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doi: 10.3934/jimo.2022021
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## Product line extension with a green added product: Impacts of segmented consumer preference on supply chain improvement and consumer surplus

 1 School of Management, Hefei University of Technology, Hefei 230009, China 2 Key Laboratory of Process Optimization and Intelligent Decision-Making of Ministry of Education, Hefei 230009, China 3 College of Economics and Management, Anhui Agricultural University, Hefei 230036, China 4 School of Economics and Management, Xiamen University of Technology, Xiamen 361024, China

*Corresponding author: Rui Zhang

Received  June 2020 Revised  October 2021 Early access February 2022

Fund Project: The work was supported by the National Natural Science Foundation of China (71801076, 71802004, 61936009, 71690230, 71771076, 72071058), National Key Research and Development Program of China (2018AAA0101604), Philosophy and Social Science Project of Anhui Province (AHSKY2016D21, AHSKY2016D25), and Fundamental Research Funds for the Central Universities (JZ2020HGTB0066)

With the enhancement of environmental protection, more and more enterprises begin to develop green products. However, the high cost of green R&D leads to an increase of product price, which reduces the competitiveness of green products. In this paper, we model a supply chain which consists of one manufacturer and one retailer providing a primary product and a substitutable green added product in the market. In order to capture the impact of consumer behavior on the supply chain members' decision-making, we classify the market into two segments and assume that high-end green consumers have higher preferences for green products than ordinary consumers. Different to existing research, we assume ordinary consumers hold a positive but lower green preference compared to the green consumers. When analyzing the impacts of consumers' green preferences, we find that there exist specific boundaries of cost and market potential which define the optimal pricing strategy and product line design. Regarding profits, we find that when the green preferences of high-end and low-end consumers increase in the same proportion, the high-end market may not bring greater supply chain revenue. In particular, the marginal profit increase of the manufacturer is always greater than that of the retailer.

Citation: Xiaoxi Zhu, Kai Liu, Miaomiao Wang, Rui Zhang, Minglun Ren. Product line extension with a green added product: Impacts of segmented consumer preference on supply chain improvement and consumer surplus. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022021
##### References:

