# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021204
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## The optimal product-line design and incentive mechanism in a supply chain with customer environmental awareness

* Corresponding author: Cui-hua Zhang

Received  April 2021 Revised  October 2021 Early access November 2021

Fund Project: The first author is supported by National Natural Science Foundation of China(NSFC) grant 71771044

Due to the increasing awareness of sustainable development, the manufacturer's product-line design gets wide attention. Nowadays, the traditional manufacturer that produces non-green products is considering whether to introduce upgraded green products. This paper studies the manufacturer's optimal product-line design considering the quality difference between non-green and green products. Besides, our model also investigates the difference in unit production cost, green research and development (R&D) investment, and market segmentation. The results show that, from the manufacturer's perspective, producing green products is a better choice when non-green products are of low quality. In addition, the retailer is always inclined to sell green products. Further, the consumers' preference for non-green and green products is divided. And the consumer surplus under different product-line designs is analysed. Finally, two contracts are proposed and compared to encourage the manufacturer to produce green products.

Citation: Zhi-tang Li, Cui-hua Zhang, Wei Kong, Ru-xia Lyu. The optimal product-line design and incentive mechanism in a supply chain with customer environmental awareness. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021204
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##### References:
The flow diagram of implement methodology
Product-line design and the sequence of events
Impact of $q_g$ and $q_n$ on product-line selection
Impact of $q_g$ and $q_n$ on consumer surplus
Impact of $q_g$ on the level of green innovation effort
Impact of $q_g$ on the profit under the contract
Impact of $k$ on the profit
Impact of $\gamma$ on the profit
Impact of $\theta$ on the profit
Revenue Share of Green Products in Philips Business Division 2017-2019 (Unit: million Euros)
Practices of the enterprise's green production
 Industry The practice of green production Automobile SAIC General Motors promotes the strategy of "greening the future". Buick and Chevrolet's 1.2L-1.6L vehicles are equipped with EcotecDVVT and S-TEC engines. Compared with the products of the same level, the manual gearboxes are high performance and fuel-efficient(https://www.saic-gm.com/www/web/saic-gm/satep.). Household appliance Philips uses green technology ranging from energy-saving lighting to TV. Compared with traditional products, its energy-saving bulbs can save 80% of electrical energy and provide sustainable lighting solutions(https://www.philips.com.cn/a-w/about-philips/sustainability.html.) Commodity Procter & Gamble reduces the use of materials by 10% through the optimization of packaging material and the weight of each diaper is greatly decreased by technological innovation (https://www.pg.com.cn/Csr/Product.aspx.). Agriculture The role of agricultural green production technologies (AGPTs) adoption rates improves low-carbon efficiency in China[8]. Green production is widely mentioned in the field of agriculture [9,10] Steel production Decarburization technology leads the development of green steel [11]. Metal processing Environmental performance in the metal processing industry could be improved by green technologies (process modifications and management practices) [12]. Fashion apparels H & M, Marks & Spencer, and Levi's, have produced low-carbon products using new technology to reduce carbon emissions during production [13,14].
 Industry The practice of green production Automobile SAIC General Motors promotes the strategy of "greening the future". Buick and Chevrolet's 1.2L-1.6L vehicles are equipped with EcotecDVVT and S-TEC engines. Compared with the products of the same level, the manual gearboxes are high performance and fuel-efficient(https://www.saic-gm.com/www/web/saic-gm/satep.). Household appliance Philips uses green technology ranging from energy-saving lighting to TV. Compared with traditional products, its energy-saving bulbs can save 80% of electrical energy and provide sustainable lighting solutions(https://www.philips.com.cn/a-w/about-philips/sustainability.html.) Commodity Procter & Gamble reduces the use of materials by 10% through the optimization of packaging material and the weight of each diaper is greatly decreased by technological innovation (https://www.pg.com.cn/Csr/Product.aspx.). Agriculture The role of agricultural green production technologies (AGPTs) adoption rates improves low-carbon efficiency in China[8]. Green production is widely mentioned in the field of agriculture [9,10] Steel production Decarburization technology leads the development of green steel [11]. Metal processing Environmental performance in the metal processing industry could be improved by green technologies (process modifications and management practices) [12]. Fashion apparels H & M, Marks & Spencer, and Levi's, have produced low-carbon products using new technology to reduce carbon emissions during production [13,14].
