Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences

Shoufeng Ji; Jinhuan Tang; Minghe Sun; Rongjuan Luo

doi:10.3934/jimo.2021051

Article Contents

2022, Volume 18, Issue 3: 1949-1977. Doi: 10.3934/jimo.2021051

This issue Previous Article Multi-aircraft cooperative path planning for maneuvering target detection Next Article Fresh produce price-setting newsvendor with bidirectional option contracts

Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences

1.
School of Business Administration, Northeastern University, Shenyang 110167, China
2.
School of Economics and Management, Shenyang Aerospace University, Shenyang 110136, China
3.
Department of Management Science and Statistics, University of Texas at San Antonio, San Antonio, TX 78249-0632, USA

^* Corresponding author: Dr Rongjuan Luo
^* Corresponding author: Dr Rongjuan Luo

Received: July 2020

Revised: January 2021

Published: May 2022

This research was supported by National Science Foundation of China [grant numbers 71572031, 71971049 and 71702112]

Abstract Full Text(HTML) Figure(7) / Table(8) Related Papers Cited by

Abstract

A combined location-routing-inventory system (CLRIS) in a three-echelon supply chain network is studied with environmental considerations. Specifically, a bi-objective mixed integer programming model is formulated for the CLRIS to deal with the trade-offs between the total cost and the carbon-capped difference (CCD). A multi-objective particle swarm optimization (MOPSO) heuristic solution procedure is developed and implemented to solve the bi-objective mixed integer programming problem. The bi-objective mixed integer programming model and the MOPSO heuristic procedure are applied to a real-life problem as an illustrative example. The approximate nondominated frontier formed by solutions not dominated by others can be used for the decision makers to make trade-offs between the total cost and the CCD. Sensitivity analyses are conducted, and the relationship among the carbon cap, CCD, the total cost and the carbon prices are examined, and relevant managerial insights are provided. Comparisons with other existing algorithms show that the MSPSO heuristic procedure has very good performance.

Keywords:

Mathematics Subject Classification: Primary: 65K05; Secondary: 90C08.

Citation:

Full Text(HTML)

Figure 1. A three-echelon supply chain network

Download: Full-size image PowerPoint slide

Figure 2. Locations of the Plants, the potential DCs and the Retailers

Download: Full-size image PowerPoint slide

Figure 3. The nondominated frontier of the CLRIS considering CCD

Download: Full-size image PowerPoint slide

Figure 4. The nondominated frontier of the CLRIS considering carbon emissions

Download: Full-size image PowerPoint slide

Figure 5. Nondominated frontiers of the model minimizing CCD by varying the carbon cap

Download: Full-size image PowerPoint slide

Figure 6. Box plots for the three evaluation indicators

Download: Full-size image PowerPoint slide

Figure 7. The obtained nondominated frontiers of the all three procedures

Download: Full-size image PowerPoint slide

Table 1. Summary of relevant literature for low carbon supply chains

Literature category	Issues considered	Related publications
Translating carbon emissions into cost	Carbon cost; carbon price; pollution cost; cap-and-trade; emissions trading scheme	Tseng and Hung [44]; Treitl et al. [43]; Alhaj et al. [1]; Bai et al. [5]; Wang, Tao and Shi [50].
Treating carbon emissions as a constraint in supply chain models	Carbon footprints; carbon-constrained	Benjaafar et al. [8]; Xu et al. [53]; Lam and Gu [23]; Martí et al. [26].
Policies for carbon emission reduction	Carbon trading; carbon tax	Bazan et al. [7]; Wang et al. [47]; Wang, Zhao and Herty [49]; Saxena et al. [34]; Xin et al. [51]; Huang et al. [18]; Samuel et al. [33].
Multiple objectives with carbon emissions	Trade-offs between cost and environment	Paksoy et al. [30]; Musavi and Bozorgi-Amiri [29]; Daryanto et al. [10].
Carbon emission reduction with coordination mechanisms	Green production; green purchasing; coordination mechanism; life cycle assessment	Palmer [31]; Jaber et al. [19]; Du et al. [13]; Xu et al. [52]; Zhang et al. [56].
Supply chain network design	Location; routing; inventory	Min et al. [27]; Wang, Tao and Shi [50]; Javid and Azad [20]; Farahani et al. [15]; Tang et al. [42]; Zhalechian et al. [55].

| Show Table

DownLoad: CSV

Table 2. Distances from the plants to the potential DCs (km)

