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Note on : Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit risk customers

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  • In the recently published paper [Gour Chandra Mahata and Sujit Kumar De, Supply chain inventory model for deteriorating items with maximum lifetime and partial trade credit to credit-risk customers, International Journal of Management Science and Engineering Management, 2017, DOI:10.1080/17509653.2015.1109482], a supplier-retailer supply chain model of a deteriorating item with maximum lifetime and partial trade credit to credit risk customers is studied. In their study, unfortunately the amount of the payable bank interest due to the deteriorated units is omitted in the retailer's profit function for making the marketing decision. Some other unrealistic studies are also found in the numerical section of the paper. In this study those non-trivial flaws are identified and technically corrected. After correction, the theoretical existence of the optimal solutions of different scenarios are established and the solutions are derived using a soft computing technique.

    Mathematics Subject Classification: Primary: 90B05; Secondary 91B60.

    Citation:

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  • Figure 1.  Pictorial representation of situation 1.1

    Figure 2.  Interest earn and paid situations for the sold units

    Figure 3.  Interest paid situation due to deteriorated units

    Figure 4.  Pictorial representation of situation 1.2

    Figure 5.  Interest earn and paid situations for the sold units

    Figure 6.  Interest paid situation due to deteriorated units

    Figure 7.  Pictorial representation of situation 1.3

    Figure 8.  Interest earn and paid situations for the sold units

    Figure 9.  Interest paid situation due to deteriorated units

    Figure 10.  Pictorial representation of situation 2.1

    Figure 11.  Interest earn and paid situations for the sold units

    Figure 12.  Interest paid situation due to deteriorated units

    Figure 13.  Pictorial representation of situation 2.2

    Figure 14.  Interest earn and paid situations for the sold units

    Figure 15.  Interest paid situation due to deteriorated units

    Table 1.  Innovation of this paper related to the exiting literature

    Article Deteriorating item Level of trade credit Pattern of trade credit Deterioration rate Item(s) has expiration time Interest paid for deteriorated units
    [8,11,15,37,38] $\surd$ $\times$ NA Constant $\times$ NA
    [35] $\surd$ $\times$ NA Constant $\surd$ NA
    [1] $\surd$ Supplier-Retailer Full credit Constant $\times$ $\times$
    [2,14,26] $\surd$ Supplier-Retailer Ordered quantity based full/ partial credit Constant $\times$ $\times$
    [3,6,13,21,25] $\surd$ Supplier-Retailer Full credit Constant $\times$ $\times$
    Retailer-Customers Full credit
    [20] $\surd$ Supplier-Retailer Full credit Constant $\times$ $\times$
    Retailer-Customers Partial credit
    [7,27,34] $\surd$ $\times$ NA Time dependent $\times$ NA
    [5] $\surd$ Supplier-Retailer Order quantity based full credit Time dependent $\times$ $\times$
    [22] $\surd$ Supplier-Retailer Full credit Time dependent $\surd$ $\times$
    Retailer-Customers Partial credit
    This Paper $\surd$ Supplier-Retailer Full credit Time dependent $\surd$ $\surd$
    Retailer-Customers Partial credit
    NA stands for ‘Not Applicable’.
     | Show Table
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    Table 2.  Results of the model

    Example Appropriate for $T^*$ $Q^*$ $TP^*(T^*)$
    5.1 Situation 1.1 $T_{11}=0.1346$ 319.396 $TP_{11}(T_{11})=9824.71$
    5.2 Situation 1.2 $T_{12}=0.1404$ 291.159 $TP_{12}(T_{12})=8643.00$
    5.3 Situation 1.3 $T_{13}=0.1365$ 296.892 $TP_{13}(T_{13})=8942.34$
    5.4 Situation 2.1 $T_{21}=0.1382$ 273.311 $TP_{21}(T_{21})=8087.69$
    5.5 Situation 2.2 $T_{22}=0.1374$ 256.299 $TP_{22}(T_{22})=7716.36$
     | Show Table
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    Table 3.  Sensitivity Analysis

    Parameter $T^*$ $Q^*$ $TP^*(T^*)$
    2000 0.1404 291.159 8643.00
    D 2500 0.1259 325.220 10991.49
    3000 0.1151 355.645 13355.68
    0.16 0.1404 291.159 8643.00
    M 0.20 0.1395 289.318 8664.18
    0.25 0.1392 288.595 8694.01
    50 0.1000 205.167 9058.72
    A 100 0.1404 291.159 8643.00
    200 0.1958 412.145 8048.82
    1 0.1404 291.159 8643.00
    m 2 0.1569 322.272 8780.27
    3 0.1670 341.100 8853.89
    0.02 0.1409 292.159 8637.78
    $I_{e}$ 0.03 0.1404 291.159 8643.00
    0.04 0.1398 289.933 8648.24
    0.05 0.1404 291.159 8643.00
    $\alpha$ 0.10 0.1402 290.779 8645.21
    0.20 0.1403 290.972 8649.619
    0.04 0.1396 289.443 8662.98
    N 0.08 0.1404 291.159 8643.00
    0.12 0.1407 291.855 8626.29
    1 0.1894 398.066 16983.74
    c 3 0.1595 332.370 12795.03
    5 0.1404 291.159 8643.00
    1 0.1569 326.853 8795.10
    h 2 0.1404 291.159 8643.00
    4 0.1189 244.171 8380.12
    0.02 0.1410 292.351 8644.47
    $I_{c}$ 0.03 0.1404 291.159 8643.00
    0.04 0.1400 290.248 8641.556
    10 0.1404 291.159 8643.00
    s 15 0.1396 289.442 18650.87
    20 0.1390 288.053 28658.77
     | Show Table
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