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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

Received  January 2022 Revised  March 2022 Early access April 2022

Fund Project: 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)

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.

Citation: Si-Han Wang, Dan-Yang Lv, Ji-Bo Wang. Research on position-dependent weights scheduling with delivery times and truncated sum-of-processing-times-based learning effect. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022066
References:
[1]

C.C. WuY. YinW.H. Wu and S.R. Cheng, Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect, European Journal of Industrial Engineering, 6 (2012), 441-453.  doi: 10.1016/j.apm.2009.12.015.

[2]

T.C.E. Cheng, C.-C. Wu, J.-C. Chen, W.-H. Wu and S.-R. Cheng, Two-machine flowshop scheduling with a truncated learning function to minimize the makespan, International Journal of Production Economics, 141 (2013), 79-86.

[3]

C.-C. WuW.-C. Lee and M.-J. Liou, Single-machine scheduling with two competing agents and learning consideration, Information Sciences, 251 (2013), 136-149.  doi: 10.1016/j.ins.2013.06.054.

[4]

J.-B. WangM. LiuN. Yin and P. Ji, Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects, Journal of Industrial and Management Optimization, 13 (2017), 1025-1039.  doi: 10.3934/jimo.2016060.

[5]

A. Azzouz, M. Ennigrou and L.B. Said, Scheduling problems under learning effects: classification and cartography, International Journal of Production Research, 56 (2018), 1642-1661.

[6]

X.-X. LiangB. ZhangJ.-B. WangN. Yin and X. Huang, Study on flow shop scheduling with sum-of-logarithm-processing-times-based learning effects, Journal of Applied Mathematics and Computing, 61 (2019), 373-388.  doi: 10.1007/s12190-019-01255-0.

[7]

J.-B. Wang, F. Liu and J.-J. Wang, Research on $m$-machine flow shop scheduling with truncated learning effects, International Transactions in Operational Research, 26 (2019), 1135-1151. doi: 10.1111/itor.12323.

[8]

J.-B. Wang, M. Gao, J.-J. Wang, L. Liu and H. He, Scheduling with a position-weighted learning effect and job release dates, Engineering Optimization, 52 (2020), 1475-1493. doi: 10.1080/0305215X.2019.1664498.

[9]

L. SunA.J. Yu and B. Wu, Single machine common flow allowance group scheduling with learning effect and resource allocation, Computers & Industrial Engineering, 139 (2020), 106126. 

[10]

D.-Y. LvS.-W. LuoJ. XueJ.-X. Xu and J.-B. Wang, A note on single machine common flow allowance group scheduling with learning effect and resource allocation, Computers & Industrial Engineering, 151 (2021), 106941. 

[11]

H.-B. Shi and J.-B. Wang, Research on common due window assignment flowshop scheduling with learning effect and resource allocation, Engineering Optimization, 52 (2020), 669-686.  doi: 10.1080/0305215X.2019.1604698.

[12]

D.-Y. Lv and J.-B. Wang, Study on resource-dependent no-wait flow shop scheduling with different due-window assignment and learning effects, Asia-Pacific Journal of Operational Research, 38 (2021), 2150008.  doi: 10.1142/s0217595921500081.

[13]

J.-B. WangD.-Y. LvJ. Xu and P. Ji anmd F. Li, Bicriterion scheduling with truncated learning effects and convex controllable processing times, International Transactions in Operational Research, 28 (2021), 1573-1593.  doi: 10.1111/itor.12888.

[14]

D. BaiX. BaiJ. YangX. ZhangT. RenC. Xie and B. Liu, Minimization of maximum lateness in a flowshop learning effect scheduling with release dates, Computers & Industrial Engineering, 158 (2021), 107309. 

[15]

Z. JiangF. Chen and X. Zhang, Single-machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect, Journal of Combinatorial Optimization, 43 (2022), 116-139.  doi: 10.1007/s10878-021-00752-y.

[16]

C. Koulamas and G.J. Kyparisis, Single-machine scheduling problems with past-sequence-dependent delivery times, International Journal of Production Economics, 126 (2010), 264-266.  doi: 10.1016/j.ejor.2006.03.066.

[17]

M. MateoJ. Teghem and D. Tuyttens, A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs, International Journal of Production Research, 56 (2018), 1030-1053. 

