Shipper collaboration in forward and reverse logistics

Xiaohui Lyu; Nengmin Wang; Zhen Yang; Haoxun Chen

doi:10.3934/jimo.2018173

Article Contents

2020, Volume 16, Issue 2: 669-705. Doi: 10.3934/jimo.2018173

This issue Previous Article Designing a hub location and pricing network in a competitive environment Next Article Vector-valued separation functions and constrained vector optimization problems: optimality and saddle points

Shipper collaboration in forward and reverse logistics

1.
School of Management, Xi'an Jiaotong University, 710049, NO.28 Xianning Road, Xian Shaanxi, China, ERC for Process Mining of Manufacturing Services in Shaanxi Province
2.
Industrial Systems Optimization Laboratory, Charles Delaunay Institute and UMR CNRS, 6281, University of Technology of Troyes, 12 rue Marie Curie, CS 42060, 10004 Troyes, France

* Corresponding author: Nengmin Wang
* Corresponding author: Nengmin Wang

Received: March 31, 2018

Revised: May 31, 2018

Early access: October 2018

Published: February 2020

Abstract Full Text(HTML) Figure(5) / Table(21) Related Papers Cited by

Abstract

In less than truckload transportation, shippers collaborate to reduce their logistics costs by consolidating their transportation requests in the procurement of transportation services from a carrier for serving the requests. In this paper, we study shipper collaboration in forward and reverse logistics, in which multiple shippers with forward or/and reverse logistics operations consolidate their transportation requests. In the forward and reverse logistics, manufacturers deliver new products to their customers and used products are collected from customers and transported to remanufacturers for repair or reproduction. This gives rise to a new vehicle routing problem with pickup and delivery requests and three different types of depots (product depots, vehicle depots and recycle depots). A hybrid approach combining greedy randomized adaptive search procedure (GRASP) and iterated local search (ILS) is proposed to find a near optimal solution of the problem. Numerical experiments on a large set of randomly generated instances with different problem sizes demonstrate that shipper collaboration in forward and reverse logistics can realize significant cost savings compared with the isolated operation of each shipper without cooperation, and the proposed approach is effective in the sense that it can find a high quality solution in a reasonable computation time.

Keywords:

Mathematics Subject Classification: Primary: 90BXX; Secondary: 90B06.

Citation:

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Figure 1. Isolated transportation planning of each shipper in forward and reverse logistics

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Figure 2. Collaborative transportation planning of all shippers in forward and reverse logistics

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Figure 3. Illustration of the insertion positions for a product depot

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Figure 4. Illustration of the insertion positions for a customer

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Figure 5. Illustration of the insertion positions for a recycle depot

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Table 1. The comparison of the first improvement and the best improvement

Instance set	Best improvement		First improvement
Instance set	CPU	Gap	CPU	Gap
I40	827.63	5.20	29.22	5.18
O40	796.54	0.62	35.18	0.58

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Table 2. The comparison of two strategies

Instance set	General strategy		Speedup strategy
Instance set	CPU	Gap	CPU	Gap
I40	327.63	5.18	29.22	5.18
O40	296.54	0.61	35.18	0.58

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Table 3. Parameter tuning according to instance size

Description	Parameter	Value
Description	Parameter	Small instances (20 requests)	Medium instances (40 requests)	Large instances (60 requests)	Large instances (100 requests)
Number of GRASP iterations	np	10	10	15	15
Number of ILS iterations	ni	5	10	15	20
RCL size	nrcl	3	5	7	7

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Table 5. Results for comparison of GRASP-ILS and CPLEX solver

Instance set	CPLEX			GRASP-ILS
	ImpIni	GapLB	CPU	ImpIni	ImpCplex	GapLB	CPU
I20	--	0.00	2101.07	--	0.00	0.00	3.17
O20	--	0.00	1077.42	--	0.00	0.00	1.92
A20	--	0.00	1350.15	--	0.00	0.00	2.49
Average		0.00	1509.55		0.00	0.00	2.53
I40	1.44	28.47	21600.00	6.57	5.18	24.58	29.22
O40	6.02	10.78	21600.00	6.37	0.58	10.27	35.18
A40	3.33	20.89	21600.00	6.61	3.58	17.91	29.94
Average	3.60	20.05	21600.00	6.52	3.11	17.59	31.45
I60	2.74	34.25	21600.00	12.45	9.99	26.73	125.42
O60	4.77	28.38	21600.00	16.85	12.63	18.00	144.84
A60	3.35	28.74	21600.00	14.78	11.81	19.18	148.35
Average	3.62	30.46	21600.00	13.70	12.47	21.30	139.54
I100	1.62	40.24	21600.00	16.85	13.00	31.27	246.32
O100	2.57	38.25	21600.00	21.11	15.24	23.55	292.72
A100	1.83	34.56	21600.00	19.52	14.68	23.17	282.45
Average	2.01	37.68	21600.00	19.16	14.31	26.00	273.83

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Table 6. Summarized results for comparison among GRASP-ILS, GRASP and ILS

Instance set
	ImpGRASP-ILS, GRASP	ImpGRASP-ILS, ILS
I20	6.51	3.17
O20	1.87	0.86
A20	7.65	3.68
Average	5.34	2.57
I40	3.95	3.71
O40	3.00	3.23
A40	6.75	3.62
Average	4.57	3.52
I60	4.09	2.65
O60	7.42	0.73
A60	6.35	4.64
Average	5.95	2.67
I100	7.20	4.19
O100	6.59	3.78
A100	5.00	4.06
Average	6.26	4.01

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Table 7. Summarized results for deviations among GRASP-ILS, GRASP and ILS

Instance set	GRASP	ILS	GRASP-ILS
	Dev	Dev	Dev
I20	1.93	4.31	0.37
O20	0.26	0.43	0.01
A20	1.21	5.23	0.76
Average	1.13	3.32	0.38
I40	4.46	7.73	0.42
O40	3.81	7.01	0.44
A40	3.68	8.65	0.89
Average	3.98	7.80	0.58
I60	6.92	11.58	0.51
O60	4.80	6.72	0.81
A60	4.09	8.66	0.92
Average	5.27	8.99	0.75
I100	7.04	12.38	0.88
O100	5.25	8.96	1.16
A100	5.40	9.31	1.12
Average	5.90	10.22	1.05

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Table 8. Summarized results of geographical distributions of customers on cost savings