	Shenbei	Yuhong	Sujiatun	Dongling
Fushun	77.5	71.1	64.6	36.5
Liaoyang	112.8	65.5	44.7	35.8

| Show Table

DownLoad: CSV

Table 3. Parameters of the potential DCs

	Shenbei	Yuhong	Sujiatun	Dongling
Lead time (days)	3	2	3	4
Service level	95%	95%	95%	95%

| Show Table

DownLoad: CSV

Table 4. Areas and fixed costs of the potential DCs

	Capacity (ton)	Fixed cost per period ()	Holding cost (/ton/day)	Areas (m2)
Shenbei	340	20000	0.20	1100
Yuhong	500	18000	0.25	1600
Sujiatun	310	11200	0.20	1000
Dongling	380	15600	0.25	1200

| Show Table

DownLoad: CSV

Table 5. Details of some typical solutions on the nondominated frontier

Solutions	Plants	DC Status				Total cost	CCD
Solutions	Plants	Shenbei	Yuhong	Sujiatun	Dongling	Total cost	CCD
1	Fushun	1	0	1	1	80153.5	4451.7
1	Liaoyang	1	0	0	0	80153.5	4451.7
2	Fushun	1	1	0	1	81875.5	3677.2
2	Liaoyang	1	1	0	0	81875.5	3677.2
3	Fushun	0	1	0	1	88125.9	3025.7
3	Liaoyang	1	1	0	0	88125.9	3025.7
4	Fushun	1	1	0	1	93750.3	2418.4
4	Liaoyang	1	1	0	1	93750.3	2418.4
5	Fushun	1	1	0	1	100104.9	1975.1
5	Liaoyang	1	1	1	0	100104.9	1975.1
6	Fushun	1	1	1	0	110139.3	1575.7
6	Liaoyang	1	0	1	0	110139.3	1575.7
7	Fushun	1	1	1	0	117697.4	1273.5
7	Liaoyang	1	1	1	0	117697.4	1273.5
8	Fushun	0	1	1	1	122385.8	968.1
8	Liaoyang	0	1	1	1	122385.8	968.1
9	Fushun	1	1	1	1	134982.2	613.9
9	Liaoyang	0	1	1	1	134982.2	613.9

| Show Table

DownLoad: CSV

Table 6. Values of the evaluation indicators for MOPSO, NSGAII and MOEA/D

	Convergence			Diversity			Dominance
	MOPSO	NSGAII	MOEA/D	MOPSO	NSGAII	MOEA/D	MOPSO	NSGAII	MOEA/D
1	0.258	0.179	2.320	0.507	0.518	0.691	0.909	0.476	0.000
2	0.126	0.251	2.261	0.520	0.494	0.775	0.878	0.466	0.000
3	0.193	0.142	1.208	0.508	0.540	0.694	0.814	0.485	0.000
4	0.170	0.254	1.273	0.516	0.482	0.841	0.828	0.441	0.000
5	0.160	0.244	1.679	0.468	0.471	0.738	0.913	0.428	0.000
6	0.158	0.260	1.741	0.559	0.479	0.808	0.820	0.463	0.000
7	0.137	0.241	1.375	0.493	0.497	0.698	0.826	0.535	0.000
8	0.177	0.106	2.207	0.480	0.627	0.817	0.775	0.517	0.000
9	0.233	0.092	1.471	0.516	0.545	0.728	0.789	0.371	0.000
10	0.250	0.103	1.050	0.455	0.493	0.713	0.834	0.526	0.000
11	0.239	0.171	1.607	0.521	0.598	0.789	0.817	0.330	0.000
12	0.106	0.179	1.800	0.485	0.557	0.804	0.892	0.326	0.000
13	0.146	0.188	1.952	0.406	0.533	0.724	0.884	0.478	0.000
14	0.131	0.181	1.667	0.490	0.493	0.704	0.871	0.448	0.000
15	0.115	0.158	2.385	0.433	0.449	0.779	0.905	0.476	0.000
16	0.158	0.195	2.158	0.530	0.482	0.662	0.868	0.557	0.000
17	0.122	0.268	1.276	0.480	0.485	0.710	0.841	0.486	0.000
18	0.193	0.169	1.727	0.489	0.517	0.663	0.892	0.546	0.000
19	0.168	0.220	1.700	0.550	0.576	0.637	0.926	0.403	0.000
20	0.172	1.295	1.333	0.478	0.567	0.787	0.833	0.353	0.000
21	0.143	1.724	1.696	0.502	0.517	0.708	0.866	0.303	0.000

| Show Table

DownLoad: CSV

Table A1. Distances from the potential DCs to the retailers (km)

