The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain

Jian Liu; Xin Wu; Jiang-Ling Lei

doi:10.3934/jimo.2021090

Article Contents

2022, Volume 18, Issue 4: 2749-2782. Doi: 10.3934/jimo.2021090

This issue Previous Article Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products Next Article An online-decision algorithm for the multi-period bank clearing problem

The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain

School of Information Management, Jiangxi University of Finance and Economics, Nanchang 330032, China

^* Corresponding author: Xin Wu
^* Corresponding author: Xin Wu

Received: December 31, 2020

Revised: February 28, 2021

Published: July 2022

The first author is supported by the National Natural Science Foundation of China grant 71761015 and the Science and Technology Research Project of Jiangxi Education Department of China grant GJJ150475

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Abstract

Consumer green preference (CGP) and fairness concern have posed significant impact on supply chain, respectively. This paper study the combined impacts of CGP and fairness concern on the supply chain that consists of a manufacturer, a green retailer, and a traditional retailer. Specifically, the optimal decision-makings are solved in seven cases, fairness neutrality (FN), the green retailer and the traditional retailer has vertical fairness concern (VFC) respectively, the two retailers has horizontal fairness concern (HFC) respectively, both retailers have vertical fairness concern (BVFC), both retailers have horizontal fairness concern (BHFC). Our main results via numerical simulation follow. (1) The improvement of CGP benefits the supply chain members except the traditional retailer. (2) The green retailer's VFC benefits itself and the whole supply chain, whereas bad for the manufacturer and the traditional retailer. However, the green retailer's HFC bad for itself, while benefits the manufacturer and the traditional retailer. (3) The traditional retailer's profits are affected by both CGP and fairness concern. (4) The high level of BVFC benefits the two retailers, but bad for the manufacturer. Conversely, the high level of BHFC will intensify competition between retailers and thus bad for them, while the manufacturer can benefit from it.

Keywords:

Mathematics Subject Classification: Primary: 90B06; Secondary: 91A35.

Citation:

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Figure 1. Proposed supply chain structure

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Figure 2. The potential demand distribution of consumers in the market

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Figure 3. Combined impacts of CGP and R1VFC on profits

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Figure 4. Combined impacts of CGP and R2VFC on profits

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Figure 5. Combined impacts of CGP and R1HFC on profits

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Figure 6. Combined impacts of CGP and R2HFC on profits

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Figure 7. Combined impacts of CGP and BVFC on profits (σ = 1.3)

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Figure 8. Combined impacts of CGP and BVFC on profits (σ = 1.9)

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Figure 9. Combined impacts of CGP and BHFC on profits (σ = 1.3)

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Figure 10. Combined impacts of CGP and BHFC on profits (σ = 1.9)

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Table 1. The literature positioning of this paper

Literature	Consumer green preference	Vertical fairness concern	Horizontal fairness concern	Both fairness concern	Three-party supply chain
Vanclay et al. [31]	√
Ghosh et al. [14]	√
Moon et al. [25]	√
Du et al. [6]	√
Cui et al. [2]		√
Du et al. [4]		√
Zhang et al. [38]		√
Savaskan et al. [28]					√
Yao et al. [32]					√
Modak et al. [24]					√
Nie et al. [26]		√	√		√
Ho et al. [17]		√	√		√
Yao et al. [33]		√			√
This paper	√	√	√	√	√

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Table 2. Symbol and notations

Notations	Definition
${{c}_{1}},{{c}_{2}}$	Unit cost for the manufacturer to produce green products and traditional products, respectively
${{w}_{1}},{{w}_{2}}$	Wholesale price of green products and traditional products, respectively
${{p}_{1}},{{p}_{2}}$	Retail price of green products and traditional products, respectively
$Q$	Potential consumers in the market
$\sigma $	Consumer green preference
${{q}_{1}},{{q}_{2}}$	Sales of green products and traditional products, respectively
${{\pi }_{m}}$	Profit function of the manufacturer
${{\pi }_{r1}}$	Profit function of the green retailer
${{\pi }_{r2}}$	Profit function of the traditional retailer
${{\pi }_{s}}$	Profit function of the whole supply chain
${{u}_{r1}}(m)$	Utility of the green retailer vertical fairness concern
${{u}_{r2}}(m)$	Utility of the traditional retailer vertical fairness concern
${{u}_{r1}}({{r}_{2}})$	Utility of the green retailer horizontal fairness concern
${{u}_{r2}}({{r}_{1}})$	Utility of the traditional retailer horizontal fairness concern
${{\lambda }_{1}},{{\lambda }_{2}},{{\lambda }_{3}},{{\lambda }_{4}}$	Coefficients of fairness concern under different scenarios

