Facility Location with Tree Topology and Radial Distance Constraints

Table 9

Numerical results for , , and algorithms for the large size instances.

#			Den.
					Ub	CPU (s)		Ub	CPU (s)	(%)		Ub	CPU (s)	(%)
Instances using radial coverage of 0.2 km
1	1000	500	10.57	26	87.34	82.69	24	86.66	7.33	0.78	25	85.66	31.45	1.97
2	1200	500	10.49	27	104.08	97.78	23	101.50	29.60	2.54	25	100.70	102.46	3.35
3	1300	500	10.56	26	111.15	102.58	25	109.18	128.19	1.80	26	105.04	369.68	5.82
4	1400	500	10.61	27	119.56	112.72	25	119.23	76.84	0.27	25	117.82	201.39	1.47
5	1500	500	10.36	27	128.46	117.14	23	128.03	82.74	0.34	26	124.94	238.19	2.82
6	1000	700	10.56	28	84.74	149.35	26	85.40	226.00	−0.77	27	83.93	273.14	0.97
7	1200	700	10.56	28	104.45	176.45	24	102.27	243.70	2.12	26	101.28	598.77	3.13
8	1300	700	11.12	28	111.94	182.19	23	109.58	112.67	2.15	25	109.52	195.97	2.21
9	1400	700	10.26	29	116.27	207.47	25	117.59	81.74	−1.13	27	113.27	387.75	2.64
10	1500	700	10.45	28	126.42	204.97	26	125.85	31.88	0.45	27	126.12	179.14	0.23
11	1000	1000	10.14	28	84.97	277.61	26	83.26	117.39	2.06	26	83.49	379.99	1.77
12	1200	1000	10.61	29	100.14	331.85	25	101.26	182.85	−1.10	29	98.15	281.68	2.03
13	1300	1000	10.63	28	107.62	354.17	25	106.83	170.39	0.74	28	105.82	518.54	1.71
14	1400	1000	10.56	30	118.58	359.51	24	117.42	57.51	0.99	26	116.20	147.08	2.05
15	1500	1000	10.32	28	124.38	394.33	24	123.45	110.95	0.76	27	123.02	207.92	1.10
Instances using radial coverage of 0.5 km
1	1000	500	49.22	6	188.96	16.44	6	185.54	29.08	1.84	6	184.39	48.22	2.48
2	1200	500	50.03	6	229.38	19.15	6	220.48	72.47	4.03	6	222.96	9.08	2.88
3	1300	500	46.71	7	247.19	21.06	6	238.58	23.96	3.61	6	242.42	14.16	1.97
4	1400	500	51.39	6	270.10	22.35	6	257.81	8.10	4.77	6	260.91	5.05	3.53
5	1500	500	48.34	6	283.52	23.90	6	273.81	113.59	3.55	6	274.10	3.08	3.44
6	1000	700	48.65	7	189.37	34.88	6	181.26	278.97	4.47	6	183.16	79.83	3.39
7	1200	700	48.04	6	227.75	35.33	6	219.55	95.28	3.74	6	220.21	79.40	3.43
8	1300	700	47.46	7	242.48	36.88	6	238.53	130.71	1.66	6	239.97	16.56	1.04
9	1400	700	46.70	7	258.40	39.01	6	252.52	112.10	2.33	6	258.84	10.01	−0.17
10	1500	700	48.50	7	281.43	40.78	6	271.28	111.47	3.74	6	275.77	38.58	2.05
11	1000	1000	48.96	7	184.28	69.86	6	182.69	282.79	0.87	6	185.89	7.31	−0.87
12	1200	1000	48.46	7	223.99	80.81	6	215.64	125.56	3.87	6	223.71	7.83	0.13
13	1300	1000	47.63	6	245.73	77.27	6	237.25	70.79	3.58	6	240.35	19.43	2.24
14	1400	1000	47.81	7	263.12	81.55	6	254.52	75.90	3.38	7	258.23	5.52	1.89
15	1500	1000	47.01	6	282.72	84.44	6	271.97	139.55	3.95	6	277.50	50.35	1.88