	Shenbei	Yuhong	Dongling
1	82.6	47.7	55.6
2	80.1	47.0	37.3
3	80.5	27.9	54.2
4	64.5	35.7	42.3
5	62.3	40.0	47.3
6	64.6	49.8	15.7
7	61.2	55.6	7.0
8	58.2	45.0	27.3
9	64.2	36.1	49.1
10	66.1	27.2	49.5
11	66.0	12.0	50.0
12	66.2	48.2	60.1
13	63.8	60.6	12.0
14	56.6	40.2	58.9
15	55.2	35.2	67.1
16	58.1	7.0	55.3
17	62.1	54.2	42.0
18	56.9	42.1	41.1
19	50.3	38.4	47.9
20	45.7	39.0	52.1
21	50.1	32.2	50.0
22	50.1	12.0	57.1
23	40.1	36.1	37.0
24	50.1	48.9	12.2
25	30.2	45.9	52.1
26	25.8	40.1	67.1
27	32.1	40.2	55.3
28	23.2	38.4	55.3
29	25.8	42.6	65.1
30	22.4	48.9	54.2
31	20.5	52.6	62.1
32	23.7	46.0	70.1
33	7.0	55.6	66.2
34	15.0	61.3	72.1

| Show Table

DownLoad: CSV

Table A2. Distances between the retailers (km)

