Table 3 Average MILP and heuristic... | Emerald Publishing

Table 3

Average MILP and heuristic performance

n	MILP (solved with Gurobi)								Heuristic
n	Time	UB	LB	Gap	Un	Un pen	QRF	Route	Time	Obj	Un	Un pen	QRF	Route
3	23	5.19	5.19	0	0.0	0	0/10	3.79	3	5.35	0.0	0	0/10	3.95
4	1,455	5.94	5.94	0	0.0	0	0/10	4.24	7	5.99	0.0	0	0/10	4.29
5	9,278	6.68	6.68	0	0.0	0	0/10	4.88	9	6.68	0.0	0	0/10	5.03
6	*	7.51	7.51	0	0.0	0	0/10	5.71	14	47.64	0.1	40	0/10	5.84
7	*	8.77	8.77	0	0.0	0	0/10	6.77	18	8.99	0.0	0	0/10	6.99
8	*	18.74	18.74	0	0.1	10	0/10	6.84	41	79.28	0.2	30	1/10	7.48
9	*	49.37	8.91	82	0.0	0	1/10	7.05	56	69.08	0.5	60	0/10	7.08
10	*	49.66	9.15	82	0	0	1/10	7.66	84	60.31	0.1	10	1/10	8.41
20	21,600	–	1.98	–	–	–	–	–	789	2976.45	0.1	2,560	10/10	14.45
30	21,600	–	0.90	–	–	–	–	–	2,554	609.40	1.1	190	10/10	17.40

n	MILP (solved with Gurobi)								Heuristic
n	Time	UB	LB	Gap	Un	Un pen	QRF	Route	Time	Obj	Un	Un pen	QRF	Route
3	23	5.19	5.19	0	0.0	0	0/10	3.79	3	5.35	0.0	0	0/10	3.95
4	1,455	5.94	5.94	0	0.0	0	0/10	4.24	7	5.99	0.0	0	0/10	4.29
5	9,278	6.68	6.68	0	0.0	0	0/10	4.88	9	6.68	0.0	0	0/10	5.03
6	*	7.51	7.51	0	0.0	0	0/10	5.71	14	47.64	0.1	40	0/10	5.84
7	*	8.77	8.77	0	0.0	0	0/10	6.77	18	8.99	0.0	0	0/10	6.99
8	*	18.74	18.74	0	0.1	10	0/10	6.84	41	79.28	0.2	30	1/10	7.48
9	*	49.37	8.91	82	0.0	0	1/10	7.05	56	69.08	0.5	60	0/10	7.08
10	*	49.66	9.15	82	0	0	1/10	7.66	84	60.31	0.1	10	1/10	8.41
20	21,600	–	1.98	–	–	–	–	–	789	2976.45	0.1	2,560	10/10	14.45
30	21,600	–	0.90	–	–	–	–	–	2,554	609.40	1.1	190	10/10	17.40

Note(s): * Alternative MILP solution method used

− Gurobi was not able to find values

See Table A2 for instance-level details

Source(s): Table by authors