Research Article
A Location-Inventory-Routing Problem in Forward and Reverse Logistics Network Design
Table 4
Results of different rate between the cost of recovered products and the cost of new products.
| Prob. ID | | | | | TS | NTS | Gap 1 (%) | UB | Time | UB | Time |
| P1 | 1 | 20 | 5 | 70 | 68142 | 3.00 | 68142 | 2.78 | 0.00 | 1.25 | 67402 | 2.68 | 67402 | 2.39 | 0.00 | 1.5 | 67211 | 2.14 | 66964 | 2.61 | −0.37 | 1.75 | 66898 | 3.15 | 66649 | 2.54 | −0.37 | 2 | 66496 | 2.76 | 66414 | 2.79 | −0.12 |
| P2 | 1 | 20 | 5 | 150 | 43008 | 3.33 | 43008 | 2.35 | 0.00 | 1.25 | 42964 | 3.11 | 42964 | 2.54 | 0.00 | 1.5 | 42934 | 2.49 | 42934 | 2.22 | 0.00 | 1.75 | 42913 | 2.40 | 42913 | 3.15 | 0.00 | 2 | 42897 | 3.55 | 42897 | 3.19 | 0.00 |
| P3 | 1 | 20 | 5 | 70 | 61680 | 2.72 | 61680 | 2.82 | 0.00 | 1.25 | 61028 | 2.46 | 61028 | 2.81 | 0.00 | 1.5 | 60595 | 2.47 | 60595 | 2.54 | 0.00 | 1.75 | 60367 | 2.59 | 60285 | 2.71 | −0.14 | 2 | 60132 | 2.52 | 60052 | 2.50 | −0.13 |
| P4 | 1 | 20 | 5 | 150 | 40458 | 2.45 | 40458 | 2.05 | 0.00 | 1.25 | 40391 | 2.18 | 40391 | 2.36 | 0.00 | 1.5 | 40346 | 2.86 | 40346 | 2.96 | 0.00 | 1.75 | 40314 | 2.69 | 40314 | 2.32 | 0.00 | 2 | 40290 | 1.92 | 40290 | 2.28 | 0.00 |
| P5 | 1 | 50 | 5 | 70 | 117832 | 26.39 | 116378 | 25.98 | −1.23 | 1.25 | 117029 | 25.68 | 114692 | 26.63 | −2.00 | 1.5 | 115617 | 26.14 | 114374 | 25.88 | −1.08 | 1.75 | 115126 | 26.70 | 114022 | 26.30 | −0.96 | 2 | 113413 | 25.84 | 112590 | 25.75 | −0.73 |
| P6 | 1 | 50 | 5 | 150 | 90053 | 22.94 | 87484 | 20.19 | −2.85 | 1.25 | 88307 | 24.22 | 86991 | 20.15 | −1.49 | 1.5 | 87796 | 23.82 | 86910 | 23.21 | −1.01 | 1.75 | 86976 | 20.81 | 86535 | 22.24 | −0.51 | 2 | 86703 | 22.88 | 86394 | 17.23 | −0.36 |
| P7 | 1 | 50 | 5 | 70 | 123939 | 18.23 | 122295 | 21.88 | −1.33 | 1.25 | 121637 | 19.25 | 120958 | 16.91 | −0.56 | 1.5 | 120474 | 18.75 | 119532 | 20.84 | −0.78 | 1.75 | 119790 | 21.88 | 118308 | 21.61 | −1.24 | 2 | 118183 | 16.95 | 117858 | 21.77 | −0.27 |
| P8 | 1 | 50 | 5 | 150 | 100524 | 17.41 | 100439 | 25.51 | −0.08 | 1.25 | 99371 | 28.59 | 99067 | 29.73 | −0.31 | 1.5 | 98231 | 24.37 | 97807 | 29.53 | −0.43 | 1.75 | 97514 | 24.48 | 96608 | 22.80 | −0.93 | 2 | 96942 | 25.15 | 96560 | 17.95 | −0.39 |
| P9 | 1 | 50 | 5 | 70 | 117880 | 27.00 | 115956 | 22.17 | −1.63 | 1.25 | 116053 | 30.39 | 114876 | 35.22 | −1.01 | 1.5 | 114690 | 24.03 | 113420 | 28.06 | −1.11 | 1.75 | 113128 | 19.20 | 112769 | 28.95 | −0.32 | 2 | 112006 | 28.62 | 111756 | 26.96 | −0.22 |
| P10 | 1 | 50 | 5 | 150 | 88057 | 23.26 | 87883 | 31.21 | −0.20 | 1.25 | 86485 | 25.83 | 86222 | 31.48 | −0.30 | 1.5 | 85367 | 31.62 | 84589 | 19.58 | −0.91 | 1.75 | 83386 | 26.10 | 83478 | 22.37 | 0.11 | 2 | 83455 | 25.45 | 83235 | 21.90 | −0.26 |
