Single Machine Problem with Multi-Rate-Modifying Activities under a Time-Dependent Deterioration

Table 1

Comparison of results from B & B; HA for 1|𝑝_𝑖𝑟,rm|𝐶_max.

n	b	Branch and bound			Heuristic algorithm		n	b	Branch and bound			Heuristic algorithm
		Optimal solution	𝑘	CPU time (s)	Var	𝑘			Optimal solution	𝑘	CPU time (s)	Var	𝑘
	0.05	231.26	3	0	0.039	2		0.05	1737.96	15	66.782	0.023	28
5	0.07	319.34	4	0	0.037	2	30	0.07	2103.11	13	67.438	0.028	4
	0.09	483.31	3	0	0.051	4		0.09	3080.54	16	66.313	0.015	21
	0.05	739.34	6	0.200	0.029	2		0.05	2177.56	19	154.984	0.016	31
10	0.07	653.29	5	0.201	0.053	2	35	0.07	2652.92	22	153.266	0.014	28
	0.09	666.42	6	0.182	0.052	3		0.09	2790.96	18	153.484	0.020	8
	0.05	801.51	9	1.656	0.025	12		0.05	2362.75	26	318.391	0.018	37
15	0.07	918.13	10	1.656	0.035	14	40	0.07	2929.35	23	317.781	0.015	10
	0.09	916.67	5	1.657	0.041	14		0.09	2532.46	22	322.297	0.034	37
	0.05	1102.83	14	7.625	0.035	2		0.05	3074.90	27	611.469	0.015	7
20	0.07	1044.45	13	7.594	0.030	18	45	0.07	3082.73	24	610.953	0.023	40
	0.09	1381.71	11	7.594	0.036	4		0.09	3568.99	21	610.282	0.031	41
	0.05	1693.42	14	25.016	0.021	4		0.05	3337.76	25	1092.14	0.025	48
25	0.07	1530.00	17	25.063	0.020	21	50	0.07	3758.05	23	1091.81	0.020	8
	0.09	2169.22	17	25.047	0.034	4		0.09	4285.62	28	1089.73	0.015	13