[18]

M. Liu, Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect, Applied Mathematical Modelling, 37 (2013), 9630-9633.  doi: 10.1016/j.apm.2013.05.025.

[19]

M. LiuS. Wang and C. Chu, Scheduling deteriorating jobs with past-sequence-dependent delivery times, International Journal of Production Economics, 144 (2013), 418-421. 

[20]

L. Shen and Y.B. Wu, Single machine past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects, Applied Mathematical Modelling, 37 (2013), 5444-5451.  doi: 10.1016/j.apm.2012.11.001.

[21]

Y.-B. Wu and J.-J. Wang, Single-machine scheduling with truncated sum-of-processing-times-based learning effect including proportional delivery times, Neural Computing & Applications, 27 (2016), 937-943. 

[22]

J.-B. WangB. CuiP. Ji and W.-W. Liu, Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times, Journal of Combinatorial Optimization, 41 (2021), 290-303.  doi: 10.1007/s10878-020-00676-z.

[23]

J.-B. WangJ. XueB. Cui and M. Gao, Single-machine scheduling problems with variable processing times and past-sequence-dependent delivery times, Asia-Pacific Journal of Operational Research, 39 (2022), 2150013. 

[24]

J. Qian and Y. Zhan, The due date assignment scheduling problem with delivery times and truncated sum-of-processing-times-based learning effect, Mathematics, 9 (2021), 3085-3098. 

[25]

W. LiuX. Hu and X.-Y. Wang, Single machine scheduling with slack due dates assignment, Engineering Optimization, 49 (2017), 709-717.  doi: 10.1080/0305215X.2016.1197611.

[26]

W.-W. Liu and C. Jiang, Flow shop resource allocation scheduling with due date assignment, learning effect and position-dependent weights, Asia-Pacific Journal of Operational Research, 37 (2020), 2050014.  doi: 10.1142/S0217595920500141.

[27]

J.-B. WangB. ZhangL. LiD. Bai and Y.-B. Feng, Due window assignment scheduling problems with position-dependent weights on a single machine, Engineering Optimization, 52 (2020), 185-193.  doi: 10.1080/0305215X.2019.1577411.

[28]

L.-Y. Wang, X. Huang, W.-W. Liu, Y.-B. Wu and J.-B. Wang, Scheduling with position-dependent weights, due-date assignment and past-sequence-dependent setup times, RAIRO-Operations Research, 55 (2021), S2747-S2758. doi: 10.1051/ro/2020117.

[29]

D.-Y. Lv and J.-B. Wang, Study on proportionate flowshop scheduling with due-date assignment and position-dependent weights, Optimization Letters, 15 (2021), 2311-2319.  doi: 10.1007/s11590-020-01670-4.

[30]

S. Zhao, Resource allocation flowshop scheduling with learning effect and slack due window assignment, Journal of Industrial and Management Optimization, 17 (2021), 2817-2835.  doi: 10.3934/jimo.2020096.

[31]

J.-B. WangB. Zhang and and H. He, A unified analysis for scheduling problems with variable processing times, Journal of Industrial and Management Optimization, 18 (2022), 1063-1077.  doi: 10.3934/jimo.2021008.

[32]

C. ZhaoY. YinT.C.E. Cheng and C.-C. Wu, Single-machine scheduling and due date assignment with rejection and position-dependent processing times, Journal of Industrial and Management Optimization, 10 (2014), 691-700.  doi: 10.3934/jimo.2014.10.691.

[33]

J.-B. WangJ.-X. XuF. Guo and M. Liu, Single-machine scheduling with job rejection, deteriorating effects, and past-sequence-dependent setup times, Engineering Optimization, 54 (2022), 471-486.  doi: 10.1080/0305215X.2021.1876041.

show all references

References:
[1]

C.C. WuY. YinW.H. Wu and S.R. Cheng, Some polynomial solvable single-machine scheduling problems with a truncation sum-of-processing-times based learning effect, European Journal of Industrial Engineering, 6 (2012), 441-453.  doi: 10.1016/j.apm.2009.12.015.

[2]

T.C.E. Cheng, C.-C. Wu, J.-C. Chen, W.-H. Wu and S.-R. Cheng, Two-machine flowshop scheduling with a truncated learning function to minimize the makespan, International Journal of Production Economics, 141 (2013), 79-86.

