Research Article
Single-Machine Scheduling to Minimize Total Completion Time and Tardiness with Two Competing Agents
Table 5
The performance of the B&B and SA algorithms (
).
| n | P | τ | R | Branch-and-bound algorithm | | | Number of nodes | CPU time | Error percentages | Error percentages | Mean | SD | Mean | SD | Mean | SD | Mean | SD |
| 16 | 0.25 | 0.25 | 0.25 | 1585.08 | 1474.52 | 0.02 | 0.02 | 0.15 | 0.91 | 0.11 | 0.73 | 0.50 | 2095.26 | 2732.66 | 0.02 | 0.03 | 0.15 | 0.50 | 0.14 | 0.59 | 0.75 | 2222.28 | 4286.49 | 0.02 | 0.04 | 0.13 | 0.61 | 0.14 | 0.58 | 0.50 | 0.25 | 2065.72 | 2321.27 | 0.02 | 0.02 | 0.10 | 0.59 | 0.09 | 0.54 | 0.50 | 4513.85 | 6357.05 | 0.04 | 0.05 | 0.05 | 0.32 | 0.17 | 0.66 | 0.75 | 8619.26 | 21890.46 | 0.07 | 0.18 | 0.11 | 0.31 | 0.19 |
0.55 | 0.5 | 0.25 | 0.25 | 1393.40 | 1012.04 | 0.01 | 0.01 | 0.27 | 1.83 | 0.15 | 1.36 | 0.50 | 1705.39 | 1475.57 | 0.02 | 0.02 | 0.44 | 2.34 | 0.45 | 2.10 | 0.75 | 2492.71 | 3162.69 | 0.02 | 0.03 | 0.40 | 1.75 | 0.20 | 1.12 | 0.50 | 0.25 | 708.37 | 1012.71 | 0.01 | 0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 2342.18 | 6513.62 | 0.02 | 0.05 | 0.23 | 0.96 | 0.31 | 1.29 | 0.75 | 4389.43 | 6513.39 | 0.03 | 0.05 | 0.14 | 0.88 | 0.17 | 0.91 |
| 20 | 0.25 | 0.25 | 0.25 | 6440.11 | 8778.62 | 0.10 | 0.13 | 0.14 | 0.69 | 0.21 | 0.83 | 0.50 | 8888.21 | 12532.10 | 0.12 | 0.16 | 0.44 | 1.19 | 0.29 | 0.93 | 0.75 | 37910.61 | 169197.47 | 0.52 | 2.44 | 0.17 | 0.59 | 0.29 | 0.85 | 0.50 | 0.25 | 31509.93 | 119592.04 | 0.41 | 1.69 | 0.20 | 0.72 | 0.24 | 0.79 | 0.50 | 77321.28 | 252992.05 | 0.98 | 3.45 | 0.19 | 0.73 | 0.22 | 0.72 | 0.75 | 107661.85 | 496233.51 | 1.33 | 6.28 | 0.14 | 0.41 | 0.19 |
0.72 | 0.5 | 0.25 | 0.25 | 6080.79 | 7331.26 | 0.09 | 0.10 | 0.24 | 1.54 | 0.15 | 1.30 | 0.50 | 12825.16 | 17350.45 | 0.16 | 0.21 | 1.05 | 3.59 | 0.96 | 3.16 | 0.75 | 30411.23 | 83195.05 | 0.37 | 1.01 | 0.58 | 2.15 | 0.53 | 2.02 | 0.50 | 0.25 | 3189.29 | 5854.18 | 0.04 | 0.06 | 0.13 | 0.93 | 0.20 | 1.07 | 0.50 | 20391.67 | 49137.99 | 0.22 | 0.55 | 0.57 | 1.76 | 0.59 | 1.85 | 0.75 | 86350.21 | 282470.70 | 0.95 | 3.22 | 0.42 | 1.19 | 0.67 | 1.47 |
| 24 | 0.25 | 0.25 | 0.25 | 28131.45 | 39702.43 | 0.59 | 8.36 | 0.26 | 0.77 | 0.24 | 0.73 | 0.50 | 100685.98 | 354838.97 | 2.15 | 84.59 | 0.31 | 0.84 | 0.21 | 0.68 | 0.75 | 281777.41 | 669598.75 | 5.79 | 131.44 | 0.21 | 0.62 | 0.19 | 0.59 | 0.50 | 0.25 | 223096.41 | 1334703.63 | 4.35 | 265.11 | 0.27 | 0.69 | 0.25 | 0.67 | 0.50 | 707912.81 | 1682584.50 | 13.42 | 327.85 | 0.31 | 0.64 | 0.26 | 0.47 | 0.75 | 2069551.88 | 4812524.50 | 47.37 | 1083.82 | 0.26 | 0.50 | 0.26 |
0.60 | 0.5 | 0.25 | 0.25 | 28694.70 | 51288.52 | 0.57 | 10.11 | 0.46 | 2.34 | 0.80 | 2.93 | 0.50 | 130640.24 | 489352.94 | 2.26 | 79.84 | 0.20 | 1.00 | 0.44 | 2.22 | 0.75 | 259434.69 | 552024.63 | 4.58 | 97.95 | 0.29 | 1.36 | 0.86 | 2.42 | 0.50 | 0.25 | 17466.58 | 29918.38 | 0.26 | 4.36 | 0.15 | 0.76 | 0.27 | 1.11 | 0.50 | 439942.63 | 1794187.38 | 6.63 | 298.29 | 0.46 | 1.22 | 0.71 | 1.75 | 0.75 | 2000465.50 | 6470223.50 | 34.15 | 1047.58 | 0.49 | 1.32 | 0.97 | 1.63 |
|
|