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Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products

  • * Corresponding author: Xuhui Xia

    * Corresponding author: Xuhui Xia 

This research was supported by the National Natural Science Foundation of China (No. 51805385) and Natural Science Foundation of Hubei Province (No. 2018CFB265)

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  • Considering the quality of recycled products, we develop a game model of a multi-level competitive recycling and remanufacturing supply chain with two manufacturers and multiple recyclers. Being focus on two mainstream game models, namely the manufacturer-recycler cooperation game model and the manufacturer-led Stackelberg game model, we explore the connection between optimal pricing decisions and performance levels of the supply chain members. Although researches indicate that the quality of recycled products will not affect the pricing decisions in the forward supply chain, it is positively related to the recycling price, the repurchase price, and the overall profit in the reverse supply chain, and the intensity of competition among manufacturers or recycled products will affect the pricing decisions and the performance levels of the two models. In the manufacturer-led Stackelberg game model, the supply chain does not reach the Pareto optimum, which uses the recycling cost sharing contract to achieve the coordination. Afterwards, the profits of the two manufacturers and multiple recyclers in the supply chain are increased, and the overall profit of the supply chain system is higher than that of the manufacturer-led Stackelberg game model. Finally, numerical analysis is conducted to verify the proposed coordination mechanism and its effectiveness.

    Mathematics Subject Classification: Primary: 90B06.

    Citation:

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  • Figure 1.  System architecture of the recycling and remanufacturing supply chain

    Figure 2.  The impact of $ \lambda $ on manufacturer's sale price

    Figure 3.  The impact of $ \lambda $ on market demand

    Figure 4.  The impact of $ \lambda $ on profits

    Figure 5.  The impact of $ \kappa $ on $ b_{m}^{MRC} $ and $ b_{m}^{MS} $

    Figure 6.  The impact of $ \kappa $ on $ \eta_{m}^{MS} $

    Figure 7.  The impact of $ \kappa $ on $ f_{R}^{MS} $

    Figure 8.  The impact of $ \kappa $ on $ f^{MRC} $

    Figure 9.  The impact of $ \kappa $ on $ f^{ MS} $

    Figure 10.  The impact of κ on f1MS

    Figure 11.  The impact of κ on f2MS

    Figure 12.  The impact of $ \lambda $ and $ \kappa $ on $ f^{ MRC} $

    Figure 13.  The impact of $ \lambda $ and $ \kappa $ on $ f^{ MS} $

    Figure 14.  The impact of $ \sigma $ on $ b_{m}^{MRC} $ and $ b_{m}^{MS} $

    Figure 15.  The impact of $ \sigma $ on $ \eta_{m}^{MS} $

    Figure 16.  The impact of $ \sigma $ on profits

    Figure 17.  The impact of θ on f1MST

    Figure 18.  The impact of θ on f2MST

    Figure 19.  The impact of $ \theta $ on $ f_{R}^{MST} $

    Table 1.  Indices

    m Manufacturer (m=1, 2)
    r Recycler (r=1, 2, 3, ...R)
     | Show Table
    DownLoad: CSV

    Table 2.  Decision variables

    $ p_{m} $ The unit sale price for new and remanufactured products of manufacturer m
    $ b_{m} $ The unit recycling price specified by the recycler for the used products needed by the manufacturer m
    $ \eta_{m} $ The unit price at which manufacturer m repurchases used products from recyclers
     | Show Table
    DownLoad: CSV

    Table 3.  Definition of Parameters

    $\textit{R}$ Number of recyclers
    $ c_{mn} $ The unit cost required by the manufacturer m to manufacture a new product
    $ c_{mz} $ The unit cost required for manufacturer m to remanufacture the product
    $ \omega_{m} $ Manufacturer m uses the used products for remanufacturing cost savings
    $ \sigma $ Remanufacturing ratio of recycled used products. It reflects the quality of recycled used products, 0$ \leq $$ \sigma $$ \leq $1
    $\textit{s}$ The government subsidies for recycler to recycle every unit of used products
    $ c_{d} $ The unit cost for recyclers to dispose of used products
    $ c_{q} $ The unit cost for recyclers to dispose of other used products that cannot be used for remanufacturing
    $ \delta_{r} $ Economies of market scale for recyclers r, 0 < $ \delta_{r} < $1
    $ \lambda $ The intensity of competition between two manufacturers that can replace new products, 0 < $ \lambda < $1, competition, the more intense the competition among manufacturers.
    $ \mu $ Market capacity, $ \mu > $0
    $ \psi $ When the recycling price is zero, the number of used products voluntarily returned by the consumer market which reflect consumers' environmental awareness, $ \psi > $0
    $ \kappa $ The intensity of recycling competition between two used products, 0 < $ \kappa < $1
     | Show Table
    DownLoad: CSV

    Table 4.  The main parameter values

    $ R $ $ S $ $ c_{d} $ $ c_{q} $ $ \delta_{1} $ $ \delta_{2} $ $ \delta_{3} $ $ \mu $
    3 2 2 3 0.1 0.2 0.3 150
    $ c_{1n} $ $ c_{1z} $ $ \omega_{1} $ $ c_{2n} $ $ c_{2z} $ $ \omega_{2} $ $ \psi $
    40 15 25 30 15 20 3
     | Show Table
    DownLoad: CSV

    Table 5.  The optimal solutions in the MRC model and the MS model before the coordination mechanism is adopted

    Decision variables $ p_{1} $ $ p_{2} $ $ b_{1} $ $ b_{2} $ $ \eta_{1} $ $ \eta_{2} $ $ f_{1} $ $ f_{2} $ $ f_{R} $ $ f $
    MRC 145 140 9.35 6.87 - - - - - 14371
    MS 118 114 2.79 1.71 11.71 9.52 6207 7072 157 13436
     | Show Table
    DownLoad: CSV

    Table 6.  The optimal solution under the coordination mechanism

    Decision variables $ p_{1} $ $ p_{2} $ $ b_{1} $ $ b_{2} $ $ \eta_{1} $ $ \eta_{2} $ $ f_{1} $ $ f_{2} $ $ f_{R} $ $ f $
    MS model 117.7 114 2.8 1.7 11.7 9.5 6207 7072 157 13436
    Coordination1 mechanism1 117.7 114 9.35 6.87 10.45 8.45 6241 7099 206 13546
    Coordination2 1mechanism2 117.7 114 9.35 6.87 9.24 7.49 6257 7109 180 13546
     | Show Table
    DownLoad: CSV
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