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

Table 8

Comparison between Gurobi and the proposed ALNS for solving Set 2 instances of 2EVRP-TN-OD.

Instance	BKS of 2EVRP	Gurobi	Proposed ALNS
			Best	Average	CPU (s)
Set 2a
E-n22-k4-s6-17	417.07	329.64	328.18	328.21	60	−21.31	−0.44
E-n22-k4-s8-14	384.96	316.96	316.96	316.96	60	−17.66	0.00
E-n22-k4-s9-19	470.6	372.77	351.51	351.69	60	−25.31	−5.70
E-n22-k4-s10-14	371.5	277.09	277.09	277.09	60	−25.41	0.00
E-n22-k4-s11-12	427.22	367.62	350.58	350.58	60	−17.94	−4.64
E-n22-k4-s12-16	392.78	311.88	306.24	306.58	60	−22.03	−1.81
E-n33-k4-s1-9	730.16	606.01	511.93	513.07	120	−29.89	−15.52
E-n33-k4-s2-13	714.63	763.04	510.77	513.83	120	−28.53	−33.06
E-n33-k4-s3-17	707.48	—	512.48	512.95	120	−27.56	—
E-n33-k4-s4-5	778.74	761.61	555.73	557.81	120	−28.64	−27.03
E-n33-k4-s7-25	756.85	612.65	536.78	536.92	120	−29.08	−12.38
E-n33-k4-s14-22	779.05	713.55	573.87	583.34	120	−26.34	−19.58
Set 2b
E-n51-k5-s2-4-17-46	530.76	—	334.54	350.99	300	−36.97	—
E-n51-k5-s2-17	597.49	—	389.54	401.84	300	−34.80	—
E-n51-k5-s4-46	530.76	—	358.97	365.06	300	−32.37	—
E-n51-k5-s6-12	554.81	—	347.34	360.41	300	−37.39	—
E-n51-k5-s6-12-32-37	531.92	—	336.03	341.66	300	−36.83	—
E-n51-k5-s11-19	581.64	—	398.27	413.28	300	−31.53	—
E-n51-k5-s11-19-27-47	527.63	—	341.57	363.55	300	−35.26	—
E-n51-k5-s27-47	538.22	—	349.85	353.78	300	−35.00	—
E-n51-k5-s32-37	552.28	—	371.96	373.12	300	−32.65	—
Set 2c
E-n51-k5-s2-4-17-46	601.39	—	485.8	491.75	300	−19.22	—
E-n51-k5-s2-17	601.39	—	448.58	452.99	300	−25.41	—
E-n51-k5-s4-46	702.33	—	534.21	540.66	300	−23.94	—
E-n51-k5-s6-12	567.42	—	415.9	421.48	300	−26.70	—
E-n51-k5-s6-12-32-37	567.42	—	463.34	473.26	300	−18.34	—
E-n51-k5-s11-19	617.42	—	452.49	461.79	300	−26.71	—
E-n51-k5-s11-19-27-47	530.76	—	421.11	428	300	−20.66	—
E-n51-k5-s27-47	530.76	—	440.76	444.43	300	−16.96	—
E-n51-k5-s32-37	752.59	—	670.74	683.62	300	−10.88	—
Average			423.10	429.02		−26.71