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Pricing new and remanufactured products based on customer purchasing behavior

  • * Corresponding author: Tao Zhou

    * Corresponding author: Tao Zhou 

The first author is supported by National Natural Science Foundation of China under grants 71871076, 71690235, 71521001

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  • Firms' pricing strategies are largely influenced by customer purchasing behavior. By considering whether to invest in customer purchasing behavior analysis, firms can choose a discriminatory or a non-discriminatory pricing model. This paper presents a two-period duopoly that the original material supplier (OS) supplying new products faces a competition of an independent material supplier (IS) providing remanufactured products to analyze each party's competitive strategy under each pricing model. We also identify situations under which the firms would obtain more profits and cause less environmental impact under the model with price discrimination compared with the model without price discrimination. A numerical study is provided to illustrate the performance of the model. A sensitivity analysis with respect to primary parameters is used to assess the stability of the model. The proposed model could be applied in many industrial fields where the managers have the full awareness of extended producer responsibility, and they are willing to engage in the project related to remanufacturing.

    Mathematics Subject Classification: Primary: 90B60; Secondary: 91B16, 91B24.

    Citation:

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  • Figure 1.  Pricing new and remanufactured products without or with price discrimination

    Figure 2.  The difference between Model B and Model A with respect to the firms' profits and environmental impact

    Figure 3.  Optimal prices as a function of $ \alpha $

    Figure 4.  Optimal demands as a function of $ \alpha $

    Figure 5.  Optimal profits as a function of $ \alpha $

    Figure 6.  Optimal environment impacts as a function of $ \alpha $

    Figure 7.  Optimal prices as a function of $ C_{s} $

    Figure 8.  Optimal demands as a function of $ C_{s} $

    Figure 9.  Optimal profits as a function of $ C_{s} $

    Figure 10.  Optimal environment impacts as a function of $ C_{s} $

    Table 1.  Some Key Literature on Remanufacturing and Pricing Strategies

    Reference Production planning Inventory management Market competition Consumer behavior
    Component remanufacturing Material remanufacturing Discount No discount Internal External WTP Switching
    Ferrer and Swaminathan [12] $ \surd $ $ \surd $ $ \surd $
    Subramanian et al. [36] $ \surd $ $ \surd $ $ \surd $
    Pranab and Harry [31] $ \surd $ $ \surd $
    Lotfi et al. [20] $ \surd $
    Lotfi et al. [21] $ \surd $
    Pervin et al. [28] $ \surd $
    Pervin et al. [29] $ \surd $
    Roy et al. [32] $ \surd $
    Pervin et al. [30] $ \surd $
    Barman et al. [8] $ \surd $
    Ferguson and Toktay [11] $ \surd $ $ \surd $ $ \surd $
    Örsdemir et al. [25] $ \surd $ $ \surd $
    Ovchinnikov [26] $ \surd $ $ \surd $ $ \surd $
    Yan et al. [44] $ \surd $ $ \surd $ $ \surd $
    Agrawal et al. [3] $ \surd $ $ \surd $ $ \surd $
    Vorasayan and Ryan [41] $ \surd $ $ \surd $ $ \surd $
    Wang et al. [42] $ \surd $ $ \surd $ $ \surd $ $ \surd $
    Abbey et al. [2] $ \surd $ $ \surd $ $ \surd $
    Abbey et al. [1] $ \surd $ $ \surd $ $ \surd $ $ \surd $
    Atasu et al. [5] $ \surd $ $ \surd $ $ \surd $ $ \surd $
    This paper $ \surd $ $ \surd $ $ \surd $ $ \surd $ $ \surd $
     | Show Table
    DownLoad: CSV

    Table 2.  Parameter settings

    Parameter Parameter values
    $ C_{s} $ 0.15 (low); 0.35 (medium); 0.55 (high)
    $ \alpha $ 0.25 (low); 0.45 (medium); 0.65 (high)
    $ C_{n} $ 0.65
    $ e_{n} $ 0.05
    $ e_{r} $ 0.01
     | Show Table
    DownLoad: CSV

