Exact Solution of the Vehicle Routing Problem with Drones
The working paper
J. Schmidt, C. Tilk, S. Irnich (2023). Exact Solution of the Vehicle Routing Problem with Drones LM-2023-03, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
uses the following instances.
Zip file with instances.
Exact Solution of the Single Picker Routing Problem with Scattered Storage
The results reported in the working paper
K. Heßler, S. Irnich (2023). Exact Solution of the Single Picker Routing Problem with Scattered Storage LM-2023-02, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
are available at GitHub.
The Single Picker Routing Problem with Scattered Storage: Modeling and Evaluation of Routing and Storage Policies
The working paper
L. Korbacher, K. Heßler, S. Irnich (2023). The Single Picker Routing Problem with Scattered Storage: Modeling and Evaluation of Routing and Storage Policies LM-2023-01, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
uses the following instances.
Zip file with instances.
A matheuristic for a 2-echelon vehicle routing problem with capacitated satellites and reverse flows
The working paper
Dorian Dumez, Christian Tilk, Stefan Irnich, Katharina Olkis, Fabien Lehuédé, and Olivier Péton
HAL archives ouvertes.fr, hal-03384261
uses the following instances.
Zip file with instances.
Modeling and Exact Solution of Picker Routing and Order Batching Problems
The working paper
K. Heßler, S. Irnich (2022). Modeling and Exact Solution of Picker Routing and Order Batching Problems LM-2022-03, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
uses the following instances.
Zip file with instances.
Partial Dominance in Branch-Price-and-Cut for the Basic Multi-Compartment Vehicle-Routing Problem
The working paper
K. Heßler, S. Irnich (2021). Partial Dominance in Branch-Price-and-Cut for the Basic Multi-Compartment Vehicle-Routing Problem LM-2021-02, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
Forthcoming in: INFORMS Journal on Computing.
uses the following instances.
Zip file with instances.
Using Public Transport in a 2-Echelon Last-Mile Delivery Network
The working paper
J. Schmidt, C. Tilk, S. Irnich (2022). Using Public Transport in a 2-Echelon Last-Mile Delivery Network, Technical Report LM-2022-01, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
uses the following instances.
Zip file with instances.
Exact Algorithms for the Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes
The working paper
Katrin Heßler (2020). Exact Algorithms for the Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes, Technical Report LM-2020-04, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
uses the following instances.
Zip file with instances.
The Last-mile Vehicle Routing Problem with Delivery Options
The working paper
Christian Tilk, Katharina Olkis, Stefan Irnich (2020). The Last-mile Vehicle Routing Problem with Delivery Options, Technical Report LM-2020-06, Chair of Logistics Management, Johannes Gutenberg University, Mainz, Germany.
uses the following instances.
Zip file with instances.
Lexicographic Bin-Packing Optimization for Loading Trucks in a Direct-Shipping System
The working paper
K. Heßler, S. Irnich, T. Kreiter, U. Pferschy (2020). Lexicographic Bin-Packing Optimization for Loading Trucks in a Direct-Shipping System. Technical Report LM-2020-05, Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Germany.
uses 110 new benchmark instances.
Zip file with instances.
Multi-Depot Vehicle Routing Problem
The working paper
JB. Gauthier, S. Irnich (2020). Inter-Depot Moves and Dynamic-Radius Search for Multi-Depot Vehicle Routing Problems. Technical Report LM-2020-03, Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Germany.
uses the following benchmark instances.
Zip file and file with instances.
Soft-Clustered Vehicle Routing Problem
The working paper
K. Heßler, S. Irnich (2020). A Branch-and-Cut Algorithm for the Soft-Clustered Vehicle Routing Problem. Technical Report LM-2020-01, Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Germany.
uses 90 new benchmark instances.
Zip files with instances.
Soft-Clustered Capacitated Arc-Routing Problem (SoftCluCARP)
The working paper
T. Hintsch, S. Irnich, L. Kiilerich (2019). Branch-Price-and-Cut for the Soft-Clustered Capacitated Arc-Routing Problem. Technical Report LM-2019-02, Chair of Logistics Management, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Germany.
uses 644 new benchmark instances.
Zip file with instances (for the format see below at the CARP instances).
Direct Delivery Scheduling Problem in a Network
The working paper
T. Gschwind, S. Irnich, C. Tilk, S. Emde (2018). Branch-Cut-and-Price for Scheduling Deliveries with Time Windows in a Direct Shipping Network. Technical Report LM-2018-03, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Mainz, Germany.
uses 120 new benchmark instances.
Zip file with instances.
Commodity-Constrained Split Delivery Vehicle Routing Problem
The working paper
T. Gschwind, N. Bianchessi, S. Irnich (2018). Stabilized Branch-Price-and-Cut for the Commodity-Constrained Split Delivery Vehicle Routing Problem. Technical report LM-2018-06, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Mainz, Germany.
uses new benchmark instances with a larger number of commodities (4, 5, and 6) that are otherwise generated in the same way as the instances introduced in
Archetti, C., Campbell, A. M., Speranza, M. G. (2016). Multicommodity vs. single-commodity routing. Transportation Science, 50(2), 461–472.
Zip file with instances including the original benchmark instances from Archetti et al.
Vector Packing Problem
The working paper
K. Heßler, T. Gschwind, S. Irnich (2017). Stabilized Branch-and-Price Algorithms for Vector Packing Problems. Technical report LM-2017-04, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Mainz, Germany.
uses 440 new benchmark instances that add larger demand to the 2-dimensional instances of
Caprara, A. and Toth, P. (2001). Lower bounds and algorithms for the 2-dimensional vector packing problem. Discrete Applied Mathematics, 111(3), 231–262.
and the 20-dimensional instances of
Brandao, F. and Pedroso, J. P. (2016). Bin packing and related problems: general arc-flow formulation with graph compression. Computers & Operations Research, 69, 56–67.
Zip file with instances.
Zip file with optimal values.
Split Delivery Vehicle Routing Problem with Time Windows
The working paper
N. Bianchessi, M.Drexl, S. Irnich (2017). The Split Delivery Vehicle Routing Problem with Time Windows and
Customer Inconvenience Constraints. Technical report LM-2017-02, Gutenberg School of Management and Economics, Johannes Gutenberg University Mainz, Mainz, Germany.
uses 560 new benchmark instances that are generated similar to Solomon's instances, but with different demand scenarios.
Zip file with instances.
Cutting Stock Problem
The GI instances were introduced in:
Gschwind, T. and Irnich, S. Dual inequalities for stabilized column generation revisited. INFORMS Journal on Computing, 28(1), 175–194, 2016, doi: 10.1287/ijoc.2015.0670
Zip file and file with instances.
Capacitated Arc Routing Problem (CARP)
Lower and upper bound values and integer solutions for CARP benchmark instances are listed below.
