
-
Previous Article
An alternating linearization bundle method for a class of nonconvex optimization problem with inexact information
- JIMO Home
- This Issue
-
Next Article
Open-loop equilibrium strategy for mean-variance portfolio selection: A log-return model
Simulated annealing and genetic algorithm based method for a bi-level seru loading problem with worker assignment in seru production systems
1. | School Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China |
2. | Graduate School of Business, Doshisha University, Karasuma-Imadegawa, Kamigyo-ku, Kyoto, 602-8580, Japan |
Seru production is one of the latest manufacturing modes arising from Japanese production practice. Seru can achieve efficiency, flexibility, and responsiveness simultaneously. To accommodate the current business environment with volatile demands and fierce competitions, seru has attracted more and more attention both from researchers and practitioners. A new planning management system, just-in-time organization system (JIT-OS), is used to manage and control a seru production system. The JIT-OS contains two decisions: seru formation and seru loading. By seru formation, a seru system with one or multiple appropriate serus is configured; by seru loading, customer ordered products are allocated to serus to implement production plans. In the process of seru formation, workers have to be assigned to serus. In this paper, a seru loading problem with worker assignment is constructed as a bi-level programming model, and the worker assignment on the upper level is to minimize total idle time while the lower level is to minimize the makespan by finding out optimal product allocation. A product lot can be splitted and allocated to different serus. The problem of this paper is shown to be NP-hard. Therefore, a simulated annealing and genetic algorithm (SA-GA) is developed. The SA is for the upper level programming and the GA is for the lower level programming. The practicality and effectiveness of the model and algorithm are verified by two numerical examples, and the results show that the SA-GA algorithm has good scalability.
References:
[1] |
A. Aboelfotoh, G. A. Süer and M. Abdullah,
Selection of Assembly Systems; Assembly Lines vs. Seru Systems, Procedia Comput. Sci., 140 (2018), 351-358.
doi: 10.1016/j.procs.2018.10.304. |
[2] |
S. Akino, Internationalization of Japanese company and change of production system, Rikkyo Econom. Rev., 51 (1997), 29-55. Google Scholar |
[3] |
C. Babayigit and G. A. Süer, Cell loading to minimize the number of tardy jobs subject to the manpower restriction, Proceedings of Group Technology/Cellular Manufacturing Symposium, OH, USA, 2003. Google Scholar |
[4] |
B. Behnia, I. Mahdavi, B. Shirazi and M. M. Paydar,
A bi-level mathematical programming for cell formation problem considering workers' interest, Internat, J. Industrial Engineering & Produc. Res., 28 (2017), 267-277.
doi: 10.22068/ijiepr.28.3.267. |
[5] |
D & M Nikkei Mechanical, The Challenge of Canon - Part 3, D & M Nikkei Mechanical, 588 (2003), 70-73. Google Scholar |
[6] |
W. M. Han, J. Chen and X. Z. Bu,
Batch splitting activity in scheduling of virtual cell with capacity constraints based on bi-level mathematical model, Appl. Mechanics & Materials, 263-266 (2013), 1257-1264.
doi: 10.4028/www.scientific.net/AMM.263-266.1257. |
[7] |
X. Han, Z. Zhang and Y. Yin, Reliability analysis for a divisional seru production system with stochastic capacity, 2018 IEEE International Conference on Industrial Engineering and Engineering Management, Bangkok, 2018.
doi: 10.1109/IEEM.2018.8607607. |
[8] |
X. Han, Z. Zhang and Y. Yin, Reliability-oriented multi-resource allocation for seru production system with stochastic capacity, Internat. J. Manufac. Res., (2019), in press. Google Scholar |
[9] |
P. Hansen, B. Jaumard and G. Savard,
New branch-and-bound rules for linear bilevel programming, SIAM J. Sci. and Stat. Comput., 13 (1992), 1194-1217.
doi: 10.1137/0913069. |
[10] |
S. Hisashi, The Change of Consciousness and Company by Cellular Manufacturing in Canon Way, Tokyo: JMAM, 2006. Google Scholar |
[11] |
J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis With Applications to Biology, Control, and Artificial Intelligence, University of Michigan Press, Ann Arbor, 1975.
![]() |
[12] |
C. J. Hsu, W. H. Kuo and D. L. Yang,
Unrelated parallel machine scheduling with past-sequence-dependent setup time and learning effects, Appl. Math. Model., 35 (2010), 1492-1496.
doi: 10.1016/j.apm.2010.09.026. |
[13] |
R. H. Huang and T. H. Yu,
An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting, Appl. Soft Comput., 57 (2017), 642-656.
doi: 10.1016/j.asoc.2017.04.062. |
[14] |
H. Iwamuro, An easy book about seru production, Nikkan Kogyo Shimbun, Tokyo, 2004. Google Scholar |
[15] |
R. G. Jeroslow,
The polynomial hierarchy and a simple model for competitive analysis, Math. Programming, 32 (1985), 146-164.
doi: 10.1007/BF01586088. |
[16] |
J. Jones and T. Soule, Comparing genetic robustness in generational vs. steady state evolutionary algorithms, Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, ACM, 2006, 143–150.
doi: 10.1145/1143997.1144024. |
[17] |
R. M. Karp, Reducibility among combinatorial problems, in Complexity of Computer Computations, The IBM Research Symposia Series, Plenum, Now York, 1972, 85–103.
doi: 10.1007/978-1-4684-2001-2_9. |
[18] |
C. Kasemset and V. Kachitvichyanukul, Bi-level multi-objective mathematical model for job-shop scheduling: the application of theory of constraints, International Journal of Production Research, 48 (2010), 6137-6154.
doi: 10.1080/00207540903176705. |
[19] |
C. Kasemset and V. Kachitvichyanukul, A PSO-based procedure for a bi-level multi-objective TOC-based job-shop scheduling problem, Int. J. Oper. Res., 14 (2012), 50-69.
doi: 10.1504/IJOR.2012.046343. |
[20] |
S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi,
Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[21] |
J. Lian, C. G. Liu, W. J. Li and Y. Yin,
A multi-skilled worker assignment problem in seru production systems considering the worker heterogeneity, Comput. Industr. Engineering, 118 (2018), 366-382.
doi: 10.1016/j.cie.2018.02.035. |
[22] |
C. G. Liu, F. Dang, W. J. Li, J. Lian, S. Evans and Y. Yin,
Production planning of multi-stage multi-option seru production systems with sustainable measures, J. Cleaner Produc., 105 (2014), 285-299.
doi: 10.1016/j.jclepro.2014.03.033. |
[23] |
C. G. Liu, J. Lian, Y. Yin and W. J. Li,
Seru Seisan - An innovation of the production management mode in Japan, Asian Journal of Technology Innovation, 18 (2010), 89-113.
doi: 10.1080/19761597.2010.9668694. |
[24] |
C. G. Liu, K. E. Stecke, J. Lian and Y. Yin,
An implementation framework for seru production, Internat. Transactions in Oper. Res., 21 (2014), 1-19.
doi: 10.1111/itor.12014. |
[25] |
C. G. Liu, N. Yang, W. J. Li, J. Lian, S. Evans and Y. Yin, Training and assignment of multi-skilled workers for implementing seru production systems, Internat. J. Advanced Manufac. Tech., 69 (2013), 937-959.
doi: 10.1007/s00170-013-5027-5. |
[26] |
C. Low, C. M. Hsu and K. I. Huang,
Benefits of lot splitting in job-shop scheduling, Internat. J. Advanced Manufac. Tech., 24 (2004), 773-780.
doi: 10.1007/s00170-003-1785-9. |
[27] |
H. Luo, A. Zhang and G. Q. Huang,
Active scheduling for hybrid flowshop with family setup time and inconsistent family formation, Jo. Intelligent Manufac., 26 (2015), 169-187.
doi: 10.1007/s10845-013-0771-9. |
[28] |
L. Luo, Z. Zhang and Y. Yin,
Modelling and numerical analysis of seru loading problem under uncertainty, European J. of Industr. Engineering, 11 (2017), 185-204.
doi: 10.1504/EJIE.2017.083255. |
[29] |
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller,
Equation of state calculations by fast computing machines, J. Chem. Physics, 21 (1953), 1087-1092.
