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

Si-Han Wang; Dan-Yang Lv; Ji-Bo Wang

doi:10.3934/jimo.2022066

Article Contents

2023, Volume 19, Issue 4: 2824-2837. Doi: 10.3934/jimo.2022066

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

School of Science, Shenyang Aerospace University, Shenyang 110136, China

^*Corresponding author: Ji-Bo Wang
^*Corresponding author: Ji-Bo Wang

Received: January 2022

Revised: March 2022

Published: April 2023

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)

Abstract Full Text(HTML) Figure(0) / Table(5) Related Papers Cited by

Abstract

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.

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

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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

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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

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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

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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

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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

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