KSHS Instances
The KSHS instances were introduced in:
M. Kiuchi, Y. Shinano, R. Hirabayashi and Y. Saruwatari (1995). An exact algorithm for the Capacitated Arc Routing Problem using Parallel Branch and Bound method. Abstracts of the 1995 Spring National Conference of the Oper. Res. Soc. of Japan, 28-29.
Zip file with instances as provided by José Manuel Belenguer and Enrique Benavent's website (see also format file).
| Lower Bounds | Upper Bounds | Integer Solutions | |||||
| Instances | Belenguer Benavent 2003 | Longo et al. 2006 | best known LB | best known UB | Beullens et al. 2003 (modified costs) | Optimal Solution | Longo et al. 2006 |
| kshs1 | 14661 | 14661 | 14661 | 14661 | 14661 | 14661 | 14661 |
| kshs2 | 9863 | 9863 | 9863 | 9863 | 9863 | 9863 | 9863 |
| kshs3 | 9320 | 9320 | 9320 | 9320 | 9320 | 9320 | 9320 |
| kshs4 | 11098 | 11498 | 11498 | 11498 | 11498 | 11498 | 11498 |
| kshs5 | 10957 | 10957 | 10957 | 10957 | 10957 | 10957 | 10957 |
| kshs6 | 10197 | 10197 | 10197 | 10197 | 10197 | 10197 | 10197 |
GDB Instances
The GDB instances were introduced in:
B.L. Golden, J.S. DeArmon and E.K. Baker (1983). Computational Experiments with Algorithms for a Class of Routing Problems. Computers & Operations Research 10 (1), 47-59.
Zip file with instances as provided by José Manuel Belenguer and Enrique Benavent's website (see also format file).
| Lower Bounds | Upper Bounds | Integer Solutions | ||||||||
| Instances | Belenguer Benavent 2003 | Longo et al. 2006 | best known LB | best known UB | Pearn 1989 | Hertz et al. 2000 | Lacomme et al. 2001* | Beullens et al. 2003 (modified costs) | Optimal Solution | Longo et al. 2006 |
| gdb1 | 316 | 316 | 316 | 316 | 316 | 316 | 316 | 316 | 316 | 316 |
| gdb2 | 339 | 339 | 339 | 339 | 345 | 339 | 339 | 339 | 339 | 339 |
| gdb3 | 275 | 275 | 275 | 275 | 275 | 275 | 275 | 275 | 275 | 275 |
| gdb4 | 287 | 287 | 287 | 287 | 287 | 287 | 287 | 287 | 287 | 287 |
| gdb5 | 377 | 377 | 377 | 377 | 383 | 377 | 377 | 377 | 377 | 377 |
| gdb6 | 298 | 298 | 298 | 298 | 315 | 298 | 298 | 298 | 298 | 298 |
| gdb7 | 325 | 325 | 325 | 325 | 325 | 325 | 325 | 325 | 325 | 325 |
| gdb8 | 344 | 348 | 348 | 348 | 356 | 352 | 348 | 348 | 348 | 348 |
| gdb9 | 303 | 303 | 303 | 303 | 339 | 317 | 303 | 303 | 303 | 303 |
| gdb10 | 275 | 275 | 275 | 275 | 275 | 275 | 275 | 275 | 275 | 275 |
| gdb11 | 395 | 395 | 395 | 395 | 406 | 395 | 395 | 395 | 395 | 395 |
| gdb12 | 450 | 458 | 458 | 458 | 560 | 458 | 458 | 456 | 458 | 458 |
| gdb13 | 536 | 536 | 536 | 536 | 554 | 544 | 538 | 536 | 536 | 536 |
| gdb14 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
| gdb15 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 | 58 |
| gdb16 | 127 | 127 | 127 | 127 | 127 | 127 | 127 | 127 | 127 | 127 |
| gdb17 | 91 | 91 | 91 | 91 | 91 | 91 | 91 | 91 | 91 | 91 |
| gdb18 | 164 | 164 | 164 | 164 | 164 | 164 | 164 | 164 | 164 | 164 |
| gdb19 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 | 55 |
| gdb20 | 121 | 121 | 121 | 121 | 123 | 121 | 121 | 121 | 121 | 121 |
| gdb21 | 156 | 156 | 156 | 156 | 156 | 156 | 156 | 156 | 156 | 156 |
| gdb22 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 | 200 |
| gdb23 | 233 | 233 | 233 | 233 | 233 | 235 | 235 | 233 | 233 | 233 |
BBCM Instances a.k.a. VAL Instances
The BBCM instances were introduced in:
E. Benavent, V. Campos, A. Corberán and E. Mota (1992). The Capacitated Chinese Postman Problem: Lower Bounds. Networks 22 (7), 669-690.
Zip file with instances as provided by José Manuel Belenguer and Enrique Benavent's website (see also format file).
| Lower Bounds | Upper Bounds | Integer Solutions | ||||||||||||||||||||||
| Instances | Benavent et al. 1992 | Belenguer Benavent 2003 | Longo et al. 2006 (LB at root node) | Longo et al. 2006 | Baldacci Maniezzo 2006 | Bartolini et al. 2012 | Bartolini et al. 2012 (end of GenRoute) | Bode Irnich 2012 (LB at root node) | Bode Irnich 2012 | best known LB | best known UB | Hertz et al. 2000 | Lacomme et al. 2001* | Beullens et al. 2003 (modified costs) | Lacomme et al. 2004 | Polacek et al. 2008 | Brandao Eglese 2008 | Offset | Optimal Solution | Longo et al. 2006 | Baldacci Maniezzo 2006 | Bartolini et al. 2012 | Bode Irnich 2012 | |
| 1A | 247 | 247 | 247 | 247 | 247 | 247 | 247 | 247 | 247 | 173 | 173 | 173 | 173 | 173 | 173 | 74 | 247 | 247 | 247 | |||||
| 1B | 247 | 247 | 247 | 247 | 247 | 247 | 247 | 247 | 247 | 173 | 173 | 173 | 173 | 173 | 173 | 74 | 247 | 247 | 247 | |||||
