Task Scheduling for Multiunit Parallel Test Using Mixed-Integer Linear Programming

Table 5

Model statistics and solution details of 7 examples.

Example	Model details			Full-space method			SBI method
	Binary variables	Continuous variables	Constraints	Optimal solution (s)	Computation time without ISF (s)	Computation time with ISF (s)	Best solution (s)	Computation time (s)	SR	ARUR
1-2	156	12	605	321	16.2	1.7	321	9.4	1.33	26.1
2-2	110	10	407	461	11.1	1.4	461	6.6	1.49	26.7
3-2	90	9	334	253	8.1	1.3	253	5.6	1.61	36.0
4-2	506	22	2065	728	485.7	66.4	728	35.3	1.53	28.5
5-2	462	21	1898	577	366.6	53.2	577	32.1	1.45	30.4
6-2	380	19	1532	732	206.2	32.8	732	24.8	1.49	29.3
7-2	992	31	4150	999	2000	1066.3	999	86.5	1.52	29.9
1-3	168	12	869	321	25.1	2.1	321	10.5	1.33	26.1
2-3	120	10	587	456	16.5	1.7	456	7.1	1.5	27.0
3-3	99	9	478	253	12.1	1.5	253	5.9	1.61	36.1
4-3	528	22	2989	658	758.5	89.6	658	44.4	1.69	31.5
5-3	483	21	2738	533	593.6	68.9	533	40	1.57	32.9
6-3	399	19	2216	619	321.6	43.1	619	30.7	1.77	34.7
7-3	1023	31	6010	None	2000	2000	815	113.5	1.87	36.7
1-4	180	12	1133	321	31.9	2.5	321	11.5	1.33	26.1
2-4	130	10	767	456	22.1	1.9	456	7.6	1.5	27.0
3-4	108	9	622	253	16.1	1.7	253	6.3	1.61	36.0
4-4	550	22	3913	577	1077.5	108	577	53.4	1.93	37.1
5-4	504	21	3578	553	844.6	83.2	533	47.9	1.57	32.9
6-4	418	19	2900	619	461.8	54.4	619	36.3	1.77	34.7
7-4	1054	31	7870	None	2000	2000	815	141.2	1.87	36.7

Solution of examples 7-2 is found by the full-space method with ISF.