doi: 10.2172/4390578. |
[30] |
Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1994.
doi: 10.1007/978-3-662-07418-3. |
[31] |
D. I. Miyake,
The shift from belt conveyor line to work-cell based assembly systems to cope with increasing demand variation in Japanese industries, Internat. J. Automotive Tech. and Management, 6 (2006), 419-439.
doi: 10.1504/IJATM.2006.012234. |
[32] |
Not only Toyota - miraculous Canon manufacturing system, Weekly Toyo Keizen, 2003. Google Scholar |
[33] |
J. Pei, X. Liu, P. M. Pardalos, A. Migdalas and S. Yang,
Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine, J. Global Optim., 67 (2017), 1-12.
doi: 10.1007/s10898-015-0320-5. |
[34] |
A. Roth, J. Singhal, K. Singhal and C. S. Tang,
Knowledge creation and dissemination in operations and supply chain management, Produc. and Oper. Management, 25 (2016), 1473-1488.
doi: 10.1111/poms.12590. |
[35] |
H. Sakamaki, The Change of Consciousness and Company by Cellular Manufacturing in Canon Way, Japan Management Association-Management Center, Tokyo, 2006. Google Scholar |
[36] |
Y. Sakazume, Is Japanese cell manufacturing a new system? A comparative study between Japanese cell manufacturing and cellular manufacturing, J. Japan Industr. Management Assoc., 55 (2005), 341-349. Google Scholar |
[37] |
L. M. Shao, Z. Zhang and Y. Yin,
A bi-objective combination optimisation model for line-seru conversion based on queuing theory, Internat. J. Manufac. Res., 11 (2016), 322-338.
doi: 10.1504/IJMR.2016.082821. |
[38] |
A. Sinha, P. Malo and K. Deb,
A review on bilevel optimization: from classical to evolutionary approaches and applications, IEEE Transactions on Evolutionary Computation, 22 (2018), 276-295.
doi: 10.1109/TEVC.2017.2712906. |
[39] |
K. E. Stecke, Y. Yin, I. Kaku and Y. Murase,
Seru: The organizational extension of JIT for a super-talent factory, Internat. J. Strategic Decision Sci., 3 (2012), 105-118.
doi: 10.4018/jsds.2012010104. |
[40] |
G. A. Süer and C. Dagli,
Intra-cell manpower transfers and cell loading in labor-intensive manufacturing cells, Comput. Industr. Engineering, 48 (2005), 643-655.
doi: 10.1016/j.cie.2003.03.006. |
[41] |
W. Sun, Y. Wu, Q. Lou and Y. Yu,
A cooperative coevolution algorithm for the seru production with minimizing makespan, IEEE Access, 7 (2019), 5662-5670.
doi: 10.1109/ACCESS.2018.2889372. |
[42] |
W. Sun, Y. Yu and J. W. Wang, Reducing the total tardiness by seru production: Model, exact and cooperative coevolution solutions, Internat. J. Produc. Res., in press. Google Scholar |
[43] |
J. Tao, Z. Chao and Y. Xi,
A semi-online algorithm and its competitive analysis for a single machine scheduling problem with bounded processing times, J. Ind. Manag. Optim., 6 (2010), 269-282.
doi: 10.3934/jimo.2010.6.269. |
[44] |
S. Treville, M. Ketokivi and V. Singhal,
Competitive manufacturing in a high-cost environment: introduction to the special issue, J. Oper. Manag., 49-51 (2017), 1-5.
doi: 10.1016/j.jom.2017.02.001. |
[45] |
L. Vicente, G. Savard and J. Judice,
Descent approaches for quadratic bilevel programming, J. Optim. Theory Appl., 81 (1994), 379-399.
doi: 10.1007/BF02191670. |
[46] |
Y. Wang and J. F. Tang,
Cost and service-level-based model for a seru production system formation problem with uncertain demand, J. Systems Sci. and Systems Engineering, 27 (2018), 519-537.
doi: 10.1007/s11518-018-5379-3. |
[47] |
X. Yang, D. Qiu and J. Shen, Solving bi-level programming problem based on electromagnetism-like algorithm, in Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering, Advances in Intelligent Systems and Computing, 2013, 923–927.
doi: 10.1007/978-3-642-31698-2_130. |
[48] |
Y. Yin, T. C. E. Cheng, J. Xu, S. R. Cheng and C. C. Wu,
Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration, J. Ind. Manag. Optim., 9 (2013), 323-339.
doi: 10.3934/jimo.2013.9.323. |
[49] |
Y. Yin, K. E. Stecke and I. Kaku,
The evolution of seru production systems throughout Canon, Oper. Manag. Education Review, 2 (2008), 27-40.
doi: 10.4135/9781526462060. |
[50] |
Y. Yin, K. E. Stecke and D. Li,
The evolution of production systems from Industry 2.0 through Industry 4.0, Internat. J. Produc. Res., 56 (2018), 848-861.
doi: 10.1080/00207543.2017.1403664. |
[51] |
Y. Yin, K. E. Stecke, M. Li and I. Kaku, Prospering in a volatile market: Meeting uncertain demand with seru, working paper, Yamagata University, 2011. Google Scholar |
[52] |
Y. Yin, K. E. Stecke, M. Swink and I. Kaku,
Lessons from seru production on manufacturing competitively in a high cost environment, J. Oper. Manag., 49-51 (2017), 67-76.
doi: 10.1016/j.jom.2017.01.003. |
[53] |
K. C. Ying and Y. J. Tsai,
Minimising total cost for training and assigning multiskilled workers in seru production systems, Internat. J. Produc. Res., 55 (2017), 2978-2989.
doi: 10.1080/00207543.2016.1277594. |
[54] |
Y. Yu, W. Sun, J. Tang, I. Kaku and J. W. Wang,
Line-seru conversion towards reducing worker(s) without increasing makespan: models, exact and meta-heuristic solutions, Internat. J. Produc. Res., 55 (2017), 2990-3007.
doi: 10.1080/00207543.2017.1284359. |
[55] |
Y. Yu, W. Sun, J. Tang and J. Wang,
Line-hybrid seru system conversion: Models, complexities, properties, solutions and insights, Comput. & Industr. Engineering, 103 (2017), 282-299.
doi: 10.1016/j.cie.2016.11.035. |
[56] |
Y. Yu, J. Tang, J. Gong, Y. Yin and I. Kaku,
Mathematical analysis and solutions for multi-objective line-cell conversion problem, European J. Oper. Res., 236 (2014), 774-786.
doi: 10.1016/j.ejor.2014.01.029. |
[57] |
Y. Yu and J. F. Tang,
Review of seru production, Frontiers of Engineering Manag., 6 (2019), 183-192.
doi: 10.1007/s42524-019-0028-1. |
[58] |
Y. Yu, J. W. Wang, K. Ma and W. Sun,
Seru system balancing: Definition, formulation, and solution, Comput. & Industr. Engineering, 122 (2018), 318-325.
doi: 10.1016/j.cie.2018.05.048. |
[59] |
X. L. Zhang, C. G. Liu, W. J. Li, S. Evans and Y. Yin,
Effects of key enabling technologies for seru production on sustainable performance, Omega, 66 (2017), 290-307.
doi: 10.1016/j.omega.2016.01.013. |
[60] |
Z. Zhang, L. Shao and Y. Yin, PSO-based algorithm for solving lot splitting in unbalanced seru production systems, Internat. J. Industrial and Systems Engineering, (2019), in press. Google Scholar |
[61] |
Z. Zhang and J. Xu,
Bi-level multiple mode resource-constrained project scheduling problems under hybrid uncertainty, J. Ind. Manag. Optim., 12 (2016), 565-593.
doi: 10.3934/jimo.2016.12.565. |
[62] |
Z. Zhang, J. Xu, H. Yang and Y. Wang, Bi-level optimization of resource-constrained multiple project scheduling problems in hydropower station construction under uncertainty, Scientia Iranica A, 22 (2014), 650-667. Google Scholar |
[63] |
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, J. Ind. Manag. Optim., 10 (2014), 691-700.
doi: 10.3934/jimo.2014.10.691. |
[64] |
P. Zwierzyński and H. Ahmad,
Seru production as an alternative to a traditional assembly line, Engineering Manag. in Produc. and Services, 10 (2018), 62-69.