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Table 3. Simulation results in R1VFC scenario $ (\sigma \rm{ = }1.3) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi}_{m}} $	87460.32	86524.90	86036.24	85740.94	85545.31	85407.17
$ {{\pi}_{r1}} $	5461.07	6860.16	7658.16	8173.59	8533.38	8798.38
$ {{u}_{r1}}(m) $	5461.07	-9072.79	-23693.07	-38366.83	-53076.16	-67810.41
$ {{\pi}_{r2}} $	4151.55	3743.56	3474.70	3283.23	3139.67	3027.98
$ {{\pi}_{s}} $	97072.94	97128.61	97169.10	97197.76	97218.36	97233.53
$ {{w}_{1}} $	950.00	940.76	935.74	932.61	930.47	928.93
$ {{w}_{2}} $	700.00	702.32	703.72	704.67	705.36	705.89
$ {{p}_{1}} $	990.48	989.44	988.47	987.64	986.96	986.39
$ {{p}_{2}} $	730.95	731.71	732.04	732.20	732.28	732.32
$ {{q}_{1}} $	134.92	140.92	145.25	148.52	151.08	153.13
$ {{q}_{2}} $	134.13	127.37	122.71	119.28	119.28	114.55

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Table 4. Simulation results in R1VFC scenario $ (\sigma \rm{ = }1.9) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi }_{m}} $	155016.84	144556.70	138807.59	135177.66	132679.87	130857.09
$ {{\pi }_{r1}} $	39855.63	51731.18	58474.09	62842.05	65909.71	68185.73
$ {{u}_{r1}}(m) $	39855.63	33166.07	26340.69	19440.69	12493.58	5514.37
$ {{\pi }_{r2}} $	1749.57	1341.72	1111.64	963.61	860.41	784.43
$ {{\pi }_{s}} $	196622.03	197629.60	198393.33	198983.32	199449.99	199827.24
$ {{w}_{1}} $	1250.00	1198.20	1169.67	1151.63	1139.20	1130.12
$ {{w}_{2}} $	700.00	707.25	711.43	714.17	716.11	717.56
$ {{p}_{1}} $	1439.39	1439.58	1438.92	1438.11	1437.33	1436.62
$ {{p}_{2}} $	728.79	732.46	734.38	735.53	736.30	736.84
$ {{q}_{1}} $	210.44	214.32	217.18	219.36	221.08	222.47
$ {{q}_{2}} $	60.77	53.22	48.44	45.10	42.62	40.69

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Table 5. Simulation results in R2VFC scenario $ (\sigma \rm{ = }1.3) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi}_{m}} $	87460.32	86899.17	86618.75	86456.23	86352.69	86282.19
$ {{\pi}_{r1}} $	5461.07	4999.86	4691.87	4470.61	4303.71	4173.24
$ {{\pi}_{r2}} $	4151.55	5123.74	5674.90	6027.98	6272.30	6450.71
$ {{u}_{r2}}(m) $	4151.55	-11231.34	-26702.65	-42228.97	-57792.01	-73380.78
$ {{\pi}_{s}} $	97072.94	97022.77	96985.52	96954.82	96928.70	96906.13
$ {{w}_{1}} $	950.00	952.33	953.75	954.72	955.43	955.97
$ {{w}_{2}} $	700.00	693.48	689.96	687.77	686.28	685.21
$ {{p}_{1}} $	990.48	991.06	991.27	991.34	991.36	991.36
$ {{p}_{2}} $	730.95	729.78	728.78	727.96	727.29	726.74
$ {{q}_{1}} $	134.92	129.10	125.06	122.07	119.77	117.94
$ {{q}_{2}} $	134.13	141.12	146.16	149.96	152.93	155.32

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Table 6. Simulation results in R2VFC scenario $ (\sigma \rm{ = }1.9) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi}_{m}} $	155016.8	155448.8	155762.9	156000.9	156187.4	156337.3
$ {{\pi}_{r1}} $	39855.6	38438.3	37444.8	36708.8	36141.3	35690.3
$ {{\pi}_{r2}} $	1749.5	1746.2	1684.0	1604.9	1524.0	1447.2
$ {{u}_{r2}}(m) $	1749.5	-28994.2	-59947.4	-91032.7	-122206.6	-153442.8
$ {{\pi}_{s}} $	196622.0	195633.3	194891.8	194314.7	193852.8	193474.8
$ {{w}_{1}} $	1250.0	1252.3	1253.9	1255.1	1256.0	1256.7
$ {{w}_{2}} $	700.0	699.0	698.6	698.4	698.3	698.3
$ {{p}_{1}} $	1439.3	1438.3	1437.5	1436.8	1436.3	1435.9
$ {{p}_{2}} $	728.7	724.3	721.1	718.6	716.7	715.2
$ {{q}_{1}} $	210.4	206.6	203.9	201.9	200.3	199.1
$ {{q}_{2}} $	60.7	69.01	74.9	79.3	82.8	85.6