| 1C | 309 | 312 | 319 | 319 | 314 | 314 | 314 | 319 | 319 | 319 | 245 | 245 | 245 | 245 | 245 | 245 | 74 | 319 | 319 | 319 | 319 | 319 | ||
| 2A | 297 | 298 | 298 | 298 | 298 | 298 | 298 | 298 | 298 | 227 | 227 | 227 | 227 | 227 | 227 | 71 | 298 | 298 | 298 | |||||
| 2B | 318 | 330 | 329 | 330 | 330 | 330 | 329 | 330 | 330 | 330 | 260 | 259 | 259 | 259 | 259 | 259 | 71 | 330 | 330 | 330 | 330 | |||
| 2C | 526 | 528 | 528 | 528 | 528 | 528 | 528 | 528 | 528 | 528 | 457 | 457 | 457 | 457 | 457 | 457 | 71 | 528 | 528 | 528 | 528 | 528 | ||
| 3A | 103 | 105 | 105 | 105 | 105 | 105 | 105 | 105 | 105 | 81 | 81 | 81 | 81 | 81 | 81 | 24 | 105 | 105 | 105 | |||||
| 3B | 108 | 111 | 111 | 111 | 111 | 111 | 111 | 111 | 111 | 87 | 87 | 87 | 87 | 87 | 87 | 24 | 111 | 111 | 111 | |||||
| 3C | 161 | 161 | 162 | 162 | 162 | 162 | 161 | 162 | 162 | 162 | 138 | 138 | 138 | 138 | 138 | 138 | 24 | 162 | 162 | 162 | 162 | 162 | ||
| 4A | 516 | 522 | 522 | 522 | 522 | 522 | 522 | 522 | 522 | 400 | 400 | 400 | 400 | 400 | 400 | 122 | 522 | 522 | 522 | |||||
| 4B | 522 | 534 | 534 | 534 | 534 | 534 | 534 | 534 | 534 | 412 | 412 | 412 | 412 | 412 | 412 | 122 | 534 | 534 | 534 | |||||
| 4C | 528 | 550 | 550 | 550 | 550 | 550 | 550 | 550 | 550 | 430 | 428 | 428 | 428 | 428 | 428 | 122 | 550 | 550 | 550 | |||||
| 4D | 644 | 648 | 649 | 649 | 647 | 650 | 650 | 652 | 546 | 530 | 530 | 530 | 530 | 530 | 122 | 650 | 650 | |||||||
| 5A | 562 | 566 | 566 | 566 | 566 | 566 | 566 | 566 | 566 | 423 | 423 | 423 | 423 | 423 | 423 | 143 | 566 | 566 | 566 | |||||
| 5B | 580 | 589 | 588 | 588 | 588 | 587 | 589 | 589 | 589 | 446 | 446 | 446 | 446 | 446 | 446 | 143 | 589 | 589 | ||||||
| 5C | 598 | 612 | 613 | 613 | 613 | 613 | 617 | 617 | 617 | 474 | 474 | 474 | 474 | 474 | 474 | 143 | 617 | 617 | ||||||
| 5D | 714 | 716 | 717 | 718 | 715 | 718 | 718 | 718 | 593 | 581 | 583 | 581 | 575 | 577 | 143 | 718 | 718 | 718 | ||||||
| 6A | 330 | 330 | 330 | 330 | 330 | 330 | 330 | 330 | 330 | 223 | 223 | 223 | 223 | 223 | 223 | 107 | 330 | 330 | 330 | |||||
| 6B | 336 | 338 | 337 | 340 | 337 | 337 | 336 | 340 | 340 | 340 | 241 | 233 | 233 | 233 | 233 | 233 | 107 | 340 | 340 | 340 | ||||
| 6C | 418 | 420 | 424 | 421 | 424 | 418 | 424 | 424 | 424 | 317 | 317 | 317 | 317 | 317 | 317 | 107 | 424 | 424 | 424 | 424 | ||||
| 7A | 382 | 382 | 382 | 382 | 382 | 382 | 382 | 382 | 382 | 279 | 279 | 279 | 279 | 279 | 279 | 103 | 382 | 382 | ||||||
| 7B | 382 | 386 | 386 | 386 | 386 | 386 | 386 | 386 | 386 | 283 | 283 | 283 | 283 | 283 | 283 | 103 | 386 | 386 | 386 | |||||
| 7C | 436 | 436 | 437 | 437 | 437 | 437 | 432 | 434 | 437 | 437 | 334 | 334 | 334 | 334 | 334 | 334 | 103 | 437 | 437 | 437 | 437 | |||
| 8A | 522 | 522 | 522 | 522 | 522 | 522 | 522 | 522 | 522 | 386 | 386 | 386 | 386 | 386 | 386 | 136 | 522 | 522 | 522 | |||||
| 8B | 531 | 531 | 531 | 531 | 531 | 531 | 531 | 531 | 531 | 395 | 395 | 395 | 395 | 395 | 395 | 136 | 531 | 531 | 531 | |||||
| 8C | 653 | 654 | 655 | 657 | 653 | 657 | 657 | 657 | 528 | 527 | 523 | 527 | 521 | 521 | 136 | 657 | 657 | 657 | ||||||
| 9A | 450 | 450 | 450 | 450 | 450 | 450 | 450 | 450 | 450 | 323 | 323 | 323 | 323 | 323 | 2323 | 127 | 450 | 450 | 450 | |||||
| 9B | 453 | 453 | 453 | 453 | 453 | 453 | 453 | 453 | 453 | 326 | 326 | 326 | 326 | 326 | 326 | 127 | 453 | 453 | 453 | |||||
| 9C | 459 | 459 | 459 | 459 | 459 | 459 | 459 | 459 | 459 | 332 | 332 | 332 | 332 | 332 | 332 | 127 | 459 | 459 | 459 | |||||
| 9D | 509 | 512 | 512 | 512 | 510 | 515 | 515 | 516 | 399 | 391 | 391 | 391 | 389 | 391 | 127 | 515 | 515 | |||||||
| 10A | 637 | 637 | 637 | 637 | 637 | 637 | 637 | 637 | 637 | 428 | 428 | 428 | 428 | 428 | 428 | 209 | 637 | 637 | 637 | |||||
| 10B | 645 | 645 | 645 | 645 | 645 | 645 | 645 | 645 | 645 | 436 | 436 | 436 | 436 | 436 | 436 | 209 | 645 | 645 | 645 | |||||
| 10C | 653 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 655 | 451 | 446 | 446 | 446 | 446 | 446 | 209 | 655 | 655 | 655 | |||||
| 10D | 732 | 734 | 734 | 734 | 734 | 734 | 734 | 734 | 536 | 530 | 529 | 528 | 525 | 528 | 209 | 734 | 734 | 734 | ||||||
EGL Instances
The EGL instances were introduced in:
L.Y.O. Li (1992). Vehicle Routeing for Winter Gritting. Ph.D. Thesis, Dept. of Management Science, Lancaster University.
L.Y.O. Li and R.W. Eglese (1996). An Interactive Algorithm for Vehicle Routeing for Winter-Gritting. Journal of the Operational Research Society 47, 217-228.