doi: 10.2478/emj-2018-0017. |
show all references
References:
[1] |
A. Aboelfotoh, G. A. Süer and M. Abdullah,
Selection of Assembly Systems; Assembly Lines vs. Seru Systems, Procedia Comput. Sci., 140 (2018), 351-358.
doi: 10.1016/j.procs.2018.10.304. |
[2] |
S. Akino, Internationalization of Japanese company and change of production system, Rikkyo Econom. Rev., 51 (1997), 29-55. Google Scholar |
[3] |
C. Babayigit and G. A. Süer, Cell loading to minimize the number of tardy jobs subject to the manpower restriction, Proceedings of Group Technology/Cellular Manufacturing Symposium, OH, USA, 2003. Google Scholar |
[4] |
B. Behnia, I. Mahdavi, B. Shirazi and M. M. Paydar,
A bi-level mathematical programming for cell formation problem considering workers' interest, Internat, J. Industrial Engineering & Produc. Res., 28 (2017), 267-277.
doi: 10.22068/ijiepr.28.3.267. |
[5] |
D & M Nikkei Mechanical, The Challenge of Canon - Part 3, D & M Nikkei Mechanical, 588 (2003), 70-73. Google Scholar |
[6] |
W. M. Han, J. Chen and X. Z. Bu,
Batch splitting activity in scheduling of virtual cell with capacity constraints based on bi-level mathematical model, Appl. Mechanics & Materials, 263-266 (2013), 1257-1264.
doi: 10.4028/www.scientific.net/AMM.263-266.1257. |
[7] |
X. Han, Z. Zhang and Y. Yin, Reliability analysis for a divisional seru production system with stochastic capacity, 2018 IEEE International Conference on Industrial Engineering and Engineering Management, Bangkok, 2018.
doi: 10.1109/IEEM.2018.8607607. |
[8] |
X. Han, Z. Zhang and Y. Yin, Reliability-oriented multi-resource allocation for seru production system with stochastic capacity, Internat. J. Manufac. Res., (2019), in press. Google Scholar |
[9] |
P. Hansen, B. Jaumard and G. Savard,
New branch-and-bound rules for linear bilevel programming, SIAM J. Sci. and Stat. Comput., 13 (1992), 1194-1217.
doi: 10.1137/0913069. |
[10] |
S. Hisashi, The Change of Consciousness and Company by Cellular Manufacturing in Canon Way, Tokyo: JMAM, 2006. Google Scholar |
[11] |
J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis With Applications to Biology, Control, and Artificial Intelligence, University of Michigan Press, Ann Arbor, 1975.
![]() |
[12] |
C. J. Hsu, W. H. Kuo and D. L. Yang,
Unrelated parallel machine scheduling with past-sequence-dependent setup time and learning effects, Appl. Math. Model., 35 (2010), 1492-1496.
doi: 10.1016/j.apm.2010.09.026. |
[13] |
R. H. Huang and T. H. Yu,
An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting, Appl. Soft Comput., 57 (2017), 642-656.
doi: 10.1016/j.asoc.2017.04.062. |
[14] |
H. Iwamuro, An easy book about seru production, Nikkan Kogyo Shimbun, Tokyo, 2004. Google Scholar |
[15] |
R. G. Jeroslow,
The polynomial hierarchy and a simple model for competitive analysis, Math. Programming, 32 (1985), 146-164.
doi: 10.1007/BF01586088. |
[16] |
J. Jones and T. Soule, Comparing genetic robustness in generational vs. steady state evolutionary algorithms, Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, ACM, 2006, 143–150.
doi: 10.1145/1143997.1144024. |
[17] |
R. M. Karp, Reducibility among combinatorial problems, in Complexity of Computer Computations, The IBM Research Symposia Series, Plenum, Now York, 1972, 85–103.
doi: 10.1007/978-1-4684-2001-2_9. |
[18] |
C. Kasemset and V. Kachitvichyanukul, Bi-level multi-objective mathematical model for job-shop scheduling: the application of theory of constraints, International Journal of Production Research, 48 (2010), 6137-6154.
doi: 10.1080/00207540903176705. |
[19] |
C. Kasemset and V. Kachitvichyanukul, A PSO-based procedure for a bi-level multi-objective TOC-based job-shop scheduling problem, Int. J. Oper. Res., 14 (2012), 50-69.
doi: 10.1504/IJOR.2012.046343. |
[20] |
S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi,
Optimization by simulated annealing, Science, 220 (1983), 671-680.
doi: 10.1126/science.220.4598.671. |
[21] |
J. Lian, C. G. Liu, W. J. Li and Y. Yin,
A multi-skilled worker assignment problem in seru production systems considering the worker heterogeneity, Comput. Industr. Engineering, 118 (2018), 366-382.
doi: 10.1016/j.cie.2018.02.035. |
[22] |
C. G. Liu, F. Dang, W. J. Li, J. Lian, S. Evans and Y. Yin,
Production planning of multi-stage multi-option seru production systems with sustainable measures, J. Cleaner Produc., 105 (2014), 285-299.
doi: 10.1016/j.jclepro.2014.03.033. |
[23] |
C. G. Liu, J. Lian, Y. Yin and W. J. Li,
Seru Seisan - An innovation of the production management mode in Japan, Asian Journal of Technology Innovation, 18 (2010), 89-113.
doi: 10.1080/19761597.2010.9668694. |
[24] |
C. G. Liu, K. E. Stecke, J. Lian and Y. Yin,
An implementation framework for seru production, Internat. Transactions in Oper. Res., 21 (2014), 1-19.
doi: 10.1111/itor.12014. |
[25] |
C. G. Liu, N. Yang, W. J. Li, J. Lian, S. Evans and Y. Yin, Training and assignment of multi-skilled workers for implementing seru production systems, Internat. J. Advanced Manufac. Tech., 69 (2013), 937-959.
doi: 10.1007/s00170-013-5027-5. |
[26] |
C. Low, C. M. Hsu and K. I. Huang,
Benefits of lot splitting in job-shop scheduling, Internat. J. Advanced Manufac. Tech., 24 (2004), 773-780.
doi: 10.1007/s00170-003-1785-9. |
[27] |
H. Luo, A. Zhang and G. Q. Huang,
Active scheduling for hybrid flowshop with family setup time and inconsistent family formation, Jo. Intelligent Manufac., 26 (2015), 169-187.
doi: 10.1007/s10845-013-0771-9. |
[28] |
L. Luo, Z. Zhang and Y. Yin,
Modelling and numerical analysis of seru loading problem under uncertainty, European J. of Industr. Engineering, 11 (2017), 185-204.
doi: 10.1504/EJIE.2017.083255. |
[29] |
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller,
Equation of state calculations by fast computing machines, J. Chem. Physics, 21 (1953), 1087-1092.
doi: 10.2172/4390578. |
[30] |
Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1994.
doi: 10.1007/978-3-662-07418-3. |
[31] |
D. I. Miyake,
The shift from belt conveyor line to work-cell based assembly systems to cope with increasing demand variation in Japanese industries, Internat. J. Automotive Tech. and Management, 6 (2006), 419-439.
doi: 10.1504/IJATM.2006.012234. |
[32] |
Not only Toyota - miraculous Canon manufacturing system, Weekly Toyo Keizen, 2003. Google Scholar |
[33] |
J. Pei, X. Liu, P. M. Pardalos, A. Migdalas and S. Yang,
Serial-batching scheduling with time-dependent setup time and effects of deterioration and learning on a single-machine, J. Global Optim., 67 (2017), 1-12.
doi: 10.1007/s10898-015-0320-5. |
[34] |
A. Roth, J. Singhal, K. Singhal and C. S. Tang,
Knowledge creation and dissemination in operations and supply chain management, Produc. and Oper. Management, 25 (2016), 1473-1488.
