A Decomposition-Based Two-Stage Optimization Algorithm for Single Machine Scheduling Problems with Deteriorating Jobs

Table 5

Comparison between the performances of the two-stage method and GTS.

Problem	100 jobs			Problem	200 jobs
	Two-stage method	GTS	Improvement (%)		Two-stage method	GTS	Improvement (%)
1	529251	543701	2.73	1	2772482	2693236	−2.86
2	580368	561897	−3.18	2	2254343	2646620	17.40
3	471791	531532	12.66	3	2549536	2808366	10.15
4	467193	552274	18.21	4	2701978	2582402	−4.43
5	498979	502002	0.61	5	2214216	2653940	19.86
6	592447	542141	−8.49	6	2991533	3263023	9.08
7	458492	486609	6.13	7	2066705	2344396	13.44
8	590894	554199	−6.21	8	2408844	2555122	6.07
9	572005	636890	11.34	9	2331178	2802221	20.21
10	366301	402192	9.80	10	2401338	2679454	11.58
Problem	500 jobs			Problem	1000 jobs
	Two-stage method	GTS	Improvement (%)		Two-stage method	GTS	Improvement (%)
1	16526240	18984561	14.88	1	82521970	89691988	8.69
2	16917170	19958887	17.98	2	78710890	84133722	6.89
3	17430260	19615766	12.54	3	83526650	89416688	7.05
4	17960130	19779356	10.13	4	82014700	86538534	5.52
5	17383250	19476219	12.04	5	76615210	84045424	9.70
6	16520930	18978797	14.88	6	79475530	86345229	8.64
7	15694230	18608654	18.57	7	82407780	84327182	2.33
8	18541230	21285024	14.80	8	73426980	80531920	9.68
9	20040810	22896113	14.25	9	81376060	90411751	11.10
10	17562700	19684769	12.08	10	72945010	80092001	9.80