Zip file with instances as provided by the José Manuel Belenguer and Enrique Benavent's website (see also format file).
| Lower Bounds | Upper Bounds | Integer Solutions | ||||||||||||||||||||||||||||
| Instances | Belenguer Benavent 2003 | Ahr 2004 | Longo et al. 2006 (LB at root node) | Longo et al. 2006 | Baldacci Maniezzo 2006 | Martinelli et al. 2011a | Bartolini et al. 2012 | Bartolini et al. 2012 (end of GenRoute) | Bode Irnich 2012 (LB at root node) | Bode Irnich 2012 | Bode Irnich 2013 | Bode Irnich 2012b (revised) |
best known LB | best known UB | Lacomme et al. 2001* | Lacomme et al. 2004 | Polacek et al. 2008 | Brandao Eglese 2008 | Tang et al. 2009 | Mei et al. 2009 | Santos et al. 2010 | Fu et al. 2010 | Bartolini et al. 2012 (best known from literature or own ub) | Bode Irnich 2012b (revised) |
Optimal Solution | Longo et al. 2006 | Baldacci Maniezzo 2006 | Bartolini et al. 2012 | Bode Irnich 2012 | Bode Irnich 2012b (revised) |
| egl-e1-a | 3515 | 3516 | 3548 | 3548 | 3548 | 3548 | 3548 | 3545 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | 3548 | ||
| egl-e1-b | 4436 | 4436 | 4468 | 4498 | 4487 | 4487 | 4498 | 4464 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | 4498 | ||
| egl-e1-c | 5453 | 5481 | 5542 | 5537 | 5580 | 5595 | 5523 | 5545 | 5555 | 5573 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | 5595 | |||||||
| egl-e2-a | 4994 | 4963 | 5011 | 5018 | 5012 | 5012 | 5012 | 4996 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | |||
| egl-e2-b | 6249 | 6271 | 6280 | 6291 | 6284 | 6284 | 6273 | 6301 | 6306 | 6317 | 6317 | 6317 | 6340 | 6340 | 6317 | 6317 | 6317 | 6317 | 6317 | 6317 | 6317 | 6317 | 6317 | |||||||
| egl-e2-c | 8114 | 8155 | 8234 | 8274 | 8319 | 8335 | 8202 | 8244 | 8303 | 8319 | 8335 | 8335 | 8415 | 8395 | 8335 | 8335 | 8335 | 8335 | 8335 | 8335 | 8335 | 8335 | 8335 | |||||||
| egl-e3-a | 5869 | 5866 | 5898 | 5898 | 5898 | 5898 | 5898 | 4894 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | 5898 | ||
| egl-e3-b | 7646 | 7649 | 7697 | 7715 | 7711 | 7711 | 7684 | 7728 | 7735 | 7744 | 7744 | 7775 | 7822 | 7816 | 7775 | 7777 | 7775 | 7787 | 7775 | 7775 | 7775 | |||||||||
| egl-e3-c | 10019 | 10119 | 10163 | 10207 | 10244 | 10244 | 10145 | 10191 | 10226 | 10236 | 10244 | 10292 | 10433 | 10369 | 10292 | 10305 | 10292 | 10305 | 10292 | 10292 | 10292 | |||||||||
| egl-e4-a | 6372 | 6378 | 6395 | 6395 | 6395 | 6395 | 6389 | 6408 | 6408 | 6408 | 6408 | 6444 | 6461 | 6461 | 6446 | 6456 | 6456 | 6461 | 6444 | 6444 | 6444 | |||||||||
| egl-e4-b | 8809 | 8839 | 8884 | 8893 | 8935 | 8935 | 8852 | 8892 | 8900 | 8919 | 8935 | 8961 | 9021 | 9021 | 8996 | 9000 | 8998 | 9026 | 8983 | 8962 | 8961 | |||||||||
| egl-e4-c | 11276 | 11376 | 11427 | 11471 | 11493 | 11493 | 11411 | 11457 | 11502 | 11512 | 11512 | 11550 | 11779 | 11779 | 11618 | 11601 | 11561 | 11598 | 11596 | 11550 | 11562 | 11529 | ||||||||
| egl-s1-a | 4992 | 5014 | 5018 | 5014 | 5018 | 5018 | 5011 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | 5018 | |||
| egl-s1-b | 6201 | 6379 | 6388 | 6388 | 6388 | 6370 | 6388 | 6388 | 6388 | 6388 | 6388 | 6435 | 6435 | 6388 | 6388 | 6388 | 6394 | 6388 | 6388 | 6388 | 6388 | 6388 | 6388 | 6388 | ||||||
| egl-s1-c | 8310 | 8480 | 8494 | 8517 | 8518 | 8418 | 8441 | 8500 | 8509 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | 8518 | ||||||||
| egl-s2-a | 9780 | 9824 | 9807 | 9825 | 9825 | 9791 | 9803 | 9806 | 9812 | 9825 | 9884 | 9995 | 9995 | 9895 | 9956 | 9895 | 9970 | 9884 | 9889 | 9884 | ||||||||||
| egl-s2-b | 12286 | 12968 | 12970 | 13017 | 13017 | 12949 | 12970 | 12982 | 12994 | 13017 | 13100 | 13174 | 13174 | 13100 | 13165 | 13147 | 13345 | 13115 | 13101 | 13100 | ||||||||||
| egl-s2-c | 16221 | 16353 | 16357 | 16407 | 16425 | 16314 | 16352 | 16380 | 16393 | 16425 | 16425 | 16795 | 16715 | 16425 | 16505 | 16430 | 16600 | 16429 | 16430 | 16425 | 16425 | 16425 | ||||||||
| egl-s3-a | 10025 | 10143 | 10146 | 10145 | 10145 | 10143 | 10160 | 10160 | 10165 | 10165 | 10220 | 10296 | 10296 | 10221 | 10260 | 10257 | 10284 | 10220 | 10227 | 10220 | ||||||||||
| egl-s3-b | 13554 | 13616 | 13623 | 13648 | 13648 | 13598 | 13631 | 13630 | 13644 | 13648 | 13682 | 14053 | 14028 | 13682 | 13807 | 13749 | 13857 | 13707 | 13695 | 13682 | ||||||||||
| egl-s3-c | 16969 | 17100 | 17115 | 17163 | 17188 | 17058 | 17097 | 17125 | 17143 | 17188 | 17188 | 17297 | 17297 | 17259 | 17234 | 17207 | 17316 | 17230 | 17194 | 17188 | 17188 | 17188 | ||||||||
| egl-s4-a | 12027 | 12143 | 12140 | 12141 | 12141 | 12126 | 12149 | 12149 | 12153 | 12153 | 12268 | 12442 | 12442 | 12292 | 12341 | 12341 | 12348 | 12268 | 12297 | 12268 | ||||||||||
| egl-s4-b | 15933 | 16093 | 16082 | 16098 | 16098 | 16066 | 16105 | 16106 | 16113 | 16113 | 16283 | 16531 | 16531 | 16321 | 16442 | 16337 | 16442 | 16336 | 16283 | 16321 | ||||||||||
| egl-s4-c | 20179 | 20375 | 20380 | 20430 | 20430 | 20340 | 20376 | 20406 | 20423 | 20430 | 20481 | 20832 | 20832 | 20582 | 20591 | 20538 | 20821 | 20517 | 20521 | 20481 | ||||||||||
EGL-Large Instances
The EGL-Large instances were introduced in:
Brandão, J., R. Eglese. (2008). A deterministic tabu search algorithm for the capacitated arc routing problem. Computers & Operations Research 35 (4) 1112-1126.