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34
1	0.0	17.1	15.9	18.7	50.2	52.5	55.6	52.5	48.9	50.2	49.5	48.9	58.8	52.5	47.9	51.1	60.0	50.1	52.5	49.1	50.2	50.2	55.3	55.3	56.3	52.1	56.3	62.3	67.3	69.2	70.1	75.2	77.1
2	17.1	0.0	18.7	7.0	10.1	18.8	50.2	20.1	15.9	15.9	24.1	52.5	55.1	18.8	19.8	45.1	53.2	47.1	20.1	50.2	50.2	51.2	53.2	54.7	55.7	53.2	54.9	66.1	66.1	67.1	67.1	69.2	70.1
3	15.9	18.7	0.0	17.3	47.5	49.9	52.1	48.5	45.2	17.3	16.6	16.8	60.0	45.2	47.5	45.7	60.0	49.9	45.1	46.2	44.1	50.3	60.3	60.0	57.3	49.8	55.1	57.3	57.3	60.1	61.3	67.1	68.9
4	18.7	7.0	17.3	0.0	7.0	55.1	40.1	30.2	25.1	7.0	15.2	32.1	41.9	30.2	27.1	25.7	41.9	56.2	30.2	29.5	35.1	26.7	36.9	36.3	41.9	39.1	36.9	50.1	53.4	57.3	59.9	64.7	66.3
5	50.2	10.1	47.5	7.0	0.0	7.0	49.6	7.2	5.9	28.1	50.5	25.8	32.6	27.1	13.8	45.1	32.6	44.3	40.1	46.2	49.9	43.2	32.6	36.6	39.8	39.8	37.6	55.3	55.3	59.9	62.0	65.0	66.0
6	52.5	18.8	49.9	55.1	7.0	0.0	18.8	8.7	20.4	24.1	29.4	48.9	55.1	55.1	57.8	35.9	54.1	55.1	54.1	32.4	48.9	58.8	57.8	48.9	53.9	54.8	55.5	58.4	58.7	62.4	67.1	68.6	68.1
7	55.6	50.2	52.1	40.1	49.6	18.8	0.0	18.8	49.6	50.2	47.1	52.1	5.1	49.6	50.2	54.1	10.0	49.8	47.1	50.1	52.1	48.6	19.8	19.6	23.8	50.1	50.2	49.2	46.3	54.1	59.2	59.2	60.1
8	52.5	20.1	48.5	30.2	7.2	8.7	18.8	0.0	6.4	15.6	20.6	28.7	19.6	14.2	20.6	35.9	19.6	24.2	22.1	20.6	28.7	19.6	20.6	28.7	30.7	32.5	34.6	50.3	45.3	50.3	54.2	55.2	66.4
9	48.9	15.9	45.2	25.1	5.9	20.4	49.6	6.4	0.0	15.2	18.9	25.8	26.8	6.4	15.2	35.6	26.8	27.8	10.1	35.6	38.9	30.2	38.9	39.7	40.1	37.8	41.1	45.6	45.8	47.6	50.2	50.6	50.9
10	50.2	15.9	17.3	7.0	28.1	24.1	50.2	15.6	15.2	0.0	5.0	17.3	55.1	15.2	5.0	15.9	45.2	36.8	15.2	36.8	38.8	39.6	45.2	43.2	43.2	40.1	43.2	45.4	47.9	47.4	45.2	52.1	52.0
11	50.2	24.1	16.6	15.2	50.5	29.4	47.1	20.6	18.9	5.0	0.0	10.0	45.9	27.1	9.0	7.1	27.1	20.1	16.9	16.9	17.5	18.9	27.1	26.7	27.1	25.9	32.2	36.5	45.9	47.2	46.2	53.1	53.0
12	48.9	52.5	16.8	32.1	25.8	48.9	52.1	28.7	25.8	17.3	10.0	0.0	60.0	25.8	9.2	10.0	50.0	40.3	25.8	11.2	12.3	40.3	49.0	45.1	44.3	40.3	44.5	40.3	50.1	53.7	56.5	58.2	59.9
13	58.8	55.1	60.0	41.9	32.6	55.1	5.1	19.6	26.8	55.1	45.9	60.0	0.0	35.6	41.9	45.9	12.1	20.3	32.6	50.1	45.9	35.6	17.0	43.1	45.1	55.1	58.1	59.8	45.1	62.8	69.1	59.8	60.2
14	52.5	18.8	45.2	30.2	27.1	55.1	49.6	14.2	6.4	15.2	27.1	25.8	35.6	0.0	6.2	15.2	45.1	16.1	5.9	23.3	29.1	20.1	40.1	38.7	38.5	29.1	32.1	37.7	39.8	42.3	45.2	46.6	47.9
15	47.9	19.8	47.5	27.1	13.8	57.8	50.2	20.6	15.2	5.0	9.0	9.2	41.9	6.2	0.0	15.2	45.7	48.9	10.2	15.6	20.1	21.2	40.7	41.2	40.2	38.0	40.2	43.5	45.1	47.9	47.1	48.2	48.9
16	51.1	45.1	45.7	25.7	45.1	35.9	54.1	35.9	35.6	15.9	7.1	10.0	45.9	15.2	15.2	0.0	37.1	29.1	25.7	10.1	11.1	23.4	37.1	32.7	33.3	23.4	30.0	31.2	36.1	46.1	45.2	47.7	49.2
17	60.0	53.2	60.0	41.9	32.6	54.1	10.0	19.6	26.8	45.2	27.1	50.0	12.1	45.1	45.7	37.1	0.0	18.7	21.1	45.2	44.5	25.6	8.8	18.7	25.5	45.2	46.6	55.8	45.1	50.1	68.1	63.1	60.0
