Discrete location problems Benchmark library  

Competitive facility location problem

Main page (Rus | Eng)   Competitive facility location problem

Test instances. Class A

For this class of instances the set of candidate sites and the set of clients are equal to the set of vertices of some random graph. Instances are generated as follows: m numbered points are randomly thrown on the unit square. Coordinates of each point are realizations of the uniformly distributed in the [0,1] random variable.The probability of two points to be connected with edge is decreasing as like as  exp(–d ²), where d is euclidean distance between the points. The length of the new edge is equal to d. The distance between connected components are assumed to be inifinite.
For each pair of vertices i, j the value r_ij is assumed to be equal to the number of vertices, which are closer (in the sence of graph distances) to vertex j than vertex i or which are located at the same distance from j and their number is smaller than i. For given j values r_ij are pairwise different integer numbers from 0 to  m – 1.
f_i  = 40;
g_i  = random integer from 25 to 35;
p_ij = b_j, if r_ij  < R_j  and 0 otherwise, where b_j  = random integer from 10 to 20, R_j = random integer from 1 to m.
Input data format:
each string contains only one value;
parameters are given in the following order: m, n, (r_ij) line by line^[1], p_ij line by line, f_i , g_i.
^[1] for example, elements of 2x2-matrix A will be ordered as follows: a₁₁, a₁₂, a₂₁, a₂₂.
Instances' codes have the following meaning: a20-01 — instance from class A, m = n = 20, unique number 01.

 

Instance code	UB	VL*	x*
a20-01	97	62	12 16 17 18
a20-02	112	53	2 6 8 11
a20-03	87	61	2 5 9 11 14 19
a20-04	144	35	2 5 9 14 19
a20-05	93	58	2 6 12
a20-06	52	51	5 8 13 18
a20-07	65	10	4 19 20
a20-08	73	38	2 5 9 12 13
a20-09	50	16	4 17
a20-10	83	29	3 4 5 6 14 17
a20-11	84	42	8 10 17 20
a20-12	59	22	2 9 14 19
a20-13	75	25	14 15 16
a20-14	124	51	10 18 20
a20-15	97	40	3 15 16 17
a20-16	74	27	1 13 20
a20-17	81	42	3 4 5 13 18
a20-18	96	50	9 10 12
a20-19	123	46	14 15 19
a20-20	74	32	10 11 15 16 20
All instances from a20

 

 

Instance code	UB	VL*	x*
a30-01	130	67	4 16 17 18 21
a30-02	110	44	1 4 21 24 25
a30-03	130	74	5 9 12 19 22 24 29 30
a30-04	101	67	2 3 4 8 12 15 20 23 30
a30-05	179	115	4 11 13 20 25
a30-06	146	41	3 9 20 29
a30-07	149	84	8 9 12 17 28
a30-08	144	56	7 8 12 13 15 18 23
a30-09	142	83	1 4 10 12 15 19 27 29
a30-10	165	67	4 7 9 16 28 30
a30-11	82	28	4 6 8 14 17
a30-12	147	43	8 15 18
a30-13	103	53	5 9 12 19 29
a30-14	190	55	14 17 20 27 30
a30-15	176	61	3 4 11 15 19 23 27
a30-16	159	93	2 5 10 14 17 22
a30-17	165	90	4 7 12 23 26
a30-18	151	82	2 6 9 11 16 19
a30-19	131	46	7 9 12 13 18
a30-20	152	98	3 7 17 19 23 24
All instances from a30

 

 

Instance code	UB	VLrecord	xrecord
a40-01	137	62	x*
a40-02	212	135	x*
a40-03	198	81	x*
a40-04	156	96	x*
a40-05	212	97	x*
a40-06	189	81	x*
a40-07	241	96	x*
a40-08	160	125	x*
a40-09	194	83	x*
a40-10	190	107	x*
a40-11	192	101	x*
a40-12	144	57	x*
a40-13	222	163	x*
a40-14	246	67	x*
a40-15	223	100	x*
a40-16	188	77	x*
a40-17	218	136	x*
a40-18	196	131	x*
a40-19	249	112	x*
a40-20	207	54	x*
All instances from a40

 

 

Instance code	UB	VLrecord	xrecord
a50-01	315	155	x*
a50-02	270	138	x*
a50-03	207	159	x*
a50-04	239	81	x*
a50-05	216	136	x*
a50-06	236	117	x*
a50-07	246	115	x*
a50-08	206	92	x*
a50-09	263	176	x*
a50-10	241	143	x*
a50-11	147	89	x*
a50-12	259	144	x*
a50-13	224	91	x*
a50-14	218	96	x*
a50-15	218	107	x*
a50-16	231	93	x*
a50-17	259	98	x*
a50-18	295	164	x*
a50-19	229	112	x*
a50-20	238	123	x*
All instances from a50