| P11 | 1 | 50 | 5 | 70 | 114793 | 20.04 | 112544 | 25.68 | −1.96 | 1.25 | 112136 | 19.99 | 111395 | 27.60 | −0.66 | 1.5 | 111087 | 20.16 | 111062 | 29.96 | −0.02 | 1.75 | 110640 | 27.13 | 109472 | 22.12 | −1.06 | 2 | 110405 | 22.60 | 108934 | 26.43 | −1.33 |
| P12 | 1 | 50 | 5 | 150 | 87232 | 24.63 | 86433 | 29.55 | −0.04 | 1.25 | 86410 | 22.09 | 86199 | 18.89 | −0.57 | 1.5 | 85173 | 27.98 | 83868 | 19.14 | −1.94 | 1.75 | 84523 | 21.53 | 83656 | 15.63 | −2.18 | 2 | 83027 | 18.38 | 82912 | 20.22 | −1.46 |
| P13 | 1 | 100 | 5 | 70 | 364895 | 155.68 | 361755 | 159.32 | −0.86 | 1.25 | 363309 | 160.69 | 360230 | 160.93 | −0.85 | 1.5 | 362096 | 163.84 | 359999 | 168.78 | −0.58 | 1.75 | 359974 | 157.96 | 356857 | 141.78 | −0.87 | 2 | 355624 | 156.57 | 339404 | 161.89 | −4.56 |
| P14 | 1 | 100 | 5 | 150 | 305053 | 164.11 | 300033 | 139.62 | −1.65 | 1.25 | 303135 | 141.89 | 296364 | 121.95 | −2.23 | 1.5 | 301834 | 139.24 | 295118 | 121.68 | −2.23 | 1.75 | 298777 | 139.76 | 294442 | 133.88 | −1.45 | 2 | 291740 | 133.99 | 276706 | 135.66 | −5.15 |
| P15 | 1 | 100 | 5 | 70 | 296619 | 124.99 | 258199 | 125.21 | −12.95 | 1.25 | 260317 | 137.47 | 254461 | 128.82 | −2.25 | 1.5 | 249922 | 115.05 | 247152 | 183.34 | −1.11 | 1.75 | 249195 | 132.22 | 244535 | 154.43 | −1.87 | 2 | 247529 | 149.44 | 241351 | 171.13 | −2.50 |
| P16 | 1 | 100 | 5 | 150 | 233346 | 120.31 | 223398 | 126.11 | −4.26 | 1.25 | 229687 | 129.75 | 220760 | 114.91 | −3.89 | 1.5 | 226932 | 127.63 | 218861 | 117.39 | −3.56 | 1.75 | 216624 | 137.42 | 214174 | 115.09 | −1.13 | 2 | 211223 | 128.79 | 205238 | 122.39 | −2.83 |
| P17 | 1 | 100 | 5 | 70 | 267713 | 134.93 | 265309 | 110.60 | −0.90 | 1.25 | 266067 | 132.17 | 262547 | 122.34 | −1.32 | 1.5 | 263994 | 130.92 | 260267 | 110.49 | −1.41 | 1.75 | 261711 | 116.78 | 259735 | 150.61 | −0.76 | 2 | 260804 | 170.99 | 252673 | 124.40 | −3.12 |
| P18 | 1 | 100 | 5 | 150 | 226178 | 124.86 | 224348 | 139.70 | −0.81 | 1.25 | 223053 | 127.08 | 219578 | 134.79 | −1.56 | 1.5 | 220970 | 115.28 | 218823 | 184.85 | −0.97 | 1.75 | 219154 | 158.19 | 216341 | 129.00 | −1.28 | 2 | 217751 | 159.37 | 209257 | 182.73 | −3.90 |
| P19 | 1 | 100 | 10 | 70 | 412240 | 135.46 | 409643 | 141.11 | −0.63 | 1.25 | 406518 | 139.13 | 403969 | 173.98 | −0.63 | 1.5 | 404199 | 137.06 | 401006 | 167.12 | −0.79 | 1.75 | 403475 | 136.64 | 400046 | 178.88 | −0.85 | 2 | 401608 | 136.54 | 394231 | 149.81 | −1.84 |
| P20 | 1 | 100 | 10 | 150 | 366576 | 105.10 | 364188 | 166.50 | −0.65 | 1.25 | 364342 | 123.15 | 362564 | 100.25 | −0.49 | 1.5 | 360397 | 153.27 | 358732 | 143.08 | −0.46 | 1.75 | 357502 | 158.04 | 356178 | 114.59 | −0.37 | 2 | 350419 | 100.43 | 345948 | 154.21 | −1.28 |
