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

Table 2

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

n	b	Branch and bound					Heuristic algorithm
		Optimal solution	𝑀	Positions	CPU time (s)	Var	𝑀	Positions
	0.05	253.11	1	2	0.031	0.011	0	—
5	0.07	255.50	1	3	0.031	0.055	0	—
	0.09	366.12	2	4, 5	0.031	0.058	1	5
	0.05	390.36	0	—	0.328	0.012	0	—
7	0.07	567.46	2	4, 5	0.344	0.037	3	5, 6, 7
	0.09	344.59	1	5	0.328	0.070	1	7
	0.05	637.21	1	7	2.672	0.025	0	—
9	0.07	451.64	1	3	2.172	0.042	1	9
	0.09	660.17	4	5, 6, 7, 8	2.719	0.049	4	6, 7, 8, 9
	0.05	559.14	1	5	26.563	0.031	0	—
11	0.07	858.35	3	6, 7, 9	31.500	0.032	5	7, 8, 9, 10, 11
	0.09	853.83	6	2, 4, 5, 6, 8, 9	31.078	0.025	6	6, 7, 8, 9, 10, 11
	0.05	826.54	1	11	486.547	0.034	1	13
13	0.07	826.22	1	10	359.484	0.048	3	11, 12, 13
	0.09	1051.81	8	2, 5, 6, 7, 8, 9, 10, 11	509.407	0.024	7	7, 8, 9, 10, 11, 12, 13
	0.05	867.21	1	9	6810.547	0.035	2	14, 15
15	0.07	1062.18	1	7	5164.200	0.013	0	—
	0.09	1117.52	6	4, 6, 8, 10, 13, 14	9923.344	0.017	7	9, 10, 11, 12, 13, 14, 15