Research Article
Task Scheduling for Multiunit Parallel Test Using Mixed-Integer Linear Programming
Table 5
Model statistics and solution details of 7 examples.
| Example | Model details | Full-space method | SBI method | Binary variables | Continuous variables | Constraints | Optimal solution (s) | Computation time without ISF (s) | Computation time with ISF (s) | Best solution (s) | Computation time (s) | SR | ARUR |
| 1-2 | 156 | 12 | 605 | 321 | 16.2 | 1.7 | 321 | 9.4 | 1.33 | 26.1 | 2-2 | 110 | 10 | 407 | 461 | 11.1 | 1.4 | 461 | 6.6 | 1.49 | 26.7 | 3-2 | 90 | 9 | 334 | 253 | 8.1 | 1.3 | 253 | 5.6 | 1.61 | 36.0 | 4-2 | 506 | 22 | 2065 | 728 | 485.7 | 66.4 | 728 | 35.3 | 1.53 | 28.5 | 5-2 | 462 | 21 | 1898 | 577 | 366.6 | 53.2 | 577 | 32.1 | 1.45 | 30.4 | 6-2 | 380 | 19 | 1532 | 732 | 206.2 | 32.8 | 732 | 24.8 | 1.49 | 29.3 | 7-2 | 992 | 31 | 4150 | 999 | 2000 | 1066.3 | 999 | 86.5 | 1.52 | 29.9 | 1-3 | 168 | 12 | 869 | 321 | 25.1 | 2.1 | 321 | 10.5 | 1.33 | 26.1 | 2-3 | 120 | 10 | 587 | 456 | 16.5 | 1.7 | 456 | 7.1 | 1.5 | 27.0 | 3-3 | 99 | 9 | 478 | 253 | 12.1 | 1.5 | 253 | 5.9 | 1.61 | 36.1 | 4-3 | 528 | 22 | 2989 | 658 | 758.5 | 89.6 | 658 | 44.4 | 1.69 | 31.5 | 5-3 | 483 | 21 | 2738 | 533 | 593.6 | 68.9 | 533 | 40 | 1.57 | 32.9 | 6-3 | 399 | 19 | 2216 | 619 | 321.6 | 43.1 | 619 | 30.7 | 1.77 | 34.7 | 7-3 | 1023 | 31 | 6010 | None | 2000 | 2000 | 815 | 113.5 | 1.87 | 36.7 | 1-4 | 180 | 12 | 1133 | 321 | 31.9 | 2.5 | 321 | 11.5 | 1.33 | 26.1 | 2-4 | 130 | 10 | 767 | 456 | 22.1 | 1.9 | 456 | 7.6 | 1.5 | 27.0 | 3-4 | 108 | 9 | 622 | 253 | 16.1 | 1.7 | 253 | 6.3 | 1.61 | 36.0 | 4-4 | 550 | 22 | 3913 | 577 | 1077.5 | 108 | 577 | 53.4 | 1.93 | 37.1 | 5-4 | 504 | 21 | 3578 | 553 | 844.6 | 83.2 | 533 | 47.9 | 1.57 | 32.9 | 6-4 | 418 | 19 | 2900 | 619 | 461.8 | 54.4 | 619 | 36.3 | 1.77 | 34.7 | 7-4 | 1054 | 31 | 7870 | None | 2000 | 2000 | 815 | 141.2 | 1.87 | 36.7 |
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Solution of examples 7-2 is found by the full-space method with ISF. |