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Impact of cap-and-trade regulation on coordinating perishable products supply chain with cost learning

  • * Corresponding author: Fanwen Meng

    * Corresponding author: Fanwen Meng 
The research is partly supported by the National Natural Science Foundation of China under grants 71771138, 71702087 and 71701154, Humanities and Social Sciences Youth Foundation of Ministry of Education of China under grant 17YJC630004, Special Foundation for Taishan Scholars of Shandong Province, China under Grant tsqn201812061, and Science and Technology Research Program for Higher Education of Shandong Province, China under Grant 2019KJI006
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  • This paper incorporates carbon emission regulation and cost learning effects to examine a manufacturer-retailer supply chain for deteriorating items over a multi-period planning horizon. We investigate their impacts on supply chain coordination under the assumption that the product demand is affected by the selling price, promotional effort and inventory level. We first propose two algorithms for determining optimal solutions of the centralized and decentralized models. We show that the decentralized system can be coordinated perfectly with a two-part tariff contract. Further, we study necessary conditions under which members of the supply chain can accept this contract. At last, we conduct numerical experiment to illustrate the obtained theoretical results in impact analysis and the robustness of the coordinated model.

    Mathematics Subject Classification: Primary: 90B60, 91A05; Secondary: 90C46.

    Citation:

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  • Figure 1.  Graphical representation of inventory level at the retailer

    Figure 2.  Intervals of contract parameters to attain the win-win outcome

    Figure 3.  Impacts of $ C $ on profit and total emissions amount

    Figure 4.  Impacts of $ c_{p} $ on profit and total emissions amount

    Figure 5.  Impacts of $ \phi $ on profit and total emissions amount

    Figure 6.  Effects plot for the SN ratio of the coordination system

    Table 1.  The optimal solution of the example

    Model $ w $ $ s $ $ p $ $ n $ Retailer's Manufacturer's Total Total emissions
    profit profit profit amount
    Centralized - 12.15 213.75 3 - - 25589.00 285270
    Decentralized 56.76 6.08 256.88 3 3622.10 17045.00 20667.10 142640
    TT contract
    $ F=9850 $ 50 12.15 213.75 3 8539.00 17050.00 25589.00 285270
    $ F=12000 $ 50 12.15 213.75 3 6389.00 19200.00 25589.00 285270
    $ F=14750 $ 50 12.15 213.75 3 3639.00 21950.00 25589.00 285270
     | Show Table
    DownLoad: CSV

    Table 2.  Calculation results of $ L_{8} $ orthogonal array experiment for the coordination model

    No. A B C D E Total profit SN ratio of Total emissions SN ratio of total
    $ h_{r} $ $ \theta $ $ \phi $ $ C $ $ c_{p} $ total profit amount emissions amount
    1 1 1 1 1 1 43394 92.75 284600 -109.085
    2 1 1 1 2 2 38191 91.64 309080 -109.801
    3 1 2 2 1 1 15727 83.93 259150 -108.271
    4 1 2 2 2 2 6371 76.08 280390 -108.955
    5 2 1 2 1 2 39551 91.94 314060 -109.940
    6 2 1 2 2 1 32531 90.25 289570 -109.235
    7 2 2 1 1 2 15409 83.76 284830 -109.092
    8 2 2 1 2 1 13943 82.89 263590 -108.419
     | Show Table
    DownLoad: CSV

    Table 3.  Analysis of variance for the total profits and its SN ratio

    (a) Analysis of variance for the total profits
    Source df SS($ \times10^{8} $) MS($ \times10^{8} $) F P
    A 1 0.0063 0.0063 0.11 0.776
    B 1 13.0604 13.0604 217.25 0.005
    C 1 0.3510 0.3510 5.84 0.137
    D 1 0.6639 0.6639 11.04 0.080
    E 1 0.0461 0.0461 0.77 0.474
    Error 2 0.1202 0.0601 - -
    Total 7 14.2480 - - -
    (b) Analysis of variance for the SN ratio of the total profits
    Source df SS MS F P
    A 1 2.450 2.450 0.43 0.581
    B 1 199.178 199.178 34.55 0.028
    C 1 9.734 9.734 1.69 0.323
    D 1 16.603 16.603 2.88 0.232
    E 1 5.109 5.109 0.89 0.446
    Error 2 11.529 5.765 - -
    Total 7 244.604 - - -
     | Show Table
    DownLoad: CSV

    Table 4.  Analysis of variance for the carbon emissions and its SN ratio

    (a) Analysis of variance for the carbon emissions
    Source df SS($ \times10^{8} $) MS($ \times10^{8} $) F P
    A 1 0.4432 0.4432 16.84 0.055
    B 1 14.9468 14.9468 567.78 0.002
    C 1 0.0014 0.0014 0.05 0.837
    D 1 0.0000 0.0000 0.00 0.998
    E 1 10.4539 10.4539 397.11 0.003
    Error 2 0.0527 0.0263 - -
    Total 7 25.8979 - - -
    (b) Analysis of variance for the SN ratio of the carbon emissions
    Source df SS MS F P
    A 1 0.0411 0.04107 157.77 0.006
    B 1 1.3819 1.3819 5307.76 0.000
    C 1 0.0000 0.0000 0.01 0.920
    D 1 0.0001 0.0001 0.25 0.669
    E 1 0.9655 0.9655 3708.69 0.000
    Error 2 0.0005 0.0003 - -
    Total 7 2.3891 - - -
     | Show Table
    DownLoad: CSV
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