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##### References:
Regions that define the product line choice in decentralized supply chain with $c_o = 0.04$ (All the regions are located with $\frac{L}{H}>\frac{3+c_o}{4}$)
Regions that define the product line choice in decentralized supply chain with $c_o = 0.2$ (All the regions are located with $\frac{L}{H}>\frac{3+c_o}{4}$).
Regions that define the product line choice in centralized supply chain with $c_o = 0.04$ (All the regions are located with $\frac{L}{H}>\frac{1+c_o}{2}$)
Regions that define the product line choice in decentralized supply chain with $c_o = 0.2$ (All the regions are located with $\frac{L}{H}>\frac{3+c_o}{4}$).
Market coverage and consumer choice ($v_1 = p_o$, $v_2 = \frac{p_g-p_o}{H x}$, and $v_3 = \frac{p_g-p_o}{L x}$ with $v_3>v2$)
Regions that define the relationship of $\frac{\partial \Pi_{M(R)}^*}{\partial H}$ and $\frac{\partial \Pi_{M(R)}^*}{\partial L}$
Product valuations in specific segments with $H>L>0$
 Segments Product ($o$) Product ($g$) Ordinary consumer ($O$) $\xi$ $\xi+Lx\xi$ Green consumer ($G$) $\xi$ $\xi+Hx\xi$
 Segments Product ($o$) Product ($g$) Ordinary consumer ($O$) $\xi$ $\xi+Lx\xi$ Green consumer ($G$) $\xi$ $\xi+Hx\xi$
Optimal results of the decentralized model
 Optimums Case $I$ Case $\mathit{II}$ Case $\mathit{III}$ Prices $p_o^*=\frac{c_o+3}{4}$; $w_o^*=\frac{c_o+1}{2}$ $\frac{c_o+3}{4}$; $w_o^*=\frac{c_o+1}{2}$ $\frac{c_o+3}{4}$; $w_o^*=\frac{c_o+1}{2}$ $p_g^*=\frac{c_o}{4}+\frac{\Theta_1}{36 k (\alpha H-\alpha L+L)^2}$ $p_g^*=\frac{c_o}{4}+\frac{\Theta_2}{4 k ((\alpha -1) L-\alpha H)}$ $p_g^*=\frac{(c_o+3)\Theta_3}{4 k (\alpha H+(1-\alpha ) L)}$ $w_g^*=\frac{c_o}{2}+\frac{\Theta_4}{18 k (\alpha H-\alpha L+L)^2}$ $w_g^*=\frac{c_o}{2}+\frac{\Theta_5}{2 k (\alpha H-\alpha L+L)^2}$ $w_g^*=\frac{\Theta_6}{2 k ((\alpha -1) L-\alpha H)^2}$ $+\frac{H^2 c_o}{2 k}+\frac{\Theta_7}{2 k (\alpha H-\alpha L+L)}$ Greenness $x^*=\frac{2 H L}{3 k (\alpha (H- L)+L)}$ $x^*=x_{D_g^O}$ $x^*=x_{D_o^G}$ Demands $D_o^{O*}=\frac{\alpha}{12} \left(\frac{10 H}{\alpha H-\alpha L+L}-9-3 c_o\right)$ $D_o^{O*}=\frac{\alpha}{4} \left(1-c_o\right)$ $D_o^{O*}=\frac{\alpha \left(c_o+3\right) (H-L)}{4 L}$ $D_g^{O*}=\frac{\alpha ((6 \alpha-5) H+6 (1-\alpha) L)}{6 (\alpha H-\alpha L+L)}$ $D_g^{O*}=0$ $D_g^{O*}=\frac{\alpha \left(4 L-H c_o-3 H\right)}{4 L}$ $D_o^{G*}=\frac{\alpha -1}{12} \left(3 c_o-\frac{10 L}{\alpha H-\alpha L+L}+9\right)$ $D_o^{G*}=\frac{(\alpha -1) \left(H c_o+3 H-4 L\right)}{4 H}$ $D_o^{G*}=0$ $D_g^{G*}=\frac{(1-\alpha) (6 \alpha H-6 \alpha L+L)}{6 (\alpha H-\alpha L+L)}$ $D_g^{G*}=\frac{(1-\alpha) (H-L)}{H}$ $D_g^{G*}=\frac{(\alpha -1) (c_o-1)}{4}$
 Optimums Case $I$ Case $\mathit{II}$ Case $\mathit{III}$ Prices $p_o^*=\frac{c_o+3}{4}$; $w_o^*=\frac{c_o+1}{2}$ $\frac{c_o+3}{4}$; $w_o^*=\frac{c_o+1}{2}$ $\frac{c_o+3}{4}$; $w_o^*=\frac{c_o+1}{2}$ $p_g^*=\frac{c_o}{4}+\frac{\Theta_1}{36 k (\alpha H-\alpha L+L)^2}$ $p_g^*=\frac{c_o}{4}+\frac{\Theta_2}{4 k ((\alpha -1) L-\alpha H)}$ $p_g^*=\frac{(c_o+3)\Theta_3}{4 k (\alpha H+(1-\alpha ) L)}$ $w_g^*=\frac{c_o}{2}+\frac{\Theta_4}{18 k (\alpha H-\alpha L+L)^2}$ $w_g^*=\frac{c_o}{2}+\frac{\Theta_5}{2 k (\alpha H-\alpha L+L)^2}$ $w_g^*=\frac{\Theta_6}{2 k ((\alpha -1) L-\alpha H)^2}$ $+\frac{H^2 c_o}{2 k}+\frac{\Theta_7}{2 k (\alpha H-\alpha L+L)}$ Greenness $x^*=\frac{2 H L}{3 k (\alpha (H- L)+L)}$ $x^*=x_{D_g^O}$ $x^*=x_{D_o^G}$ Demands $D_o^{O*}=\frac{\alpha}{12} \left(\frac{10 H}{\alpha H-\alpha L+L}-9-3 c_o\right)$ $D_o^{O*}=\frac{\alpha}{4} \left(1-c_o\right)$ $D_o^{O*}=\frac{\alpha \left(c_o+3\right) (H-L)}{4 L}$ $D_g^{O*}=\frac{\alpha ((6 \alpha-5) H+6 (1-\alpha) L)}{6 (\alpha H-\alpha L+L)}$ $D_g^{O*}=0$ $D_g^{O*}=\frac{\alpha \left(4 L-H c_o-3 H\right)}{4 L}$ $D_o^{G*}=\frac{\alpha -1}{12} \left(3 c_o-\frac{10 L}{\alpha H-\alpha L+L}+9\right)$ $D_o^{G*}=\frac{(\alpha -1) \left(H c_o+3 H-4 L\right)}{4 H}$ $D_o^{G*}=0$ $D_g^{G*}=\frac{(1-\alpha) (6 \alpha H-6 \alpha L+L)}{6 (\alpha H-\alpha L+L)}$ $D_g^{G*}=\frac{(1-\alpha) (H-L)}{H}$ $D_g^{G*}=\frac{(\alpha -1) (c_o-1)}{4}$
Optimal results of the centralized model
 Optimums Case $\tilde{I}$ Case $\tilde{\mathit{II}}$ Case $\tilde{\mathit{III}}$ Prices $\tilde{p}_o^*=\frac{c_o+3}{4}$; $\tilde{p}_o^*=\frac{c_o+3}{4}$; $\tilde{p}_o^*=\frac{c_o+3}{4}$; $\tilde{p}_g^*=\frac{c_o}{2}+\frac{\tilde{\Theta}_1}{18 k (\alpha H-\alpha L+L)^2}$ $\tilde{p}_g^*=\frac{c_o}{2}+\frac{\tilde{\Theta}_2}{2 k ((\alpha -1) L-\alpha H)}$ $\tilde{p}_g^*=\left(c_o+1\right) (\frac{H^2 c_o}{k}$ $\qquad\quad+\frac{\tilde{\Theta}_3}{2 k ((\alpha -1) L-\alpha H)})$ Greenness $\tilde{x}^*=\frac{2 H L}{3 k (\alpha (H- L)+L)}$ $\tilde{x}^*=x_{D_g^O}$ $\tilde{x}^*=x_{D_o^G}$ Demands $\tilde{D}_o^{O*}=\frac{\alpha }{6} \left(\frac{4 H}{\alpha H-\alpha L+L}-3 c_o-3\right)$ $\tilde{D}_o^{O*}=\frac{1}{2} \alpha \left(1-c_o\right)$ $\tilde{D}_o^{O*}=\frac{\alpha \left(c_o+1\right) (H-L)}{2 L}$ $\tilde{D}_g^{O*}=\frac{\alpha ((3 \alpha-2) H+3 (1-\alpha) L)}{3 (\alpha H-\alpha L+L)}$ $\tilde{D}_g^{O*}=0$ $\tilde{D}_g^{O*}=\frac{\alpha \left(2 L-H c_o+H\right)}{2 L}$ $\tilde{D}_o^{G*}=\frac{1}{6} (\alpha -1) \left(3 c_o-\frac{4 L}{\alpha H-\alpha L+L}+3\right)$ $\tilde{D}_o^{G*}=\frac{(\alpha -1) \left(H c_o+H-2 L\right)}{2 H}$ $\tilde{D}_o^{G*}=0$ $\tilde{D}_g^{G*}=-\frac{(\alpha -1) (3 \alpha H-3 \alpha L+L)}{3 (\alpha H-\alpha L+L)}$ $\tilde{D}_g^{G*}=\frac{(1-\alpha) (H-L)}{H}$ $\tilde{D}_g^{G*}=\frac{1}{2} (\alpha -1) \left(c_o-1\right)$
 Optimums Case $\tilde{I}$ Case $\tilde{\mathit{II}}$ Case $\tilde{\mathit{III}}$ Prices $\tilde{p}_o^*=\frac{c_o+3}{4}$; $\tilde{p}_o^*=\frac{c_o+3}{4}$; $\tilde{p}_o^*=\frac{c_o+3}{4}$; $\tilde{p}_g^*=\frac{c_o}{2}+\frac{\tilde{\Theta}_1}{18 k (\alpha H-\alpha L+L)^2}$ $\tilde{p}_g^*=\frac{c_o}{2}+\frac{\tilde{\Theta}_2}{2 k ((\alpha -1) L-\alpha H)}$ $\tilde{p}_g^*=\left(c_o+1\right) (\frac{H^2 c_o}{k}$ $\qquad\quad+\frac{\tilde{\Theta}_3}{2 k ((\alpha -1) L-\alpha H)})$ Greenness $\tilde{x}^*=\frac{2 H L}{3 k (\alpha (H- L)+L)}$ $\tilde{x}^*=x_{D_g^O}$ $\tilde{x}^*=x_{D_o^G}$ Demands $\tilde{D}_o^{O*}=\frac{\alpha }{6} \left(\frac{4 H}{\alpha H-\alpha L+L}-3 c_o-3\right)$ $\tilde{D}_o^{O*}=\frac{1}{2} \alpha \left(1-c_o\right)$ $\tilde{D}_o^{O*}=\frac{\alpha \left(c_o+1\right) (H-L)}{2 L}$ $\tilde{D}_g^{O*}=\frac{\alpha ((3 \alpha-2) H+3 (1-\alpha) L)}{3 (\alpha H-\alpha L+L)}$ $\tilde{D}_g^{O*}=0$ $\tilde{D}_g^{O*}=\frac{\alpha \left(2 L-H c_o+H\right)}{2 L}$ $\tilde{D}_o^{G*}=\frac{1}{6} (\alpha -1) \left(3 c_o-\frac{4 L}{\alpha H-\alpha L+L}+3\right)$ $\tilde{D}_o^{G*}=\frac{(\alpha -1) \left(H c_o+H-2 L\right)}{2 H}$ $\tilde{D}_o^{G*}=0$ $\tilde{D}_g^{G*}=-\frac{(\alpha -1) (3 \alpha H-3 \alpha L+L)}{3 (\alpha H-\alpha L+L)}$ $\tilde{D}_g^{G*}=\frac{(1-\alpha) (H-L)}{H}$ $\tilde{D}_g^{G*}=\frac{1}{2} (\alpha -1) \left(c_o-1\right)$