Geographical distributions of customers	Non-collaboration Nv	Collaboration Nv	$\phi$
I20	4.3	2.3	22.57
O20	4.1	2	17.90
A20	4.2	2.1	10.76
I40	8	6	31.02
O40	7.3	3.5	24.19
A40	7.5	3.9	16.35
I60	11	6.3	33.31
O60	10.1	4.9	28.22
A60	10.1	5.2	24.42
I100	17.8	9.8	41.37
O100	14.1	8.4	33.79
A100	13.8	8.7	30.96

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Table 9. Summarized results of number of requests on the cost savings

Customer Requests	Non-collaboration Nv	Collaboration Nv	$\phi$
I20	4.3	2.3	22.57
I40	8	6	31.02
I60	11	6.3	33.31
I100	17.8	9.8	41.37
Average	4.2	2.1	17.08
O20	4.1	2	17.90
O40	7.3	3.5	24.19
O60	10.1	4.9	28.22
O100	14.1	8.4	33.79
Average	7.6	4.4	23.85
A20	4.2	2.1	10.76
A40	7.5	3.9	16.35
A60	10.1	5.2	24.42
A100	13.8	8.7	30.96
Average	10.4	5.5	28.65

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Table 10. Detailed results of CPLEX solver and GRASP-ILS for instances with 20 requests

Instance	CPLEX					GRASP-ILS
Instance	Ini	UB	LB	CPU	GapLB	Zmin	CPU	Zavg	CPUavg	ImpCplex	GapLB
I20-2-1-0	/	459.26	459.26	6727.61	0.00	459.26	6.24	459.26	7.25	0.00	0.00
I20-2-1-1	/	366.66	366.66	142.44	0.00	366.66	2.23	366.66	4.47	0.00	0.00
I20-2-1-2	/	478.19	478.19	1360.56	0.00	478.19	6.64	478.19	8.24	0.00	0.00
I20-2-1-3	/	360.24	360.24	128.19	0.00	360.24	1.86	365.33	1.89	0.00	0.00
I20-2-1-4	/	383.24	383.24	8933.10	0.00	383.24	1.67	383.24	2.01	0.00	0.00
I20-2-1-5	/	343.70	343.70	369.21	0.00	343.70	1.41	350.76	1.81	0.00	0.00
I20-2-1-6	/	344.51	344.51	366.51	0.00	344.51	1.59	344.51	1.77	0.00	0.00
I20-2-1-7	/	354.59	354.59	266.03	0.00	354.59	1.75	355.59	3.11	0.00	0.00
I20-2-1-8	/	351.37	351.37	2202.84	0.00	351.37	1.40	351.37	1.77	0.00	0.00
I20-2-1-9	/	476.32	476.32	514.23	0.00	476.32	6.97	476.32	8.15	0.00	0.00
Avg				2101.07	0.00		3.17
O20-2-1-0	/	240.46	240.46	817.75	0.00	240.46	2.18	240.46	2.51	0.00	0.00
O20-2-1-1	/	260.84	260.84	727.20	0.00	260.84	1.84	260.84	2.13	0.00	0.00
O20-2-1-2	/	250.62	250.62	945.73	0.00	250.62	2.50	250.62	2.66	0.00	0.00
O20-2-1-3	/	254.79	254.79	1213.25	0.00	254.79	1.50	254.79	1.83	0.00	0.00
O20-2-1-4	/	273.79	273.79	563.98	0.00	273.79	2.03	273.85	1.99	0.00	0.00
O20-2-1-5	/	269.61	269.61	2227.00	0.00	269.61	1.46	269.61	2.05	0.00	0.00
O20-2-1-6	/	260.31	260.31	1456.89	0.00	260.31	1.64	260.41	2.33	0.00	0.00
O20-2-1-7	/	245.95	245.95	1323.50	0.00	245.95	1.69	246.06	2.32	0.00	0.00
O20-2-1-8	/	240.28	240.28	685.00	0.00	240.28	1.70	240.28	2.28	0.00	0.00
O20-2-1-9	/	229.92	229.92	813.89	0.00	229.92	2.70	229.96	2.41	0.00	0.00
Avg				1077.42	0.00		1.92			0.00	0.00
A20-2-1-0	/	362.31	362.31	987.80	0.00	362.31	1.59	366.24	1.85	0.00	0.00
A20-2-1-1	/	444.80	444.80	1188.06	0.00	444.80	7.26	444.80	8.29	0.00	0.00
A20-2-1-2	/	329.67	329.67	2358.72	0.00	329.67	1.37	334.31	1.85	0.00	0.00
A20-2-1-3	/	363.62	363.62	1206.36	0.00	363.62	4.06	372.23	5.38	0.00	0.00
A20-2-1-4	/	343.77	343.77	2440.98	0.00	343.77	1.66	343.77	1.91	0.00	0.00
A20-2-1-5	/	287.74	287.74	1266.59	0.00	287.74	1.99	294.17	1.55	0.00	0.00
A20-2-1-6	/	338.23	338.23	821.69	0.00	338.23	1.56	338.23	1.70	0.00	0.00
A20-2-1-7	/	290.21	290.21	985.11	0.00	290.21	1.40	292.05	1.59	0.00	0.00
A20-2-1-8	/	314.20	314.20	1324.84	0.00	314.20	2.13	314.20	1.70	0.00	0.00
A20-2-1-9	/	323.60	323.60	921.38	0.00	323.60	1.93	323.60	2.18	0.00	0.00
Avg				1350.15	0.00		2.49			0.00	0.00

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Table 11. Detailed results of CPLEX solver and GRASP-ILS for instances with 40 requests