| P21 | 1 | 100 | 10 | 70 | 337749 | 113.31 | 334240 | 100.11 | −1.04 | 1.25 | 333248 | 114.45 | 330768 | 112.04 | −0.74 | 1.5 | 330981 | 127.66 | 329900 | 133.01 | −0.33 | 1.75 | 329982 | 143.46 | 325218 | 139.32 | −1.44 | 2 | 327911 | 189.02 | 322382 | 150.34 | −1.69 |
| P22 | 1 | 100 | 10 | 150 | 300245 | 112.22 | 297406 | 94.24 | −0.95 | 1.25 | 293642 | 127.66 | 291212 | 119.95 | −0.83 | 1.5 | 290938 | 186.05 | 287471 | 192.95 | −1.19 | 1.75 | 288716 | 183.72 | 285885 | 127.07 | −0.98 | 2 | 286473 | 132.29 | 281933 | 125.07 | −1.58 |
| P23 | 1 | 100 | 10 | 70 | 369343 | 127.38 | 364871 | 132.22 | −1.21 | 1.25 | 364871 | 152.70 | 359677 | 141.96 | −1.42 | 1.5 | 359613 | 147.70 | 355286 | 152.78 | −1.20 | 1.75 | 358094 | 155.05 | 354980 | 142.97 | −0.87 | 2 | 341610 | 146.96 | 320343 | 172.26 | −6.23 |
| P24 | 1 | 100 | 10 | 150 | 328663 | 124.91 | 299018 | 132.71 | −9.02 | 1.25 | 325042 | 125.13 | 295553 | 137.29 | −9.07 | 1.5 | 323847 | 156.83 | 291860 | 135.43 | −9.88 | 1.75 | 299214 | 135.60 | 288433 | 157.16 | −3.60 | 2 | 294706 | 121.22 | 281938 | 168.67 | −4.33 |
| P25 | 1 | 200 | 10 | 70 | 665281 | 829.11 | 653633 | 1026.07 | −1.75 | 1.25 | 657935 | 834.27 | 652114 | 1061.26 | −0.88 | 1.5 | 655818 | 823.79 | 651574 | 984.23 | −0.65 | 1.75 | 649604 | 820.10 | 646761 | 1055.81 | −0.44 | 2 | 642489 | 820.87 | 641864 | 1139.61 | −0.10 |
| P26 | 1 | 200 | 10 | 150 | 581623 | 611.52 | 580270 | 618.26 | −0.23 | 1.25 | 579961 | 608.25 | 569283 | 626.20 | −1.84 | 1.5 | 574684 | 604.60 | 536008 | 613.79 | −6.73 | 1.75 | 556955 | 621.66 | 535570 | 623.55 | −3.84 | 2 | 554052 | 621.92 | 528999 | 622.53 | −4.52 |
| P27 | 1 | 200 | 10 | 70 | 773781 | 793.09 | 662523 | 778.08 | −14.38 | 1.25 | 713012 | 819.64 | 655573 | 803.25 | −8.06 | 1.5 | 681260 | 804.27 | 642081 | 739.51 | −5.75 | 1.75 | 635834 | 770.17 | 632602 | 723.11 | −0.51 | 2 | 632061 | 739.14 | 623493 | 704.85 | −1.36 |
| P28 | 1 | 200 | 10 | 150 | 576983 | 666.69 | 555923 | 987.24 | −3.65 | 1.25 | 568736 | 675.82 | 546433 | 859.83 | −3.92 | 1.5 | 564064 | 674.70 | 543330 | 859.83 | −3.68 | 1.75 | 560726 | 914.60 | 535818 | 761.02 | −4.44 | 2 | 534830 | 977.03 | 522356 | 795.76 | −2.33 |
| P29 | 1 | 200 | 10 | 70 | 666957 | 790.82 | 636582 | 820.80 | −4.55 | 1.25 | 658832 | 832.47 | 633813 | 1119.70 | −3.80 | 1.5 | 653454 | 1149.63 | 621988 | 965.82 | −4.82 | 1.75 | 622078 | 801.89 | 619907 | 825.17 | −0.35 | 2 | 616051 | 863.47 | 608644 | 1080.37 | −1.20 |
| P30 | 1 | 200 | 10 | 150 | 542071 | 734.01 | 540384 | 705.36 | −0.31 | 1.25 | 525159 | 727.55 | 524172 | 786.56 | −0.19 | 1.5 | 521758 | 716.37 | 510933 | 763.03 | −2.07 | 1.75 | 518474 | 787.04 | 506479 | 752.31 | −2.31 | 2 | 515142 | 755.66 | 502884 | 698.85 | −2.38 |
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