Zip file with instances as provided by Marcus Poggi de Aragão. We have transformed the instances into the standard format (see also format file).
| Lower Bounds | Upper Bounds | Integer Solutions | ||||||
| Instances | Martinelli et al. 2011b | Bode Irnich 2012b | best known LB | best known UB | Brandao Eglese 2008 | Mei et al. 2009 | Martinelli et al. 2011a | Optimal Solution |
| egl-g1-a | 970495 | 976907 | 976907 | 1004864 | 1049708 | 1025765 | 1004864 | |
| egl-g1-b | 1085097 | 1093884 | 1093884 | 1129937 | 1140692 | 1135873 | 1129937 | |
| egl-g1-c | 1201030 | 1212151 | 1212151 | 1262888 | 1282270 | 1271894 | 1262888 | |
| egl-g1-d | 1325317 | 1341918 | 1341918 | 1398958 | 1420126 | 1402433 | 1398958 | |
| egl-g1-e | 1461469 | 1482176 | 1482176 | 1543804 | 1583133 | 1558548 | 1543804 | |
| egl-g2-a | 1061103 | 1069536 | 1069536 | 1115339 | 1129229 | 1125602 | 1115339 | |
| egl-g2-b | 1173286 | 1185221 | 1185221 | 1226645 | 1255907 | 1242542 | 1226645 | |
| egl-g2-c | 1295036 | 1311339 | 1311339 | 1371004 | 1418145 | 1401583 | 1371004 | |
| egl-g2-d | 1430267 | 1446680 | 1446680 | 1509990 | 1516103 | 1516072 | 1509990 | |
| egl-g2-e | 1557159 | 1581459 | 1581459 | 1659217 | 1701681 | 1668348 | 1659217 | |
BMCV Instances
The BMCV instances were introduced in:
Beullens, P., L. Muyldermans, D. Cattrysse, D. Van Oudheusden. (2003). A guided local search heuristic for the capacitated arc routing problem. European Journal of Operations Research 147(3) 629-643.
Zip file with instances as provided by Luc Muyldermans. We have transformed the instances into the standard format (see also format file).
| Lower Bounds | Upper Bounds | Integer Solutions | ||||||||||||||||||
| Instances | Beullens et al. 2003 (modified costs) | Bartolini et al. 2012 | Bartolini et al. 2012 (end of GenRoute) | Bartolini et al. 2012 (end of GenRoute) round to multiple of 5 | Bode Irnich 2013 | Bode Irnich 2012b (revised) | Bode Irnich 2012b (rev.) round to multiple of 5 | best known LB | best known UB | Beullens et al. 2003 | Brandao Eglese 2008 | Tang et al. 2009 | Mei et al. 2009 | Santos et al. 2010 | Bartolini et al. 2012 (best known from literature or own ub) | Offset | Optimal Solution | Bartolini et al. 2012 | Bode Irnich 2013 | Bode Irnich 2012b (revised) |
| C1 | 4080 | 4105 | 4105 | 4105 | 4144 | 4145 | 4145 | 4145 | 4150 | 1660 | 1660 | 1660 | 1660 | 1660 | 4150 | 2490 | 4150 | 4150 | ||
| C2 | 3135 | 3135 | 3135 | 3135 | 3135 | 3135 | 3135 | 3135 | 3135 | 1095 | 1095 | 1095 | 1095 | 1095 | 3135 | 2040 | 3135 | 3135 | 3135 | 3135 |
| C3 | 2525 | 2567 | 2575 | 2575 | 2575 | 2575 | 2575 | 2575 | 2575 | 925 | 925 | 925 | 925 | 925 | 2575 | 1650 | 2575 | 2575 | 2575 | 2575 |
| C4 | 3455 | 3478 | 3478 | 3480 | 3510 | 3510 | 3510 | 3510 | 3510 | 1340 | 1340 | 1340 | 1340 | 1340 | 3510 | 2170 | 3510 | 3510 | 3510 | |
| C5 | 5305 | 5365 | 5365 | 5365 | 5365 | 5365 | 5365 | 5365 | 5365 | 2475 | 2470 | 2470 | 2470 | 2470 | 5365 | 2895 | 5365 | 5365 | 5365 | 5365 |
| C6 | 2495 | 2532 | 2535 | 2535 | 2535 | 2535 | 2535 | 2535 | 2535 | 895 | 895 | 895 | 895 | 895 | 2535 | 1640 | 2535 | 2535 | 2535 | 2535 |
| C7 | 4015 | 4063 | 4075 | 4075 | 4075 | 4075 | 4075 | 4075 | 4075 | 1795 | 1795 | 1795 | 1795 | 1795 | 4075 | 2280 | 4075 | 4075 | 4075 | 4075 |
| C8 | 4000 | 4083 | 4090 | 4090 | 4090 | 4090 | 4090 | 4090 | 4090 | 1730 | 1730 | 1730 | 1730 | 1730 | 4090 | 2360 | 4090 | 4090 | 4090 | 4090 |
| C9 | 5215 | 5233 | 5233 | 5235 | 5244 | 5245 | 5245 | 5245 | 5260 | 1825 | 1820 | 1820 | 1830 | 1830 | 5260 | 3440 | ||||
| C10 | 4620 | 4660 | 4700 | 4700 | 4700 | 4700 | 4700 | 4700 | 4700 | 2290 | 2270 | 2270 | 2270 | 2270 | 4700 | 2430 | 4700 | 4700 | 4700 | 4700 |
| C11 | 4550 | 4583 | 4583 | 4585 | 4608 | 4617 | 4620 | 4615 | 4630 | 1815 | 1815 | 1815 | 1805 | 1810 | 4635 | 2825 | ||||
| C12 | 4140 | 4209 | 4209 | 4210 | 4234 | 4239 | 4240 | 4235 | 4240 | 1610 | 1610 | 1610 | 1610 | 1610 | 4240 | 2630 | 4240 | 4240 | ||
| C13 | 2895 | 2940 | 2955 | 2955 | 2955 | 2955 | 2955 | 2955 | 2955 | 1110 | 1110 | 1110 | 1110 | 1110 | 2955 | 1845 | 2955 | 2955 | 2955 | 2955 |