[3]

C.-C. WuW.-C. Lee and M.-J. Liou, Single-machine scheduling with two competing agents and learning consideration, Information Sciences, 251 (2013), 136-149.  doi: 10.1016/j.ins.2013.06.054.

[4]

J.-B. WangM. LiuN. Yin and P. Ji, Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects, Journal of Industrial and Management Optimization, 13 (2017), 1025-1039.  doi: 10.3934/jimo.2016060.

[5]

A. Azzouz, M. Ennigrou and L.B. Said, Scheduling problems under learning effects: classification and cartography, International Journal of Production Research, 56 (2018), 1642-1661.

[6]

X.-X. LiangB. ZhangJ.-B. WangN. Yin and X. Huang, Study on flow shop scheduling with sum-of-logarithm-processing-times-based learning effects, Journal of Applied Mathematics and Computing, 61 (2019), 373-388.  doi: 10.1007/s12190-019-01255-0.

[7]

J.-B. Wang, F. Liu and J.-J. Wang, Research on $m$-machine flow shop scheduling with truncated learning effects, International Transactions in Operational Research, 26 (2019), 1135-1151. doi: 10.1111/itor.12323.

[8]

J.-B. Wang, M. Gao, J.-J. Wang, L. Liu and H. He, Scheduling with a position-weighted learning effect and job release dates, Engineering Optimization, 52 (2020), 1475-1493. doi: 10.1080/0305215X.2019.1664498.

[9]

L. SunA.J. Yu and B. Wu, Single machine common flow allowance group scheduling with learning effect and resource allocation, Computers & Industrial Engineering, 139 (2020), 106126. 

[10]

D.-Y. LvS.-W. LuoJ. XueJ.-X. Xu and J.-B. Wang, A note on single machine common flow allowance group scheduling with learning effect and resource allocation, Computers & Industrial Engineering, 151 (2021), 106941. 

[11]

H.-B. Shi and J.-B. Wang, Research on common due window assignment flowshop scheduling with learning effect and resource allocation, Engineering Optimization, 52 (2020), 669-686.  doi: 10.1080/0305215X.2019.1604698.

[12]

D.-Y. Lv and J.-B. Wang, Study on resource-dependent no-wait flow shop scheduling with different due-window assignment and learning effects, Asia-Pacific Journal of Operational Research, 38 (2021), 2150008.  doi: 10.1142/s0217595921500081.

[13]

J.-B. WangD.-Y. LvJ. Xu and P. Ji anmd F. Li, Bicriterion scheduling with truncated learning effects and convex controllable processing times, International Transactions in Operational Research, 28 (2021), 1573-1593.  doi: 10.1111/itor.12888.

[14]

D. BaiX. BaiJ. YangX. ZhangT. RenC. Xie and B. Liu, Minimization of maximum lateness in a flowshop learning effect scheduling with release dates, Computers & Industrial Engineering, 158 (2021), 107309. 

[15]

Z. JiangF. Chen and X. Zhang, Single-machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect, Journal of Combinatorial Optimization, 43 (2022), 116-139.  doi: 10.1007/s10878-021-00752-y.

[16]

C. Koulamas and G.J. Kyparisis, Single-machine scheduling problems with past-sequence-dependent delivery times, International Journal of Production Economics, 126 (2010), 264-266.  doi: 10.1016/j.ejor.2006.03.066.

[17]

M. MateoJ. Teghem and D. Tuyttens, A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs, International Journal of Production Research, 56 (2018), 1030-1053. 

[18]

M. Liu, Parallel-machine scheduling with past-sequence-dependent delivery times and learning effect, Applied Mathematical Modelling, 37 (2013), 9630-9633.  doi: 10.1016/j.apm.2013.05.025.

[19]

M. LiuS. Wang and C. Chu, Scheduling deteriorating jobs with past-sequence-dependent delivery times, International Journal of Production Economics, 144 (2013), 418-421. 

[20]

L. Shen and Y.B. Wu, Single machine past-sequence-dependent delivery times scheduling with general position-dependent and time-dependent learning effects, Applied Mathematical Modelling, 37 (2013), 5444-5451.  doi: 10.1016/j.apm.2012.11.001.

