Table 3.

Optimality gap results using lb, ub, and lb+ub for $\mathbf{R}$ and $\mathbf{S}$ under different budget levels.

Budget	Exp	CutTime		Time		MIPgap		GapImp${}^1$		Igap	Rgap	GapImp${}^2$
		(CPU sec)		(CPU sec)		(%)		(%)		(%)	(%)	(%)
		R	S	R	S	R	S	R	S		R	R
$30M	cpx	0		7203		13.1				13.9
	lb	797	1330	8098	8536	13.1	13.3	0.1	0.0		13.2	4.9
	ub	848	1306	8068	8524	8.1	7.9	38.3	39.4		13.9	0.0
	lb+ub	965	1331	8294	8535	8.0	9.3	38.6	29.0		13.2	4.9
$35M	cpx	0		7203		9.3				10.3
	lb	171	1234	7476	8438	9.3	13.4	0.0	0.0		9.4	9.0
	ub	157	1314	7393	8530	8.3	7.8	10.4	15.8		10.3	0.0
	lb+ub	178	1270	7501	8481	8.3	10.1	11.0	0.0		9.4	9.0
$40M	cpx	0		7204		9.6				10.7
	lb	434	1080	7736	8282	9.5	13.3	0.4	0.0		9.5	10.7
	ub	434	1098	7654	8302	8.3	7.8	13.4	19.1		10.7	0.0
	lb+ub	434	1088	7754	8291	8.3	9.2	13.1	4.0		9.5	10.7
$45M	cpx	0		7203		9.3				10.4
	lb	1381	1354	8682	8358	9.3	13.4	0.1	0.0		9.2	12.1
	ub	1252	1132	8458	8334	8.1	8.0	13.0	14.4		10.4	0.0
	lb+ub	1335	1121	8639	8324	8.2	7.7	12.2	17.8		9.2	12.1
$50M	cpx	1		6775		0.0				1.1
	lb	204	982	7086	8188	0.0	13.4	0.0	0.0		0.0	100.0
	ub	215	969	7424	8172	0.0	7.4	0.0	0.0		1.1	0.0
	lb+ub	220	956	7524	8168	0.0	7.1	0.0	0.0		0.0	100.0
Average	cpx	0		7118		8.3				9.3
	lb	598	1156	7816	8360	8.2	13.4	0.1	0.0		8.3	27.3
	ub	581	1164	7799	8372	6.6	7.8	15.0	17.7		9.3	0.0
	lb+ub	626	1153	7942	8360	6.6	8.7	15.0	10.2		8.3	27.3