Instance	CPLEX						GRASP-ILS
Instance	Ini	UB	LB	CPU	ImpIni	GapLB	Zmin	CPU	Zavg	CPUavg	ImpIni	ImpCplex	GapLB
I40-2-1-0	764.73	733.02	554.38	21600.00	4.15	24.37	706.64	31.77	722.04	35.64	7.60	3.60	21.55
I40-2-1-1	617.81	617.81	432.47	21600.00	0.00	30.00	600.90	30.07	607.03	33.09	2.74	2.74	28.03
I40-2-1-2	776.04	776.04	526.08	21600.00	0.00	32.21	729.24	31.07	729.24	33.12	6.03	6.03	27.86
I40-2-1-3	718.16	702.54	545.94	21600.00	2.18	22.29	651.55	26.00	651.55	28.16	9.28	7.26	16.21
I40-2-1-4	720.41	716.43	519.91	21600.00	0.55	27.43	699.59	26.37	699.59	27.97	2.89	2.35	25.68
I40-2-1-5	748.66	748.66	475.02	21600.00	0.00	36.55	647.36	27.67	647.36	31.16	13.53	13.53	26.62
I40-2-1-6	615.92	615.92	435.58	21600.00	0.00	29.28	590.24	29.90	591.42	32.15	4.17	4.17	26.20
I40-2-1-7	664.83	662.64	432.11	21600.00	0.33	34.79	612.68	28.53	613.44	29.29	7.84	7.54	29.47
I40-2-1-8	634.10	594.85	447.33	21600.00	6.19	24.80	573.59	32.61	574.75	34.14	9.54	3.57	22.01
I40-2-1-9	611.25	604.84	466.03	21600.00	1.05	22.95	598.44	28.16	601.82	31.40	2.10	1.06	22.13
Avg				21600.00	1.44	28.47		29.22		31.61	6.57	5.18	24.58
O40-2-1-0	590.88	494.73	486.52	21600.00	16.27	1.66	494.73	30.31	497.25	32.04	16.27	0.00	1.66
O40-2-1-1	484.61	443.19	390.45	21600.00	9.99	11.90	434.04	36.80	439.23	35.30	10.44	2.06	10.04
O40-2-1-2	452.71	445.80	401.58	21600.00	1.53	9.92	445.80	34.44	445.80	36.68	1.53	0.00	9.92
O40-2-1-3	604.15	529.67	456.10	21600.00	12.33	13.89	523.35	36.44	523.35	37.24	13.37	1.19	12.85
O40-2-1-4	551.18	550.47	458.60	21600.00	0.13	16.69	549.35	37.96	549.35	41.00	0.33	0.20	16.52
O40-2-1-5	627.43	576.14	486.90	21600.00	8.17	15.49	573.11	34.70	573.11	36.25	8.66	0.53	15.04
O40-2-1-6	496.89	492.06	422.04	21600.00	0.97	14.23	489.14	39.24	489.14	41.56	1.56	0.59	13.72
O40-2-1-7	545.21	532.03	492.50	21600.00	2.78	7.43	528.80	31.72	542.87	36.13	3.01	0.61	6.86
O40-2-1-8	441.62	427.55	427.55	21600.00	3.19	0.00	427.55	32.20	427.82	40.79	3.19	0.00	0.00
O40-2-1-9	611.65	582.21	485.50	21600.00	4.81	16.61	578.85	37.98	579.14	37.03	5.36	0.58	16.13
Avg				21600.00	6.02	10.78		35.18		37.40	6.37	0.58	10.27
A40-2-1-0	595.16	581.93	463.33	21600.00	2.22	20.38	550.20	26.67	563.08	29.48	7.55	5.45	15.79
A40-2-1-1	617.54	617.54	428.57	21600.00	0.00	30.60	597.17	29.64	601.48	32.31	3.30	3.30	28.23
A40-2-1-2	685.71	593.58	508.05	21600.00	13.44	14.41	582.03	32.10	582.03	36.22	15.12	1.95	12.71
A40-2-1-3	511.22	511.22	383.62	21600.00	0.00	24.96	505.21	31.86	505.21	34.47	1.18	1.18	24.07
A40-2-1-4	574.55	569.49	460.72	21600.00	0.88	19.10	567.77	33.23	568.40	33.13	1.18	0.30	18.85
A40-2-1-5	626.75	626.75	484.73	21600.00	0.00	22.66	617.34	28.18	617.38	30.09	1.50	1.50	21.48
A40-2-1-6	574.52	572.59	457.56	21600.00	1.90	20.09	537.91	32.50	560.92	37.04	6.37	6.06	14.94
A40-2-1-7	615.58	552.47	494.52	21600.00	10.90	10.49	542.06	30.23	548.20	28.19	11.94	1.88	8.77
A40-2-1-8	642.09	630.61	480.02	21600.00	1.79	23.88	600.61	27.93	600.61	29.57	6.46	4.76	20.08
A40-2-1-9	714.16	698.33	542.39	21600.00	2.22	22.33	632.33	27.06	635.86	30.86	11.46	9.45	14.22
Avg				21600.00	3.33	20.89		29.94		32.14	6.61	3.58	17.91

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Table 12. Detailed results of CPLEX solver and GRASP-ILS for instances with 60 requests

