Complexity

Research Article

Facility Location with Tree Topology and Radial Distance Constraints

Table 7

Numerical results for , , and for the instances in Table 1.


#				CPU (s)
#				CPU (s)		Ub	CPU (s)	(%)		Ub	CPU (s)	(%)		Ub	CPU (s)	(%)

Instances using radial coverage of 0.2 km
1	500	50	56.20	6.60	16	58.71	1.63	4.46	14	63.02	1.29	12.13	15	63.03	1.34	12.15
2	600	50	63.83	5.59	17	63.92	2.11	0.14	14	72.97	1.46	14.32	15	70.82	1.51	10.95
3	700	50	84.28	8.44	15	84.67	2.01	0.46	11	100.05	1.29	18.70	12	94.11	1.47	11.66
4	800	50	85.13	8.99	16	89.62	2.48	5.27	12	105.11	1.40	23.47	12	102.91	1.67	20.89
5	1000	50	105.24	16.47	16	107.64	2.99	2.28	13	117.36	2.17	11.52	13	115.74	2.33	9.98
6	500	100	49.81	22.79	20	50.82	4.78	2.04	15	58.86	2.70	18.17	15	57.69	2.97	15.82
7	600	100	56.95	27.83	21	60.00	5.75	5.34	14	70.28	3.22	23.39	16	65.53	3.76	15.06
8	700	100	67.01	236.14	20	71.41	6.30	6.57	15	77.72	3.81	15.99	16	80.02	4.14	19.43
9	800	100	76.62	54.16	21	78.40	6.96	2.32	16	89.97	4.35	17.42	16	89.50	4.73	16.82
10	1000	100	93.87	73.87	21	98.88	8.25	5.34	15	116.93	4.90	24.57	16	109.91	5.55	17.09
11	500	200	45.05	406.80	24	47.65	13.43	5.76	17	54.04	7.60	19.96	19	51.75	8.53	14.87
12	600	200	52.38	257.96	25	55.12	15.53	5.22	15	66.39	7.75	26.74	19	64.30	8.96	22.75
13	700	200	62.07	640.04	23	66.47	19.94	7.09	16	76.39	10.16	23.06	18	72.16	12.13	16.25
14	800	200	70.70	986.03	24	74.15	21.42	4.88	17	84.40	12.29	19.38	18	83.23	13.90	17.73
15	1000	200	87.50	1324.35	24	91.48	23.30	4.55	16	106.65	13.68	21.87	18	102.06	15.89	16.63
16	1000	300	84.99	7200	25	89.15	42.05	4.90	18	101.61	25.03	19.55	21	96.68	28.72	13.75
17	1200	300	102.25	7200	25	105.67	48.78	3.35	19	122.93	29.05	20.23	20	120.33	32.44	17.69
18	1300	300	119.96	7200	24	114.47	52.28	—	19	130.38	32.54	8.69	20	126.33	36.63	5.32
19	1400	300	117.08	7200	25	120.94	61.71	3.29	18	142.07	29.92	21.34	19	138.97	35.71	18.70
20	1500	300	765.22	7200	26	130.42	57.17	—	18	155.11	33.59	–	20	148.99	39.44	—

Instances using radial coverage of 0.5 km
1	500	50	99.83	13.12	5	102.04	0.43	2.22	4	102.05	0.34	2.23	4	102.05	0.34	2.23
2	600	50	122.36	11.43	5	126.51	0.47	3.39	4	132.93	0.35	8.64	4	132.93	0.37	8.64
3	700	50	138.68	15.35	5	144.73	0.55	4.36	4	151.77	0.41	9.44	4	156.96	0.41	13.18
4	800	50	163.48	24.80	5	163.75	0.70	0.16	4	169.21	0.50	3.50	4	169.92	0.52	3.94
5	1000	50	201.94	26.66	5	205.42	0.77	1.72	4	214.12	0.60	6.03	4	214.12	0.59	6.03
6	500	100	97.20	60.15	5	102.71	0.96	5.67	4	105.66	0.79	8.71	4	105.73	0.76	8.78
7	600	100	116.65	98.19	5	117.44	1.11	0.68	6	119.35	0.86	2.31	6	119.35	0.93	2.31
8	700	100	131.50	102.31	6	134.68	1.41	2.42	6	137.15	1.11	4.29	6	137.15	1.18	4.29
9	800	100	157.34	148.20	5	159.02	1.39	1.07	5	162.97	1.11	3.58	5	162.97	1.14	3.58
10	1000	100	192.27	222.71	6	195.68	1.76	1.78	5	208.04	1.40	8.20	5	211.09	1.34	9.79
11	500	200	93.32	419.36	6	98.62	2.23	5.68	6	101.43	1.82	8.69	6	100.97	1.90	8.20
12	600	200	110.63	740.69	6	114.30	2.72	3.31	6	123.37	2.11	11.51	6	117.45	2.16	6.16
13	700	200	133.28	1061.54	6	135.63	3.51	1.77	6	137.15	2.65	2.90	6	135.39	2.85	1.58
14	800	200	152.25	1174.40	6	155.98	3.89	2.45	5	161.24	3.05	5.90	6	154.78	3.25	1.67
15	1000	200	188.15	1664.89	6	193.28	4.66	2.73	6	198.10	3.62	5.29	6	195.45	3.76	3.88
16	1000	300	184.02	5364.37	6	190.37	8.55	3.45	6	197.37	7.10	7.25	6	191.07	6.72	3.83
17	1200	300	219.90	6747.17	6	228.88	8.89	4.08	6	239.72	7.13	9.01	6	233.02	7.65	5.97
18	1300	300	237.04	6044.67	6	251.54	9.52	6.11	6	257.77	7.95	8.75	6	250.70	8.19	5.76
19	1400	300	701.78	7200	6	264.27	10.44	—	6	281.32	8.35	—	6	277.52	8.60	—
20	1500	300	728.30	7200	7	280.24	11.25	—	5	297.51	8.79	—	6	290.08	9.39	—