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A production inventory model for high-tech products involving two production runs and a product variation

  • *Corresponding author: Mijanur Rahaman Seikh

    *Corresponding author: Mijanur Rahaman Seikh 
Abstract Full Text(HTML) Figure(7) / Table(2) Related Papers Cited by
  • This paper explores a production inventory model considering two high-tech products of the same kind. One is the primary product and the other is the updated version of that primary product. Due to continuous development in technology, the life-cycle of some high-tech products, like, smartphone, tablet, laptop, etc. have become shorter. We witness the launching of new products more frequently in this field. This prompts the manufacturers to release an updated or pro version of their existing products after a certain time to compete in the market. The reputation of the primary product (in terms of quality and performance) plays an important role in generating the demand for the updated product. Due to the short life-cycle of the products, the proposed model considers only two consecutive production runs. One for the primary product and one for the updated product. Here the demands of both the products depend on the respective selling prices. Moreover, the demand of the updated product is also dependent on the quality of the primary product. Shortages for the primary product are allowed. Those shortages are backlogged partially with the updated product. Also, the possibility of imperfect production during regular production runs is considered. The selling prices, production rates, and the production run times for both the products are considered here as decision variables. Due to the complexity in the resulting optimization problem, the quantum-behaved particle swarm optimization technique is applied to derive the optimal profit. The concavity natures of the profit function are shown graphically. A numerical illustration is presented for the economic validation of the model. Finally, sensitivity analysis of the optimal solutions concerning the key inventory parameters is conducted for identifying several managerial implications.

    Note: The affiliations of the three authors have been corrected online.

    Mathematics Subject Classification: Primary: 90B05, 90B30; Secondary: 80M50.

    Citation:

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  • Figure 1.  Behaviour of the inventory level over time

    Figure 2.  Concavity of the profit function w.r.t. selling price and time

    Figure 3.  Concavity of the profit function w.r.t. production rate and time

    Figure 4.  Effect of changing $ t_3 $ on optimal solutions

    Figure 5.  Effect of changing $ \beta $ on optimal lot size

    Figure 6.  Effect of changing $ r_1 $ on optimal solution

    Figure 7.  Effect of changing $ b_1 $ on optimal solution

    Table 1.  Summary of literature review

    Author(s) EOQ/ EPQ Nature of demand Defective product? Single/ multi product? product updation considered? Demand of updated product depends on quality of primary product? Shor-tages
    Datta [11] EPQ price & quality dependent yes single no NA no
    Khara et al. [20] EPQ price, reliability & advertisement dependent yes single no NA no
    Liu et al. [23] EOQ price & quality dependent no single no NA no
    Banerjee & Agarwal [4] EOQ price & freshness dependent no single no NA yes
    Masache [30] EOQ deterministic no two no NA no
    Stavrulaki [62] EOQ stochastic no two no NA no
    Aggarwal et al. [1] EOQ deterministic no two yes no no
    Chanda & Aggarwal [6] EOQ deterministic no two yes no no
    Chiu et al. [9] EPQ deterministic yes multi no no no
    Proposed model EPQ price & quality dependent yes two yes yes yes
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    Table 2.  Sensitivity analysis

    Parameter Changes $ t_1 $ $ t_5 $ $ p_1 $ $ p_2 $ Profit $ Q_1 $ $ Q_2 $ $ T $
    $ t_3 $ 7.0 5.23913 11.47573 249.30 318.49 9201.75 1149.88 969.58 12.45178
    8.0 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    9.0 8.26835 14.60134 227.05 312.29 8744.92 1814.74 1213.42 15.56001
    $ \beta $ 0.08 7.20770 10.88072 228.66 325.62 8035.87 1581.95 624.05 11.99597
    0.09 7.14791 11.70929 229.03 321.76 8420.30 1568.82 803.54 12.78338
    1.0 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    $ A_1 $ 560 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    570 7.36848 12.03052 233.79 319.83 9687.66 1617.23 873.13 12.93037
    580 7.48057 11.00804 240.83 325.77 10564.71 1641.83 651.63 11.84619
    $ A_2 $ 520 7.24766 10.74417 228.39 322.95 7921.57 1590.72 594.47 11.76943
    530 7.09583 11.06169 230.14 321.93 8353.59 1557.39 780.23 12.69032
    540 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    $ r_1 $ 0.7 7.52533 8.63797 227.84 353.82 10037.19 1651.66 138.20 8.72560
    0.75 7.40191 10.30894 227.36 329.26 9323.61 1624.57 500.19 11.13030
    0.80 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    $ b_1 $ 1.3 7.38216 8.36716 264.23 375.81 14380.91 1620.24 123.37 8.41877
    1.4 7.25239 10.00467 248.81 334.35 10932.50 1591.76 434.27 10.62091
    1.5 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    $ b_2 $ 1.5 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    1.6 7.21987 10.47846 229.30 318.94 7653.91 1584.62 536.91 11.40339
    1.7 7.37527 8.50460 228.27 360.32 7093.80 1618.72 112.83 8.54607
    $ a $ 0.2 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    0.22 6.25516 12.52256 243.34 324.01 7730.56 1372.88 979.72 13.68868
    0.24 5.33047 11.74581 258.78 334.01 6649.15 1169.93 811.46 13.04623
    $ M_1 $ 120 7.44172 10.67127 227.19 330.36 10638.59 1633.31 578.68 11.45049
    125 7.33320 11.94581 227.62 321.13 9715.03 1609.49 854.78 12.86613
    130 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    $ M_2 $ 150 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    155 7.07835 11.73647 231.02 327.66 8401.95 1553.56 809.43 12.78843
    160 7.11430 10.76954 230.57 338.94 8009.73 1561.45 599.94 11.81604
    $ \delta $ 0.6 6.82219 13.03966 234.36 318.36 8928.81 1497.33 1091.74 14.10543
    0.7 7.04729 13.32953 231.39 314.59 8897.09 1546.74 1154.54 14.35523
    0.8 7.27322 13.54918 228.21 311.69 8867.08 1596.33 1202.12 14.53423
     | Show Table
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