Instance	CPLEX						GRASP-ILS
Instance	Ini	UB	LB	CPU	ImpIni	GapLB	Zmin	CPU	Zavg	CPUavg	ImpIni	ImpCplex	GapLB
I60-2-1-0	1075.15	1011.77	647.03	21600.00	5.89	36.05	911.77	99.40	914.95	114.83	15.20	9.88	29.04
I60-2-1-1	1190.63	1187.76	774.42	21600.00	0.24	34.80	987.76	118.70	988.14	130.24	17.04	16.84	21.60
I60-2-1-2	950.96	939.23	602.05	21600.00	1.23	35.90	877.23	131.62	879.37	139.26	7.75	6.60	31.37
I60-2-1-3	1088.70	1082.44	690.16	21600.00	0.57	36.24	882.44	137.82	889.93	122.66	18.95	18.48	21.79
I60-2-1-4	1047.69	1000.73	685.00	21600.00	4.48	31.55	896.87	108.94	900.72	119.33	14.40	10.38	23.62
I60-2-1-5	1026.03	1026.03	632.75	21600.00	0.00	38.33	996.95	138.59	997.19	135.02	2.83	2.83	36.53
I60-2-1-6	1214.28	1143.88	758.39	21600.00	5.80	33.70	1043.88	119.96	1046.20	126.73	14.03	8.74	27.35
I60-2-1-7	993.02	993.02	642.58	21600.00	0.00	35.29	944.32	132.32	960.94	137.32	4.90	4.90	31.95
I60-2-1-8	946.14	918.94	625.61	21600.00	2.87	31.92	818.94	132.87	826.45	119.74	13.44	10.88	23.61
I60-2-1-9	1029.63	965.24	687.93	21600.00	6.25	28.73	865.24	133.94	867.75	135.43	15.97	10.36	20.49
Avg				21600.00	2.74	34.25		125.42			12.45	9.99	26.73
O60-2-1-0	778.81	742.35	556.24	21600.00	4.68	25.07	652.35	146.37	672.06	140.72	16.24	12.12	14.73
O60-2-1-1	860.37	792.55	585.30	21600.00	7.88	26.15	746.22	144.23	750.48	150.35	13.27	5.85	21.56
O60-2-1-2	883.39	832.49	606.55	21600.00	5.76	27.14	732.49	138.82	736.08	137.72	17.08	12.01	17.19
O60-2-1-3	975.67	897.76	686.25	21600.00	7.99	23.56	787.76	128.96	795.54	144.19	19.26	12.25	12.89
O60-2-1-4	889.25	832.01	565.60	21600.00	6.44	32.02	727.32	159.57	734.02	163.88	18.21	12.58	22.24
O60-2-1-5	891.08	852.47	631.60	21600.00	4.33	25.91	752.74	150.60	755.68	145.87	15.53	11.70	16.09
O60-2-1-6	813.00	813.00	542.76	21600.00	0.00	33.24	680.46	129.71	680.46	147.45	16.30	16.30	20.24
O60-2-1-7	935.69	881.76	640.60	21600.00	5.76	27.35	752.96	162.61	761.11	172.49	19.53	14.61	14.92
O60-2-1-8	850.19	835.58	571.37	21600.00	1.72	31.62	695.58	134.58	696.81	139.18	18.19	16.75	17.86
O60-2-1-9	850.23	823.61	562.61	21600.00	3.13	31.69	723.61	152.90	727.63	150.04	14.89	12.14	22.25
Avg				21600.00	4.77	28.38		144.84			16.85	12.63	18.00
A60-2-1-0	936.24	936.24	594.70	21600.00	0.00	36.48	836.54	161.45	836.60	163.57	10.65	10.65	28.91
A60-2-1-1	1072.31	1072.31	663.76	21600.00	0.00	38.1	911.33	161.93	941.39	158.79	15.01	15.01	27.17
A60-2-1-2	859.84	803.79	620.37	21600.00	6.52	22.82	703.79	135.40	703.85	151.11	18.15	12.44	11.85
A60-2-1-3	950.17	881.73	663.68	21600.00	7.20	24.73	781.73	122.15	782.94	123.85	17.73	11.34	15.10
A60-2-1-4	912.08	902.08	622.80	21600.00	1.10	30.96	793.69	148.34	806.85	147.38	12.98	12.02	21.53
A60-2-1-5	908.24	908.24	611.25	21600.00	0.00	32.7	740.28	148.01	741.38	148.81	18.49	18.49	17.43
A60-2-1-6	919.06	854.71	676.50	21600.00	7.00	20.85	754.71	146.15	756.53	157.06	17.88	11.70	10.36
A60-2-1-7	942.98	880.28	647.62	21600.00	6.65	26.43	780.28	155.59	796.40	155.86	17.25	11.36	17.00
A60-2-1-8	799.61	799.61	594.75	21600.00	0.00	25.62	751.38	140.81	757.58	142.27	6.03	6.03	20.85
A60-2-1-9	817.71	776.45	553.61	21600.00	5.05	28.7	705.99	163.67	712.95	157.17	13.66	9.07	21.58
Avg				21600.00	3.35	28.74		148.35			14.78	11.81	19.18

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Table 13. Detailed results of CPLEX solver and GRASP-ILS for instances with 100 requests

Instance	CPLEX						GRASP-ILS
Instance	Ini	UB	LB	CPU	ImpIni	GapLB	Zmin	CPU	Zavg	CPUavg	ImpIni	ImpCplex	GapLB
I100-2-1-0	1735.62	1680.34	1041.47	21600.00	3.29	38.02	1500.16	242.56	1509.42	254.82	15.70	10.72	30.58
I100-2-1-1	1651.57	1634.89	1015.27	21600.00	1.02	37.90	1399.61	244.23	1409.80	271.59	18.00	14.39	27.46
I100-2-1-2	1668.99	1668.99	907.93	21600.00	0.00	45.60	1481.37	264.12	1491.31	270.40	12.67	11.24	38.71
I100-2-1-3	1764.60	1689.42	1077.17	21600.00	4.45	36.24	1406.15	200.51	1412.52	228.29	25.49	16.77	23.40
I100-2-1-4	1686.00	1686.00	985.47	21600.00	0.00	41.55	1471.77	231.05	1479.38	237.84	14.56	12.71	33.04
I100-2-1-5	1700.66	1700.66	878.73	21600.00	0.00	48.33	1465.71	265.97	1488.23	273.44	16.03	13.82	40.05
I100-2-1-6	1692.38	1691.53	1017.12	21600.00	0.05	39.87	1482.92	258.92	1503.80	271.70	14.12	12.33	31.41
I100-2-1-7	1645.66	1645.66	900.34	21600.00	0.00	45.29	1439.77	227.63	1442.38	242.32	14.30	12.51	37.47
I100-2-1-8	1505.41	1478.50	927.61	21600.00	1.82	37.26	1277.58	261.05	1283.99	274.56	17.83	13.59	27.39
I100-2-1-9	1541.52	1460.33	987.62	21600.00	5.56	32.37	1286.29	267.15	1315.68	277.42	19.84	11.92	23.22
Avg				21600.00	1.62	40.24		246.32			16.85	13.00	31.27
O100-2-1-0	1467.93	1420.49	950.02	21600.00	3.34	33.12	1215.92	278.27	1225.50	288.86	20.73	14.40	21.87
O100-2-1-1	1309.79	1309.79	836.30	21600.00	0.00	36.15	1113.13	316.97	1124.36	328.01	17.67	15.01	24.87
O100-2-1-2	1283.48	1230.45	831.54	21600.00	4.31	32.42	1066.12	254.79	1068.68	263.26	20.39	13.36	22.00
O100-2-1-3	1284.46	1321.90	810.99	21600.00	0.00	38.65	1166.47	300.23	1186.02	278.56	13.32	11.76	30.48
O100-2-1-4	1382.26	1338.36	909.82	21600.00	3.28	32.02	1146.62	287.89	1151.50	298.72	20.55	14.33	20.65
O100-2-1-5	1494.38	1431.12	903.18	21600.00	4.42	36.89	1223.53	294.71	1245.41	298.48	22.14	14.51	26.18
O100-2-1-6	1318.96	1264.83	831.75	21600.00	4.28	34.24	1062.43	311.91	1064.81	321.69	24.15	16.00	21.71
O100-2-1-7	1435.95	1432.51	894.75	21600.00	0.24	37.54	1224.31	306.67	1230.86	324.67	17.29	14.53	26.92
O100-2-1-8	1254.70	1221.48	779.18	21600.00	2.72	36.21	971.56	296.99	1002.10	317.68	29.14	20.46	19.80
O100-2-1-9	1381.18	1339.26	866.90	21600.00	3.13	35.27	1098.25	278.80	1119.88	283.29	25.76	18.00	21.06
Avg				21600.00	2.57	35.25		292.72			21.11	15.24	23.55
A100-2-1-0	1415.28	1404.33	863.94	21600.00	0.78	38.48	1212.68	235.67	1230.21	256.89	16.71	13.65	28.76
A100-2-1-1	1696.07	1627.24	1168.36	21600.00	4.23	28.20	1271.73	269.87	1291.68	279.07	33.37	21.85	8.13
A100-2-1-2	1328.88	1283.69	849.55	21600.00	3.52	33.82	1129.63	308.04	1132.34	325.42	17.64	12.00	24.79
A100-2-1-3	1364.97	1360.34	865.59	21600.00	0.34	36.37	1162.85	263.527	1179.11	269.85	17.38	14.52	25.56
A100-2-1-4	1433.15	1417.56	886.68	21600.00	1.10	37.45	1190.23	270.33	1197.46	281.37	20.41	16.04	25.50
A100-2-1-5	1320.79	1320.79	802.64	21600.00	0.00	39.23	1093.48	267.46	1116.72	344.65	20.79	17.21	26.60
A100-2-1-6	1450.78	1400.91	972.51	21600.00	3.56	30.58	1208.76	258.22	1212.17	356.84	20.02	13.72	19.54
A100-2-1-7	1404.69	1371.23	920.23	21600.00	2.44	32.89	1174.24	364.28	1193.54	380.21	19.63	14.37	21.63
A100-2-1-8	1334.8	1321.19	847.28	21600.00	1.03	35.87	1154.51	266.66	1177.15	345.79	15.62	12.62	26.61
A100-2-1-9	1382.94	1365.60	918.36	21600.00	1.27	32.75	1217.18	320.42	1218.88	329.73	13.62	10.87	24.55
Avg				21600.00	1.83	34.56		282.45			19.52	14.68	23.17