| C14 | 3970 | 4030 | 4030 | 4030 | 4024 | 4030 | 4030 | 4030 | 4030 | 1680 | 1680 | 1680 | 1680 | 1680 | 4030 | 2350 | 4030 | 4030 | 4030 | |
| C15 | 4845 | 4912 | 4912 | 4915 | 4918 | 4923 | 4925 | 4920 | 4940 | 1860 | 1860 | 1860 | 1860 | 1860 | 4940 | 3080 | ||||
| C16 | 1470 | 1475 | 1475 | 1475 | 1475 | 1475 | 1475 | 1475 | 1475 | 585 | 585 | 585 | 585 | 585 | 1475 | 890 | 1475 | 1475 | 1475 | 1475 |
| C17 | 3535 | 3555 | 3555 | 3555 | 3555 | 3555 | 3555 | 3555 | 3555 | 1610 | 1610 | 1610 | 1610 | 1610 | 3555 | 1945 | 3555 | 3555 | 3555 | 3555 |
| C18 | 5550 | 5577 | 5577 | 5580 | 5570 | 5570 | 5570 | 5580 | 5620 | 2410 | 2410 | 2390 | 2425 | 2385 | 5620 | 3235 | ||||
| C19 | 3065 | 3096 | 3096 | 3100 | 3115 | 3115 | 3115 | 3115 | 3115 | 1395 | 1395 | 1395 | 1395 | 1395 | 3115 | 1720 | 3115 | 3115 | 3115 | |
| C20 | 2120 | 2120 | 2120 | 2120 | 2120 | 2120 | 2120 | 2120 | 2120 | 665 | 665 | 665 | 665 | 665 | 2120 | 1455 | 2120 | 2120 | 2120 | 2120 |
| C21 | 3950 | 3960 | 3960 | 3960 | 3970 | 3970 | 3970 | 3970 | 3970 | 1725 | 1725 | 1725 | 1725 | 1725 | 3970 | 2245 | 3970 | 3970 | 3970 | |
| C22 | 2245 | 2245 | 2245 | 2245 | 2245 | 2245 | 2245 | 2245 | 2245 | 1070 | 1070 | 1070 | 1070 | 1070 | 2245 | 1175 | 2245 | 2245 | 2245 | 2245 |
| C23 | 4015 | 4032 | 4032 | 4035 | 4073 | 4078 | 4080 | 4075 | 4085 | 1690 | 1700 | 1690 | 1700 | 1690 | 4085 | 2395 | ||||
| C24 | 3370 | 3384 | 3384 | 3385 | 3400 | 3400 | 3400 | 3400 | 3400 | 1360 | 1360 | 1360 | 1360 | 1360 | 3400 | 2040 | 3400 | 3400 | 3400 | |
| C25 | 2310 | 2310 | 2310 | 2310 | 2310 | 2310 | 2310 | 2310 | 2310 | 905 | 905 | 905 | 905 | 905 | 2310 | 1405 | 2310 | 2310 | 2310 | 2310 |
| D1 | 3215 | 3215 | 3215 | 3215 | 3215 | 3215 | 3215 | 3215 | 3215 | 725 | 740 | 745 | 740 | 725 | 3215 | 2490 | 3215 | 3215 | 3215 | 3215 |
| D2 | 2520 | 2520 | 2520 | 2520 | 2520 | 2520 | 2520 | 2520 | 2520 | 480 | 480 | 480 | 480 | 480 | 2520 | 2040 | 2520 | 2520 | 2520 | 2520 |
| D3 | 2065 | 2065 | 2065 | 2065 | 2065 | 2065 | 2065 | 2065 | 2065 | 415 | 415 | 415 | 415 | 415 | 2065 | 1650 | 2065 | 2065 | 2065 | 2065 |
| D4 | 2785 | 2785 | 2785 | 2785 | 2785 | 2785 | 2785 | 2785 | 2785 | 615 | 615 | 615 | 615 | 615 | 2785 | 2170 | 2785 | 2785 | 2785 | 2785 |
| D5 | 3935 | 3935 | 3935 | 3935 | 3935 | 3935 | 3935 | 3935 | 3935 | 1040 | 1040 | 1040 | 1040 | 1040 | 3935 | 2895 | 3935 | 3935 | 3935 | 3935 |
| D6 | 2125 | 2125 | 2125 | 2125 | 2125 | 2125 | 2125 | 2125 | 2125 | 485 | 485 | 485 | 485 | 485 | 2125 | 1640 | 2125 | 2125 | 2125 | 2125 |
| D7 | 3015 | 3078 | 3115 | 3115 | 3108 | 3108 | 3110 | 3115 | 3115 | 835 | 835 | 835 | 835 | 845 | 3115 | 2280 | 3115 | 3115 | ||
| D8 | 2975 | 2995 | 2995 | 2995 | 3045 | 3045 | 3045 | 3045 | 3045 | 685 | 685 | 685 | 685 | 685 | 3045 | 2360 | 3045 | 3045 | 3045 | |
| D9 | 4120 | 4120 | 4120 | 4120 | 4120 | 4120 | 4120 | 4120 | 4120 | 680 | 680 | 680 | 680 | 680 | 4120 | 3440 | 4120 | 4120 | 4120 | 4120 |
| D10 | 3330 | 3335 | 3340 | 3340 | 3340 | 3340 | 3340 | 3340 | 3340 | 910 | 910 | 910 | 910 | 910 | 3340 | 2430 | 3340 | 3340 | 3340 | 3340 |
| D11 | 3745 | 3745 | 3745 | 3745 | 3745 | 3745 | 3745 | 3745 | 3745 | 930 | 940 | 920 | 930 | 920 | 3745 | 2825 | 3745 | 3745 | 3745 | 3745 |
| D12 | 3310 | 3310 | 3310 | 3310 | 3310 | 3310 | 3310 | 3310 | 3310 | 680 | 680 | 680 | 680 | 680 | 3310 | 2630 | 3310 | 3310 | 3310 | 3310 |
| D13 | 2535 | 2535 | 2535 | 2535 | 2535 | 2535 | 2535 | 2535 | 2535 | 690 | 690 | 690 | 690 | 690 | 2535 | 1845 | 2535 | 2535 | 2535 | 2535 |
| D14 | 3270 | 3272 | 3272 | 3275 | 3280 | 3280 | 3280 | 3280 | 3280 | 930 | 930 | 930 | 930 | 930 | 3280 | 2350 | 3280 | 3280 | 3280 | |
| D15 | 3990 | 3990 | 3990 | 3990 | 3990 | 3990 | 3990 | 3990 | 3990 | 910 | 950 | 910 | 920 | 910 | 3990 | 3080 | 3990 | 3990 | 3990 | 3990 |
| D16 | 1060 | 1060 | 1060 | 1060 | 1060 | 1060 | 1060 | 1060 | 1060 | 170 | 170 | 170 | 170 | 170 | 1060 | 890 | 1060 | 1060 | 1060 | 1060 |
| D17 | 2620 | 2620 | 2620 | 2620 | 2620 | 2620 | 2620 | 2620 | 2620 | 675 | 675 | 675 | 675 | 675 | 2620 | 1945 | 2620 | 2620 | 2620 | 2620 |