18	52.1	50.2	45.2	39.1	49.8	18.8	10.0	22.1	25.9	40.1	23.1	48.9	15.0	25.9	57.8	31.2	11.9	7.7	18.8	40.1	44.4	21.8	7.5	44.4	24.5	43.1	46.8	48.7	40.1	45.1	55.1	58.1	58.7
19	50.1	47.1	49.9	56.2	44.3	55.1	49.8	24.2	27.8	36.8	20.1	40.3	20.3	16.1	48.9	29.1	18.7	0.0	7.4	35.9	40.6	10.0	22.7	20.0	24.7	27.8	35.7	40.7	49.7	50.7	52.3	57.9	58.7
20	52.5	20.1	45.1	30.2	40.1	54.1	47.1	22.1	10.1	15.2	16.9	25.8	32.6	5.9	10.2	25.7	21.1	7.4	0.0	20.1	25.5	5.6	27.6	28.7	32.5	30.7	35.7	45.1	45.0	43.1	48.7	49.2	50.1
21	49.1	50.2	46.2	29.5	46.2	32.4	50.1	20.6	35.6	36.8	16.9	11.2	50.1	23.3	15.6	10.1	45.2	35.9	20.1	0.0	8.5	22.2	40.7	34.5	32.1	18.7	24.5	38.0	42.7	43.0	43.7	45.6	46.5
22	50.2	50.2	44.1	35.1	49.9	48.9	52.1	28.7	38.9	38.8	17.5	12.3	45.9	29.1	20.1	11.1	44.5	40.6	25.5	8.5	0.0	27.8	45.2	40.1	38.1	18.9	26.0	30.1	44.1	44.6	45.0	46.7	48.0
23	50.2	51.2	50.3	26.7	43.2	58.8	48.6	19.6	30.2	39.6	18.9	40.3	35.6	20.1	21.2	23.4	25.6	10.0	5.6	22.2	27.8	0.0	27.1	14.2	15.8	20.7	24.2	33.3	38.9	40.1	43.3	45.1	45.2
24	55.3	53.2	60.3	36.9	32.6	57.8	19.8	20.6	38.9	45.2	27.1	49.0	17.0	40.1	40.7	37.1	8.8	22.7	27.6	40.7	45.2	27.1	0.0	13.6	19.5	33.2	34.8	45.2	33.8	38.5	46.1	55.1	50.1
25	55.3	54.7	60.0	36.3	36.6	48.9	19.6	28.7	39.7	43.2	26.7	45.1	43.1	38.7	41.2	32.7	18.7	20.0	28.7	34.5	40.1	14.2	13.6	0.0	6.1	18.9	17.0	41.8	20.0	25.0	40.0	45.2	46.1
26	56.3	55.7	57.3	41.9	39.8	53.9	23.8	30.7	40.1	43.2	27.1	44.3	45.1	38.5	40.2	33.3	25.5	24.7	32.5	32.1	38.1	15.8	19.5	6.1	0.0	20.0	17.9	36.1	30.1	36.1	36.2	37.1	38.2
27	52.1	53.2	49.8	39.1	39.8	54.8	50.1	32.5	37.8	40.1	25.9	40.3	55.1	29.1	38.0	23.4	45.2	27.8	30.7	18.7	18.9	20.7	33.2	18.9	20.0	0.0	7.3	18.2	36.2	38.1	38.1	40.2	44.2
28	56.3	54.9	55.1	36.9	37.6	55.5	50.2	34.6	41.1	43.2	32.2	44.5	58.1	32.1	40.2	30.0	46.6	35.7	35.7	24.5	26.0	24.2	34.8	17.0	17.9	7.3	0.0	13.5	30.1	36.9	40.2	42.1	43.5
29	62.3	66.1	57.3	50.1	55.3	58.4	49.2	50.3	45.6	45.4	36.5	40.3	59.8	37.7	43.5	31.2	55.8	40.7	45.1	38.0	30.1	33.3	45.2	41.8	36.1	18.2	13.5	0.0	35.6	37.3	20.0	45.2	46.2
30	67.3	66.1	57.3	53.4	55.3	58.7	46.3	45.3	45.8	47.9	45.9	50.1	45.1	39.8	45.1	36.1	45.1	49.7	45.0	42.7	44.1	38.9	33.8	20.0	30.1	36.2	30.1	35.6	0.0	7.2	37.3	30.2	32.1
31	69.2	67.1	60.1	57.3	59.9	62.4	54.1	50.3	47.6	47.4	47.2	53.7	62.8	42.3	47.9	46.1	50.1	50.7	43.1	43.0	44.6	40.1	38.5	25.0	36.1	38.1	36.9	37.3	7.2	0.0	25.6	20.1	26.1
32	70.1	67.1	61.3	59.9	62.0	67.1	59.2	54.2	50.2	45.2	46.2	56.5	69.1	45.2	47.1	45.2	68.1	52.3	48.7	43.7	45.0	43.3	46.1	40.0	36.2	38.1	40.2	20.0	37.3	25.6	0.0	38.2	45.6
33	75.2	69.2	67.1	64.7	65.0	68.6	59.2	55.2	50.6	52.1	53.1	58.2	59.8	46.6	48.2	47.7	63.1	57.9	49.2	45.6	46.7	45.1	55.1	45.2	37.1	40.2	42.1	45.2	30.2	20.1	38.2	0.0	8.2
34	77.1	70.1	68.9	66.3	66.0	68.1	60.1	66.4	50.9	52.0	53.0	59.9	60.2	47.9	48.9	49.2	60.0	58.7	50.1	46.5	48.0	45.2	50.1	46.1	38.2	44.2	43.5	46.2	32.1	26.1	45.6	8.2	0.0