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Table 14. Meta-heuristics results for instances with 20 requests

Instance	GRASP		ILS		GRASP-ILS
Instance	Zmin	Zavg	Zmin	Zavg	Zmin	ImpGRASP-ILS, GRASP	ImpGRASP-ILS, ILS
I20-2-1-0	459.26	459.26	459.26	459.26	459.26	0.00	0.00
I20-2-1-1	449.88	449.88	366.66	366.66	366.66	22.70	0.00
I20-2-1-2	478.19	478.19	478.19	478.19	478.19	0.00	0.00
I20-2-1-3	449.29	459.44	360.24	415.28	360.24	24.72	0.00
I20-2-1-4	387.33	413.78	387.33	412.08	383.24	1.07	1.07
I20-2-1-5	364.89	370.22	364.89	373.59	343.70	6.17	6.17
I20-2-1-6	344.51	344.51	344.51	344.51	344.51	0.00	0.00
I20-2-1-7	379.50	407.70	426.47	479.74	354.59	7.03	20.27
I20-2-1-8	363.34	368.28	366.19	376.44	351.37	3.41	4.22
I20-2-1-9	476.32	476.32	476.32	494.04	476.32	0.00	0.00
Avg						6.51	3.17
O20-2-1-0	240.46	240.46	240.46	240.46	240.46	0.00	0.00
O20-2-1-1	261.02	261.02	278.50	278.56	260.84	0.07	6.77
O20-2-1-2	250.62	250.62	251.75	251.75	250.62	0.00	0.45
O20-2-1-3	254.79	254.79	254.79	254.79	254.79	0.00	0.00
O20-2-1-4	273.98	274.99	275.45	275.56	273.79	0.07	0.61
O20-2-1-5	269.61	269.61	269.61	269.61	269.61	0.00	0.00
O20-2-1-6	260.87	260.92	260.87	261.21	260.31	0.22	0.22
O20-2-1-7	245.95	246.37	246.97	246.97	245.95	0.00	0.41
O20-2-1-8	265.74	265.74	240.28	244.44	240.28	10.60	0.00
O20-2-1-9	247.82	247.97	230.15	235.51	229.92	7.79	0.10
Avg						1.87	0.86
A20-2-1-0	367.97	367.97	367.91	379.79	362.31	1.56	1.55
A20-2-1-1	444.8	444.80	444.80	444.80	444.80	0.00	0.00
A20-2-1-2	364.77	375.31	364.77	404.68	329.67	10.65	10.65
A20-2-1-3	412.44	439.21	423.93	456.66	363.62	13.43	16.59
A20-2-1-4	415.4	415.40	343.77	397.64	343.77	20.84	0.00
A20-2-1-5	295.37	297.82	299.91	305.22	287.74	2.65	4.23
A20-2-1-6	340.74	340.74	338.23	338.74	338.23	0.74	0.00
A20-2-1-7	298.51	304.03	301.26	304.94	290.21	2.86	3.81
A20-2-1-8	314.20	314.20	314.20	314.20	314.20	0.00	0.00
A20-2-1-9	400.40	400.40	323.60	361.33	323.60	23.73	0.00
Avg						7.65	3.68

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Table 15. Meta-heuristics results for instances with 40 requests