doi: 10.1111/poms.12590. |
[35] |
H. Sakamaki, The Change of Consciousness and Company by Cellular Manufacturing in Canon Way, Japan Management Association-Management Center, Tokyo, 2006. Google Scholar |
[36] |
Y. Sakazume, Is Japanese cell manufacturing a new system? A comparative study between Japanese cell manufacturing and cellular manufacturing, J. Japan Industr. Management Assoc., 55 (2005), 341-349. Google Scholar |
[37] |
L. M. Shao, Z. Zhang and Y. Yin,
A bi-objective combination optimisation model for line-seru conversion based on queuing theory, Internat. J. Manufac. Res., 11 (2016), 322-338.
doi: 10.1504/IJMR.2016.082821. |
[38] |
A. Sinha, P. Malo and K. Deb,
A review on bilevel optimization: from classical to evolutionary approaches and applications, IEEE Transactions on Evolutionary Computation, 22 (2018), 276-295.
doi: 10.1109/TEVC.2017.2712906. |
[39] |
K. E. Stecke, Y. Yin, I. Kaku and Y. Murase,
Seru: The organizational extension of JIT for a super-talent factory, Internat. J. Strategic Decision Sci., 3 (2012), 105-118.
doi: 10.4018/jsds.2012010104. |
[40] |
G. A. Süer and C. Dagli,
Intra-cell manpower transfers and cell loading in labor-intensive manufacturing cells, Comput. Industr. Engineering, 48 (2005), 643-655.
doi: 10.1016/j.cie.2003.03.006. |
[41] |
W. Sun, Y. Wu, Q. Lou and Y. Yu,
A cooperative coevolution algorithm for the seru production with minimizing makespan, IEEE Access, 7 (2019), 5662-5670.
doi: 10.1109/ACCESS.2018.2889372. |
[42] |
W. Sun, Y. Yu and J. W. Wang, Reducing the total tardiness by seru production: Model, exact and cooperative coevolution solutions, Internat. J. Produc. Res., in press. Google Scholar |
[43] |
J. Tao, Z. Chao and Y. Xi,
A semi-online algorithm and its competitive analysis for a single machine scheduling problem with bounded processing times, J. Ind. Manag. Optim., 6 (2010), 269-282.
doi: 10.3934/jimo.2010.6.269. |
[44] |
S. Treville, M. Ketokivi and V. Singhal,
Competitive manufacturing in a high-cost environment: introduction to the special issue, J. Oper. Manag., 49-51 (2017), 1-5.
doi: 10.1016/j.jom.2017.02.001. |
[45] |
L. Vicente, G. Savard and J. Judice,
Descent approaches for quadratic bilevel programming, J. Optim. Theory Appl., 81 (1994), 379-399.
doi: 10.1007/BF02191670. |
[46] |
Y. Wang and J. F. Tang,
Cost and service-level-based model for a seru production system formation problem with uncertain demand, J. Systems Sci. and Systems Engineering, 27 (2018), 519-537.
doi: 10.1007/s11518-018-5379-3. |
[47] |
X. Yang, D. Qiu and J. Shen, Solving bi-level programming problem based on electromagnetism-like algorithm, in Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering, Advances in Intelligent Systems and Computing, 2013, 923–927.
doi: 10.1007/978-3-642-31698-2_130. |
[48] |
Y. Yin, T. C. E. Cheng, J. Xu, S. R. Cheng and C. C. Wu,
Single-machine scheduling with past-sequence-dependent delivery times and a linear deterioration, J. Ind. Manag. Optim., 9 (2013), 323-339.
doi: 10.3934/jimo.2013.9.323. |
[49] |
Y. Yin, K. E. Stecke and I. Kaku,
The evolution of seru production systems throughout Canon, Oper. Manag. Education Review, 2 (2008), 27-40.
doi: 10.4135/9781526462060. |
[50] |
Y. Yin, K. E. Stecke and D. Li,
The evolution of production systems from Industry 2.0 through Industry 4.0, Internat. J. Produc. Res., 56 (2018), 848-861.
doi: 10.1080/00207543.2017.1403664. |
[51] |
Y. Yin, K. E. Stecke, M. Li and I. Kaku, Prospering in a volatile market: Meeting uncertain demand with seru, working paper, Yamagata University, 2011. Google Scholar |
[52] |
Y. Yin, K. E. Stecke, M. Swink and I. Kaku,
Lessons from seru production on manufacturing competitively in a high cost environment, J. Oper. Manag., 49-51 (2017), 67-76.
doi: 10.1016/j.jom.2017.01.003. |
[53] |
K. C. Ying and Y. J. Tsai,
Minimising total cost for training and assigning multiskilled workers in seru production systems, Internat. J. Produc. Res., 55 (2017), 2978-2989.
doi: 10.1080/00207543.2016.1277594. |
[54] |
Y. Yu, W. Sun, J. Tang, I. Kaku and J. W. Wang,
Line-seru conversion towards reducing worker(s) without increasing makespan: models, exact and meta-heuristic solutions, Internat. J. Produc. Res., 55 (2017), 2990-3007.
doi: 10.1080/00207543.2017.1284359. |
[55] |
Y. Yu, W. Sun, J. Tang and J. Wang,
Line-hybrid seru system conversion: Models, complexities, properties, solutions and insights, Comput. & Industr. Engineering, 103 (2017), 282-299.
doi: 10.1016/j.cie.2016.11.035. |
[56] |
Y. Yu, J. Tang, J. Gong, Y. Yin and I. Kaku,
Mathematical analysis and solutions for multi-objective line-cell conversion problem, European J. Oper. Res., 236 (2014), 774-786.
doi: 10.1016/j.ejor.2014.01.029. |
[57] |
Y. Yu and J. F. Tang,
Review of seru production, Frontiers of Engineering Manag., 6 (2019), 183-192.
doi: 10.1007/s42524-019-0028-1. |
[58] |
Y. Yu, J. W. Wang, K. Ma and W. Sun,
Seru system balancing: Definition, formulation, and solution, Comput. & Industr. Engineering, 122 (2018), 318-325.
doi: 10.1016/j.cie.2018.05.048. |
[59] |
X. L. Zhang, C. G. Liu, W. J. Li, S. Evans and Y. Yin,
Effects of key enabling technologies for seru production on sustainable performance, Omega, 66 (2017), 290-307.
doi: 10.1016/j.omega.2016.01.013. |
[60] |
Z. Zhang, L. Shao and Y. Yin, PSO-based algorithm for solving lot splitting in unbalanced seru production systems, Internat. J. Industrial and Systems Engineering, (2019), in press. Google Scholar |
[61] |
Z. Zhang and J. Xu,
Bi-level multiple mode resource-constrained project scheduling problems under hybrid uncertainty, J. Ind. Manag. Optim., 12 (2016), 565-593.
doi: 10.3934/jimo.2016.12.565. |
[62] |
Z. Zhang, J. Xu, H. Yang and Y. Wang, Bi-level optimization of resource-constrained multiple project scheduling problems in hydropower station construction under uncertainty, Scientia Iranica A, 22 (2014), 650-667. Google Scholar |
[63] |
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, J. Ind. Manag. Optim., 10 (2014), 691-700.
doi: 10.3934/jimo.2014.10.691. |
[64] |
P. Zwierzyński and H. Ahmad,
Seru production as an alternative to a traditional assembly line, Engineering Manag. in Produc. and Services, 10 (2018), 62-69.
