Journal of the Operational Research Society - Table 3 for article: Single machine scheduling with time deteriorating job values

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Single machine scheduling with time deteriorating job values

S Raut, J N D Gupta and S Swami

Table 3. Maximum optimality gap of the proposed algorithms for small problems

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	n	H	HI	HIT ^*	F	FI	FIT ^*	R	RI	RIT ^*	V	VI	VIT ^*
Linear	5	12.10	4.72	2.54	1.71	0.69	0.27	8.92	3.78	1.63	15.34	4.72	2.54
truncated	10	5.72	5.32	2.81	0.53	0.51	0.51	4.58	2.01	1.72	13.78	2.01	1.72
	15	5.35	3.26	1.92	0.40	0.34	0.34	3.61	1.54	1.13	9.88	1.56	1.08
	20	4.36	3.00	2.17	0.45	0.37	0.37	3.85	1.76	1.31	11.47	1.76	1.31
Overall		12.10	5.32	2.81	1.71	0.69	0.51	8.92	3.78	1.72	15.34	4.72	2.54

Capacitated	5	12.64	12.29	7.19	4.36	3.30	2.68	13.88	7.19	7.19	19.84	12.29	8.40
linear	10	12.13	6.18	3.80	3.65	2.14	1.70	9.54	5.26	3.80	16.34	5.26	3.80
	15	13.65	5.36	3.02	2.97	1.84	1.84	10.19	5.46	2.17	15.78	5.52	2.80
	20	11.40	5.59	3.36	3.13	2.32	1.86	8.89	7.33	3.92	13.35	4.85	2.58
Overall		13.65	12.29	7.19	4.36	3.30	2.68	13.88	7.33	7.19	19.84	12.29	8.40

Capacitated	5	8.91	6.16	3.88	2.61	2.06	2.06	7.25	6.16	3.88	14.82	6.16	3.88
linear	10	8.09	7.55	4.72	2.69	1.70	1.70	7.10	4.91	2.46	11.51	4.36	2.57
truncated	15	8.89	8.48	2.24	2.48	2.19	1.84	6.56	5.65	2.24	10.93	5.49	2.24
	20	10.22	9.68	5.21	5.33	5.25	4.71	8.84	7.16	5.32	12.86	6.34	4.59
Overall		10.22	9.68	5.21	5.33	5.25	4.71	8.84	7.16	5.32	14.82	6.34	4.59

Exponential	5	23.95	22.83		14.05	13.25		35.50	22.83		38.29	22.83
	10	16.98	11.80		8.41	5.79		25.43	5.58		48.57	4.78
	15	12.65	5.86		7.22	5.27		23.61	3.13		38.03	2.18
	20	12.38	3.81		4.32	2.35		11.67	0.59		31.94	0.84
Overall		23.95	22.83		14.05	13.25		35.50	22.83		48.57	22.83

Exponential	5	26.85	23.56	22.24	14.30	14.30	3.83	26.85	24.19	22.24	37.07	24.19	22.24
truncated	10	16.84	12.72	11.82	6.02	2.84	2.84	18.89	7.18	3.35	40.54	7.18	4.72
	15	13.63	9.42	7.69	3.99	2.60	2.60	9.46	4.39	2.82	36.07	4.39	2.82
	20	18.56	10.05	7.86	4.30	3.00	3.00	9.07	3.53	1.77	42.47	3.53	1.27
Overall		26.85	23.56	22.24	14.30	14.30	3.83	26.85	24.19	22.24	42.47	24.19	22.24

Capacitated	5	30.45	17.96	10.64	17.10	14.55	6.39	34.67	19.11	13.26	50.57	14.55	7.28
exponential	10	31.08	17.81	8.07	12.76	10.90	5.33	31.06	16.25	9.24	48.45	14.51	9.24
	15	20.46	16.12	6.63	11.14	9.76	5.28	32.76	18.22	7.42	39.70	9.23	6.09
	20	22.09	17.42	7.45	14.70	9.60	5.71	32.66	13.71	6.85	46.31	13.13	5.66
Overall		31.08	17.96	10.64	17.10	14.55	6.39	34.67	19.11	13.26	50.57	14.55	9.24

Capacitated	5	30.27	23.88	8.59	14.94	7.70	6.17	33.18	22.86	4.48	48.07	22.86	5.39
exponential	10	30.70	21.37	6.38	8.53	5.29	3.70	21.29	11.96	6.94	46.76	11.96	7.02
truncated	15	20.21	16.91	5.24	7.29	6.09	4.14	14.87	10.70	4.67	38.27	9.93	5.34
	20	22.16	17.48	5.64	9.17	6.89	3.52	17.64	12.89	4.39	43.32	13.12	5.11
Overall		30.70	23.88	8.59	14.94	7.70	6.17	33.18	22.86	6.94	48.07	22.86	7.02

* Depending on the specific case being considered, T represents the use of algorithm T, C, or TC.

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TABLE 3

Single machine scheduling with time deteriorating job values

Table 3. Maximum optimality gap of the proposed algorithms for small problems