Instance	GRASP		ILS		GRASP-ILS
Instance	Zmin	Zavg	Zmin	Zavg	Zmin	ImpGRASP-ILS, GRASP	ImpGRASP-ILS, ILS
I40-2-1-0	733.03	769.61	741.58	773.84	706.64	3.73	4.94
I40-2-1-1	617.81	617.81	610.54	675.38	600.90	2.81	1.60
I40-2-1-2	756.99	806.65	755.90	772.53	729.24	3.81	3.66
I40-2-1-3	651.55	681.20	718.16	718.16	651.55	0.00	10.22
I40-2-1-4	699.59	731.00	720.42	720.42	699.59	0.00	2.98
I40-2-1-5	718.38	761.48	672.90	771.28	647.36	10.97	3.95
I40-2-1-6	605.91	639.66	627.27	700.22	590.24	4.35	6.27
I40-2-1-7	653.35	653.35	612.68	686.02	612.68	6.64	0.00
I40-2-1-8	601.37	635.83	582.26	645.55	573.59	4.84	1.51
I40-2-1-9	612.71	654.01	610.28	677.78	598.44	2.38	1.98
Avg						3.95	3.71
O40-2-1-0	573.13	607.63	530.77	613.94	494.73	15.85	7.28
O40-2-1-1	451.96	479.67	476.94	535.79	434.04	4.13	9.88
O40-2-1-2	465.61	486.61	452.72	499.94	445.80	4.44	1.55
O40-2-1-3	523.35	523.35	523.35	523.35	523.35	0.00	0.00
O40-2-1-4	549.35	549.35	549.35	549.35	549.35	0.00	0.00
O40-2-1-5	577.85	601.43	603.35	666.88	573.11	0.83	5.28
O40-2-1-6	492.06	525.27	492.06	492.06	489.14	0.60	0.60
O40-2-1-7	545.21	550.93	545.21	545.21	528.80	3.10	3.10
O40-2-1-8	431.92	455.46	430.07	473.46	427.55	1.02	0.59
O40-2-1-9	579.27	602.79	601.79	668.05	578.85	0.07	3.96
Avg						3.00	3.23
A40-2-1-0	636.15	636.28	551.33	631.55	550.20	15.62	0.21
A40-2-1-1	606.64	644.56	616.86	622.47	597.17	1.59	3.30
A40-2-1-2	587.75	587.75	582.03	583.37	582.03	0.98	0.00
A40-2-1-3	506.85	506.85	508.34	559.68	505.21	0.32	0.62
A40-2-1-4	573.67	573.78	568.42	570.30	567.77	1.04	0.11
A40-2-1-5	683.98	697.73	617.34	703.95	617.34	10.79	0.00
A40-2-1-6	587.71	660.17	569.77	572.96	537.91	9.26	5.92
A40-2-1-7	615.47	645.69	605.92	703.23	542.06	13.54	11.78
A40-2-1-8	624.30	670.44	624.30	702.84	600.61	3.94	3.94
A40-2-1-9	697.84	724.57	697.60	816.89	632.33	10.36	10.32
Avg						6.75	3.62

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Table 16. Meta-heuristics results for instances with 60 requestss

Instance	GRASP		ILS		GRASP-ILS
Instance	Zmin	Zavg	Zmin	Zavg	Zmin	ImpGRASP-ILS, GRASP	ImpGRASP-ILS, ILS
I60-2-1-0	971.76	930.24	954.90	1040.17	911.77	6.58	4.73
I60-2-1-1	997.55	990.98	997.55	1070.57	987.76	0.99	0.99
I60-2-1-2	893.43	879.02	897.08	1033.44	877.23	1.85	2.26
I60-2-1-3	907.53	902.23	901.81	1008.95	882.44	2.84	2.20
I60-2-1-4	979.14	967.49	975.61	1121.17	896.87	9.17	8.78
I60-2-1-5	1004.53	997.95	1004.53	1065.50	996.95	0.76	0.76
I60-2-1-6	1061.43	1051.96	1056.81	1093.90	1043.88	1.68	1.24
I60-2-1-7	1005.16	981.49	950.37	1110.89	944.32	6.44	0.64
I60-2-1-8	882.39	854.26	854.36	965.17	818.94	7.75	4.33
I60-2-1-9	890.19	877.62	870.52	1028.26	865.24	2.88	0.61
Avg						4.09	2.65
O60-2-1-0	713.15	746.03	703.50	758.65	652.35	9.32	3.73
O60-2-1-1	820.25	872.50	782.50	820.53	746.22	9.92	0.55
O60-2-1-2	782.26	799.70	761.74	868.31	732.49	6.79	0.15
O60-2-1-3	847.18	875.98	820.05	853.67	787.76	7.54	0.52
O60-2-1-4	776.48	845.20	771.15	817.65	727.32	6.76	0.64
O60-2-1-5	820.66	851.19	763.93	844.07	752.74	9.02	0.40
O60-2-1-6	708.48	714.50	680.46	680.46	680.46	4.12	0.00
O60-2-1-7	816.27	830.39	781.70	811.56	752.96	8.41	1.16
O60-2-1-8	723.94	759.78	715.02	806.47	695.58	4.08	0.00
O60-2-1-9	783.28	871.56	747.26	771.70	723.61	8.25	0.18
Avg						7.42	0.73
A60-2-1-0	858.31	858.31	836.63	929.83	836.54	2.60	0.01
A60-2-1-1	956.96	1024.04	952.71	1049.60	911.33	5.01	4.54
A60-2-1-2	719.41	741.14	776.51	778.37	703.79	2.22	10.33
A60-2-1-3	849.45	928.96	802.22	912.04	781.73	8.66	2.62
A60-2-1-4	857.32	880.81	841.54	899.44	793.69	8.02	6.03
A60-2-1-5	808.57	830.08	761.17	803.11	740.28	9.22	2.82
A60-2-1-6	803.29	862.81	803.29	871.89	754.71	6.44	6.44
A60-2-1-7	853.23	853.23	802.72	905.31	780.28	9.35	2.88
A60-2-1-8	780.61	815.35	772.43	843.73	751.38	3.89	2.80
A60-2-1-9	763.12	795.25	762.09	825.88	705.99	8.09	7.95
Avg						6.35	4.64

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Table 17. Meta-heuristics results for instances with 100 requests