doi: 10.2478/emj-2018-0017. |












Level | Algorithm | Parameters | |
Upper | SA | ||
Lower | GA | ||
Level | Algorithm | Parameters | |
Upper | SA | ||
Lower | GA | ||
Product | Worker's processing time (min) | Demand | Setup (min) |
||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |||
1 | 23 | 23 | 21 | 22 | 21 | 24 | 22 | – | 21 | 24 | 22 | – | 24 | 24 | 23 | 95 | 4 |
2 | – | 32 | 37 | 32 | – | 34 | 37 | 31 | 34 | 31 | – | 31 | 36 | 36 | 37 | 100 | 9 |
3 | 41 | 43 | – | – | 44 | 47 | 42 | 42 | – | 41 | 47 | 45 | 44 | 42 | – | 130 | 8 |
4 | 29 | 28 | 29 | 28 | 26 | 27 | 26 | 27 | 27 | 28 | 26 | 31 | 31 | – | 28 | 105 | 6 |
5 | 17 | – | 17 | 16 | 19 | 17 | – | 18 | 16 | 16 | 20 | 20 | 18 | 16 | 17 | 120 | 5 |
6 | 42 | 23 | 20 | 33 | 38 | 33 | 27 | 29 | – | 34 | 33 | 29 | 30 | 36 | 19 | 145 | 6 |
7 | – | 68 | 48 | 63 | 43 | 71 | 49 | 21 | 66 | 59 | 53 | – | – | 70 | 83 | 50 | 4 |
8 | 14 | 15 | 14 | 20 | – | 19 | 19 | 17 | 22 | 19 | 17 | 18 | – | 15 | 10 | 115 | 1 |
1 The '-' means that the worker cannot produce the product. |
Product | Worker's processing time (min) | Demand | Setup (min) |
||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |||
1 | 23 | 23 | 21 | 22 | 21 | 24 | 22 | – | 21 | 24 | 22 | – | 24 | 24 | 23 | 95 | 4 |
2 | – | 32 | 37 | 32 | – | 34 | 37 | 31 | 34 | 31 | – | 31 | 36 | 36 | 37 | 100 | 9 |
3 | 41 | 43 | – | – | 44 | 47 | 42 | 42 | – | 41 | 47 | 45 | 44 | 42 | – | 130 | 8 |
4 | 29 | 28 | 29 | 28 | 26 | 27 | 26 | 27 | 27 | 28 | 26 | 31 | 31 | – | 28 | 105 | 6 |
5 | 17 | – | 17 | 16 | 19 | 17 | – | 18 | 16 | 16 | 20 | 20 | 18 | 16 | 17 | 120 | 5 |
6 | 42 | 23 | 20 | 33 | 38 | 33 | 27 | 29 | – | 34 | 33 | 29 | 30 | 36 | 19 | 145 | 6 |
7 | – | 68 | 48 | 63 | 43 | 71 | 49 | 21 | 66 | 59 | 53 | – | – | 70 | 83 | 50 | 4 |
8 | 14 | 15 | 14 | 20 | – | 19 | 19 | 17 | 22 | 19 | 17 | 18 | – | 15 | 10 | 115 | 1 |
1 The '-' means that the worker cannot produce the product. |
![]() |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
1 | – | 100 | – | – | 80 | – | 50 | 115 |
2 | – | – | 130 | – | – | 116 | – | – |
3 | 95 | – | – | 105 | 40 | 29 | – | – |
![]() |
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
1 | – | 100 | – | – | 80 | – | 50 | 115 |
2 | – | – | 130 | – | – | 116 | – | – |
3 | 95 | – | – | 105 | 40 | 29 | – | – |
Product | 1 | 2 | 3 | 4 | 5 |
Seru | 3 | 1 | 2 | 3 | 1 |
Starting time | Monday 8:00 | Monday 8:00 | Monday 8:00 | Tuesday 9:13 | Tuesday10:22 |
Finishing time | Tuesday 9:07 | Tuesday 10:17 | Wednesday 11:30 | Wednesday 15:54 | Tuesday 16:09 |
Product | 5 | 6 | 6 | 7 | 8 |
Seru | 3 | 2 | 3 | 1 | 1 |
Starting time | Wednesday 15:59 | Wednesday 11:36 | Thursday 9:25 | Tuesday 16:13 | Thursday 8:05 |
Finishing time | Thursday 9:19 | Thursday 17:12 | Thursday 16:29 | Thursday 8:04 | Thursday 17:07 |
Product | 1 | 2 | 3 | 4 | 5 |
Seru | 3 | 1 | 2 | 3 | 1 |
Starting time | Monday 8:00 | Monday 8:00 | Monday 8:00 | Tuesday 9:13 | Tuesday10:22 |
Finishing time | Tuesday 9:07 | Tuesday 10:17 | Wednesday 11:30 | Wednesday 15:54 | Tuesday 16:09 |
Product | 5 | 6 | 6 | 7 | 8 |
Seru | 3 | 2 | 3 | 1 | 1 |
Starting time | Wednesday 15:59 | Wednesday 11:36 | Thursday 9:25 | Tuesday 16:13 | Thursday 8:05 |
Finishing time | Thursday 9:19 | Thursday 17:12 | Thursday 16:29 | Thursday 8:04 | Thursday 17:07 |
No. | Idle time (min) | Makespan (min) | CPU time (s) |
1 | 2381.7 | 1910 | 8242.5 |
2 | 2629.4 | 1907.8 | 8193.5 |
3 | 2438.6 | 1932.3 | 8222.2 |
4 | 2446 | 1936 | 8228 |
5 | 2723.1 | 1933 | 8228.6 |
6 | 2022.3 | 1893 | 8064.8 |
7 | 2461.2 | 1895 | 8095.2 |
8 | 2300 | 1906.3 | 8098.5 |
9 | 2819 | 1859.5 | 8051.9 |
10 | 2566.8 | 1874.1 | 8135 |
Average | 2478.81 | 1904.7 | 8156.02 |
SD | 214.16 | 24.07 | 70.94 |
No. | Idle time (min) | Makespan (min) | CPU time (s) |
1 | 2381.7 | 1910 | 8242.5 |
2 | 2629.4 | 1907.8 | 8193.5 |
3 | 2438.6 | 1932.3 | 8222.2 |
4 | 2446 | 1936 | 8228 |
5 | 2723.1 | 1933 | 8228.6 |
6 | 2022.3 | 1893 | 8064.8 |
7 | 2461.2 | 1895 | 8095.2 |
8 | 2300 | 1906.3 | 8098.5 |
9 | 2819 | 1859.5 | 8051.9 |
10 | 2566.8 | 1874.1 | 8135 |
Average | 2478.81 | 1904.7 | 8156.02 |
SD | 214.16 | 24.07 | 70.94 |
No. | Idle time (min) | Makespan (min) | CPU time (s) |
1 | 2519.5 | 1913.8 | 8220.8 |
2 | nonconvergent | ||
3 | 2384.4 | 1851.8 | 8278.8 |
4 | 2375.6 | 1898.3 | 8230.3 |
5 | nonconvergent | ||
6 | 2409.5 | 1829 | 8284.8 |
7 | 2882 | 1894.2 | 9085.2 |
8 | 2213.2 | 1941.3 | 8244.5 |
9 | 2526 | 1941 | 8190.9 |
10 | 2526.9 | 1918 | 8289.3 |
Average | 2479.64 | 1898.43 | 8353.08 |
SD | 181.55 | 37.55 | 278.59 |
No. | Idle time (min) | Makespan (min) | CPU time (s) |
1 | 2519.5 | 1913.8 | 8220.8 |
2 | nonconvergent | ||
3 | 2384.4 | 1851.8 | 8278.8 |
4 | 2375.6 | 1898.3 | 8230.3 |
5 | nonconvergent | ||
6 | 2409.5 | 1829 | 8284.8 |
7 | 2882 | 1894.2 | 9085.2 |
8 | 2213.2 | 1941.3 | 8244.5 |
9 | 2526 | 1941 | 8190.9 |
10 | 2526.9 | 1918 | 8289.3 |
Average | 2479.64 | 1898.43 | 8353.08 |
SD | 181.55 | 37.55 | 278.59 |
Worker | Workers' processing time for each product (min) | |||||||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
