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An integrated inventory model with variable holding cost under two levels of trade-credit policy

* Corresponding author: sankroy2006@gmail.com
The reviewing process of this paper was handled by Associate Editors A. (Nima) Mirzazadeh, Kharazmi University, Tehran, Iran, and Gerhard-Wilhelm Weber, Middle East Technical University, Ankara, Turkey. "This paper was for the occasion of The 12th International Conference on Industrial Engineering (ICIE 2016), which was held in Tehran, Iran during 25-26 January, 2016".The author, Magfura Pervin is very much thankful to University Grants Commission (UGC) of India for providing financial support to continue this research work under [MANF(UGC)] scheme: Sanctioned letter number [F1-17.1/2012-13/MANF-2012-13-MUS-WES-19170/(SA-Ⅲ/Website)] dated 28/02/2013

The research of Gerhard-Wilhelm Weber (Institute of Applied Mathematics, Middle East Technical University, 06800, Ankara, Turkey) is partially supported by the Portuguese Foundation for Science and Technology ("FCT-Fundação para a Ciência e a Tecnologia"), through the CIDMA -Center for Research and Development in Mathematics and Applications, within project UID/MAT/ 04106/2013

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  • This paper presents an integrated vendor-buyer model for deteriorating items. We assume that the deterioration follows a constant rate with respect to time. The vendor allows a certain credit period to buyer in order to promote the market competition. Keeping in mind the competition of modern age, the stock-dependent demand rate is included in the formulated model which is a new policy to attract more customers. Shortages are allowed for the model to give the model more realistic sense. Partial backordering is offered for the interested customers, and there is a lost-sale cost during the shortage interval. The traditional parameter of holding cost is considered here as time-dependent. Henceforth, an easy solution procedure to find the optimal order quantity is presented so that the total relevant cost per unit time will be minimized. The mathematical formation is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution for important parameters is also carried out to modify the result of the model.

    Mathematics Subject Classification: Primary: 90B05, 91B70; Secondary: 91B24.

    Citation:

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  • Figure 1.  Graphical representation of Inventory model for a Vendor

    Figure 2.  Graphical representation of a Buyer's Inventory model

    Figure 5.  The convexity of the integrated cost described in Example 1. Included are $T$ , $M$ and the integrated cost $TC$ , along the x-axis, the y-axis and the z-axis, respectively

    Figure 6.  The convexity of the integrated cost showed in Example 2. Represented are $T$ , $M$ and the integrated cost $TC$ , along the x-axis, the y-axis and the z-axis, respectively

    Figure 7.  The convexity of the integrated cost presented in Example 3. Followed are $T$ , $M$ and the integrated cost $TC$ , along the x-axis, the y-axis and the z-axis, respectively

    Figure 3.  $TC$ vs. $T$ at $M = 0.1091$

    Figure 4.  $TC$ vs. $M$ at $T = 0.0870$

    Figure 8.  Sensitivity analysis of $\theta$

    Figure 9.  Sensitivity analysis of $\alpha$

    Figure 10.  Sensitivity analysis of $h$

    Figure 11.  Schematic view of all parameters

    Table 1.  Previous works of different authors in this field including our work

    Author(s)
    Aggarwal and Jaggi [1] $\surd$ $\surd$
    Ouyang et al. [23] $\surd$
    Huang et al. [13] $\surd$ $\surd$
    Tripathi and Pandey [30] $\surd$ $\surd$
    Mahata [22] $\surd$ $\surd$
    Goswami and Chaudhuri [9] $\surd$ $\surd$
    Teng and Chang [29] $\surd$ $\surd$
    Law and Wee [18] $\surd$ $\surd$ $\surd$
    Jolai et al. [15] $\surd$ $\surd$ $\surd$
    Lo et al. [21] $\surd$ $\surd$
    Pervin et al. [24] $\surd$ $\surd$
    Pervin et al. [25] $\surd$ $\surd$ $\surd$
    Our paper $\surd$ $\surd$ $\surd$ $\surd$ $\surd$ $\surd$
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    Table 2.  Sensitivity analysis for different parameters involved in Example 1

    Parameter parametric value after % change $T$ $M$ $TC_V$ $TC_B$ $TC$
    $A$ 375 0.0910 0.1129 4527.31 4032.05 3461.12
    312.5 0.0873 0.1091 4578.44 4113.10 3478.69
    275 0.0821 0.1051 4629.73 4150.03 3510.85
    $s$ 1.35 0.0674 0.1104 4655.28 4187.46 3382.38
    1.125 0.0763 0.1096 4022.38 3810.14 3412.19
    0.99 0.0791 0.1052 4065.19 3843.52 3487.71
    $c$ 120 0.0683 0.1027 4122.16 3874.00 3560.31
    100 0.0724 0.1035 4203.23 3890.64 3619.41
    88 0.0812 0.1037 4247.11 3915.26 3670.10
    $a$ 0.9 0.0690 0.1366 3877.35 3682.34 3510.94
    0.75 0.0728 0.1380 3852.55 3650.34 3422.30
    0.66 0.0749 0.1418 3796.21 3614.57 3392.62
    $b$ 1.2 0.0467 0.1510 3785.04 3654.87 3473.22
    1.0 0.0511 0.1572 3751.39 3627.95 3376.99
    0.88 0.0585 0.1618 3728.45 3567.53 3108.04
    $c_1$ 60 0.0814 0.1136 4242.33 3735.10 3630.44
    50 0.0889 0.1219 4407.61 3846.72 3780.00
    44 0.0926 0.1305 4521.17 3918.34 3822.35
    $c_2$ 90 0.0672 0.1158 4176.88 3839.15 3610.23
    75 0.0779 0.1227 4366.08 3882.46 3679.14
    66 0.0837 0.1293 4541.00 3918.27 3746.22
    $\alpha$ 450 0.0832 0.1745 3983.52 3728.61 3555.22
    375 0.0811 0.1659 3875.00 3984.17 3487.20
    330 0.0768 0.1633 3854.33 3729.26 3390.38
    $\beta$ 1.05 0.0577 0.1594 4539.74 4218.40 3671.99
    0.875 0.0597 0.1677 4487.23 4179.30 3647.19
    0.77 0.0649 0.1626 4435.41 4027.64 3557.73
    $I_e$ 0.285 0.0855 0.1547 4923.07 4500.68 3750.08
    0.2375 0.0732 0.1588 4846.31 4483.47 3921.39
    0.209 0.0611 0.1470 4736.58 4375.07 3982.63
    $\theta$ 1.35 0.0769 0.1720 4739.13 4460.53 3699.28
    1.125 0.0732 0.1693 4688.57 4379.24 3642.57
    0.99 0.0684 0.1647 4635.14 4316.20 3571.26
    $\delta$ 0.9 0.0592 0.1281 4037.45 3658.74 3429.50
    0.75 0.0633 0.1357 4168.70 3791.26 3557.35
    0.66 0.0748 0.1414 4231.05 3834.00 3658.10
     | Show Table
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