| D18 | 4165 | 4165 | 4165 | 4165 | 4165 | 4165 | 4165 | 4165 | 4165 | 930 | 930 | 930 | 950 | 930 | 4165 | 3235 | 4165 | 4165 | 4165 | 4165 |
| D19 | 2370 | 2393 | 2393 | 2395 | 2400 | 2400 | 2400 | 2400 | 2400 | 680 | 680 | 680 | 680 | 680 | 2400 | 1720 | 2400 | 2400 | 2400 | |
| D20 | 1870 | 1870 | 1870 | 1870 | 1870 | 1870 | 1870 | 1870 | 1870 | 415 | 415 | 415 | 415 | 415 | 1870 | 1455 | 1870 | 1870 | 1870 | 1870 |
| D21 | 2940 | 2985 | 2985 | 2985 | 3005 | 3011 | 3015 | 3005 | 3050 | 805 | 815 | 810 | 810 | 805 | 3050 | 2245 | ||||
| D22 | 1865 | 1865 | 1865 | 1865 | 1865 | 1865 | 1865 | 1865 | 1865 | 690 | 690 | 690 | 690 | 690 | 1865 | 1175 | 1865 | 1865 | 1865 | 1865 |
| D23 | 3110 | 3114 | 3114 | 3115 | 3126 | 3126 | 3130 | 3130 | 3130 | 735 | 735 | 735 | 735 | 735 | 3130 | 2395 | ||||
| D24 | 2660 | 2676 | 2676 | 2680 | 2704 | 2710 | 2710 | 2705 | 2710 | 670 | 670 | 670 | 670 | 670 | 2710 | 2040 | 2710 | 2710 | ||
| D25 | 1815 | 1815 | 1815 | 1815 | 1815 | 1815 | 1815 | 1815 | 1815 | 410 | 410 | 410 | 410 | 410 | 1815 | 1405 | 1815 | 1815 | 1815 | 1815 |
| E1 | 4830 | 4885 | 4885 | 4885 | 4898 | 4903 | 4905 | 4900 | 4910 | 1940 | 1935 | 1935 | 1935 | 1935 | 4910 | 2975 | ||||
| E2 | 3960 | 3978 | 3990 | 3990 | 3990 | 3990 | 3990 | 3990 | 3990 | 1610 | 1610 | 1610 | 1610 | 1610 | 3990 | 2380 | 3990 | 3990 | 3990 | 3990 |
| E3 | 2015 | 2015 | 2015 | 2015 | 2015 | 2015 | 2015 | 2015 | 2015 | 750 | 750 | 750 | 750 | 750 | 2015 | 1265 | 2015 | 2015 | 2015 | 2015 |
| E4 | 4125 | 4154 | 4155 | 4155 | 4155 | 4155 | 4155 | 4155 | 4155 | 1610 | 1615 | 1610 | 1610 | 1610 | 4155 | 2545 | 4155 | 4155 | 4155 | 4155 |
| E5 | 4555 | 4585 | 4585 | 4585 | 4585 | 4585 | 4585 | 4585 | 4585 | 2170 | 2160 | 2160 | 2185 | 2170 | 4585 | 2425 | 4585 | 4585 | 4585 | 4585 |
| E6 | 2055 | 2055 | 2055 | 2055 | 2055 | 2055 | 2055 | 2055 | 2055 | 670 | 670 | 670 | 670 | 670 | 2055 | 1385 | 2055 | 2055 | 2055 | 2055 |
| E7 | 4035 | 4133 | 4155 | 4155 | 4155 | 4155 | 4155 | 4155 | 4155 | 1900 | 1900 | 1900 | 1900 | 1900 | 4155 | 2255 | 4155 | 4155 | 4155 | 4155 |
| E8 | 4640 | 4702 | 4710 | 4710 | 4710 | 4710 | 4710 | 4710 | 4710 | 2150 | 2150 | 2150 | 2150 | 2150 | 4710 | 2560 | 4710 | 4710 | 4710 | 4710 |
| E9 | 5745 | 5780 | 5780 | 5780 | 5802 | 5809 | 5810 | 5805 | 5820 | 2250 | 2295 | 2235 | 2285 | 2235 | 5820 | 3585 | ||||
| E10 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 1690 | 1690 | 1690 | 1690 | 1690 | 3605 | 1915 | 3605 | 3605 | 3605 | 3605 |
| E11 | 4630 | 4637 | 4637 | 4640 | 4650 | 4650 | 4650 | 4650 | 4650 | 1850 | 1840 | 1850 | 1850 | 1835 | 4655 | 2820 | 4650 | 4650 | 4650 | |
| E12 | 4065 | 4161 | 4180 | 4180 | 4170 | 4179 | 4180 | 4180 | 4180 | 1710 | 1705 | 1710 | 1715 | 1710 | 4180 | 2485 | 4180 | 4180 | ||
| E13 | 3320 | 3337 | 3345 | 3345 | 3345 | 3345 | 3345 | 3345 | 3345 | 1325 | 1325 | 1325 | 1325 | 1325 | 3345 | 2020 | 3345 | 3345 | 3345 | 3345 |
| E14 | 4085 | 4115 | 4115 | 4115 | 4115 | 4115 | 4115 | 4115 | 4115 | 1810 | 1810 | 1810 | 1810 | 1810 | 4115 | 2305 | 4115 | 4115 | 4115 | 4115 |
| E15 | 4170 | 4189 | 4189 | 4190 | 4199 | 4202 | 4205 | 4200 | 4205 | 1610 | 1610 | 1595 | 1610 | 1590 | 4205 | 2615 | 4205 | 4205 | ||
| E16 | 3735 | 3755 | 3755 | 3755 | 3775 | 3775 | 3775 | 3775 | 3775 | 1825 | 1825 | 1825 | 1825 | 1825 | 3775 | 1950 | 3775 | 3775 | 3775 | |
| E17 | 2740 | 2740 | 2740 | 2740 | 2740 | 2740 | 2740 | 2740 | 2740 | 1290 | 1290 | 1290 | 1290 | 1290 | 2740 | 1450 | 2740 | 2740 | 2740 | 2740 |
| E18 | 3825 | 3825 | 3825 | 3825 | 3825 | 3832 | 3835 | 3835 | 3835 | 1610 | 1610 | 1610 | 1610 | 1610 | 3835 | 2225 | ||||
| E19 | 3200 | 3222 | 3222 | 3225 | 3235 | 3235 | 3235 | 3235 | 3235 | 1435 | 1435 | 1435 | 1435 | 1435 | 3235 | 1800 | 3235 | 3235 | 3235 | |
| E20 | 2785 | 2802 | 2802 | 2805 | 2825 | 2825 | 2825 | 2825 | 2825 | 990 | 990 | 990 | 990 | 990 | 2825 | 1835 | 2825 | 2825 | 2825 | |
| E21 | 3725 | 3728 | 3728 | 3730 | 3730 | 3730 | 3730 | 3730 | 3730 | 1705 | 1705 | 1705 | 1705 | 1705 | 3730 | 2025 | 3730 | 3730 | ||
| E22 | 2440 | 2470 | 2470 | 2470 | 2470 | 2470 | 2470 | 2470 | 2470 | 1185 | 1185 | 1185 | 1185 | 1185 | 2470 | 1285 | 2470 | 2470 | 2470 | 2470 |