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Table 7. Simulation results in R1HFC scenario $ (\sigma \rm{ = }1.3) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi }_{m}} $	87460.32	88162.13	88670.59	89055.92	89358.01	89601.20
$ {{\pi }_{r1}} $	5461.07	4804.17	4323.18	3955.74	3665.87	3431.35
$ {{u}_{r1}}({{r}_{2}}) $	5461.07	4914.64	4323.11	3702.96	3063.48	2410.34
$ {{\pi }_{r2}} $	4151.55	4251.80	4323.35	4377.05	4418.87	4452.37
$ {{\pi }_{s}} $	97072.94	97218.10	97317.12	97388.71	97442.75	97484.92
$ {{w}_{1}} $	950.00	952.61	954.51	955.96	957.10	958.01
$ {{w}_{2}} $	700.00	697.39	695.52	694.10	692.99	692.10
$ {{p}_{1}} $	990.48	988.05	986.29	984.96	983.91	983.07
$ {{p}_{2}} $	730.95	728.72	727.10	725.88	724.92	724.15
$ {{q}_{1}} $	134.92	135.55	136.02	136.40	136.70	136.94
$ {{q}_{2}} $	134.13	135.74	136.87	137.72	138.38	138.90

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Table 8. Simulation results in R1HFC scenario $ (\sigma \rm{ = }1.9) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi }_{m}} $	155016.84	156077.52	156896.16	157542.60	158064.30	158493.43
$ {{\pi }_{r1}} $	39855.63	38221.01	36996.40	36046.73	35289.49	34671.87
$ {{u}_{r1}}({{r}_{2}}) $	39855.63	45435.93	50817.12	56069.28	61233.10	66333.79
$ {{\pi }_{r2}} $	1749.57	2146.42	2444.61	2675.82	2859.98	3009.96
$ {{\pi }_{s}} $	196622.03	196444.95	196337.17	196265.15	196213.77	196175.26
$ {{w}_{1}} $	1250.00	1252.66	1254.86	1256.67	1258.18	1259.44
$ {{w}_{2}} $	700.00	691.75	685.91	681.55	678.18	675.48
$ {{p}_{1}} $	1439.39	1435.49	1432.54	1430.24	1428.40	1426.90
$ {{p}_{2}} $	728.79	723.63	719.94	717.16	714.98	713.24
$ {{q}_{1}} $	210.44	209.05	208.22	207.68	207.31	207.04
$ {{q}_{2}} $	134.13	127.37	122.71	119.28	119.28	114.55

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Table 9. Simulation results in R2HFC scenario $ (\sigma \rm{ = }1.3) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi }_{m}} $	87460.32	88162.13	88670.59	89055.92	89358.01	89601.20
$ {{\pi }_{r1}} $	5461.07	5511.81	5550.75	5581.37	5605.99	5626.19
$ {{u}_{r2}}({{r}_{1}}) $	4151.55	3544.17	3095.78	2751.42	2478.75	2257.54
$ {{\pi }_{r2}} $	4151.55	3150.64	2113.79	1053.45	-23.04	-1111.10
$ {{\pi }_{s}} $	97072.94	97218.11	97317.12	97388.71	97442.75	97484.93
$ {{w}_{1}} $	950.00	947.39	945.49	944.04	942.90	941.99
$ {{w}_{2}} $	700.00	702.61	704.48	705.90	707.01	707.90
$ {{p}_{1}} $	990.48	988.05	986.29	984.96	983.91	983.07
$ {{p}_{2}} $	730.95	728.72	727.10	725.88	724.92	724.15
$ {{q}_{1}} $	134.92	135.55	136.02	136.40	136.70	136.94
$ {{q}_{2}} $	134.13	135.74	136.87	137.72	138.38	138.90

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Table 10. Simulation results in R2HFC scenario $ (\sigma \rm{ = }1.9) $

$ \lambda $	0	0.2	0.4	0.6	0.8	1
$ {{\pi }_{m}} $	155016.84	156077.52	156896.16	157542.60	158064.30	158493.43
$ {{\pi }_{r1}} $	39855.63	39331.98	39020.85	38819.46	38680.82	38580.82
$ {{u}_{r2}}({{r}_{1}}) $	1749.57	1035.45	420.15	-96.91	-531.35	-898.98
$ {{\pi }_{r2}} $	1749.57	-6623.86	-15020.13	-23446.73	-31901.08	-40378.78
$ {{\pi }_{s}} $	196622.04	196444.95	196337.16	196265.15	196213.77	196175.27
$ {{w}_{1}} $	1250.00	1247.34	1245.14	1243.32	1241.82	1240.56
$ {{w}_{2}} $	700.00	708.25	714.09	718.45	721.82	724.52
$ {{p}_{1}} $	1439.39	1435.49	1432.54	1430.24	1428.40	1426.90
$ {{p}_{2}} $	728.79	723.63	719.94	717.16	714.98	713.24
$ {{q}_{1}} $	210.44	209.05	208.22	207.68	207.31	207.04
$ {{q}_{2}} $	134.13	135.74	136.87	137.72	138.38	138.90

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