Table 2.

Conditional dominance inequality analysis

Status	Column	Budget	Group	Cuts Soln	No Cuts Soln	No Cuts	Cuts	Obj$_{\text{c}}^{}>$ Obj$_{\text{nc}}^{}$	N$_{\text{nc}}^{}$ - N$_{\text{c}}^{}$	N$_{\text{c}}^{}$ - N$_{\text{nc}}^{}$
(both)	prices	proportion	size	time (s)	time (s)	faster	faster	count	max	max
OPTIMAL	LOW	0.75	12	$<1$	$<1$	7	4	–	0	0
	LOW	0.50	12	16.27	16.06	5	7	–	326	83,997
	LOW	0.25	6	7.75	8.19	3	3	–	16,143	15,131
	MEDIUM	0.75	12	2.04	2.27	5	7	–	17,640	9,618
	MEDIUM	0.50	6	1.65	2.02	5	1	–	6,170	1,193
	MEDIUM	0.25	6	40.92	39.08	4	2	–	48,428	128,249
	HIGH	0.75	12	9.50	9.66	6	6	–	34,296	24,356
	HIGH	0.50	6	2.99	3.37	5	1	–	6,904	1,155
	HIGH	0.25	6	6.36	6.82	4	2	–	8,482	2,435
TIME_LIMIT	LOW	0.25	6	600	600	–	–	1	964,750	196,695
	MEDIUM	0.50	6	600	600	–	–	2	598,087	290,328
	MEDIUM	0.25	6	600	600	–	–	2	897,771	122,405
	HIGH	0.50	6	600	600	–	–	3	2,157,927	2,301,566
	HIGH	0.25	6	600	600	–	–	4	1,895,997	914,481

We excluded matrices with 10 rows or 10 columns, as solution times were small. With N denoting node count, the last two columns refer to the worse case additional nodes one method required over the other. We remark that the node count for the first group is 1 for all instances, as the problem was sufficiently easy to solve without a branch-and-cut procedure. We set the time limit of 10 min in these experiments