# American Institute of Mathematical Sciences

• Previous Article
A study on vector variational-like inequalities using convexificators and application to its bi-level form
• JIMO Home
• This Issue
• Next Article
Effect of service quality on software sales and coordination mechanism in IT service supply chain
doi: 10.3934/jimo.2022066
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## 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. Wu, Y. Yin, W.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. Wu, W.-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. Wang, M. Liu, N. 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. Liang, B. Zhang, J.-B. Wang, N. 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. Sun, A.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. Lv, S.-W. Luo, J. Xue, J.-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. Wang, D.-Y. Lv, J. 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. Bai, X. Bai, J. Yang, X. Zhang, T. Ren, C. 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. Jiang, F. 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. Mateo, J. 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. Liu, S. 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. Wang, B. Cui, P. 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. Wang, J. Xue, B. 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. Liu, X. 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. Wang, B. Zhang, L. Li, D. 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. Wang, B. 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. Zhao, Y. Yin, T.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. Wang, J.-X. Xu, F. 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. Wu, Y. Yin, W.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. Wu, W.-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. Wang, M. Liu, N. 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. Liang, B. Zhang, J.-B. Wang, N. 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. Sun, A.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. Lv, S.-W. Luo, J. Xue, J.-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. Wang, D.-Y. Lv, J. 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. Bai, X. Bai, J. Yang, X. Zhang, T. Ren, C. 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. Jiang, F. 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. Mateo, J. 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. Liu, S. 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. Wang, B. Cui, P. 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. Wang, J. Xue, B. 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. Liu, X. 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. Wang, B. Zhang, L. Li, D. 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. Wang, B. 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. Zhao, Y. Yin, T.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. Wang, J.-X. Xu, F. 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.
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
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
$\overbrace{con}$ 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
$\overbrace{slk}$ 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
$\overbrace{dif}$ 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
 [1] Chuanli Zhao, Yunqiang Yin, T. C. E. Cheng, Chin-Chia Wu. Single-machine scheduling and due date assignment with rejection and position-dependent processing times. Journal of Industrial and Management Optimization, 2014, 10 (3) : 691-700. doi: 10.3934/jimo.2014.10.691 [2] Mehmet Duran Toksari, Emel Kizilkaya Aydogan, Berrin Atalay, Saziye Sari. Some scheduling problems with sum of logarithm processing times based learning effect and exponential past sequence dependent delivery times. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1795-1807. doi: 10.3934/jimo.2021044 [3] Shuang Zhao. Resource allocation flowshop scheduling with learning effect and slack due window assignment. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2817-2835. doi: 10.3934/jimo.2020096 [4] Xianyu Yu, Dar-Li Yang, Dequn Zhou, Peng Zhou. Multi-machine scheduling with interval constrained position-dependent processing times. Journal of Industrial and Management Optimization, 2018, 14 (2) : 803-815. doi: 10.3934/jimo.2017076 [5] Ji-Bo Wang, Dan-Yang Lv, Shi-Yun Wang, Chong Jiang. Resource allocation scheduling with deteriorating jobs and position-dependent workloads. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022011 [6] Shan-Shan Lin. Due-window assignment scheduling with learning and deterioration effects. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2567-2578. doi: 10.3934/jimo.2021081 [7] Ran Ma, Lu Zhang, Yuzhong Zhang. A best possible algorithm for an online scheduling problem with position-based learning effect. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021144 [8] Yunqiang Yin, T. C. E. Cheng, Jianyou Xu, Shuenn-Ren Cheng, Chin-Chia Wu. Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration. Journal of Industrial and Management Optimization, 2013, 9 (2) : 323-339. doi: 10.3934/jimo.2013.9.323 [9] Hongwei Li, Yuvraj Gajpal, C. R. Bector. A survey of due-date related single-machine with two-agent scheduling problem. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1329-1347. doi: 10.3934/jimo.2019005 [10] Ping Yan, Ji-Bo Wang, Li-Qiang Zhao. Single-machine bi-criterion scheduling with release times and exponentially time-dependent learning effects. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1117-1131. doi: 10.3934/jimo.2018088 [11] Sachiko Ishida. Global existence and boundedness for chemotaxis-Navier-Stokes systems with position-dependent sensitivity in 2D bounded domains. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3463-3482. doi: 10.3934/dcds.2015.35.3463 [12] Chunlai Liu, Yanpeng Fan, Chuanli Zhao, Jianjun Wang. Multiple common due-dates assignment and optimal maintenance activity scheduling with linear deteriorating jobs. Journal of Industrial and Management Optimization, 2017, 13 (2) : 713-720. doi: 10.3934/jimo.2016042 [13] Bin Zheng, Min Fan, Mengqi Liu, Shang-Chia Liu, Yunqiang Yin. Parallel-machine scheduling with potential disruption and positional-dependent processing times. Journal of Industrial and Management Optimization, 2017, 13 (2) : 697-711. doi: 10.3934/jimo.2016041 [14] Ji-Bo Wang, Mengqi Liu, Na Yin, Ping Ji. Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects. Journal of Industrial and Management Optimization, 2017, 13 (2) : 1025-1039. doi: 10.3934/jimo.2016060 [15] Leiyang Wang, Zhaohui Liu. Heuristics for parallel machine scheduling with batch delivery consideration. Journal of Industrial and Management Optimization, 2014, 10 (1) : 259-273. doi: 10.3934/jimo.2014.10.259 [16] Wael Bahsoun, Christopher Bose, Anthony Quas. Deterministic representation for position dependent random maps. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 529-540. doi: 10.3934/dcds.2008.22.529 [17] Reza Alizadeh Foroutan, Javad Rezaeian, Milad Shafipour. Bi-objective unrelated parallel machines scheduling problem with worker allocation and sequence dependent setup times considering machine eligibility and precedence constraints. Journal of Industrial and Management Optimization, 2021  doi: 10.3934/jimo.2021190 [18] Jiayu Shen, Yuanguo Zhu. An uncertain programming model for single machine scheduling problem with batch delivery. Journal of Industrial and Management Optimization, 2019, 15 (2) : 577-593. doi: 10.3934/jimo.2018058 [19] Ganggang Li, Xiwen Lu, Peihai Liu. The coordination of single-machine scheduling with availability constraints and delivery. Journal of Industrial and Management Optimization, 2016, 12 (2) : 757-770. doi: 10.3934/jimo.2016.12.757 [20] Ji-Bo Wang, Bo Zhang, Hongyu He. A unified analysis for scheduling problems with variable processing times. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1063-1077. doi: 10.3934/jimo.2021008

2021 Impact Factor: 1.411