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Research on position-dependent weights scheduling with delivery times and truncated sum-of-processing-times-based learning effect

  • *Corresponding author: Ji-Bo Wang

    *Corresponding author: Ji-Bo Wang

This Work Was Supported by LiaoNing Revitalization Talents Program (grant no. XLYC2002017) and the Natural Science Foundation of LiaoNing Province in China (grant no. 2020-MS-233)

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  • This paper considers single-machine position-dependent weights scheduling problem with past-sequence-dependent delivery times and truncated sum-of-processing-times-based learning effect. The objective is to minimize the weighted sum of due date, and the number of early jobs and tardy jobs, where the weights are position-dependent weights. Under the common due date, slack due date and different due date assignments, the optimal properties are given, and the corresponding optimal solution algorithms are respectively proposed to obtain the optimal sequence and optimal due dates of jobs.

    Mathematics Subject Classification: Primary: 90B35; Secondary: 90C26.

    Citation:

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  • Table 1.  Data of Example 1

    $i$ $i=1$ $i=2$ $i=3$ $i=4$ $i=5$
    $\vartheta_{i}$ 5 4 9 8 2
    $\upsilon_{i}$ 6 10 12 9 6
    $\gamma_{i}$ 4 8 1 7 4
     | Show Table
    DownLoad: CSV

    Table 2.  Results of Example 1

    $\overline{J}_{i}$ $\overline{J}_5$ $\overline{J}_1$ $\overline{J}_3$ $\overline{J}_2$ $\overline{J}_4$
    $p_{i}^A$ 2 2.2795 3.1947 3.6000 4.2000
    $q_{i}$ 0 0.6000 1.2839 2.2423 3.3223
    $W_{i}$ 0 2.0000 4.2795 7.4742 11.0742
    $C_{i}$ 2 4.8795 8.7581 13.3165 18.5965
     | Show Table
    DownLoad: CSV

    Table 3.  $\overbrace{con}$ results of Example 1

    $k$ $1$ $2$ $3$ $4$ $5$
    $d$ 2 4.8795 8.7581 13.3165 18.5965
    $G$ 85 149.1080 234.1944 343.5960 472.3160
     | Show Table
    DownLoad: CSV

    Table 4.  $\overbrace{slk}$ results of Example 1

    $k$ $1$ $2$ $3$ $4$ $5$
    $q$ 0 2.6000 5.5634 9.7165 14.3965
    $G$ 37 94.4000 157.5216 257.1960 371.5160
     | Show Table
    DownLoad: CSV

    Table 5.  $\overbrace{dif}$ results of Example 1

    $\overline{J}_{i}$ $\overline{J}_{5}$ $\overline{J}_{1}$ $\overline{J}_{3}$ $\overline{J}_{2}$ $\overline{J}_{4}$
    $d_{i}$ 0 0 8.7581 0 0
    $X_{i}$ 8 39.0360 8.7581 93.2155 74.3860
    $Y_{i}$ 6 10 12 9 6
    $G_{i}$ 6 10 8.7581 9 6
     | Show Table
    DownLoad: CSV
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