Multi Stage Uncapacitated Facility Location Problem

Instances on random quadruples of facilities

and transportation matrix

type Gap-C  (R4-GapC)

One of the most difficult class of instances for the Multi Stage Uncapacitated Facility Location Problem is created as class Gap-C for the Simple Plant Location Problem. Each customer can be served by one of the 10 admissible facility paths. Each path can be used for servicing at most 10 customers. Each path consists of  4 facilities which are selected like Steiner systems. In other words, any pair of facilities can appear at most once. The fixed cost of arbitrary facility is 3000. The dimension of the instances is 50 facilities, 100 admissible facility paths, 100 customers.

Table shows the input data and results for 30 benchmarks. The first column of the table is codes of input data and hyperlinks to text files. The second column is the optimal value of the objective function. The third column is the duality gap. The fourth column is the optimal set of open facilities.

All instances type St4-GapC.zip 118 Kb

 Code The optimal value Duality Gap (%) The optimal set of open facilities 471 78174 61,9 1, 2, 4, 5, 8, 11, 12, 16, 18, 20, 23, 24, 27, 28, 29, 30, 33, 34, 36, 39, 41, 42, 44, 45, 47, 50 472 81127 62,5 3, 6, 9, 10, 11, 12, 19, 20, 23, 24, 26, 28, 30, 31, 32, 33, 35, 38, 40, 41, 43, 44, 45, 46, 47, 49, 50 473 81119 62,2 1, 4, 6, 7, 8, 10, 11, 13, 15, 16, 17, 18, 19, 20, 22, 25, 26, 29, 30, 33, 35, 36, 44, 45, 47, 48, 49 474 78130 61,4 3, 5, 6, 7, 9, 11, 12, 22, 26, 27, 28, 30, 32, 33, 35, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 50 475 78141 61,2 2, 5, 7, 9, 11, 12, 14, 16, 18, 19, 22, 23, 24, 25, 27, 28, 30, 32, 34, 35, 36, 37, 38, 39, 41, 44 476 81123 61,5 2, 4, 5, 7, 8, 9, 12, 14, 15, 16, 18, 20, 21, 22, 24, 27, 29, 30, 31, 36, 40, 41, 42, 43, 45, 47, 49 477 81113 63,2 1, 2, 3, 4, 5, 9, 10, 11, 13, 16, 17, 18, 21, 23, 26, 30, 31, 34, 35, 36, 41, 43, 44, 46, 47, 49, 50 478 81128 63,2 1, 3, 4, 6, 7, 8, 9, 11, 14, 15, 17, 20, 24, 30, 31, 32, 33, 34, 37, 38, 39, 42, 43, 44, 47, 49, 50 479 81130 62,3 2, 6, 8, 15, 16, 18, 19, 21, 23, 24, 25, 26, 30, 32, 33, 34, 35, 36, 37, 38, 39, 41, 43, 44, 46, 48, 50 480 81106 62,8 1, 2, 7, 8, 9, 10, 12, 14, 16, 22, 25, 26, 27, 29, 30, 32, 36, 37, 40, 42, 43, 44, 46, 47, 48, 49, 50 481 81130 63,8 1, 2, 3, 6, 12, 18, 19, 22, 23, 24, 25, 28, 31, 33, 34, 37, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50 482 81131 63,0 2, 3, 6, 7, 10, 11, 13, 16, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 34, 36, 40, 41, 42, 43, 44, 48 483 78147 61,2 2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 16, 18, 19, 20, 22, 23, 26, 33, 35, 36, 38, 40, 43, 44, 49, 50 484 75162 60,1 1, 2, 4, 7, 8, 9, 10, 13, 14, 17, 18, 19, 21, 22, 23, 24, 29, 33, 35, 37, 39, 41, 45, 47, 49 485 81119 63,8 1, 2, 4, 5, 9, 10, 11, 12, 13, 15, 16, 17, 19, 22, 23, 26, 30, 36, 37, 40, 42, 43, 45, 46, 48, 49, 50 486 78141 61,1 1, 2, 3, 4, 6, 7, 8, 9, 12, 15, 18, 19, 21, 23, 27, 29, 35, 36, 37, 42, 43, 45, 47, 48, 49, 50 487 81130 61,0 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 15, 16, 19, 20, 21, 28, 30, 32, 33, 34, 36, 42, 43, 45, 49, 50 488 81111 62,3 2, 3, 4, 5, 6, 7, 10, 14, 15, 16, 17, 18, 19, 24, 26, 28, 29, 31, 32, 33, 35, 36, 38, 39, 43, 46, 48 489 78150 60,4 2, 3, 4, 5, 6, 7, 9, 10, 11, 15, 16, 19, 20, 21, 24, 25, 28, 31, 32, 34, 41, 42, 45, 46, 48, 50 490 81105 62,7 2, 3, 6, 9, 10, 11, 13, 14, 15, 16, 18, 19, 21, 22, 23, 26, 27, 33, 35, 36, 37, 39, 41, 42, 46, 48, 50 491 75143 60,2 2, 3, 5, 6, 7, 8, 9, 10, 12, 13, 18, 20, 21, 22, 26, 28, 31, 33, 35, 38, 44, 45, 47, 49, 50 492 78119 62,2 2, 3, 5, 14, 17, 19, 20, 21, 22, 24, 25, 27, 28, 29, 30, 31, 33, 38, 39, 42, 43, 44, 46, 47, 48, 49 493 81133 62,7 1, 2, 3, 4, 5, 9, 13, 16, 18, 19, 22, 27, 28, 30, 31, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46 494 81119 63,0 1, 3, 4, 5, 7, 9, 14, 16, 19, 21, 22, 23, 24, 25, 27, 31, 32, 33, 34, 35, 37, 38, 40, 41, 43, 47, 50 495 78149 61,2 1, 3, 4, 5, 8, 9, 11, 13, 17, 18, 20, 22, 23, 27, 29, 30, 32, 35, 37, 38, 39, 41, 42, 45, 48, 50 496 81130 62,0 1, 2, 3, 5, 8, 12, 13, 15, 17, 21, 22, 23, 25, 26, 28, 29, 30, 33, 35, 36, 39, 40, 42, 44, 48, 49, 50 497 78144 60,5 1, 2, 7, 9, 12, 13, 14, 15, 21, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 44, 48, 49, 50 498 81130 62,9 1, 4, 6, 9, 10, 15, 17, 19, 21, 22, 25, 28, 29, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 47, 48, 49, 50 499 78142 61,1 1, 2, 3, 5, 6, 7, 8, 9, 11, 12, 13, 15, 19, 23, 25, 26, 30, 33, 35, 37, 38, 40, 41, 47, 49, 50 500 78136 61,2 1, 3, 4, 9, 13, 16, 19, 20, 21, 23, 24, 28, 29, 30, 31, 32, 33, 36, 37, 39, 40, 42, 43, 45, 46, 50