Relative running time of the considered filters
 Paper Product-line design Green level Pricing strategy Quality-based model Coordination Game theory Chen et al. [17] Y N Y N N N Yenipazarli and Vakharia. [33] N N Y N N Y Ozinci et al. [34] N N Y N N Y Zhang et al. [18] Y Y Y N N N Shen et al. [15] Y N Y Y N Y Zhang et al. [35] N N Y N N Y Zou et al. [16] Y N Y Y N Y Tirkolaee et al. [39] N Y N N N N Sinayi and Rasti-Barzoki. [41] N Y Y N Y Y Chen et al. [42] N Y Y N Y Y Yu et al. [43] N N Y N Y Y Zhu et al. [44] N Y Y N N Y Zu et al. [45] N N Y N N Y Chen. [47] N N Y Y N Y Zhang et al. [48] N N Y Y N Y Gouda et al. [49] Y N Y Y N Y Murali et al. [50] N N Y Y N Y Xu et al. [19] N N Y N Y Y Zhou and Ye. [20] N N Y N Y Y He et al. [21] N N Y N Y Y Li et al. [22] N N Y N Y Y Yang et al. [23] N N Y N Y Y Moon et al. [24] N N Y N Y Y Our paper Y Y Y Y Y Y
 Paper Product-line design Green level Pricing strategy Quality-based model Coordination Game theory Chen et al. [17] Y N Y N N N Yenipazarli and Vakharia. [33] N N Y N N Y Ozinci et al. [34] N N Y N N Y Zhang et al. [18] Y Y Y N N N Shen et al. [15] Y N Y Y N Y Zhang et al. [35] N N Y N N Y Zou et al. [16] Y N Y Y N Y Tirkolaee et al. [39] N Y N N N N Sinayi and Rasti-Barzoki. [41] N Y Y N Y Y Chen et al. [42] N Y Y N Y Y Yu et al. [43] N N Y N Y Y Zhu et al. [44] N Y Y N N Y Zu et al. [45] N N Y N N Y Chen. [47] N N Y Y N Y Zhang et al. [48] N N Y Y N Y Gouda et al. [49] Y N Y Y N Y Murali et al. [50] N N Y Y N Y Xu et al. [19] N N Y N Y Y Zhou and Ye. [20] N N Y N Y Y He et al. [21] N N Y N Y Y Li et al. [22] N N Y N Y Y Yang et al. [23] N N Y N Y Y Moon et al. [24] N N Y N Y Y Our paper Y Y Y Y Y Y
Notations for model parameters
 Abbreviations Description $N/n$ The production of the non-green product $G/g$ The production of the green product $m$ The manufacturer $r$ The retailer Variables $w_i$ The unit wholesale price of the product $i$, where $i=n,g$ $p_i$ The unit retail price of the product $i$, where $i=n,g$ $e$ Green effort of the green product Parameters $q_i$ Product quality for the product $i$, where $i=n,g$ $c_i$ The unit production cost for the product $i$, where $i=n,g$ $v$ Consumer's willingness to pay for the product $k$ Coefficient of manufacturer's green R&D effort cost $\gamma$ Sensitivity coefficient of green R&D effort to market demand, $\gamma > 0$ denotes consumers' green preference towards the green effort. $\theta$ The proportion of green consumers in the market Functions $U_{ns}^j$ Consumer's utility obtained from the product $j$ in the non-green segment, where $j=N,G$ $U_{gs}^{j}$ Consumer's utility obtained from the product $j$ in the green segment, where $j=N,G$ $D_i$ Demand for the product $i$, where $i=n,g$ $\pi_m^j$ The profit of the manufacturer from producing the product $j$, where $j=N,G$ $\pi_r^j$ The profit of the retailer from selling the product $j$, where $j=N,G$ $CS^j$ Consumer surplus obtained from purchasing the product $j$, where $j=N,G$
 Abbreviations Description $N/n$ The production of the non-green product $G/g$ The production of the green product $m$ The manufacturer $r$ The retailer Variables $w_i$ The unit wholesale price of the product $i$, where $i=n,g$ $p_i$ The unit retail price of the product $i$, where $i=n,g$ $e$ Green effort of the green product Parameters $q_i$ Product quality for the product $i$, where $i=n,g$ $c_i$ The unit production cost for the product $i$, where $i=n,g$ $v$ Consumer's willingness to pay for the product $k$ Coefficient of manufacturer's green R&D effort cost $\gamma$ Sensitivity coefficient of green R&D effort to market demand, $\gamma > 0$ denotes consumers' green preference towards the green effort. $\theta$ The proportion of green consumers in the market Functions $U_{ns}^j$ Consumer's utility obtained from the product $j$ in the non-green segment, where $j=N,G$ $U_{gs}^{j}$ Consumer's utility obtained from the product $j$ in the green segment, where $j=N,G$ $D_i$ Demand for the product $i$, where $i=n,g$ $\pi_m^j$ The profit of the manufacturer from producing the product $j$, where $j=N,G$ $\pi_r^j$ The profit of the retailer from selling the product $j$, where $j=N,G$ $CS^j$ Consumer surplus obtained from purchasing the product $j$, where $j=N,G$
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