Sensitivity results on demands and profits when $H>L>0$
 Cases $D_o^{O*}$ $D_g^{O*}$ $D_o^{G*}$ $D_g^{G*}$ $\Pi_M^*$ $\Pi_R^*$ $\alpha$ $(\uparrow)$ $\uparrow(\downarrow)^{(1)}$ $\uparrow(\downarrow)^{(2)}$ $\uparrow(\downarrow)^{(1)}$ $\uparrow(\downarrow)^{(2)}$ $\downarrow$ $\downarrow$ $H$ $(\uparrow)$ $\uparrow$ $\downarrow$ $\downarrow$ $\uparrow$ $\uparrow$ $\uparrow$ $L$ $(\uparrow)$ $\downarrow$ $\uparrow$ $\uparrow$ $\downarrow$ $\uparrow$ $\uparrow$ $"\uparrow"$ denotes increases and $"\downarrow"$ denotes decreases;${(1)}$: $\uparrow (\downarrow)$ if $\frac{HL}{(\alpha H-\alpha L+L)^2} >(<)\frac{9+c_o}{10}$ and ${(2)}$: $\uparrow (\downarrow)$ if $\frac{HL}{(\alpha H-\alpha L+L)^2} >(<)\frac{6}{5}$.
 Cases $D_o^{O*}$ $D_g^{O*}$ $D_o^{G*}$ $D_g^{G*}$ $\Pi_M^*$ $\Pi_R^*$ $\alpha$ $(\uparrow)$ $\uparrow(\downarrow)^{(1)}$ $\uparrow(\downarrow)^{(2)}$ $\uparrow(\downarrow)^{(1)}$ $\uparrow(\downarrow)^{(2)}$ $\downarrow$ $\downarrow$ $H$ $(\uparrow)$ $\uparrow$ $\downarrow$ $\downarrow$ $\uparrow$ $\uparrow$ $\uparrow$ $L$ $(\uparrow)$ $\downarrow$ $\uparrow$ $\uparrow$ $\downarrow$ $\uparrow$ $\uparrow$ $"\uparrow"$ denotes increases and $"\downarrow"$ denotes decreases;${(1)}$: $\uparrow (\downarrow)$ if $\frac{HL}{(\alpha H-\alpha L+L)^2} >(<)\frac{9+c_o}{10}$ and ${(2)}$: $\uparrow (\downarrow)$ if $\frac{HL}{(\alpha H-\alpha L+L)^2} >(<)\frac{6}{5}$.
Notations
 Parameters Descriptions $D_o^i$ The demand of product "o" on segment "$i$", where $i=O, G$ $D_g^i$ The demand of product "g" on segment "$i$", where $i=O, G$ $\alpha$ $\alpha$ and $1-\alpha$ denotes the market size of segments "$O$" and "$G$" $k$ The cost factor related for the green added product $c_o$ The unit production cost of producing a primary product $H, L$ The consumers' preference of the added greenness of the product. $w_o, p_o$ Unit wholesale price and retail price of the primary product $w_g, p_g$ Unit wholesale price and retail price of the green product $x$ The green level of the products designed by the manufacturer. $D_o$ Total demand of product "o" across the two segments, $D_o=\sum D_o^i$ $D_g$ Total demand of product "g" across the two segments, $D_g=\sum D_g^i$ $\tilde{\Pi}_C$ The total profit of the integrated supply chain $\Pi_M$ The profit of the manufacturer under decentralized supply chain $\Pi_R$ The profit of the retailer under decentralized supply chain
 Parameters Descriptions $D_o^i$ The demand of product "o" on segment "$i$", where $i=O, G$ $D_g^i$ The demand of product "g" on segment "$i$", where $i=O, G$ $\alpha$ $\alpha$ and $1-\alpha$ denotes the market size of segments "$O$" and "$G$" $k$ The cost factor related for the green added product $c_o$ The unit production cost of producing a primary product $H, L$ The consumers' preference of the added greenness of the product. $w_o, p_o$ Unit wholesale price and retail price of the primary product $w_g, p_g$ Unit wholesale price and retail price of the green product $x$ The green level of the products designed by the manufacturer. $D_o$ Total demand of product "o" across the two segments, $D_o=\sum D_o^i$ $D_g$ Total demand of product "g" across the two segments, $D_g=\sum D_g^i$ $\tilde{\Pi}_C$ The total profit of the integrated supply chain $\Pi_M$ The profit of the manufacturer under decentralized supply chain $\Pi_R$ The profit of the retailer under decentralized supply chain
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