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Quality competition and coordination in a VMI supply chain with two risk-averse manufacturers

  • * Corresponding author: Fuyou Huang

    * Corresponding author: Fuyou Huang 

The paper is supported by the Science and Technology Project of Sichuan Province (Grant No.20CXTD0081) and the Science and Technology Project of Transportation Department of Sichuan Province (Grant No.2019-D-05)

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  • Quality competition and risk aversion have become more and more common in today's many industries, making it a challenge to supply chain management and coordination. This paper considers a vendor-managed inventory (VMI) supply chain comprising two risk-averse manufacturers who sell their competing products through a common retailer. Market demand shared by each manufacturer is dependent on the quality level of its own product as well as on the competitor's product quality. The Conditional Value-at-Risk (CVaR) criterion is employed to formulate the risk aversion of manufacturers. This study first develops basic models without coordination mechanism and analyzes the effect of the quality sensitivity, competition intensity, risk aversion degree and cost coefficient of quality improvement on equilibrium decisions and supply chain efficiency. Further, a combined contract composed of option and cost-sharing is proposed to investigate the supply chain coordination issue. The results reveal that the combined contract can coordinate the supply chain and achieve a win-win outcome only when the manufacturers are low in risk aversion, and the system-wide profit of the supply chain can be allocated arbitrarily only by the option price. Also, this research examines the effect of the quality sensitivity, competition intensity, risk aversion degree and cost coefficient of quality improvement on the feasible region of option price.

    Mathematics Subject Classification: Primary: 90B50; Secondary: 91B30.

    Citation:

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  • Figure 1.  Structure of the supply chain

    Figure 2.  Effect of the option price on profit allocation under channel coordination

    Table 1.  Differences between this paper and other relevant papers

    Literature [1] [16] [24] [26] [37] [43] [46] This paper
    Product quality Yes Yes No Yes Yes Yes No Yes
    Competition Yes No No No No Yes No Yes
    Stochastic demand No No Yes Yes No No Yes Yes
    Risk aversion No No Yes No No No Yes Yes
    Coordination No Yes Yes Yes Yes No Yes Yes
     | Show Table
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    Table 2.  Notations

    Symbol Definition
    $ i $ Index for product, $ i = 1, 2 $
    $ {d_i} $ Quality dependent deterministic demand for the $ i $th product
    $ {D_i} $ Demand faced by the retailer for the $ i $th product
    $ {c_i} $ Production cost per unit of the $ i $th product
    $ {w_i} $ Wholesale price per unit of the $ i $th product
    $ {p_i} $ Retail price per unit of the $ i $th product
    $ {\upsilon _i} $ Salvage value per unit of the $ i $th product
    $ {x_i} $ Random demand faced by the retailer for the $ i $th product
    $ {L_i}, {U_i} $ Lower bound and upper bound on $ {x_i} $
    $ {f_i}({x_i}) $ Probability density function of the random variable $ {x_i} $
    $ {F_i}({x_i}) $ Cumulative distribution function of the random variable $ {x_i} $
    $ {a_i} $ Initial market size of the $ i $th product
    $ \alpha $ Demand sensitivity of product $ i $'s own quality improvement level
    $ \beta $ Competition intensity
    $ {s_i} $ Quality improvement level of the $ i $th product
    $ {Q_i} $ Production quantity for the $ i $th product
    $ {\eta _i} $ Risk aversion coefficient of the $ i $th manufacturer
    $ {k_i} $ Cost coefficient of investment in quality improvement of product $ i $
     | Show Table
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    Table 3.  Effect of the quality sensitivity on the expected profits and supply chain efficiency

    $ \alpha $ $ E\pi _r^{wp*} $ $ E\pi _m^{wp*} $ $ E\pi _{sc}^{wp*} $ $ E\pi _{sc}^{I*} $ $ {E_f} $
    1 24133 7722 39577 46960 84.28%
    2 26053 7962 41977 49960 84.02%
    3 28933 8362 45657 54960 83.07%
    4 32773 8922 51576 61960 81.69%
    5 37573 9642 56857 70960 80.13%
     | Show Table
    DownLoad: CSV

    Table 4.  Effect of the competition intensity on the expected profits and supply chain efficiency

    $ \beta $ $ E\pi _r^{wp*} $ $ E\pi _m^{wp*} $ $ E\pi _{sc}^{wp*} $ $ {E_f} $
    1 37573 9642 56857 80.13%
    2 39973 9402 58777 82.83%
    3 42373 9002 60377 85.09%
    4 44773 8442 61657 86.89%
    5 47173 7722 62617 88.24%
    6 49573 6842 63257 89.14%
    7 51973 5802 63577 89.60%
    8 54373 4602 63577 89.60%
    9 56773 3242 63257 89.14%
    10 59173 1722 62617 88.24%
     | Show Table
    DownLoad: CSV

    Table 5.  Effect of the risk aversion degree on the expected profits and supply chain efficiency

    $ \eta $ $ E\pi _r^{wp*} $ $ E\pi _m^{wp*} $ $ E\pi _{sc}^{wp*} $ $ {E_f} $
    1 38148 9833 57814 81.47%
    0.95 37861 9738 57337 80.80%
    0.9 37573 9642 56857 80.13%
    0.85 37286 9546 56378 79.45%
    0.8 36998 9451 55900 78.78%
     | Show Table
    DownLoad: CSV

    Table 6.  Effect of the cost coefficient of quality improvement on the expected profits and supply chain efficiency

    $ k $ $ E\pi _r^{wp*} $ $ E\pi _m^{wp*} $ $ E\pi _{sc}^{wp*} $ $ E\pi _{sc}^{I*} $ $ {E_f} $
    0.1 51973 11562 75097 95960 78.23%
    0.2 37573 9642 56857 70960 80.13%
    0.3 32773 9002 50777 62627 81.08%
    0.4 30373 8682 47737 58460 81.66%
    0.5 28933 8490 45913 55960 82.05%
     | Show Table
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    Table 7.  Effect of the quality sensitivity on the feasible region of option price

    $ \alpha $ 1 2 3 4 5
    feasible region of $ o $ $ [3.76, 4.16] $ [3.75, 4.17] [3.75, 4.20] [3.74, 4.23] [3.73, 4.27]
     | Show Table
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    Table 8.  Effect of the competition intensity on the feasible region of option price

    $ \beta $ 1 2 3 4 5
    feasible region of $ o $ [3.73, 4.27] [3.73, 4.23] [3.72, 4.20] [3.72, 4.17] [3.71, 4.16]
    $ \beta $ 6 7 8 9 10
    feasible region of $ o $ [3.69, 4.16] [3.68, 4.19] [3.66, 4.26] [3.63, 4.38] [3.59, 4.59]
     | Show Table
    DownLoad: CSV

    Table 9.  Effect of the risk aversion degree on the feasible region of option price

    $ \eta $ 0.94 0.92 0.90 0.88 0.86
    feasible region of $ o $ [3.24, 3.97] [3.49, 4.12] [3.73, 4.27] [3.98, 4.42] [4.24, 4.57]
     | Show Table
    DownLoad: CSV

    Table 10.  Effect of the cost coefficient of quality improvement on the feasible region of option price

    $ k $ 0.1 0.2 0.3 0.4 0.5
    feasible region of $ o $ [3.72, 4.33] [3.73, 4.27] [3.74, 4.24] [3.75, 4.22] [3.75, 4.21]
     | Show Table
    DownLoad: CSV
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