Journal of Advanced Transportation

Research Article

Presenting a Multi-Start Hybrid Heuristic for Solving the Problem of Two-Echelon Location-Routing Problem with Simultaneous Pickup and Delivery (2E-LRPSPD)

Table 4

Comparison of proposed heuristic and B&C on Barreto’s LRPSPD instances.


Instance	DSS		B&C [34]		MHH-PR
Instance	DSS		Gap (%)	CPU		Gap (%)	CPU

Srivastava86_82		625.43	0.00	0.38	625.43	0.00	1.09
Srivastava86_82		625.43	0.00	0.26	625.43	0.00	1.03
Perl83_122		242.41	0.00	0.60	242.41	0.00	3.05
Perl83_122		242.41	0.00	0.55	242.41	0.00	2.21
Gaskell67_215		454.48	0.00	13.34	454.48	0.00	7.51
Gaskell67_215		454.48	0.00	8.98	454.48	0.00	6.08
Gaskell67_225		629.51	0.00	109.62	629.51	0.00	5.17
Gaskell67_225		629.51	0.00	64.99	629.51	0.00	5.04
Min92_275		2998.80	0.00	91.87	2998.80	0.00	4.95
Min92_275		2998.80	0.00	190.62	2998.80	0.00	6.61
Gaskell67_295		490.34	0.00	6.63	490.34	0.00	4.65
Gaskell67_295		490.34	0.00	6.57	490.34	0.00	5.99
Gaskell67_325_1		563.47	0.00	18.77	563.47	0.00	6.83
Gaskell67_325_1		563.47	0.00	27.31	563.47	0.00	6.98
Gaskell67_325_2		507.03	0.00	13.72	507.03	0.00	5.88
Gaskell67_325_2		507.03	0.00	7.87	507.03	0.00	5.30
Gaskell67_365		494.86	0.00	18.36	503.16	1.68	7.20
Gaskell67_365		494.86	0.00	18.13	501.05	1.25	13.62
Ghristofides69_505		576.69	2.40	14400.00	612.58	6.22	15.38
Ghristofides69_505		578.97	2.69	14400.00	600.25	3.67	16.42
Perl83_5515		985.56	2.94	14400.00	999.06	1.37	57.50
Perl83_5515		988.06	3.14	14400.00	1002.17	1.43	55.07
Christofides69_7510		888.16	10.33	14400.00	896.51	0.94	47.96
Christofides69_7510		884.00	8.90	14400.00	890.80	0.77	62.06
Perl83_857		1381.57	5.88	14400.00	1386.52	0.36	131.55
Perl83_857		1368.64	4.96	14400.00	1412.78	3.22	114.98
Daskin95_888		399.17	11.20	14400.00	406.68	1.88	109.69
Daskin95_888		401.98	0.00	14068.40	419.60	4.38	134.31
Christofides69_10010		880.18	7.45	14400.00	884.16	0.45	151.00
Christofides69_10010		880.89	6.17	14400.00	902.04	2.40	115.67

Average			2.20	5768.90	814.68	1.00	37.03

In this table, the first column represents the names of the LRPSPD instances. The name of each instance is represented by the coding structure of the author, Author, who generated the instance; year of the instance, Year; the number of customers, ; and the number of depots, (i.e., Author–Year-). The names of instances can not be set in bold.