| Show Table

DownLoad: CSV

Related Papers

Cited by

References

[1]	M. A. Alhaj, D. Svetinovic and A. Diabat, A carbon-sensitive two-echelon-inventory supply chain model with stochastic demand, Resources Conservation & Recycling, 108 (2016), 82-87. doi: 10.1016/j.resconrec.2015.11.011.
[2]	M. J. Amoshahy, M. Shamsi and M. H. Sedaaghi, A novel flexible inertia weight particle swarm optimization algorithm, PLoS One, 11 (2016), e0161558. doi: 10.1371/journal.pone.0161558.
[3]	Z. N. Ansari and R. Kant, A state-of-art literature review reflecting 15 years of focus on sustainable supply chain management, Journal of Cleaner Production, 142 (2017), 2524-2543. doi: 10.1016/j.jclepro.2016.11.023.
[4]	V. Artale, C. L. Milazzo, C. Orlando and A. Ricciardello, Comparison of GA and PSO approaches for the direct and LQR tuning of a multirotor PD controller, Journal of Industrial & Management Optimization, 13 (2017), 2067-2091. doi: 10.3934/jimo.2017032.
[5]	Q. Bai, J. Xu, F. Meng and N. Yu, Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning, Journal of Industrial & Management Optimization, 2020. doi: 10.3934/jimo.2020126.
[6]	J. C. Bansal, P. Singh, M. Saraswat, A. Verma, S. S. Jadon and A. Abraham, Inertia weight strategies in particle swarm optimization, in Third World Congress on Nature and Biologically Inspired Computing, Salamanca, 2011,633-640. doi: 10.1109/NaBIC.2011.6089659.
[7]	E. Bazan, M. Y. Jaber and S. Zanoni, Carbon emissions and energy effects on a two-level manufacturer-retailer closed-loop supply chain model with remanufacturing subject to different coordination mechanisms, International Journal of Production Economics, 183 (2017), 394-408. doi: 10.1016/j.ijpe.2016.07.009.
[8]	S. Benjaafar, Y. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transactions on Automation Science and Engineering, 10 (2012), 99-116. doi: 10.1109/TASE.2012.2203304.
[9]	J. Cong, T. Pang and H. Peng, Optimal strategies for capital constrained low-carbon supply chains under yield uncertainty, Journal of Cleaner Production, 256 (2020), 120339. doi: 10.1016/j.jclepro.2020.120339.
[10]	Y. Daryanto, H. M. Wee and R. D. Astanti, Three-echelon supply chain model considering carbon emission and item deterioration, Transportation Research Part E: Logistics and Transportation Review, 122 (2019), 368-383. doi: 10.1016/j.tre.2018.12.014.
[11]	K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: Nsga-II, IEEE Transactions on Evolutionary Computation, 6 (2002), 182-197. doi: 10.1109/4235.996017.
[12]	M. Desrochers and G. Laporte, Improvements and extensions to the miller-tucker-zemlin subtour elimination constraints, Operations Research Letters, 10 (1991), 27-36. doi: 10.1016/0167-6377(91)90083-2.
[13]	S. Du, J. Zhu, H. Jiao and W. Ye, Game-theoretical analysis for supply chain with consumer preference to low carbon, International Journal of Production Research, 53 (2015), 3753-3768. doi: 10.1080/00207543.2014.988888.
[14]	R. M. Everson, J. E. Fieldsend and S. Singh, Full elite sets for multi-objective optimisation, in I. C. Parmee (ed.), Adaptive Computing in Design and Manufacture, Springer, 2002,343-354. doi: 10.1007/978-0-85729-345-9_29.
[15]	R. Z. Farahani, H. Rashidi Bajgan, B. Fahimnia and M. Kaviani, Location-inventory problem in supply chains: A modelling review, International Journal of Production Research, 53 (2015), 3769-3788. doi: 10.1080/00207543.2014.988889.
[16]	A. Ghorbani and M. R. A. Jokar, A hybrid imperialist competitive-simulated annealing algorithm for a multisource multi-product location-routing-inventory problem, Computers & Industrial Engineering, 101 (2016), 116-127. doi: 10.1016/j.cie.2016.08.027.
[17]	K. Hoen, T. Tan, J. Fransoo and G. Van Houtum, Effect of carbon emission regulations on transport mode selection under stochastic demand, Flexible Services and Manufacturing Journal, 26 (2014), 170-195. doi: 10.1007/s10696-012-9151-6.
[18]	Y.-S. Huang, C. C. Fang and Y. A. Lin, Inventory management in supply chains with consideration of logistics, green investment and different carbon emissions policies, Computers & Industrial Engineering, 139 (2020), 106207. doi: 10.1016/j.cie.2019.106207.
[19]	M. Y. Jaber, C. H. Glock and A. M. El. Saadany, Supply chain coordination with emissions reduction incentives, International Journal of Production Research, 51 (2013), 69-82. doi: 10.1080/00207543.2011.651656.
