Optimization Model Based on Reachability Guarantee for Emergency Facility Location and Link Reinforcement

Table 3

Solutions for different G and ω (P: primary facility, B: backup facility).

G	ω			CF	CL	Set of reinforced links RL		J
								3	8	10	13	14	18	22
300	[0.1, 0.2]	507	10.54	106	193	(1-2), (4-5), (6–8), (10-11), (3–12), (7–18)	P	9	9	9	9	17	9	17
							B	17	17	17	17	9	17	9
	[0.3, 0.5]	357	9.10	108	191	(1-2), (4-5), (6–8), (3–12), (7–18), (20-21)	P	9	9	9	21	21	9	21
							B	21	21	21	9	9	21	9
	[0.6, 0.9]	304	6.89	115	180	(1-2), (4-5), (6–8), (3–12), (7–18), (23-24)	P	9	9	9	23	23	9	23
							B	23	23	23	9	9	23	9
350	0.1	396	10.85	131	215	(1-2), (4-5), (6–8), (3–12), (7–18), (16–18), (21-22)	P	16	16	15	15	15	16	15
							B	15	15	16	16	16	15	16
	0.2	304	10.13	165	182	(1-2), (4-5), (6–8), (3–12), (7–18), (16–18), (18–20)	P	9	9	9	23	23	9	23
							B	17	17	17	17	9	17	9
	[0.3, 0.5]	260	9.57	176	168	(1-2), (4-5), (6–8), (9-10), (3–12), (7–18)	P	9	9	9	23	23	16	23
							B	16	16	16	9	16	9	9
	[0.6, 0.9]	219	6.69	191	151	(1-2), (4-5), (6–8), (3–12), (7–18)	P	4	16	16	23	23	16	23
							B	16	4	4	16	16	4	16
400	0.1	396	11.73	131	269	(1-2), (4-5), (6–8), (10-11), (3–12), (12-13), (7–18), (16–18), (21-22)	P	16	16	15	15	15	16	15
							B	15	15	16	16	16	15	16
	[0.2, 0.3]	260	10.82	176	222	(1-2), (3-4), (6–8), (5–9), (12-13), (7–18)	P	9	9	9	23	23	16	23
							B	16	16	16	16	16	9	9
	0.4	219	9.83	241	151	(1-2), (4-5), (6–8), (3–12), (7–18)	P	4	16	16	23	23	16	23
							B	17	17	17	16	16	17	17
	[0.5, 0.9]	209	9.43	247	151	(1-2), (4-5), (6–8), (3–12), (7–18)	P	4	9	9	23	23	16	23
							B	16	16	16	16	16	21	16
450	0.1	313	12.03	169	275	(1-2), (4-5), (6–8), (3–12), (11–14), (7–18), (21-22)	P	9	9	9	21	21	16	21
							B	15	15	16	16	16	15	16
	0.2	260	11.60	176	274	(1-2), (3-4), (6–8), (5–9), (7–18), (16–18), (21-22)	P	9	9	9	23	23	16	23
							B	16	16	16	9	16	9	16
	[0.3, 0.5]	219	10.91	191	258	(1-2), (3-4), (6–8), (5–9), (7–18), (21-22)	P	4	16	16	23	23	16	23
							B	16	4	4	4	16	4	16
	0.6	209	10.27	247	199	(1-2), (4-5), (6–8), (3–12), (7–18), (21-22)	P	4	9	9	23	23	16	23
							B	16	16	16	16	4	9	16
	[0.7, 0.9]	200	9.46	258	187	(1-2), (4-5), (6–8), (3–12), (7–18), (22-23)	P	4	9	9	23	23	7	23
							B	7	7	7	7	4	9	7
500	[0.1, 0.2]	260	12.47	176	324	(1-2), (4-5), (6–8), (8-9), (10-11), (3–12), (8–16), (7-18)	P	9	9	9	23	23	16	23
							B	16	16	16	9	16	9	9
	[0.3, 0.4]	219	11.74	191	308	(1-2), (3-4), (6–8), (5–9), (12-13), (7-18), (18–20), (21-22), (13-24)	P	4	16	16	23	23	16	23
							B	16	4	4	16	16	4	16
	0.5	209	11.3	247	246	(1-2), (3-4), (6–8), (5–9), (7–18), (22-23)	P	4	9	9	23	23	16	23
							B	16	16	16	16	4	4	16
	0.6	202	10.76	299	199	(1-2), (4-5), (6–8), (3–12), (7–18), (21-22)	P	4	9	9	23	23	16	21
							B	21	16	16	16	4	21	16
	[0.7, 0.9]	193	9.46	310	187	(1-2), (4-5), (6–8), (3–12), (7–18), (22-23)	P	4	9	9	23	23	7	21
							B	7	7	7	7	21	21	7