 |
10 |
0, 4, 1, 6, 5, 7, 3, 2, 0, 0 |
468 |
|
|
8 |
10 |
1, 0, 0, 6, 2, 4, 8, 5, 3, 7 |
724 |
|
|
9 |
10 |
0, 6, 1, 3, 8, 7, 4, 2, 9, 5 |
866 |
|
|
10 |
10 |
2, 8, 10, 7, 9, 5, 4, 1, 6, 3 |
1132 |
|
|
10 |
12 |
0, 5, 1, 6, 4, 3, 10, 2, 8, 7, 9, 0 |
1272 |
|
|
10 |
15 |
0, 9, 7, 8, 2, 10, 3, 4, 6, 1, 5, 0, 0, 0, 0 |
1378 |
|
|
10 |
20 |
0, 0, 1, 6, 5, 4, 3, 10, 2, 8, 7, 9, 0, 0, 0, 0, 0, 0, 0, 0 |
1402 |
|
|
10 |
25 |
0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 5, 4, 3, 10, 2, 8, 7, 9, 0, 0, 0, 0, 0, 0, 0 |
1402 |
|
|
10 |
30 |
7, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 5, 4, 3, 10, 2, 8 |
1402 |
|
|
15 |
20 |
11, 9, 14, 8, 7, 4, 6, 5, 1, 0, 0, 0, 0, 0, 3, 10, 15, 2, 13, 12 |
4818 |
|
|
15 |
30 |
0, 0, 0, 0, 5, 1, 4, 6, 7, 8, 14, 9, 11, 12, 13, 2, 10, 15, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
5134 |
|
|
20 |
30 |
0, 0, 0, 0, 0, 0, 4, 12, 1, 11, 16, 5, 18, 15, 6, 20, 19, 13, 9, 14, 8, 7, 3, 17, 2, 10, 0, 0, 0, 0 |
12600 |
|
|
12 |
20 |
0, 0, 0, 0, 0, 0, 0, 2, 9, 1, 3, 5, 12, 4, 6, 10, 7, 11, 8, 0 |
4409 |
|
|
13 |
20 |
0, 0, 0, 0, 0, 11, 7, 6, 10, 5, 4, 13, 2, 9, 12, 3, 1, 8, 0, 0 |
5781 |
|
|
13 |
30 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 1, 3, 12, 9, 2, 13, 4, 5, 10, 6, 7, 11, 0, 0 |
5897 |
|
|
14 |
20 |
6, 14, 12, 4, 5, 13, 2, 9, 3, 1, 8, 0, 0, 0, 0, 0, 0, 11, 7, 10 |
7027 |
|
|
15 |
20 |
0, 0, 0, 10, 11, 7, 6, 14, 12, 4, 5, 13, 9, 1, 3, 2, 15, 8, 0, 0 |
8377 |
|
|
16 |
20 |
0, 0, 8, 15, 13, 2, 9, 3, 1, 5, 4, 16, 12, 6, 14, 7, 10, 11, 0, 0 |
10044 |
|
|
17 |
20 |
15, 1, 3, 8, 0, 0, 0, 12, 16, 10, 6, 14, 11, 7, 17, 4, 5, 13, 9, 2 |
11567 |
|
|
18 |
20 |
1, 3, 18, 8, 16, 12, 0, 0, 10, 6, 14, 11, 7, 17, 4, 13, 5, 2, 9, 15 |
13208 |
|
|
19 |
20 |
0, 16, 12, 18, 8, 3, 1, 9, 15, 2, 19, 4, 13, 17, 11, 7, 14, 10, 6, 5 |
15000 |
|
|
20 |
30 |
0, 0, 0, 0, 0, 0, 0, 0, 11, 7, 14, 6, 5, 17, 4, 13, 10, 16, 12, 20, 18, 9, 2, 15, 3, 1, 19, 8, 0, 0 |
21234 |
|
|
21 |
30 |
0, 0, 0, 0, 0, 11, 7, 14, 6, 5, 17, 13, 4, 10, 16, 12, 20, 18, 9, 2, 15, 3, 1, 19, 8, 21, 0, 0, 0, 0 |
23896 |
|
|
22 |
30 |
0, 0, 0, 0, 0, 0, 21, 8, 19, 1, 3, 18, 9, 2, 15, 20, 16, 12, 5, 13, 4, 10, 14, 6, 17, 7, 22, 11, 0, 0 |
27021 |
|
|
23 |
30 |
0, 0, 0, 0, 0, 19, 8, 21, 1, 18, 20, 9, 2, 15, 3, 16, 12, 23, 5, 13, 4, 6, 14, 10, 17, 7, 22, 11, 0, 0 |
30613 |
|
|
24 |
30 |
0, 0, 0, 0, 0, 19, 11, 24, 7, 22, 17, 10, 14, 4, 6, 12, 16, 23, 13, 5, 3, 15, 2, 9, 20, 18, 1, 21, 8, 0 |
34004 |
|
|
25 |
30 |
0, 0, 0, 0, 0, 20, 15, 2, 9, 21, 18, 8, 1, 19, 3, 5, 25, 16, 12, 23, 24, 6, 14, 4, 10, 7, 22, 17, 13, 11 |
37444 |
|
|
6 |
6 |
6, 2, 3, 1, 5, 4 |
1063 |
|
|
6 |
10 |
0, 0, 6, 2, 3, 4, 1, 5, 0, 0 |
1372 |
|
|
7 |
10 |
0, 4, 5, 6, 2, 3, 7, 1, 0, 0 |
1733 |
|
|
8 |
10 |
0, 4, 3, 2, 7, 6, 8, 5, 1, 0 |
2088 |
|
|
9 |
10 |
2, 8, 6, 5, 7, 0, 1, 4, 9, 3 |
2432 |
|
|
10 |
10 |
9, 6, 10, 2, 1, 5, 7, 8, 3, 4 |
2711 |
|
|
10 |
20 |
0, 0, 0, 0, 0, 0, 1, 5, 2, 10, 7, 4, 8, 3, 6, 9, 0, 0, 0, 0 |
3508 |
|
|
11 |
11 |
1, 3, 2, 4, 6, 8, 9, 7, 5, 10, 11 |
3083 |
|
|
11 |
12 |
1, 3, 0, 2, 4, 6, 8, 9, 7, 5, 10, 11 |
3350 |
|
|
11 |
20 |