[20]	A. A. Javid and N. Azad, Incorporating location, routing and inventory decisions in supply chain network design, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 582-597.
[21]	S. F. Ji, R. J. Luo and X. S. Peng, A probability guided evolutionary algorithm for multi-objective green express cabinet assignment in urban last-mile logistics, International Journal of Production Research, 57 (2019), 3382-3404. doi: 10.1080/00207543.2018.1533653.
[22]	J. Kennedy and R. Eberhart, Particle swarm optimization, in, IEEE International Conference on Neural Networks, Perth, Australia, 1995, 1942-1948. doi: 10.1109/ICNN.1995.488968.
[23]	J. S. L. Lam and Y. Gu, A market-oriented approach for intermodal network optimisation meeting cost, time and environmental requirements, International Journal of Production Economics, 171 (2016), 266-274. doi: 10.1016/j.ijpe.2015.09.024.
[24]	H. F. Ling, X. Z. Zhou, X. L. Jiang and Y. H. Xiao, Improved constrained multi-objective particle swarm optimization algorithm, Journal of Computer Applications, 32 (2012), 1320-1324. doi: 10.3724/SP.J.1087.2012.01320.
[25]	R. J. Luo, S. F. Ji and B. L. Zhu, A Pareto evolutionary algorithm based on incremental learning for a kind of multi-objective multidimensional knapsack problem, Computers & Industrial Engineering, 135 (2019), 537-559. doi: 10.1016/j.cie.2019.06.027.
[26]	J. M. C. Martí, J. S. Tancrez and R. W. Seifert, Carbon footprint and responsiveness trade-offs in supply chain network design, International Journal of Production Economics, 166 (2015), 129-142.
[27]	H. Min, V. Jayaraman and R. Srivastava, Combined location-routing problems: A synthesis and future research directions, European Journal of Operational Research, 108 (1998), 1-15. doi: 10.1016/S0377-2217(97)00172-0.
[28]	S. M. Mousavi, A. Bahreininejad, S. N. Musa and F. Yusof, A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network, Journal of Intelligent Manufacturing, 28 (2017), 191-206. doi: 10.1007/s10845-014-0970-z.
[29]	M. Musavi and A. Bozorgi-Amiri, A multi-objective sustainable hub location-scheduling problem for perishable food supply chain, Computers & Industrial Engineering, 113 (2017), 766-778. doi: 10.1016/j.cie.2017.07.039.
[30]	T. Paksoy, E. }Ozceylan and G. W. Weber, A multi objective model for optimization of a green supply chain network, AIP Conference Proceedings, 311 (2010), 1239. doi: 10.1063/1.3459765.
[31]	A. Palmer, The Development of an Integrated Routing and Carbon Dioxide Emissions Model for Goods Vehicles, Ph.D thesis, Cranfield University, London, 2007.
[32]	B. Qian, L. Wang, D.-X. Huang and X. Wang, Scheduling multi-objective job shops using a memetic algorithm based on differential evolution, The International Journal of Advanced Manufacturing Technology, 35 (2008), 1014-1027. doi: 10.1007/s00170-006-0787-9.
[33]	C. N. Samuel, U. Venkatadri, C. Diallo and A. Khatab, Robust closed-loop supply chain design with presorting, return quality and carbon emission considerations, Journal of Cleaner Production, 247 (2020), 119086. doi: 10.1016/j.jclepro.2019.119086.
[34]	L. K. Saxena, P. K. Jain and A. K. Sharma, Tactical supply chain planning for tyre remanufacturing considering carbon tax policy, The International Journal of Advanced Manufacturing Technology, 97 (2018), 1505-1528. doi: 10.1007/s00170-018-1972-3.
[35]	B. L. Shankar, S. Basavarajappa, J. C. Chen and R. S. Kadadevaramath, Location and allocation decisions for multi-echelon supply chain network-a multi-objective evolutionary approach, Expert Systems with Applications, 40 (2013), 551-562. doi: 10.1016/j.eswa.2012.07.065.
[36]	Y. Shi and R. C. Eberhart, Empirical study of particle swarm optimization, in Proceedings of Twelfth IEEE International Conference on Artificial Intelligence (IJCA), Washington, D. C., USA, 1999, 1945-1950. doi: 10.1109/CEC.1999.785511.
[37]	M. R. Sierra and C. A. C. Coello, Improving Pso-Based Multi-Objective Optimization Using Crowding, Mutation and $\varepsilon$-dominance, in, Third International Conference on Evolutionary Multi-Criterion Optimization, Evolutionary Multi-Criterion Optimization, Guanajuato, Mexico, 2005.
[38]	R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Applications, John Wiley and Sons, New York, 1986.