| E23 | 3675 | 3686 | 3686 | 3690 | 3704 | 3707 | 3710 | 3710 | 3710 | 1430 | 1435 | 1435 | 1430 | 1430 | 3710 | 2280 | ||||
| E24 | 3930 | 4001 | 4001 | 4005 | 4020 | 4020 | 4020 | 4020 | 4020 | 1785 | 1785 | 1785 | 1785 | 1785 | 4020 | 2235 | 4020 | 4020 | 4020 | |
| E25 | 1615 | 1615 | 1615 | 1615 | 1615 | 1615 | 1615 | 1615 | 1615 | 655 | 655 | 655 | 655 | 655 | 1615 | 960 | 1615 | 1615 | 1615 | 1615 |
| F1 | 4040 | 4040 | 4040 | 4040 | 4040 | 4040 | 4040 | 4040 | 4040 | 1065 | 1070 | 1065 | 1065 | 1065 | 4040 | 2975 | 4040 | 4040 | 4040 | 4040 |
| F2 | 3300 | 3300 | 3300 | 3300 | 3300 | 3300 | 3300 | 3300 | 3300 | 920 | 920 | 920 | 920 | 920 | 3300 | 2380 | 3300 | 3300 | 3300 | 3300 |
| F3 | 1665 | 1665 | 1665 | 1665 | 1665 | 1665 | 1665 | 1665 | 1665 | 400 | 400 | 400 | 400 | 400 | 1665 | 1265 | 1665 | 1665 | 1665 | 1665 |
| F4 | 3475 | 3476 | 3476 | 3480 | 3485 | 3485 | 3485 | 3485 | 3485 | 940 | 945 | 940 | 950 | 940 | 3485 | 2545 | 3485 | 3485 | 3485 | |
| F5 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 3605 | 1180 | 1180 | 1180 | 1180 | 1180 | 3605 | 2425 | 3605 | 3605 | 3605 | 3605 |
| F6 | 1875 | 1875 | 1875 | 1875 | 1875 | 1875 | 1875 | 1875 | 1875 | 490 | 490 | 490 | 490 | 490 | 1875 | 1385 | 1875 | 1875 | 1875 | 1875 |
| F7 | 3335 | 3335 | 3335 | 3335 | 3335 | 3335 | 3335 | 3335 | 3335 | 1080 | 1080 | 1080 | 1080 | 1080 | 3335 | 2255 | 3335 | 3335 | 3335 | 3335 |
| F8 | 3695 | 3690 | 3690 | 3690 | 3705 | 3705 | 3705 | 3705 | 3705 | 1145 | 1145 | 1145 | 1145 | 1145 | 3705 | 2560 | 3705 | 3705 | 3705 | |
| F9 | 4730 | 4730 | 4730 | 4730 | 4730 | 4730 | 4730 | 4730 | 4730 | 1145 | 1155 | 1145 | 1145 | 1145 | 4730 | 3585 | 4730 | 4730 | 4730 | 4730 |
| F10 | 2925 | 2925 | 2925 | 2925 | 2925 | 2925 | 2925 | 2925 | 2925 | 1010 | 1010 | 1010 | 1010 | 1010 | 2925 | 1915 | 2925 | 2925 | 2925 | 2925 |
| F11 | 3835 | 3835 | 3835 | 3835 | 3835 | 3835 | 3835 | 3835 | 3835 | 1015 | 1015 | 1015 | 1015 | 1015 | 3835 | 2820 | 3835 | 3835 | 3835 | 3835 |
| F12 | 3385 | 3390 | 3390 | 3390 | 3395 | 3395 | 3395 | 3395 | 3395 | 910 | 910 | 910 | 910 | 910 | 3395 | 2485 | 3395 | 3395 | 3395 | |
| F13 | 2855 | 2855 | 2855 | 2855 | 2855 | 2855 | 2855 | 2855 | 2855 | 835 | 835 | 835 | 835 | 835 | 2855 | 2020 | 2855 | 2855 | 2855 | 2855 |
| F14 | 3330 | 3330 | 3330 | 3330 | 3330 | 3330 | 3330 | 3330 | 3330 | 1025 | 1035 | 1025 | 1035 | 1025 | 3330 | 2305 | 3330 | 3330 | 3330 | 3330 |
| F15 | 3560 | 3560 | 3560 | 3560 | 3560 | 3560 | 3560 | 3560 | 3560 | 945 | 965 | 945 | 945 | 945 | 3560 | 2615 | 3560 | 3560 | 3560 | 3560 |
| F16 | 2725 | 2725 | 2725 | 2725 | 2725 | 2725 | 2725 | 2725 | 2725 | 775 | 775 | 775 | 775 | 775 | 2725 | 1950 | 2725 | 2725 | 2725 | 2725 |
| F17 | 2055 | 2005 | 2055 | 2055 | 2055 | 2055 | 2055 | 2055 | 2055 | 605 | 605 | 605 | 605 | 605 | 2055 | 1450 | 2055 | 2055 | 2055 | 2055 |
| F18 | 3060 | 3063 | 3063 | 3065 | 3065 | 3065 | 3065 | 3065 | 3075 | 850 | 850 | 850 | 850 | 850 | 3075 | 2225 | ||||
| F19 | 2485 | 2500 | 2500 | 2500 | 2515 | 2515 | 2515 | 2515 | 2525 | 725 | 725 | 725 | 725 | 725 | 2525 | 1800 | ||||
| F20 | 2445 | 2445 | 2445 | 2445 | 2445 | 2445 | 2445 | 2445 | 2445 | 610 | 610 | 610 | 610 | 610 | 2445 | 1835 | 2445 | 2445 | 2445 | 2445 |
| F21 | 2930 | 2930 | 2930 | 2930 | 2930 | 2930 | 2930 | 2930 | 2930 | 905 | 905 | 905 | 905 | 905 | 2930 | 2025 | 2930 | 2930 | 2930 | 2930 |
| F22 | 2075 | 2075 | 2075 | 2075 | 2075 | 2075 | 2075 | 2075 | 2075 | 790 | 790 | 790 | 790 | 790 | 2075 | 1285 | 2075 | 2075 | 2075 | 2075 |
| F23 | 2982 | 2994 | 2994 | 2995 | 3003 | 3003 | 3005 | 3005 | 3005 | 725 | 730 | 725 | 725 | 725 | 3005 | 2280 | ||||
| F24 | 3210 | 3210 | 3210 | 3210 | 3210 | 3210 | 3210 | 3210 | 3210 | 975 | 1010 | 975 | 1005 | 975 | 3210 | 2235 | 3210 | 3210 | 3210 | 3210 |
| F25 | 1390 | 1390 | 1390 | 1390 | 1390 | 1390 | 1390 | 1390 | 1390 | 430 | 430 | 430 | 430 | 430 | 1390 | 960 | 1390 | 1390 | 1390 | 1390 |
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* Computational Results for Egl instances presented in Belenguer Benavent 2003.