1 | 22 | 39 | 47 | 29 | - | 34 | 64 | 23 | 50 | 71 | 20 | 21 | 11 | 32 | 39 | 15 | 20 | 27 | 29 | 24 |
2 | 23 | 37 | 47 | 29 | 20 | 35 | 54 | 21 | 55 | 77 | 24 | 20 | 12 | 30 | 38 | 19 | 21 | 21 | 26 | 20 |
3 | 22 | 38 | 46 | - | 22 | 35 | 50 | 26 | 56 | 77 | 24 | 15 | 11 | 34 | 43 | - | 17 | 23 | 29 | 21 |
4 | - | 37 | 46 | 32 | - | 35 | 56 | - | 50 | 78 | 22 | 19 | 12 | 34 | 42 | 17 | 21 | 21 | 25 | 23 |
5 | 23 | 40 | 47 | 27 | - | 34 | 59 | 20 | 50 | 81 | - | 17 | 10 | 34 | 42 | 15 | 17 | 22 | 28 | - |
6 | 22 | 38 | 47 | 29 | 23 | 33 | 61 | 25 | - | - | 21 | 20 | 10 | 32 | 39 | 18 | 17 | 27 | 28 | 21 |
7 | 21 | 37 | - | 28 | 19 | 32 | 59 | - | 52 | 73 | 23 | 21 | 11 | 30 | 35 | 16 | 22 | 22 | 25 | 19 |
8 | 23 | 38 | 49 | 27 | 18 | - | - | 22 | 48 | 78 | 21 | 20 | 10 | 31 | 44 | 18 | - | 23 | 26 | 22 |
9 | 21 | 40 | 50 | - | 21 | 33 | 56 | 26 | 53 | 87 | - | 18 | 10 | 32 | 40 | 17 | 22 | 21 | 27 | 20 |
10 | 24 | - | 49 | 28 | 19 | 38 | 58 | 26 | 52 | - | 24 | 18 | 10 | 37 | 41 | - | 17 | 25 | 26 | 23 |
11 | 22 | 38 | 47 | 30 | 18 | 33 | 61 | 27 | 53 | 77 | 21 | 19 | - | 33 | 41 | - | 19 | 21 | 29 | 23 |
12 | 23 | 36 | 49 | 29 | 21 | 34 | 57 | 22 | 53 | 86 | 21 | 20 | 10 | 33 | 36 | 17 | 21 | 21 | 27 | 24 |
13 | 23 | 39 | 47 | 29 | 22 | - | 65 | 21 | 53 | 86 | 22 | 19 | 12 | 30 | 38 | 15 | 19 | 22 | 27 | 21 |
14 | 23 | 39 | - | 31 | 18 | 30 | 50 | 29 | 57 | 85 | 24 | - | 10 | 37 | 36 | 19 | 21 | 27 | 27 | 21 |
15 | 21 | 36 | 49 | 30 | - | 36 | 59 | 24 | 50 | 81 | 24 | 17 | 11 | 37 | 35 | 18 | 19 | 26 | 26 | 22 |
16 | 25 | 36 | 49 | 31 | 19 | 37 | 58 | 22 | 54 | 82 | 24 | 19 | 12 | 39 | 39 | 17 | 18 | 23 | 29 | 22 |
17 | - | 37 | 45 | 30 | 22 | 38 | 60 | 23 | 55 | - | 21 | 18 | - | 37 | 44 | - | 21 | 22 | 27 | - |
18 | 23 | 37 | 49 | 31 | 21 | 37 | 61 | - | 48 | - | 21 | 21 | 12 | 34 | - | 17 | 17 | - | 26 | 20 |
19 | 21 | 35 | 48 | - | 19 | 37 | 61 | 28 | 48 | 69 | 20 | 19 | 10 | 33 | 36 | 18 | 22 | 25 | 25 | 20 |
20 | 21 | 38 | - | 30 | 23 | 32 | 55 | 29 | 53 | 72 | 22 | 16 | 10 | - | 35 | 16 | 17 | 21 | 29 | 23 |
21 | 21 | 36 | 50 | 30 | 22 | 35 | 64 | 29 | 53 | 86 | 22 | 17 | 11 | 39 | - | 17 | 18 | 24 | 26 | 23 |
22 | 22 | 38 | 50 | 29 | - | 33 | 61 | 22 | 48 | 69 | 23 | 17 | 11 | 40 | - | 15 | - | 22 | 28 | 21 |
23 | 25 | 39 | 47 | 29 | 19 | 37 | 59 | 26 | - | - | 24 | 16 | 12 | 39 | - | 17 | 22 | 25 | 25 | 23 |
24 | 20 | 37 | 49 | 29 | 22 | 30 | 62 | 22 | 47 | 71 | 21 | 18 | 12 | 40 | 42 | 19 | 21 | 27 | 25 | 21 |
25 | 23 | 39 | 47 | 30 | 21 | 38 | 63 | - | 55 | - | 23 | 15 | 11 | 31 | 38 | 19 | 22 | 27 | 27 | 24 |
26 | - | 37 | - | 32 | 23 | 32 | 58 | 28 | 50 | 72 | 24 | 16 | 11 | 32 | 44 | 17 | 19 | 22 | 25 | - |
27 | 24 | 37 | 49 | 30 | 22 | - | 56 | 30 | 51 | 78 | 24 | 19 | 11 | 34 | 40 | - | 19 | - | 29 | 21 |
28 | 24 | 39 | 47 | - | 18 | 37 | - | 24 | 47 | 85 | 23 | 16 | 10 | 39 | 35 | 17 | 22 | 20 | 26 | 20 |
29 | 25 | - | 47 | 29 | 19 | 36 | 54 | 20 | 49 | 79 | 24 | 16 | 11 | 35 | 41 | 18 | - | 23 | 25 | - |
30 | 20 | 37 | 47 | 28 | 22 | 40 | 51 | 22 | 51 | 78 | - | 21 | 11 | 37 | 39 | 16 | 18 | - | 25 | - |
31 | 23 | 38 | 48 | 29 | 19 | 35 | 53 | 20 | 56 | 72 | 22 | 16 | 11 | - | 37 | 16 | 20 | 25 | 25 | 20 |
32 | 23 | 36 | 45 | 29 | - | 37 | 63 | 29 | 50 | 79 | 20 | 16 | 11 | 37 | - | 18 | 21 | 27 | 29 | 25 |
33 | 23 | 38 | 47 | 30 | 23 | 40 | 59 | 26 | 56 | 78 | 23 | 18 | 11 | 41 | 40 | - | 21 | 22 | - | 23 |
34 | 21 | 35 | 50 | 27 | 23 | 38 | 65 | 22 | 47 | 71 | 24 | 16 | 10 | 38 | 36 | 16 | 20 | 27 | 27 | 24 |
35 | 20 | 35 | 48 | 32 | 21 | 33 | 61 | 25 | - | - | 21 | 21 | 10 | 38 | - | 19 | 18 | 24 | 29 | 19 |
36 | - | 38 | 45 | 30 | 19 | 31 | 63 | 24 | 56 | 85 | 23 | - | 10 | 41 | 37 | 19 | 19 | 24 | 26 | 21 |
37 | 24 | 36 | - | 30 | 22 | 38 | 55 | 24 | 50 | 87 | 23 | 19 | 12 | - | 39 | 17 | 20 | 26 | - | 25 |
38 | 24 | 39 | 49 | 32 | 21 | 37 | 52 | - | - | 71 | 24 | 19 | 12 | 35 | 38 | 15 | 19 | 23 | 25 | 22 |
39 | 21 | 39 | 49 | 31 | 19 | 35 | 57 | 29 | 55 | 77 | 21 | 19 | 11 | 40 | 43 | 15 | 19 | - | 28 | 19 |
40 | 25 | 35 | 47 | 30 | 20 | 34 | 59 | 25 | 48 | 72 | 23 | - | 10 | 41 | 35 | 18 | 20 | 20 | 26 | 18 |
41 | 22 | 36 | 48 | 32 | 20 | - | 55 | 25 | 49 | 71 | 23 | 19 | 12 | 31 | 43 | 17 | 19 | 22 | 26 | 24 |
42 | 23 | 39 | 47 | 27 | 19 | 39 | 64 | 24 | 53 | 74 | 24 | 21 | 12 | 32 | - | 19 | 18 | - | 29 | 22 |
43 | 23 | 36 | 46 | 32 | 20 | 35 | - | 21 | 55 | 80 | 21 | 16 | 12 | 32 | 40 | 18 | 20 | 23 | 26 | 22 |
44 | - | - | 45 | 31 | 22 | 37 | 52 | - | 57 | 72 | 22 | 16 | 11 | 37 | - | 18 | 22 | 20 | 27 | 24 |
45 | 20 | 40 | 47 | 29 | 21 | 32 | 52 | 29 | 55 | 82 | 21 | 15 | 10 | 33 | - | 16 | 20 | 27 | - | 19 |
46 | 20 | 40 | - | 30 | 20 | 38 | 58 | 23 | 50 | 82 | 23 | 20 | 11 | 31 | 38 | 19 | - | - | 25 | 19 |
47 | 23 | 39 | 49 | - | 21 | 39 | 61 | 25 | - | 78 | 24 | 19 | 11 | 38 | 39 | 17 | 22 | 27 | 27 | 25 |
48 | 22 | 38 | 49 | 28 | 18 | 33 | - | 25 | 49 | 74 | 23 | 18 | 12 | 30 | 43 | 16 | 20 | 21 | 29 | - |
49 | 20 | 39 | 47 | 29 | 21 | - | 60 | 22 | 52 | 81 | 23 | 21 | 12 | 30 | 40 | 16 | 20 | 24 | 25 | 19 |
50 | 22 | - | 47 | 28 | 20 | 32 | 64 | 27 | 49 | 77 | - | 18 | 10 | 33 | 37 | 17 | 20 | 20 | 25 | 24 |
