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Joint decision on pricing and waste emission level in industrial symbiosis chain

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  • Based on a monopoly model in industrial symbiosis chain including one upstream manufacturer and one downstream manufacturer, the price sensitive-environmental concern demand is introduced into the paper. The decision behaviors of the manufacturers in industrial symbiosis chain under environmental regulations imposed by the policy makers or the government in waste emission standard, waste emission tax and subsidy for waste usage are investigated. The results show the operational factors of the manufacturers must be taken into account in the right formulation of waste emission standard, and the simultaneous implementation of waste emission tax and subsidy for external environmental performance of the manufacturers is superior to a single policy. Environmental concerned consumers with stronger green attitude who are more willing to buy environmentally friendly products could pressurize the manufacturers into decreasing waste emission level, and the manufacturers will affirmatively involve in industrial symbiosis chain due to the intervention of environmental regulations. Especially, integrated industrial symbiosis becomes the optimal decision for the manufacturers to boost both economic benefit and environmental performance. Waste emission contract and quantity discount contract can be techniques to improve the performance of non-integrated industrial symbiosis chain.

    Mathematics Subject Classification: Primary: 90B30; Secondary: 91B38, 91B42, 91B76.


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  • Figure 1.  Environmental regulations and waste flow in industrial symbiosis chain

    Figure 2.  Effect of $\alpha_{2}$ on price of product A

    Figure 3.  Effect of $\alpha_{2}$ on waste emission level of product A

    Figure 4.  Effect of $\beta_{2}$ on price of product B

    Figure 5.  Effect of $\beta_{2}$ on waste emission level of product B

    Figure 6.  Effect of $\alpha_{2}$ and $\beta_{2}$ on the system profit

    Figure 7.  Effect of $\alpha_{1}$ on price of product A

    Figure 8.  Effect of $\alpha_{1}$ on waste emission level of product A

    Figure 9.  Effect of $\beta_{1}$ on price of product B

    Figure 10.  Effect of $\beta_{1}$ on waste emission level of product B

    Figure 11.  Effect of $\alpha_{1}$ and $\beta_{1}$ on the system profit

    Table 1.  The optimal interval of waste emission standard (only for product A)

    Waste emission standardOptimal waste emission level and price
    $\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}\le\bar\gamma_{A}^{I} < \bar U_{A}^{I}$$\gamma_{A}^{I^{*}}=\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}$
    $\underline U_{A}^{I} < \bar\gamma_{A}^{I} < \frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}\tau)}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}\tau)^{2}}$$\gamma_{A}^{I^{*}}=\bar\gamma_{A}^{I}$
    $\bar\gamma_{A}^{I}\ge\bar U_{A}^{I}$ or $\bar\gamma_{A}^{I}\le\underline U_{A}^{I}$withdraw from the market
    $\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}\le\bar\gamma_{A}^{NI} < \bar U_{A}^{NI}$$\gamma_{A}^{NI^{*}}=\frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}$
    $\underline U_{A}^{NI} < \bar\gamma_{A}^{NI} < \frac{4\alpha_{1}m_{A}\gamma_{A}^{0}-(a-\alpha_{1}c_{A})(\alpha_{2}-\alpha_{1}p_{W})}{4\alpha_{1}m_{A}-(\alpha_{2}-\alpha_{1}p_{W})^{2}}$$\gamma_{A}^{NI^{*}}=\bar\gamma_{A}^{NI}$
    $\bar\gamma_{A}^{NI}\ge\bar U_{A}^{NI}$ or $\bar\gamma_{A}^{NI}\le\underline U_{A}^{NI}$withdraw from the market
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    Table 2.  The optimal price, waste emission level and system profit

    Price of product A188140.51128.13
    Waste emission level of product A3835.8936.60
    Price of product B124.86124.57138.86
    Waste emission level of product B17.4317.2924.43
    System profit8427.8624173.9023115.00
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