The Two-Echelon Vehicle Routing Problem with Transshipment Nodes and Occasional Drivers: Formulation and Adaptive Large Neighborhood Search Heuristic

Table 4

Comparative results for solving 2EVRP set 3 instances.

Instance	BKS	Hemmelmayr et al. [24]		Breunig et al. [42]		Enthoven et al. [14]		Proposed ALNS			Avg. Gap to BKS (%)	Best gap to BKS (%)
		Best	CPU (s)	Best	CPU (s)	Best	CPU (s)	Avg. 5	Best	CPU (s)
Set 3a
E-n22-k4-s13-14	526.15	526.15	43	526.15	60	526.15	70	532.25	526.15	60	1.16	0.00
E-n22-k4-s13-16	521.09	521.09	44	521.09	60	521.09	64	521.96	521.09	60	0.17	0.00
E-n22-k4-s13-17	496.38	496.38	49	496.38	60	496.38	65	511.59	496.39	60	3.06	0.00
E-n22-k4-s14-19	498.8	498.8	43	498.8	60	498.8	63	518.63	498.80	60	3.98	0.00
E-n22-k4-s17-19	512.81	512.81	26	512.81	60	512.81	72	526.15	512.81	60	2.60	0.00
E-n22-k4-s19-21	520.42	520.42	34	520.42	60	520.42	62	525.93	520.42	60	1.06	0.00
E-n33-k4-s16-22	672.17	672.17	76	672.17	60	672.17	114	677.53	672.17	60	0.80	0.00
E-n33-k4-s16-24	666.02	666.02	77	666.02	60	666.02	106	692.45	666.02	60	3.97	0.00
E-n33-k4-s19-26	680.36	680.36	84	680.36	60	680.36	79	681.16	680.37	60	0.12	0.00
E-n33-k4-s22-26	680.37	680.37	77	680.37	60	680.37	136	683.34	680.37	60	0.44	0.00
E-n33-k4-s24-28	670.43	670.43	88	670.43	60	670.43	77	679.16	670.43	60	1.30	0.00
E-n33-k4-s25-28	650.58	650.58	63	650.58	60	650.58	112	675.43	650.58	60	3.82	0.00
Set 3b
E-n51-k5-s12-18	690.59	690.59	147	690.59	60	690.59	125	693.62	690.57	60	0.44	0.00
E-n51-k5-s12-41	683.05	683.05	133	683.05	60	683.05	239	690.74	683.05	60	1.13	0.00
E-n51-k5-s12-43	710.41	710.41	217	710.41	60	710.41	137	710.83	710.41	60	0.06	0.00
E-n51-k5-s39-41	728.54	728.54	155	728.54	60	728.54	179	736.08	728.54	60	1.03	0.00
E-n51-k5-s40-41	723.75	723.75	154	723.75	60	723.75	129	736.46	723.75	60	1.76	0.00
E-n51-k5-s40-43	752.15	752.15	158	752.15	60	752.15	242	763.2	752.15	60	1.47	0.00
Set 3c
E-n51-k5-s13-19	560.73			560.73	60	560.73	119	566.35	560.73	60	1.00	0.00
E-n51-k5-s13-42	564.45			564.45	60	564.45	174	568.69	564.45	60	0.75	0.00
E-n51-k5-s13-44	564.45			564.45	60	564.45	121	571.14	564.45	60	1.19	0.00
E-n51-k5-s40-42	746.31			746.31	60	746.31	122	749.71	746.31	60	0.46	0.00
E-n51-k5-s41-42	771.56			771.56	60	771.56	203	775.65	771.56	60	0.53	0.00
E-n51-k5-s41-44	802.91			802.91	60	802.91	169	807.64	802.91	60	0.59	0.00
Average	641.44	632.45	92	641.44	60	641.44	124	649.82	641.44	60.00	1.37	0.00