Worker | Workers' processing time for each product (min) | |||||||||||||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | |
1 | 22 | 39 | 47 | 29 | - | 34 | 64 | 23 | 50 | 71 | 20 | 21 | 11 | 32 | 39 | 15 | 20 | 27 | 29 | 24 |
2 | 23 | 37 | 47 | 29 | 20 | 35 | 54 | 21 | 55 | 77 | 24 | 20 | 12 | 30 | 38 | 19 | 21 | 21 | 26 | 20 |
3 | 22 | 38 | 46 | - | 22 | 35 | 50 | 26 | 56 | 77 | 24 | 15 | 11 | 34 | 43 | - | 17 | 23 | 29 | 21 |
4 | - | 37 | 46 | 32 | - | 35 | 56 | - | 50 | 78 | 22 | 19 | 12 | 34 | 42 | 17 | 21 | 21 | 25 | 23 |
5 | 23 | 40 | 47 | 27 | - | 34 | 59 | 20 | 50 | 81 | - | 17 | 10 | 34 | 42 | 15 | 17 | 22 | 28 | - |
6 | 22 | 38 | 47 | 29 | 23 | 33 | 61 | 25 | - | - | 21 | 20 | 10 | 32 | 39 | 18 | 17 | 27 | 28 | 21 |
7 | 21 | 37 | - | 28 | 19 | 32 | 59 | - | 52 | 73 | 23 | 21 | 11 | 30 | 35 | 16 | 22 | 22 | 25 | 19 |
8 | 23 | 38 | 49 | 27 | 18 | - | - | 22 | 48 | 78 | 21 | 20 | 10 | 31 | 44 | 18 | - | 23 | 26 | 22 |
9 | 21 | 40 | 50 | - | 21 | 33 | 56 | 26 | 53 | 87 | - | 18 | 10 | 32 | 40 | 17 | 22 | 21 | 27 | 20 |
10 | 24 | - | 49 | 28 | 19 | 38 | 58 | 26 | 52 | - | 24 | 18 | 10 | 37 | 41 | - | 17 | 25 | 26 | 23 |
11 | 22 | 38 | 47 | 30 | 18 | 33 | 61 | 27 | 53 | 77 | 21 | 19 | - | 33 | 41 | - | 19 | 21 | 29 | 23 |
12 | 23 | 36 | 49 | 29 | 21 | 34 | 57 | 22 | 53 | 86 | 21 | 20 | 10 | 33 | 36 | 17 | 21 | 21 | 27 | 24 |
13 | 23 | 39 | 47 | 29 | 22 | - | 65 | 21 | 53 | 86 | 22 | 19 | 12 | 30 | 38 | 15 | 19 | 22 | 27 | 21 |
14 | 23 | 39 | - | 31 | 18 | 30 | 50 | 29 | 57 | 85 | 24 | - | 10 | 37 | 36 | 19 | 21 | 27 | 27 | 21 |
15 | 21 | 36 | 49 | 30 | - | 36 | 59 | 24 | 50 | 81 | 24 | 17 | 11 | 37 | 35 | 18 | 19 | 26 | 26 | 22 |
16 | 25 | 36 | 49 | 31 | 19 | 37 | 58 | 22 | 54 | 82 | 24 | 19 | 12 | 39 | 39 | 17 | 18 | 23 | 29 | 22 |
17 | - | 37 | 45 | 30 | 22 | 38 | 60 | 23 | 55 | - | 21 | 18 | - | 37 | 44 | - | 21 | 22 | 27 | - |
18 | 23 | 37 | 49 | 31 | 21 | 37 | 61 | - | 48 | - | 21 | 21 | 12 | 34 | - | 17 | 17 | - | 26 | 20 |
19 | 21 | 35 | 48 | - | 19 | 37 | 61 | 28 | 48 | 69 | 20 | 19 | 10 | 33 | 36 | 18 | 22 | 25 | 25 | 20 |
20 | 21 | 38 | - | 30 | 23 | 32 | 55 | 29 | 53 | 72 | 22 | 16 | 10 | - | 35 | 16 | 17 | 21 | 29 | 23 |
21 | 21 | 36 | 50 | 30 | 22 | 35 | 64 | 29 | 53 | 86 | 22 | 17 | 11 | 39 | - | 17 | 18 | 24 | 26 | 23 |
22 | 22 | 38 | 50 | 29 | - | 33 | 61 | 22 | 48 | 69 | 23 | 17 | 11 | 40 | - | 15 | - | 22 | 28 | 21 |
23 | 25 | 39 | 47 | 29 | 19 | 37 | 59 | 26 | - | - | 24 | 16 | 12 | 39 | - | 17 | 22 | 25 | 25 | 23 |
24 | 20 | 37 | 49 | 29 | 22 | 30 | 62 | 22 | 47 | 71 | 21 | 18 | 12 | 40 | 42 | 19 | 21 | 27 | 25 | 21 |
25 | 23 | 39 | 47 | 30 | 21 | 38 | 63 | - | 55 | - | 23 | 15 | 11 | 31 | 38 | 19 | 22 | 27 | 27 | 24 |
26 | - | 37 | - | 32 | 23 | 32 | 58 | 28 | 50 | 72 | 24 | 16 | 11 | 32 | 44 | 17 | 19 | 22 | 25 | - |
27 | 24 | 37 | 49 | 30 | 22 | - | 56 | 30 | 51 | 78 | 24 | 19 | 11 | 34 | 40 | - | 19 | - | 29 | 21 |
28 | 24 | 39 | 47 | - | 18 | 37 | - | 24 | 47 | 85 | 23 | 16 | 10 | 39 | 35 | 17 | 22 | 20 | 26 | 20 |
29 | 25 | - | 47 | 29 | 19 | 36 | 54 | 20 | 49 | 79 | 24 | 16 | 11 | 35 | 41 | 18 | - | 23 | 25 | - |
30 | 20 | 37 | 47 | 28 | 22 | 40 | 51 | 22 | 51 | 78 | - | 21 | 11 | 37 | 39 | 16 | 18 | - | 25 | - |
31 | 23 | 38 | 48 | 29 | 19 | 35 | 53 | 20 | 56 | 72 | 22 | 16 | 11 | - | 37 | 16 | 20 | 25 | 25 | 20 |
32 | 23 | 36 | 45 | 29 | - | 37 | 63 | 29 | 50 | 79 | 20 | 16 | 11 | 37 | - | 18 | 21 | 27 | 29 | 25 |
33 | 23 | 38 | 47 | 30 | 23 | 40 | 59 | 26 | 56 | 78 | 23 | 18 | 11 | 41 | 40 | - | 21 | 22 | - | 23 |
34 | 21 | 35 | 50 | 27 | 23 | 38 | 65 | 22 | 47 | 71 | 24 | 16 | 10 | 38 | 36 | 16 | 20 | 27 | 27 | 24 |
35 | 20 | 35 | 48 | 32 | 21 | 33 | 61 | 25 | - | - | 21 | 21 | 10 | 38 | - | 19 | 18 | 24 | 29 | 19 |
36 | - | 38 | 45 | 30 | 19 | 31 | 63 | 24 | 56 | 85 | 23 | - | 10 | 41 | 37 | 19 | 19 | 24 | 26 | 21 |
37 | 24 | 36 | - | 30 | 22 | 38 | 55 | 24 | 50 | 87 | 23 | 19 | 12 | - | 39 | 17 | 20 | 26 | - | 25 |
38 | 24 | 39 | 49 | 32 | 21 | 37 | 52 | - | - | 71 | 24 | 19 | 12 | 35 | 38 | 15 | 19 | 23 | 25 | 22 |
39 | 21 | 39 | 49 | 31 | 19 | 35 | 57 | 29 | 55 | 77 | 21 | 19 | 11 | 40 | 43 | 15 | 19 | - | 28 | 19 |
40 | 25 | 35 | 47 | 30 | 20 | 34 | 59 | 25 | 48 | 72 | 23 | - | 10 | 41 | 35 | 18 | 20 | 20 | 26 | 18 |
41 | 22 | 36 | 48 | 32 | 20 | - | 55 | 25 | 49 | 71 | 23 | 19 | 12 | 31 | 43 | 17 | 19 | 22 | 26 | 24 |
42 | 23 | 39 | 47 | 27 | 19 | 39 | 64 | 24 | 53 | 74 | 24 | 21 | 12 | 32 | - | 19 | 18 | - | 29 | 22 |
43 | 23 | 36 | 46 | 32 | 20 | 35 | - | 21 | 55 | 80 | 21 | 16 | 12 | 32 | 40 | 18 | 20 | 23 | 26 | 22 |
44 | - | - | 45 | 31 | 22 | 37 | 52 | - | 57 | 72 | 22 | 16 | 11 | 37 | - | 18 | 22 | 20 | 27 | 24 |
45 | 20 | 40 | 47 | 29 | 21 | 32 | 52 | 29 | 55 | 82 | 21 | 15 | 10 | 33 | - | 16 | 20 | 27 | - | 19 |
46 | 20 | 40 | - | 30 | 20 | 38 | 58 | 23 | 50 | 82 | 23 | 20 | 11 | 31 | 38 | 19 | - | - | 25 | 19 |
47 | 23 | 39 | 49 | - | 21 | 39 | 61 | 25 | - | 78 | 24 | 19 | 11 | 38 | 39 | 17 | 22 | 27 | 27 | 25 |
48 | 22 | 38 | 49 | 28 | 18 | 33 | - | 25 | 49 | 74 | 23 | 18 | 12 | 30 | 43 | 16 | 20 | 21 | 29 | - |
49 | 20 | 39 | 47 | 29 | 21 | - | 60 | 22 | 52 | 81 | 23 | 21 | 12 | 30 | 40 | 16 | 20 | 24 | 25 | 19 |
