Facility Location with Tree Topology and Radial Distance Constraints

Table 1

Numerical results for and .

#			Den.				CPU (s)		CPU (s)			CPU (s)		CPU (s)	(%)	(%)
Instances using radial coverage of 0.2 km
1	500	50	11.26	14	56.20	113	9.61	47.63	0.78	56.20	83	6.60	55.03	1.79	15.25	2.08
2	600	50	10.61	17	63.83	123	10.33	54.63	0.98	63.83	12	5.59	63.26	1.65	14.41	0.89
3	700	50	11.02	14	84.28	166	15.46	73.40	1.14	84.28	13	8.44	83.15	2.64	12.91	1.35
4	800	50	11.02	16	85.13	65	11.81	75.25	1.39	85.13	89	8.99	84.79	3.07	11.61	0.40
5	1000	50	10.86	16	105.24	573	29.09	90.41	1.90	105.24	142	16.47	104.14	3.90	14.09	1.04
6	500	100	10.53	20	49.81	387	24.65	35.85	1.51	49.81	277	22.79	47.97	7.57	28.03	3.69
7	600	100	10.40	21	56.95	307	47.41	40.21	1.97	56.95	130	27.83	55.16	9.19	29.39	3.14
8	700	100	10.24	20	67.01	4402	260.79	47.29	2.28	67.01	5547	236.14	64.46	15.02	29.43	3.80
9	800	100	10.59	20	76.62	633	94.77	56.29	2.61	76.62	176	54.16	74.49	17.74	26.53	2.78
10	1000	100	10.20	20	93.87	225	91.34	68.47	3.79	93.87	159	73.87	91.93	24.74	27.05	2.06
11	500	200	10.19	23	45.05	2331	727.94	26.17	4.41	45.05	219	406.80	41.67	107.66	41.91	7.50
12	600	200	9.97	25	52.38	599	405.91	29.89	4.95	52.38	273	257.96	49.50	135.94	42.93	5.50
13	700	200	10.20	23	62.07	1898	884.70	35.45	5.73	62.07	175	640.04	58.50	193.37	42.90	5.75
14	800	200	10.47	22	70.70	4269	4296.99	38.52	6.58	70.70	346	986.03	66.93	246.15	45.51	5.33
15	1000	200	10.08	23	87.50	2441	1653.07	49.17	9.86	87.50	1226	1324.35	83.87	358.33	43.81	4.16
16	1000	300	10.35	24	85.16	222	7200	41.25	18.95	84.99	101	7200	-	1008.92	51.56	-
17	1200	300	10.81	25	102.77	127	7200	48.09	23.99	102.25	51	7200			53.20
18	1300	300	11.01	21	119.96	90	7200	54.21	27.86	633.94	8	7200			54.81
19	1400	300	10.70	24	119.61	127	7200	55.51	29.75	117.08	30	7200			53.59
20	1500	300	10.59	1	766.47	11	7200	60.52	31.06	765.22	2	7200			92.10
Instances using radial coverage of 0.5 km
1	500	50	51.18	5	99.83	15	16.74	46.17	0.83	99.83	3	13.12	96.61	3.87	53.75	3.23
2	600	50	44.08	4	122.36	0	14.12	62.68	0.97	122.36	0	11.43	121.36	4.87	48.78	0.82
3	700	50	53.39	4	138.68	0	17.04	70.69	1.59	138.68	0	15.35	138.03	5.96	49.03	0.47
4	800	50	46.12	4	163.48	38	29.89	77.24	1.36	163.48	11	24.80	158.58	8.98	52.75	2.99
5	1000	50	51.92	5	201.94	0	29.91	98.40	2.33	201.94	0	26.66	201.22	13.82	51.27	0.35
6	500	100	48.91	5	97.20	0	65.99	35.74	1.72	97.20	0	60.15	96.14	21.78	63.23	1.09
7	600	100	49.33	5	116.65	40	101.18	44.57	2.04	116.65	0	98.19	113.68	30.03	61.79	2.54
8	700	100	43.54	6	131.50	0	106.99	46.58	2.53	131.50	0	102.31	130.60	45.29	64.58	0.69
9	800	100	47.64	5	157.34	15	154.19	59.78	2.98	157.34	3	148.20	154.90	50.81	62.00	1.55
10	1000	100	52.61	5	192.27	27	231.91	68.04	3.65	192.27	7	222.71	189.23	88.52	64.61	1.58
11	500	200	48.30	6	93.32	0	419.36	26.51	4.90	93.32	0	522.18	91.83	249.68	71.59	1.60
12	600	200	47.85	6	110.63	37	777.41	30.98	5.58	110.63	33	740.69	108.48	401.20	72.00	1.94
13	700	200	49.38	6	133.28	55	1158.32	35.24	7.60	133.28	19	1061.54	129.97	548.92	73.56	2.48
14	800	200	47.90	6	152.25	39	1273.34	41.22	10.16	152.25	4	1174.40	149.29	640.60	72.93	1.94
15	1000	200	47.48	6	188.15	36	2104.82	49.17	12.39	188.15	13	1664.89	182.83	1005.08	73.87	2.83
16	1000	300	46.43	6	184.02	91	6892.81	40.91	23.32	184.02	18	5364.37			77.77
17	1200	300	48.88	1	551.27	0	7200	49.02	24.77	219.90	17	6747.17			91.11
18	1300	300	47.10	1	768.33	0	7200	53.42	38.84	237.04	0	6044.67			93.05
19	1400	300	47.21	1	701.78	0	7200	56.48	43.06	701.78	0	7200			91.95
20	1500	300	48.17	1	728.30	0	7200	61.02	53.02	728.30	0	7200			91.62

Instance not solved. -, CPLEX could not solve the problem.