Research Article
A Branch-and-Price Algorithm for an Integrated Online and Offline Retailing Distribution System with Product Return
Table 3
Performance comparison of CPLEX solver and the proposed algorithm with Set 1.
| Instance | Sum (Inv) | Sum (Sd) | Sum (Cd) | Sum (Re) | CPLEX | The proposed algorithm | %dev | Best | k | Time (s) | Avg. 10 | k | Time (s) |
| T-S3-D9-R1 | 39 | 197 | 36 | 1 | 188368 | 1 | 195 | 188368 | 1 | 7.2 | 0.0 | R-S3-D9-R1 | 63 | 197 | 36 | 1 | 174472 | 1 | 227 | 174472 | 1 | 7.1 | 0.0 | A-S3-D9-R1 | 108 | 197 | 36 | 1 | 174472 | 1 | 176 | 174472 | 1 | 9.5 | 0.0 | T-S3-D9-R2 | 42 | 197 | 36 | 10 | 184656 | 1 | 300 | 180688 | 1 | 8.5 | −2.2 | R-S3-D9-R2 | 66 | 197 | 36 | 10 | 180395 | 1 | 300 | 176669 | 1 | 8.5 | −2.1 | A-S3-D9-R2 | 108 | 197 | 36 | 10 | 180395 | 1 | 300 | 176669 | 1 | 10.0 | −2.1 | T-S3-D9-R3 | 48 | 197 | 36 | 5 | 193772 | 1 | 300 | 193772 | 1 | 12.8 | 0.0 | R-S3-D9-R3 | 60 | 197 | 36 | 5 | 191047 | 1 | 300 | 191047 | 1 | 10.0 | 0.0 | A-S3-D9-R3 | 108 | 197 | 36 | 5 | 191047 | 1 | 300 | 191047 | 1 | 19.7 | 0.0 | T-S3-D9-R4 | 48 | 197 | 36 | 12 | 191583 | 1 | 300 | 191583 | 1 | 10.0 | 0.0 | R-S3-D9-R4 | 66 | 197 | 36 | 12 | 188858 | 1 | 300 | 188858 | 1 | 10.5 | 0.0 | A-S3-D9-R4 | 108 | 197 | 36 | 12 | 188858 | 1 | 300 | 188858 | 1 | 13.4 | 0.0 | T-S3-D9-R5 | 42 | 197 | 36 | 14 | 203714 | 1 | 300 | 203714 | 1 | 13.4 | 0.0 | R-S3-D9-R5 | 57 | 197 | 36 | 14 | 201916 | 1 | 300 | 200312 | 1 | 15.5 | −0.8 | A-S3-D9-R5 | 108 | 197 | 36 | 14 | 200312 | 1 | 300 | 200312 | 1 | 34.6 | 0.0 | T-S4-D12-R1 | 56 | 206 | 52 | 10 | 192523 | 2 | 300 | 192523 | 2 | 17.7 | 0.0 | R-S4-D12-R1 | 100 | 206 | 52 | 10 | 192523 | 2 | 300 | 192523 | 2 | 14.7 | 0.0 | A-S4-D12-R1 | 208 | 206 | 52 | 10 | 192523 | 2 | 300 | 192523 | 2 | 21.1 | 0.0 | T-S4-D12-R3 | 56 | 206 | 52 | 21 | 211098 | 2 | 300 | 211098 | 2 | 18.9 | 0.0 | R-S4-D12-R3 | 84 | 206 | 52 | 21 | 209391 | 2 | 300 | 209391 | 2 | 10.9 | 0.0 | A-S4-D12-R3 | 208 | 206 | 52 | 21 | 209573 | 2 | 300 | 207960 | 2 | 14.0 | −0.8 | T-S4-D12-R4 | 72 | 206 | 52 | 23 | 255768 | 2 | 300 | 254073 | 2 | 17.5 | −0.7 | R-S4-D12-R4 | 80 | 206 | 52 | 23 | 235864 | 2 | 300 | 230901 | 2 | 33.0 | −2.1 | A-S4-D12-R4 | 208 | 206 | 52 | 23 | 246404 | 2 | 300 | 223166 | 2 | 13.5 | −9.4 | T-S4-D12-R5 | 68 | 206 | 52 | 21 | 260354 | 2 | 300 | 254570 | 2 | 27.7 | −2.2 | R-S4-D12-R5 | 80 | 206 | 52 | 21 | 259689 | 2 | 300 | 254580 | 2 | 24.5 | −2.0 | A-S4-D12-R5 | 208 | 206 | 52 | 21 | 264646 | 2 | 300 | 258683 | 2 | 60.0 | −2.3 | T-S4-D12-R6 | 68 | 206 | 52 | 31 | 256079 | 2 | 300 | 255026 | 2 | 37.1 | −0.4 | R-S4-D12-R6 | 100 | 206 | 52 | 31 | 255035 | 2 | 300 | 254482 | 2 | 39.5 | −0.2 | A-S4-D12-R6 | 208 | 206 | 52 | 31 | 291126 | 2 | 300 | 260144 | 2 | 46.5 | −10.6 | Avg. | 95.8 | 201.5 | 44.0 | 14.8 | 212215.4 | 1.5 | 289.9 | 209082.8 | 1.5 | 19.6 | −1.3 |
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