[21]

Y.-B. Wu and J.-J. Wang, Single-machine scheduling with truncated sum-of-processing-times-based learning effect including proportional delivery times, Neural Computing & Applications, 27 (2016), 937-943. 

[22]

J.-B. WangB. CuiP. Ji and W.-W. Liu, Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times, Journal of Combinatorial Optimization, 41 (2021), 290-303.  doi: 10.1007/s10878-020-00676-z.

[23]

J.-B. WangJ. XueB. Cui and M. Gao, Single-machine scheduling problems with variable processing times and past-sequence-dependent delivery times, Asia-Pacific Journal of Operational Research, 39 (2022), 2150013. 

[24]

J. Qian and Y. Zhan, The due date assignment scheduling problem with delivery times and truncated sum-of-processing-times-based learning effect, Mathematics, 9 (2021), 3085-3098. 

[25]

W. LiuX. Hu and X.-Y. Wang, Single machine scheduling with slack due dates assignment, Engineering Optimization, 49 (2017), 709-717.  doi: 10.1080/0305215X.2016.1197611.

[26]

W.-W. Liu and C. Jiang, Flow shop resource allocation scheduling with due date assignment, learning effect and position-dependent weights, Asia-Pacific Journal of Operational Research, 37 (2020), 2050014.  doi: 10.1142/S0217595920500141.

[27]

J.-B. WangB. ZhangL. LiD. Bai and Y.-B. Feng, Due window assignment scheduling problems with position-dependent weights on a single machine, Engineering Optimization, 52 (2020), 185-193.  doi: 10.1080/0305215X.2019.1577411.

[28]

L.-Y. Wang, X. Huang, W.-W. Liu, Y.-B. Wu and J.-B. Wang, Scheduling with position-dependent weights, due-date assignment and past-sequence-dependent setup times, RAIRO-Operations Research, 55 (2021), S2747-S2758. doi: 10.1051/ro/2020117.

[29]

D.-Y. Lv and J.-B. Wang, Study on proportionate flowshop scheduling with due-date assignment and position-dependent weights, Optimization Letters, 15 (2021), 2311-2319.  doi: 10.1007/s11590-020-01670-4.

[30]

S. Zhao, Resource allocation flowshop scheduling with learning effect and slack due window assignment, Journal of Industrial and Management Optimization, 17 (2021), 2817-2835.  doi: 10.3934/jimo.2020096.

[31]

J.-B. WangB. Zhang and and H. He, A unified analysis for scheduling problems with variable processing times, Journal of Industrial and Management Optimization, 18 (2022), 1063-1077.  doi: 10.3934/jimo.2021008.

[32]

C. ZhaoY. YinT.C.E. Cheng and C.-C. Wu, Single-machine scheduling and due date assignment with rejection and position-dependent processing times, Journal of Industrial and Management Optimization, 10 (2014), 691-700.  doi: 10.3934/jimo.2014.10.691.

[33]

J.-B. WangJ.-X. XuF. Guo and M. Liu, Single-machine scheduling with job rejection, deteriorating effects, and past-sequence-dependent setup times, Engineering Optimization, 54 (2022), 471-486.  doi: 10.1080/0305215X.2021.1876041.

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
$i$ $i=1$ $i=2$ $i=3$ $i=4$ $i=5$
$\vartheta_{i}$ 5 4 9 8 2
$\upsilon_{i}$ 6 10 12 9 6
$\gamma_{i}$ 4 8 1 7 4
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
$\overline{J}_{i}$ $\overline{J}_5$ $\overline{J}_1$ $\overline{J}_3$ $\overline{J}_2$ $\overline{J}_4$
$p_{i}^A$ 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
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
$k$ $1$ $2$ $3$ $4$ $5$
$d$ 2 4.8795 8.7581 13.3165 18.5965
$G$ 85 149.1080 234.1944 343.5960 472.3160
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
$k$ $1$ $2$ $3$ $4$ $5$
$q$ 0 2.6000 5.5634 9.7165 14.3965
$G$ 37 94.4000 157.5216 257.1960 371.5160
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
$\overline{J}_{i}$ $\overline{J}_{5}$ $\overline{J}_{1}$ $\overline{J}_{3}$ $\overline{J}_{2}$ $\overline{J}_{4}$
$d_{i}$ 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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