    Table 3.  The optimal solution and comparison of profit

    OS's total profits IS's total profits Comparison between OS & IS
    $ \pi^{B\ast}_{o} $ $ \pi^{A\ast}_{o} $ $ \pi^{B\ast}_{o}-\pi^{A\ast}_{o} $ $ \pi^{B\ast}_{i} $ $ \pi^{A\ast}_{i} $ $ \pi^{B\ast}_{i}-\pi^{A\ast}_{i} $ $ \pi^{B\ast}_{o}-\pi^{B\ast}_{i} $ $ \pi^{A\ast}_{o}-\pi^{A\ast}_{i} $
    $ C_{s}=0.15 $ $ \alpha=0.25 $ 0.4919 0.54 -0.0481 0.2481 0.24 +0.0081 +0.2438 +0.3
    $ \alpha=0.45 $ 0.3341 0.3646 -0.0305 0.1987 0.198 +0.0007 +0.1354 +0.1666
    $ \alpha=0.65 $ 0.1792 0.1921 -0.0129 0.1522 0.1587 -0.0065 +0.0270 +0.0334
    $ C_{s}=0.35 $ $ \alpha=0.25 $ 0.3679 0.3919 -0.024 0.3408 0.3585 -0.0177 +0.0271 +0.0334
    $ \alpha=0.45 $ 0.2215 0.2273 -0.0058 0.3027 0.3273 -0.0246 -0.0812 -0.1
    $ \alpha=0.65 $ 0.091 0.0778 +0.0132 0.2806 0.3111 -0.0305 -0.1896 -0.2333
    $ C_{s}=0.55 $ $ \alpha=0.25 $ 0.2689 0.2674 +0.0015 0.4585 0.5007 -0.0422 -0.1896 -0.2333
    $ \alpha=0.45 $ 0.143 0.1222 +0.0208 0.4409 0.4889 -0.048 -0.2979 -0.3667
    $ \alpha=0.65 $ 0.0563 0.0143 +0.042 0.4626 0.5143 -0.0517 -0.4063 -0.5
     | Show Table
    DownLoad: CSV

    Table 4.  The optimal solution and comparison of environment impact

    OS's environment impact IS's environment impact Comparison between OS & IS
    $ E^{B\ast}_{o} $ $ E^{A\ast}_{o} $ $ E^{B\ast}_{o}-E^{A\ast}_{o} $ $ E^{B\ast}_{i} $ $ E^{A\ast}_{i} $ $ E^{B\ast}_{i}-E^{A\ast}_{i} $ $ E^{B\ast}_{o}-E^{B\ast}_{i} $ $ E^{A\ast}_{o}-E^{A\ast}_{i} $
    $ C_{s}=0.15 $ $ \alpha=0.25 $ 0.0612 0.06 +0.0012 0.0078 0.008 -0.0002 +0.0534 +0.052
    $ \alpha=0.45 $ 0.0585 0.0576 +0.0009 0.0083 0.0085 -0.0002 +0.0502 +0.0491
    $ \alpha=0.65 $ 0.0527 0.0524 +0.0003 0.0095 0.0095 0 +0.0432 +0.0429
    $ C_{s}=0.35 $ $ \alpha=0.25 $ 0.0512 0.0511 +0.0001 0.0098 0.0098 0 +0.0414 +0.0413
    $ \alpha=0.45 $ 0.0449 0.0455 -0.0006 0.011 0.0109 +0.0001 +0.0339 +0.0346
    $ \alpha=0.65 $ 0.0313 0.0333 -0.002 0.0138 0.0133 +0.0005 +0.0175 +0.02
    $ C_{s}=0.55 $ $ \alpha=0.25 $ 0.0412 0.0422 -0.001 0.0118 0.0116 +0.0002 +0.0294 +0.0306
    $ \alpha=0.45 $ 0.0312 0.0333 -0.0021 0.0138 0.0133 +0.0005 +0.0174 +0.02
    $ \alpha=0.65 $ 0.0098 0.0143 -0.0045 0.018 0.0171 +0.0009 –0.0082 -0.0028
     | Show Table
    DownLoad: CSV
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