50 | 22 | - | 47 | 28 | 20 | 32 | 64 | 27 | 49 | 77 | - | 18 | 10 | 33 | 37 | 17 | 20 | 20 | 25 | 24 |
Product | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Setup time (min) | 4 | 9 | 8 | 6 | 5 | 6 | 4 | 1 | 10 | 12 | 24 | 2 | 5 | 7 | 11 | 3 | 15 | 4 | 2 | 7 |
Demand | 145 | 107 | 134 | 105 | 140 | 145 | 115 | 87 | 145 | 126 | 125 | 150 | 118 | 106 | 75 | 80 | 132 | 83 | 65 | 89 |
Product | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Setup time (min) | 4 | 9 | 8 | 6 | 5 | 6 | 4 | 1 | 10 | 12 | 24 | 2 | 5 | 7 | 11 | 3 | 15 | 4 | 2 | 7 |
Demand | 145 | 107 | 134 | 105 | 140 | 145 | 115 | 87 | 145 | 126 | 125 | 150 | 118 | 106 | 75 | 80 | 132 | 83 | 65 | 89 |
No. | Idle time (min) | Makespan (min) | CPU time (s) |
1 | 5587.3 | 1932 | 16236 |
2 | 5457.4 | 1848.30 | 16376 |
3 | 5164.9 | 1865.4 | 16221 |
4 | 5258.9 | 1919 | 15754 |
5 | 5757.2 | 1806 | 15743 |
Average | 5445.14 | 1874.14 | 16066 |
SD | 214.92 | 46.36 | 264.84 |
No. | Idle time (min) | Makespan (min) | CPU time (s) |
1 | 5587.3 | 1932 | 16236 |
2 | 5457.4 | 1848.30 | 16376 |
3 | 5164.9 | 1865.4 | 16221 |
4 | 5258.9 | 1919 | 15754 |
5 | 5757.2 | 1806 | 15743 |
Average | 5445.14 | 1874.14 | 16066 |
SD | 214.92 | 46.36 | 264.84 |
[1] |
Yahia Zare Mehrjerdi. A new methodology for solving bi-criterion fractional stochastic programming. Numerical Algebra, Control & Optimization, 2020 doi: 10.3934/naco.2020054 |
[2] |
Guo Zhou, Yongquan Zhou, Ruxin Zhao. Hybrid social spider optimization algorithm with differential mutation operator for the job-shop scheduling problem. Journal of Industrial & Management Optimization, 2021, 17 (2) : 533-548. doi: 10.3934/jimo.2019122 |
[3] |
Shengxin Zhu, Tongxiang Gu, Xingping Liu. AIMS: Average information matrix splitting. Mathematical Foundations of Computing, 2020, 3 (4) : 301-308. doi: 10.3934/mfc.2020012 |
[4] |
Yunfeng Geng, Xiaoying Wang, Frithjof Lutscher. Coexistence of competing consumers on a single resource in a hybrid model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 269-297. doi: 10.3934/dcdsb.2020140 |
[5] |
Franck Davhys Reval Langa, Morgan Pierre. A doubly splitting scheme for the Caginalp system with singular potentials and dynamic boundary conditions. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 653-676. doi: 10.3934/dcdss.2020353 |
[6] |
Tien-Yu Lin, Bhaba R. Sarker, Chien-Jui Lin. An optimal setup cost reduction and lot size for economic production quantity model with imperfect quality and quantity discounts. Journal of Industrial & Management Optimization, 2021, 17 (1) : 467-484. doi: 10.3934/jimo.2020043 |
[7] |
Wolfgang Riedl, Robert Baier, Matthias Gerdts. Optimization-based subdivision algorithm for reachable sets. Journal of Computational Dynamics, 2021, 8 (1) : 99-130. doi: 10.3934/jcd.2021005 |
[8] |
Hui Lv, Xing'an Wang. Dissipative control for uncertain singular markovian jump systems via hybrid impulsive control. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 127-142. doi: 10.3934/naco.2020020 |
[9] |
Yasmine Cherfaoui, Mustapha Moulaï. Biobjective optimization over the efficient set of multiobjective integer programming problem. Journal of Industrial & Management Optimization, 2021, 17 (1) : 117-131. doi: 10.3934/jimo.2019102 |
[10] |
Pablo Neme, Jorge Oviedo. A note on the lattice structure for matching markets via linear programming. Journal of Dynamics & Games, 2020 doi: 10.3934/jdg.2021001 |
[11] |
Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semi-infinite programming. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021012 |
[12] |
Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li, Bowen Li. An adaptive dynamic programming method for torque ripple minimization of PMSM. Journal of Industrial & Management Optimization, 2021, 17 (2) : 827-839. doi: 10.3934/jimo.2019136 |
[13] |
Mehdi Badsi. Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem. Kinetic & Related Models, 2021, 14 (1) : 149-174. doi: 10.3934/krm.2020052 |
[14] |
Wenbin Li, Jianliang Qian. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020073 |
[15] |
Ali Mahmoodirad, Harish Garg, Sadegh Niroomand. Solving fuzzy linear fractional set covering problem by a goal programming based solution approach. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020162 |
[16] |
Lingfeng Li, Shousheng Luo, Xue-Cheng Tai, Jiang Yang. A new variational approach based on level-set function for convex hull problem with outliers. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020070 |
[17] |
Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021013 |
[18] |
Masaru Hamano, Satoshi Masaki. A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1415-1447. doi: 10.3934/dcds.2020323 |
[19] |
Peter Frolkovič, Viera Kleinová. A new numerical method for level set motion in normal direction used in optical flow estimation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 851-863. doi: 10.3934/dcdss.2020347 |
[20] |
Tetsuya Ishiwata, Takeshi Ohtsuka. Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 893-907. doi: 10.3934/dcdss.2020390 |
2019 Impact Factor: 1.366
Tools
Article outline
Figures and Tables
[Back to Top]