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Pricing strategy in an interval-valued production inventory model for high-tech products under demand disruption and price revision

  • *Corresponding author: Mijanur Rahaman Seikh

    *Corresponding author: Mijanur Rahaman Seikh 
Abstract Full Text(HTML) Figure(7) / Table(2) Related Papers Cited by
  • Due to continuous development in technology, new and updated products are launching in the market more frequently in the area of some high-tech products such as smartphones, laptops, etc. It is noticed that after a certain period of releasing a new product by a particular company some other company develops a similar type of product at a lesser selling price. Customers generally become attracted to buy that updated product causing a sudden disruption in the demand for the first product. The demand for a normal product may also suddenly vanish as we have experienced during the COVID-19 lockdown period. The manufacturer is then compelled to reduce the selling price to sell the remaining products. This paper aims at developing a single period production inventory model addressing this particular market condition. This paper also considers carbon emissions from different inventory processes and examines the optimal inventory policies under the cap and trade regulatory policy. Again, in a real-life production system, the various inventory cost components and the carbon emission rates from different inventory processes are not fixed always. To incorporate this issue, the proposed model considers these quantities as interval numbers. The resulting optimization problem is thus also interval-valued and has been solved by using the quantum-behaved particle swarm optimization technique. A numerical illustration is provided to validate the proposed model. Finally, a sensitivity analysis with respect to key inventory parameters is performed to derive some key managerial implications. It is found that the frequency of launching new products is inversely proportional to the optimum profit of the manufacturer. Also, a higher carbon tax rate is found to be beneficial from an environmental point of view.

    Mathematics Subject Classification: Primary: 90B05, 90B30; Secondary: 49N30, 90C59.

    Citation:

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  • Figure 1.  Research scheme of our paper

    Figure 2.  Behaviour of the inventory level with respect to time

    Figure 3.  Concavity of the profit function w.r.t. $ t_1 $ and $ m $

    Figure 4.  Impact on the optimal profit and optimal carbon emission due to changes in $ \alpha $

    Figure 5.  Impact on the optimal profit and optimal cycle length due to changes in $ \beta $

    Figure 6.  Impact on the optimal profit and optimal cycle length due to changes in $ t_3 $

    Figure 7.  Impact on the optimal profit and optimal carbon emission due to changes in $ \bar{c_1} $

    Table 1.  Summary of literature survey

    References Demand depends on Demand disruption Pricing strategy Imprecise cost parameter Carbon emission Imprecise emission rate Cap and trade policy
    Rana et al. [37] time $ \checkmark $
    Ali et al. [1] price & service level $ \checkmark $ $ \checkmark $
    Wu et al. [61] price $ \checkmark $ $ \checkmark $
    Cao [5] price $ \checkmark $ $ \checkmark $
    Bhunia et. al [4] price, time & advertisement $ \checkmark $
    San-Jos$ \acute{e} $ et al. [45] price, time & advertisement $ \checkmark $
    Sepehri and Gholamian [46] price $ \checkmark $ $ \checkmark $ $ \checkmark $
    Qu et al. [35] price & warranty period $ \checkmark $ $ \checkmark $ $ \checkmark $
    Ruidas et al. [39] price $ \checkmark $ $ \checkmark $ $ \checkmark $ $ \checkmark $ $ \checkmark $
    Gupta et al. [19] price, advertisement & stock level $ \checkmark $
    Ruidas et al. [43] price, time & advertisement $ \checkmark $ $ \checkmark $
    Proposed model price, time & advertisement $ \checkmark $ $ \checkmark $ $ \checkmark $ $ \checkmark $ $ \checkmark $ $ \checkmark $
     | Show Table
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    Table 2.  Sensitivity analysis

    Para meter Changes $ t_1^* $ $ m^* $ $ p^* $ Optimal profit $ T^* $ Lot size Carbon emission
    $ \alpha $ 355 0.17270 1.45493 104.03 [114.67, 287.68] 2.39599 120.89 [1477.52, 1643.34]
    360 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    365 0.16861 1.45521 104.05 [285.23, 500.86] 1.72357 118.03 [1946.66, 2152.35]
    $ \beta $ 2.9 0.17100 1.46419 104.69 [410.73, 643.00] 1.62241 119.70 [2109.67, 2331.19]
    3.0 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    3.1 0.17291 1.44652 103.42 [34.62, 199.66] 2.60076 121.04 [1381.65, 1540.06]
    $ t_3 $ 1.4 0.17171 1.46581 104.81 [178.32, 356.10] 2.27236 120.20 [1537.92, 1708.13]
    1.5 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    1.6 0.17219 1.44637 103.40 [213.47, 414.15] 1.93925 120.53 [1777.45, 1969.25]
    $ X $ 680 0.17707 1.45472 104.01 [196.64, 385.00] 2.09719 120.41 [1652.65, 1832.80]
    700 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    720 0.16697 1.45542 104.06 [194.48, 382.66] 2.10102 120.22 [1649.15, 1829.14]
    $ C $ 35 0.16796 1.45036 103.70 [190.90, 379.31] 2.02636 117.57 [1670.54, 1850.51]
    40 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    45 0.17633 1.46035 104.43 [200.25, 389.50] 2.17013 123.43 [1639.34, 1820.61]
    $ A $ 7 0.17060 1.45949 104.35 [182.14, 363.09] 2.19535 119.42 [1578.43, 1752.02]
    8 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    9 0.17309 1.45125 103.95 [207.52, 403.22] 2.01279 121.16 [1722.83, 1909.47]
    $ \lambda $ 0.45 0.16777 1.43493 102.60 [262.57, 461.62] 1.78169 117.44 [1880.62, 2080.04]
    0.50 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    0.55 0.17371 1.47242 105.28 [134.10, 318.82] 2.34277 121.60 [1512.42, 1681.33]
    $ l $ 0.93 0.16039 1.44121 103.05 [173.02, 379.07] 1.72905 112.27 [1869.26, 2065.62]
    0.95 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    0.97 0.18164 1.46798 104.96 [224.87, 403.38] 2.42734 127.15 [1516.83, 1688.15]
    $ \bar{c_0} $ [1090,1110] 0.17109 1.45410 103.97 [199.84, 389.07] 2.07352 119.76 [1663.27, 1844.20]
    [1100,1120] 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    [1110,1130] 0.17270 1.45596 104.10 [191.22, 378.63] 2.12447 120.89 [1639.34, 1818.63]
    $ \bar{c_1} $ [68.5, 69.5] 0.16815 1.46492 101.81 [305.21, 527.76] 1.65435 117.70 [2018.39, 2230.60]
    [70.5, 71.5] 0.17187 1.45506 104.04 [195.52, 383.80] 2.09882 120.31 [1651.05, 1831.13]
    [72.5, 73.5] 0.17219 1.44174 105.97 [97.90, 268.87] 2.43368 120.53 [1455.07, 1618.96]
     | Show Table
    DownLoad: CSV
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