Table 8.

Statistical lower bounds, upper bounds and the estimators for quality evaluation in the sensitivity analysis with changing weight combination.

Weight	Goal	Lower bound		Upper bound		Gap estimators
		${\overline{f}}_{Q,R}$	${\sigma }_{{\overline{f}}_{Q,R}}^2$	${\hat{f}}_{Q^{’}}\left(\hat{x}\right)$	${\sigma }_{{\hat{f}}_{Q^{’}}\left(\hat{x}\right)}^2$	$ga{p}_{Q,R,Q^{’}}\left(\hat{x}\right)$	%	${\sigma }_{gap}^2$
w1 = 1	Cost	43,252,268	86,316	43,250,895	809434	−1373	0	814,023
	Risk	119,952,310	967,360	119,895,022	10,839,277	−57,288	−0.05	10,882,358
w1 = 0.9	Cost	43,475,060	148,551	43,281,984	813,666	−193,076	−0.44	827,115
	Risk	117,960,070	1,269,067	118,560,005	10,703,293	599,935	0.51	10,778,266
w1 = 0.8	Cost	43,425,067	120,239	43,349,774	815,638	−75,293	−0.17	824,452
	Risk	117,384,540	964,128	104,244,613	9,809,252	51,613	0.05	9824,419
w1 = 0.7	Cost	45,115,179	100,370	45,090,960	809,304	−24,219	−0.05	815,504
	Risk	104,193,000	545,693	104,244,613	9,809,252	51,613	0.05	9,824,419
w1 = 0.6	Cost	45,151,484	105,368	45,132,280	814,186	−19,204	−0.04	820,976
	Risk	103,933,240	594,219	104,066,758	9,783,581	133,518	0.13	9,801,610
w1 = 0.5	Cost	46,497,296	999,620	47,088,714	803,281	591,418	1.27	1,282,381
	Risk	100,656,751	2,256,733	99,560,882	9,314,344	−1,095,869	−1.09	9,583,833
w1 = 0.4	Cost	47,281,433	309,679	47,106,247	806,902	−175,186	−0.37	864,287
	Risk	99,134,692	1,046,516	99,528,192	9,309,252	393,500	0.40	9,367,890
w1 = 0.3	Cost	47,304,111	299,695	47,118,668	810,118	−185,443	−0.39	863,776
	Risk	99,106,560	1,042,259	99,512,380	9,304,577	405,820	0.41	9,362,770
w1 = 0.2	Cost	47,313,976	296,886	47,133,044	811,360	−180,932	−0.38	863,971
	Risk	99,099,020	1,041,099	99,501,415	9,303,115	402,395	0.41	9,361,188
w1 = 0.1	Cost	50,023,629	3,383,297	53,930,043	813,174	3,906,414	7.81	3,479,648
	Risk	98,370,287	818,338	97,516,075	8,681,971	−854,212	−0.87	8,720,453
w1 = 0	Cost	59,850,556	3,259,162	60,620,437	825,052	769,880	1.29	3,361,970
	Risk	97,723,873	651,248	97,513,812	8,681,283	−210,061	−0.22	8,705,676