0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 11, 10, 5, 7, 9, 8, 2, 4, 6, 0 |
4022 |
|
|
12 |
12 |
10, 7, 2, 8, 3, 1, 4, 11, 9, 12, 5, 6 |
3677 |
|
|
12 |
20 |
11, 4, 1, 12, 0, 0, 0, 0, 0, 0, 0, 0, 7, 2, 10, 6, 8, 5, 9, 3 |
4765 |
|
|
13 |
13 |
8, 5, 7, 9, 3, 4, 12, 2, 13, 1, 10, 6, 11 |
4196 |
|
|
13 |
20 |
0, 0, 0, 0, 0, 6, 1, 13, 11, 10, 2, 12, 8, 5, 4, 9, 3, 7, 0, 0 |
5367 |
|
|
14 |
14 |
5, 10, 11, 13, 4, 8, 1, 2, 14, 12, 6, 7, 3, 9 |
4926 |
|
|
14 |
20 |
0, 0, 0, 8, 4, 10, 11, 5, 9, 3, 7, 13, 1, 2, 6, 14, 12, 0, 0, 0 |
6179 |
|
|
15 |
20 |
0, 0, 0, 0, 13, 9, 7, 15, 1, 14, 2, 3, 5, 8, 12, 11, 10, 4, 6, 0 |
6884 |
|
|
15 |
30 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 8, 10, 11, 12, 5, 3, 2, 14, 1, 15, 7, 9, 13, 0, 0, 0, 0, 0 |
7359 |
|
|
20 |
30 |
0, 0, 0, 0, 0, 0, 8, 4, 7, 11, 18, 12, 2, 20, 19, 15, 17, 3, 14, 5, 13, 10, 9, 1, 16, 6, 0, 0, 0, 0 |
11885 |
|
|
25 |
30 |
2, 0, 0, 0, 0, 0, 4, 13, 21, 15, 14, 9, 3, 5, 11, 25, 10, 7, 24, 6, 12, 23, 1, 8, 16, 20, 22, 17, 19, 18 |
18011 |
|
|
30 |
30 |
16, 3, 27, 11, 29, 20, 30, 9, 6, 14, 4, 17, 8, 24, 23, 21, 13, 26, 2, 12, 28, 10, 19, 5, 18, 22, 1, 7, 15, 25 |
21086 |
|
|
30 |
60 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 15, 18, 5, 7, 2, 10, 19, 1, 22, 26, 25, 3, 12, 16, 27, 20, 30, 6, 14, 9, 8, 23, 13, 17, 24, 4, 21, 11, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
27673 |
|
|
35 |
60 |
0, 0, 0, 0, 0, 0, 1, 7, 35, 5, 29, 28, 33, 8, 10, 11, 3, 20, 32, 22, 26, 6, 2, 9, 18, 17, 23, 15, 27, 14, 25, 12, 30, 4, 19, 34, 16, 31, 21, 13, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
38014 |
|
|
40 |
60 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 13, 25, 10, 17, 1, 11, 27, 31, 2, 14, 22, 38, 18, 6, 7, 28, 3, 24, 9, 12, 39, 20, 32, 4, 40, 33, 5, 8, 29, 19, 16, 35, 37, 30, 21, 15, 23, 36, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
46333 |
|
|
45 |
60 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 16, 34, 36, 35, 2, 8, 29, 39, 18, 5, 3, 1, 4, 6, 45, 26, 14, 33, 43, 42, 9, 13, 22, 37, 23, 32, 10, 30, 28, 15, 7, 40, 31, 24, 38, 11, 17, 21, 19, 44, 41, 25, 27, 20, 0, 0, 0, 0 |
58810 |
|
|
50 |
60 |
32, 12, 24, 26, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 4, 20, 19, 38, 27, 49, 34, 22, 33, 3, 50, 29, 44, 9, 40, 31, 10, 18, 2, 41, 21, 16, 15, 6, 43, 46, 36, 39, 13, 11, 5, 17, 14, 45, 48, 37, 25, 23, 1, 47, 42, 28, 7, 35 |
73309 |
|
|
60 |
100 |
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 43, 15, 14, 36, 45, 9, 37, 32, 2, 7, 28, 22, 4, 42, 57, 60, 21, 55, 11, 1, 5, 8, 41, 44, 40, 39, 19, 17, 47, 48, 46, 30, 52, 31, 20, 23, 10, 12, 6, 58, 29, 24, 27, 13, 18, 26, 35, 51, 3, 16, 33, 34, 38, 59, 49, 56, 54, 50, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
111207 |
References:
[1] M. F. Anjos, A. Kennings, A. Vannelli, A semidefinite optimization ap
proach for the single-row layout problem with unequal dimensions, Discrete
Optimization 2 (2) (2005) 113–122.
[2] M. F. Anjos, G. Yen, Provably near-optimal solutions for very large single
row facility layout problems, Optimization Methods & Software 24 (4-5)
(2009) 805–817.
This page was created on January 23, 2024.