Research Article
Ridesharing Problem with Flexible Pickup and Delivery Locations for App-Based Transportation Service: Mathematical Modeling and Decomposition Methods
Table 2
Numerical results for multiscale instances.
| | Instance | Value | CF | CT | CP | Ctotal | Solution Time (sec) | Gap (%) |
| | 100-20-20 | Ave | 534.0 | 12.1 | 2.3 | 548.4 | 775.4 | 0.59 | | SD | 12.0 | 1.3 | 1.1 | 12.0 | 117.1 | 0.30 | | 100-20-30 | Ave | 834.0 | 17.1 | 4.3 | 855.4 | 804.4 | 2.63 | | SD | 12.0 | 1.6 | 0.6 | 13.5 | 169.8 | 0.64 | | 100-20-40 | Ave | 1086.0 | 22.3 | 4.3 | 1112.6 | 1264.5 | 3.05 | | SD | 22.4 | 1.2 | 1.2 | 22.2 | 120.1 | 0.21 | | 100-30-20 | Ave | 504.0 | 13.6 | 2.1 | 519.7 | 671.6 | 2.82 | | SD | 12.0 | 0.4 | 1.2 | 11.7 | 218.8 | 0.12 | | 100-30-30 | Ave | 750.0 | 18.7 | 3.5 | 772.2 | 1079.7 | 3.28 | | SD | 32.9 | 1.1 | 0.6 | 33.9 | 159.1 | 1.35 | | 100-30-40 | Ave | 1002.0 | 25.1 | 5.3 | 1032.4 | 1768.7 | 5.66 | | SD | 24.0 | 0.7 | 1.1 | 23.1 | 170.0 | 1.53 | | 100-40-20 | Ave | 480.0 | 14.1 | 2.7 | 496.9 | 1215.7 | 2.18 | | SD | 0.0 | 0.6 | 0.5 | 0.8 | 590.6 | 0.51 | | 100-40-30 | Ave | 726.0 | 20.1 | 4.2 | 750.4 | 1370.2 | 3.20 | | SD | 39.8 | 0.9 | 0.6 | 36.4 | 273.3 | 0.67 | | 100-40-40 | Ave | 996.0 | 27.0 | 5.5 | 1028.5 | 1433.8 | 3.97 | | SD | 29.4 | 1.0 | 1.5 | 28.2 | 217.1 | 0.62 | | 400-20-20 | Ave | 580.0 | 15.0 | 2.1 | 597.0 | 1151.8 | 2.05 | | SD | 14.1 | 1.0 | 1.2 | 13.5 | 356.9 | 0.36 | | 400-20-30 | Ave | 870.0 | 23.2 | 3.3 | 896.5 | 1279.0 | 2.91 | | SD | 0.0 | 1.2 | 1.5 | 0.9 | 332.9 | 0.07 | | 400-20-40 | Ave | 1162.5 | 29.2 | 3.8 | 1195.5 | 1336.0 | 4.22 | | SD | 32.7 | 1.2 | 2.4 | 31.5 | 459.5 | 0.81 | | 400-30-20 | Ave | 565.0 | 20.8 | 2.3 | 588.1 | 1552.4 | 2.83 | | SD | 20.6 | 1.6 | 1.2 | 19.1 | 408.4 | 0.63 | | 400-30-30 | Ave | 858.0 | 33.0 | 4.7 | 895.6 | 1876.5 | 3.13 | | SD | 14.7 | 2.9 | 0.2 | 16.7 | 628.9 | 0.73 | | 400-30-40 | Ave | 1140.0 | 42.0 | 4.7 | 1186.7 | 1963.0 | 4.18 | | SD | 19.0 | 1.8 | 1.3 | 19.5 | 399.8 | 0.52 | | 400-40-20 | Ave | 540.0 | 25.2 | 2.1 | 567.3 | 1981.3 | 2.45 | | SD | 19.0 | 3.3 | 0.7 | 21.8 | 293.8 | 0.45 | | 400-40-30 | Ave | 840.0 | 35.5 | 2.6 | 878.1 | 2415.5 | 3.83 | | SD | 26.8 | 2.9 | 1.4 | 26.5 | 867.6 | 0.83 | | 400-40-40 | Ave | 1152.0 | 49.4 | 2.7 | 1204.0 | 4223.5 | 4.24 | | SD | 40.7 | 3.1 | 2.3 | 42.1 | 392.9 | 1.34 | | 900-20-20 | Ave | 588.0 | 15.4 | 1.4 | 604.8 | 1018.5 | 2.98 | | SD | 14.7 | 1.5 | 1.4 | 14.5 | 373.9 | 0.24 | | 900-20-30 | Ave | 882.0 | 24.2 | 2.1 | 908.3 | 1980.1 | 3.91 | | SD | 14.7 | 2.0 | 1.6 | 14.4 | 860.4 | 0.02 | | 900-20-40 | Ave | 1188.0 | 33.3 | 2.2 | 1223.6 | 2234.3 | 4.80 | | SD | 14.7 | 1.6 | 2.0 | 14.1 | 731.8 | 0.37 | | 900-30-20 | Ave | 588.0 | 24.7 | 1.2 | 613.8 | 1883.7 | 4.50 | | SD | 14.7 | 3.0 | 1.2 | 15.4 | 713.3 | 0.30 | | 900-30-30 | Ave | 882.0 | 37.3 | 1.3 | 920.6 | 2153.5 | 5.67 | | SD | 14.7 | 2.5 | 1.4 | 13.5 | 541.2 | 0.17 | | 900-30-40 | Ave | 1170.0 | 48.7 | 4.4 | 1223.0 | 3080.2 | 6.31 | | SD | 19.0 | 1.6 | 2.2 | 17.0 | 1348.9 | 0.45 | | 900-40-20 | Ave | 588.0 | 31.6 | 0.4 | 619.9 | 2484.6 | 4.83 | | SD | 14.7 | 4.1 | 0.5 | 15.3 | 1096.1 | 0.07 | | 900-40-30 | Ave | 888.0 | 47.9 | 1.2 | 937.1 | 4222.2 | 6.00 | | SD | 14.7 | 3.3 | 1.7 | 11.6 | 975.3 | 0.75 | | 900-40-40 | Ave | 1158.0 | 63.8 | 3.9 | 1225.7 | 4817.4 | 7.22 | | SD | 14.7 | 4.5 | 2.1 | 15.2 | 1901.5 | 0.67 |
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