Instance	GRASP		ILS		GRASP-ILS
Instance	Zmin	Zavg	Zmin	Zavg	Zmin	ImpGRASP-ILS, GRASP	ImpGRASP-ILS, ILS
I100-2-1-0	1638.35	1704.61	1609.09	1890.61	1500.16	9.21	7.26
I100-2-1-1	1475.76	1550.51	1462.03	1720.88	1399.61	5.44	4.46
I100-2-1-2	1549.56	1714.37	1519.43	1792.65	1481.37	4.60	2.57
I100-2-1-3	1541.71	1630.81	1516.8	1799.58	1406.15	9.64	7.87
I100-2-1-4	1586.41	1607.53	1501.97	1774.75	1471.77	7.79	2.05
I100-2-1-5	1547.53	1591.87	1476.42	1763.20	1465.71	5.58	0.73
I100-2-1-6	1594.07	1622.95	1501.05	1791.06	1482.92	7.50	1.22
I100-2-1-7	1568.12	1653.99	1508.18	1741.59	1439.77	8.91	4.75
I100-2-1-8	1340.87	1424.62	1358.42	1513.15	1277.58	4.95	6.33
I100-2-1-9	1393.89	1430.99	1346.03	1604.42	1286.29	8.37	4.64
Avg						7.20	4.19
O100-2-1-0	1279.18	1347.70	1252.87	1352.97	1215.92	5.20	3.04
O100-2-1-1	1169.86	1255.83	1149.36	1236.94	1113.13	5.10	3.25
O100-2-1-2	1123.63	1191.98	1098.08	1156.11	1066.12	5.39	3.00
O100-2-1-3	1272.18	1320.34	1209.93	1297.75	1166.47	9.06	3.73
O100-2-1-4	1278.7	1376.42	1206.94	1273.12	1146.62	11.52	5.26
O100-2-1-5	1282.2	1310.21	1264.78	1444.76	1223.53	4.80	3.37
O100-2-1-6	1112.92	1195.06	1099.75	1266.59	1062.43	4.75	3.51
O100-2-1-7	1271.97	1338.24	1231.68	1310.19	1224.31	3.89	0.60
O100-2-1-8	1071.1	1141.54	1000.51	1190.17	971.56	10.25	2.98
O100-2-1-9	1163.25	1211.45	1197.58	1339.77	1098.25	5.92	9.04
Avg						6.59	3.78
A100-2-1-0	1280.19	1361.66	1265.52	1359.89	1212.68	5.57	4.36
A100-2-1-1	1362.77	1431.84	1362.04	1541.04	1271.73	7.16	7.10
A100-2-1-2	1183.91	1240.90	1159.67	1326.68	1129.63	4.81	2.66
A100-2-1-3	1214.65	1288.61	1198.17	1355.01	1162.85	2.73	3.04
A100-2-1-4	1236.76	1325.19	1243.54	1400.64	1190.23	3.91	4.48
A100-2-1-5	1177.71	1241.31	1144.83	1228.66	1093.48	7.70	4.70
A100-2-1-6	1270.56	1328.54	1256.54	1336.74	1208.76	5.11	3.95
A100-2-1-7	1227.98	1308.64	1221.57	1316.30	1174.24	4.58	4.03
A100-2-1-8	1210.54	1298.73	1192.27	1288.85	1154.51	3.99	3.27
A100-2-1-9	1271.11	1320.95	1253.95	1419.94	1217.18	4.43	3.02
Avg						5.00	4.06

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Table 18. Cost savings for instances with 20 requests

Instance	Non-collaboration		Collaboration
Instance	Cost	NV	Cost	NV	$\phi$
I20-2-1-0	528.74	5	459.26	3	13.14
I20-2-1-1	477.54	4	366.66	2	23.22
I20-2-1-2	612.48	4	478.19	3	21.93
I20-2-1-3	481.75	4	360.24	2	25.22
I20-2-1-4	491.83	4	383.24	2	22.08
I20-2-1-5	427.16	4	343.7	2	19.54
I20-2-1-6	453.01	5	344.51	2	23.95
I20-2-1-7	476.59	4	354.59	2	25.60
I20-2-1-8	484.62	4	351.37	2	27.50
I20-2-1-9	622.55	5	476.32	3	23.49
Avg		4.3		2.3	22.57
O20-2-1-0	283.63	4	240.46	2	15.22
O20-2-1-1	299.27	4	260.84	2	12.84
O20-2-1-2	336.31	4	250.62	2	25.48
O20-2-1-3	316.26	4	254.79	2	19.44
O20-2-1-4	329.42	5	273.79	2	16.89
O20-2-1-5	323.26	4	269.61	2	16.60
O20-2-1-6	293.28	4	260.31	2	11.24
O20-2-1-7	348.76	4	245.95	2	29.48
O20-2-1-8	296.46	4	240.28	2	18.95
O20-2-1-9	263.93	4	229.92	2	12.89
Avg		4.1		2	17.90
A20-2-1-0	403.54	4	362.31	2	10.22
A20-2-1-1	494.62	4	444.8	3	10.07
A20-2-1-2	383.46	5	329.67	2	14.03
A20-2-1-3	410.31	5	363.62	2	11.38
A20-2-1-4	386.48	4	343.77	2	11.05
A20-2-1-5	302.36	4	287.74	2	4.83
A20-2-1-6	371.57	4	338.23	2	8.97
A20-2-1-7	333.01	4	290.21	2	12.85
A20-2-1-8	358.15	4	314.2	2	12.27
A20-2-1-9	367.36	4	323.6	2	11.91
Avg		4.2			10.76

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Table 19. Cost savings for instances with 40 requests

Instance	Non- collaboration		Collaboration
Instance	Cost	NV	Cost	NV	$\phi$
I40-2-1-0	1021.39	8	706.64	6	30.82
I40-2-1-1	861.87	8	600.90	6	30.28
I40-2-1-2	1006.32	8	729.24	6	27.53
I40-2-1-3	943.17	8	651.55	6	30.92
I40-2-1-4	1062.08	8	699.59	6	34.13
I40-2-1-5	930.23	8	647.36	6	30.41
I40-2-1-6	874.73	8	590.24	6	32.52
I40-2-1-7	910.38	8	612.68	6	32.70
I40-2-1-8	841.23	8	573.59	6	31.82
I40-2-1-9	843.80	8	598.44	6	29.08
Avg		8		6	31.02
O40-2-1-0	650.32	7	494.73	3	23.93
O40-2-1-1	574.51	7	434.04	3	24.45
O40-2-1-2	578.02	7	445.80	3	22.87
O40-2-1-3	692.40	8	523.35	4	24.42
O40-2-1-4	749.51	7	549.35	4	26.71
O40-2-1-5	750.72	8	573.11	4	23.66
O40-2-1-6	636.65	7	492.06	4	22.71
O40-2-1-7	734.12	7	528.80	3	27.97
O40-2-1-8	553.40	7	427.55	3	22.74
O40-2-1-9	746.28	8	578.85	4	22.43
Avg		7.3		3.5	24.19
A40-2-1-0	686.52	8	550.2	4	19.86
A40-2-1-1	730.78	7	597.17	4	18.28
A40-2-1-2	708.31	8	582.03	4	17.83
A40-2-1-3	662.45	8	505.21	4	23.74
A40-2-1-4	667.54	8	567.77	4	14.95
A40-2-1-5	714.79	7	617.34	4	13.63
A40-2-1-6	610.43	7	537.91	3	11.88
A40-2-1-7	639.30	7	542.06	4	15.21
A40-2-1-8	695.09	7	600.61	4	13.59
A40-2-1-9	739.69	8	632.33	4	14.51
Avg		7.5		3.9	16.35

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Table 20. Cost savings for instances with 60 requests