[39]	M. Sun, Interactive Multiple Objective Programming Procedures Via Adaptive Random Search and Feed-Forward Artificial Neural Networks, Ph.D. dissertation, the University of Georgia, Athens, GA, 1992.
[40]	M. Sun, Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures, European Journal of Operational Research, 162 (2005), 468-483. doi: 10.1016/j.ejor.2003.08.058.
[41]	M. Sun, Multiple objective programming, in J. Wang (ed.), Encyclopedia of Business Analytics and Optimization, IGI Global, Hershey, PA, 3 (2014), 1585-1604.
[42]	J. Tang, S. Ji and L. Jiang, The design of a sustainable location-routing-inventory model considering consumer environmental behavior, Sustainability, vol. 8, no. 3,211-231, 2016. doi: 10.3390/su8030211.
[43]	S. Treitl, P. C. Nolz, and W. Jammernegg, Incorporating environmental aspects in an inventory routing problem. a case study from the petrochemical industry, Flexible Services and Manufacturing Journal, 26 (2014), 143-169. doi: 10.1007/s10696-012-9158-z.
[44]	S. C. Tseng and S. W. Hung, A strategic decision-making model considering the social costs of carbon dioxide emissions for sustainable supply chain management, Journal of Environmental Management, 133 (2014), 315-322. doi: 10.1016/j.jenvman.2013.11.023.
[45]	S. Validi, A. Bhattacharya and P. Byrne, Integrated low-carbon distribution system for the demand side of a product distribution supply chain: A DoE-guided mopso optimiser-based solution approach, International Journal of Production Research, 52 (2014), 3074-3096. doi: 10.1080/00207543.2013.864054.
[46]	S. Prasanna Venkatesan and S. Kumanan, A multi-objective discrete particle swarm optimisation algorithm for supply chain network design, International Journal of Logistics Systems and Management, 11 (2012), 375-406. doi: 10.1504/IJLSM.2012.045919.
[47]	C. Wang, W. Wang and R. Huang, Supply chain enterprise operations and government carbon tax decisions considering carbon emissions, Journal of Cleaner Production, 152 (2017), 271-280. doi: 10.1016/j.jclepro.2017.03.051.
[48]	H. Wang and M. K. Lim, Two stage heuristic algorithm for logistics network optimization of integrated location-routing-inventory, in Recent Advances in Intelligent Manufacturing, Springer, 2018,209-217. doi: 10.1007/978-981-13-2396-6_19.
[49]	M. Wang, L. Zhao and M. Herty, Modelling carbon trading and refrigerated logistics services within a fresh food supply chain under carbon cap-and-trade regulation, International Journal of Production Research, 56 (2018), 4207-4225.
[50]	S. Wang, F. Tao and Y. Shi, Optimization of location-routing problem for cold chain logistics considering carbon footprint, International Journal of Environmental Research and Public Health, 15 (2018), 86-103. doi: 10.3390/ijerph15010086.
[51]	B. Xin, W. Peng and M. Sun, Optimal coordination strategy for international production planning and pollution abating under cap-and-trade regulations, International Journal of Environmental Research and Public Health, 16 (2019), article 3490 (21 pages). doi: 10.3390/ijerph16183490.
[52]	J. Xu, Q. Qi and Q. Bai, Coordinating a dual-channel supply chain with price discount contracts under carbon emission capacity regulation, Applied Mathematical Modelling, 56 (2018), 449-468. doi: 10.1016/j.apm.2017.12.018.
[53]	Z. Xu, A. Elomri, S. Pokharel, Q. Zhang, X. Ming and W. Liu, Global reverse supply chain design for solid waste recycling under uncertainties and carbon emission constraint, Waste Management, 64 (2017), 358-370. doi: 10.1016/j.wasman.2017.02.024.
[54]	H. Yu, Y. Tan, J. Zeng, C. Sun and Y. Jin, Surrogate-assisted hierarchical particle swarm optimization, Information Sciences, 454 (2018), 59-72. doi: 10.1016/j.ins.2018.04.062.
[55]	M. Zhalechian, R. Tavakkoli-Moghaddam, B. Zahiri and M. Mohammadi, Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty, Transportation Research Part E: Logistics and Transportation Review, 89 (2016), 182-214. doi: 10.1016/j.tre.2016.02.011.
[56]	M. Zhang, M. Sun, D. Bi and T. Liu, Green logistics development decision-making: Factor identification and hierarchical framework construction, IEEE Access, 2020, 127897-127912.
[57]	Q. Zhang and H. Li, MOEA/D: A multiobjective evolutionary algorithm based on decomposition, IEEE Transactions on Evolutionary Computation, 11 (2007), 712-731.