Instance	Non- collaboration		Collaboration
Instance	Cost	NV	Cost	NV	$\phi$
I60-2-1-0	1405.67	11	911.77	6	35.14
I60-2-1-1	1466.10	10	987.76	7	32.63
I60-2-1-2	1326.57	12	877.23	6	33.87
I60-2-1-3	1381.98	12	882.44	6	36.15
I60-2-1-4	1341.28	11	896.87	5	33.13
I60-2-1-5	1438.62	11	996.95	7	30.70
I60-2-1-6	1575.24	13	1043.88	7	33.73
I60-2-1-7	1384.43	10	944.32	6	31.79
I60-2-1-8	1245.97	10	818.94	5	34.27
I60-2-1-9	1266.52	10	865.24	8	31.68
Avg		11		6.3	33.31
O60-2-1-0	920.63	8	652.35	5	29.14
O60-2-1-1	1049.04	11	742.55	4	29.22
O60-2-1-2	1092.15	11	732.49	5	32.93
O60-2-1-3	1083.86	11	787.76	5	27.32
O60-2-1-4	1031.74	11	727.32	5	29.51
O60-2-1-5	981.97	10	752.74	5	23.34
O60-2-1-6	956.39	9	680.46	5	28.85
O60-2-1-7	1052.40	11	752.96	5	28.45
O60-2-1-8	977.50	9	695.58	5	28.84
O60-2-1-9	959.39	10	723.61	5	24.58
Avg		10.1	4.9	4.9	28.22
A60-2-1-0	1133.63	11	836.54	6	26.21
A60-2-1-1	1187.66	10	911.33	6	23.27
A60-2-1-2	956.53	10	703.79	5	26.42
A60-2-1-3	969.58	10	781.73	5	19.37
A60-2-1-4	1074.74	10	793.69	5	26.15
A60-2-1-5	984.88	9	740.28	5	24.84
A60-2-1-6	999.87	10	754.71	5	24.52
A60-2-1-7	1061.10	11	780.28	5	26.46
A60-2-1-8	962.43	11	751.38	5	21.93
A60-2-1-9	941.98	9	705.99	5	25.05
Avg		10.1	5.2	5.2	24.42

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Table 21. Cost savings for instances with 100 requests

Instance	Non- collaboration		Collaboration
Instance	Cost	NV	Cost	NV	$\phi$
I100-2-1-0	2741.02	20	1500.16	10	45.27
I100-2-1-1	2308.06	17	1399.61	10	39.36
I100-2-1-2	2634.95	19	1481.37	10	43.78
I100-2-1-3	2517.73	18	1406.15	10	44.15
I100-2-1-4	2275.46	17	1471.77	9	35.32
I100-2-1-5	2393.39	17	1465.71	10	38.76
I100-2-1-6	2635.37	19	1482.92	10	43.73
I100-2-1-7	2628.76	19	1439.77	10	45.23
I100-2-1-8	1910.26	15	1277.58	9	33.12
I100-2-1-9	2337.01	17	1286.29	10	44.96
Avg		17.8		9.8	41.37
O100-2-1-0	1791.81	15	1215.92	9	32.14
O100-2-1-1	1692.20	14	1113.13	8	34.22
O100-2-1-2	1690.38	14	1066.12	8	36.93
O100-2-1-3	1803.45	15	1166.47	9	35.32
O100-2-1-4	1641.55	14	1146.62	9	30.15
O100-2-1-5	1924.70	15	1223.53	9	36.43
O100-2-1-6	1606.09	14	1062.43	8	33.85
O100-2-1-7	1786.01	14	1224.31	9	31.45
O100-2-1-8	1538.25	13	971.56	7	36.84
O100-2-1-9	1582.04	13	1098.25	8	30.58
Avg		14.1		8.4	33.79
A100-2-1-0	1760.57	14	1212.68	9	31.12
A100-2-1-1	1809.52	15	1271.73	9	29.72
A100-2-1-2	1717.81	14	1129.63	8	34.24
A100-2-1-3	1497.94	10	1162.85	8	22.37
A100-2-1-4	1611.69	14	1190.23	9	26.15
A100-2-1-5	1613.52	14	1093.48	8	32.23
A100-2-1-6	1895.50	15	1208.76	9	36.23
A100-2-1-7	1764.98	14	1174.24	8	33.47
A100-2-1-8	1764.23	14	1154.51	9	34.56
A100-2-1-9	1727.48	14	1217.18	10	29.54
Avg		13.8		8.7	30.96

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Table 4. Notations of performance indicators and their description

Notations	Description
UB	The best cost obtained by CPLEX solver in a preset running time.
LB	The lower bound obtained by CPLEX solver in a preset running time
Ini	The cost of the best initial solution obtained by GRASP-ILS
Zmin	The best cost of 10 runs for each meta-heuristic
Zavg	The average cost of 10 runs for each meta-heuristic
Dev	The standard deviation of the costs obtained in ten runs by each meta-heuristic.
$Imp_{Ini}$	The improvement of best cost over Ini. For CPLEX solver $Imp_{Ini}$ is calculated by ${{(UB - Ini)} / {UB}}100\%$ For meta-heuristics, $Imp_{Ini}$ is calculated by$ {{({z_{min}} - Ini)} /{{z_{min}}}}100\%$
$Gap_{LB}$	The percentage gap between the best cost and LB. For CPLEX solver, $Gap_{LB}$ is calculated by $Gap_{LB} = {{(UB - Ini)} /{UB}}100\%$ For meta-heuristics, $Gap_{LB}$ is calculated by$ {{({z_{min}} - LB)} /{{z_{min}}}}100\%$
$Imp_{Cplex}$	The improvement of the best cost obtained by meta-heuristics over the best cost obtained by CPLEX solver.$Imp_{Cplex}$ is calculated as:${{(UB - {z_{min}})} /{UB}}*100\%$
$Imp_{GRASP-ILS,GRASP}$	The improvement of over. It is calculated as: ${{({Z_{min,GRASP}} - {z_{min,GRASP - ILS}})} / {{z_{min,GRASP - ILS}}}}*100\%$
$Imp_{GRASP-ILS,ILS}$	The improvement of over. It is calculated as: ${{({Z_{min,ILS}} - {z_{min,GRASP - ILS}})} / {{z_{min,GRASP - ILS}}}}*100\%$
NV	The average total number of vehicles used in the transportation
$Cost_{N}$	The total transportation cost of the shippers without collaboration obtained by CPLEX solver.
$Cost_{C}$	The total transportation cost of the shippers with collaboration, which is the best objective value of CPLEX solver and GRASP-ILS.
$\phi$	The cost savings in percentage achieved by the collaboration among the shippers. is defined as: ${{({Cost_N} - {Cost_C})} /{{Cost_N}}}*100\%$
$CPU_{avg}$	The average execution time in seconds for meta-heuristics

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