Skip to main content

A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines

Abstract

The analytical evaluation of production system performance measures is a difficult task. Over the years, various methods have been developed to solve specific cases of very short production lines. However, formulae for estimating the mean production rate (throughput) are lacking. Recent developments in artificial intelligence simplify their use in the solution of symbolic regression problems. In this work, we use genetic programming (GP) to obtain approximate formulae for calculating the throughput of short reliable approximately balanced production lines, for which the processing times are exponentially distributed. A hybrid GP&GA scheme reduces the search space, in which GP uses genetic algorithms (GA) as a search engine. The scheme produces polynomial formulae for throughput estimation for the first time. To train the GP algorithm we use MARKOV, an accurate algorithm for calculating numerically the exact throughput of short exponential production lines. A few formulae, not previously reported in the literature, are presented. These formulae give close results to the exact results from the MARKOV algorithm, for short (up to five stations) reliable approximately balanced production lines without intermediate buffers. Also, the robustness of these formulae is satisfactory. In addition, the proposed hybrid GP&GA scheme is useful for design/production engineers to adjust the formulae to other ranges of the mean processing rates; the algorithms are quickly retrained to generate a new approximate formula.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Availability of data and materials

All data as well as materials and software application used for training and testing the algorithms are available by the authors upon request.

Code availability

The code of the algorithms developed in this study is available by the authors upon request.

References

  1. Alhayani, B. S. A., & Llhan, H. (2021). Visual sensor intelligent module based image transmission in industrial manufacturing for monitoring and manipulation problems. Journal of Intelligent Manufacturing, 32(2), 597–610. https://doi.org/10.1007/s10845-020-01590-1

    Article  Google Scholar 

  2. Alkaff, A., & Muth, E. J. (1987). The throughput rate of multistation production lines with stochastic servers. Probability in the Engineering and Informational Sciences, 1(3), 309–326. https://doi.org/10.1017/S0269964800000085

    Article  Google Scholar 

  3. Alkaff, A., Qomarudin, M. N., & Wiratno, S. E. (2020). Matrix-analytic solutions in production lines without buffers. Computers & Operations Research, 119, 104903. https://doi.org/10.1016/j.cor.2020.104903

    Article  Google Scholar 

  4. Altiok, T. (1997). Performance analysis of manufacturing systems. Springer. https://doi.org/10.1007/978-1-4612-1924-8

    Book  Google Scholar 

  5. Angeline, P. J., & Kinnear, K. E. (Eds.). (1996). Advances in genetic programming (Vol. 2). MIT Press. https://doi.org/10.7551/mitpress/1109.001.0001

    Book  Google Scholar 

  6. Askin, R. G., & Standridge, C. R. (1993). Modeling and analysis of manufacturing systems. Wiley.

    Google Scholar 

  7. Baker, K. R., Powell, S. G., & Pyke, D. F. (1994). A predictive model for the throughput of unbalanced, unbuffered three-station serial lines. IIE Transactions, 26(4), 62–71. https://doi.org/10.1080/07408179408966619

    Article  Google Scholar 

  8. Basu, R. N. (1977). The interstage buffer storage capacity of non-powered assembly lines A simple mathematical approach. International Journal of Production Research, 15(4), 365–382. https://doi.org/10.1080/00207547708943136

    Article  Google Scholar 

  9. Bingöl, S., & Kılıçgedik, H. Y. (2018). Application of gene expression programming in hot metal forming for intelligent manufacturing. Neural Computing and Applications, 30(3), 937–945. https://doi.org/10.1007/s00521-016-2718-5

    Article  Google Scholar 

  10. Bitran, G. R., & Dasu, S. (1992). A review of open queueing network models of manufacturing systems. Queueing Systems, 12(1), 95–133. https://doi.org/10.1007/BF01158637

    Article  Google Scholar 

  11. Blumenfeld, D. E. (1990). A simple formula for estimating throughput of serial production lines with variable processing times and limited buffer capacity. International Journal of Production Research, 28(6), 1163–1182. https://doi.org/10.1080/00207549008942783

    Article  Google Scholar 

  12. Blumenfeld, D. E., & Li, J. (2005). An analytical formula for throughput of a production line with identical stations and random failures. Mathematical Problems in Engineering, 2005(3), 293–308. https://doi.org/10.1155/mpe.2005.293

    Article  Google Scholar 

  13. Boulas, K., Dounias, G., Papadopoulos, C., & Tsakonas, A. (2015). Acquisition of accurate or approximate throughput formulas for serial production lines through genetic programming. In Proceedings of the 4th international symposium & 26th national conference on operational research (Vol. 1, pp. 128–133). Hellenic Operational Research Society. http://mde-lab.aegean.gr/research-material

  14. Boulas, K., Dounias, G., & Papadopoulos, C. (2017). Approximating throughput of small production lines using genetic programming. In E. Grigoroudis & M. Doumpos (Eds.), Operational research in business and economics: 4th international symposium and 26th national conference on operational research, Chania, Greece, June 2015 (pp. 185–204). Springer. https://doi.org/10.1007/978-3-319-33003-7_9

  15. Boulas, K., Tzanetos, A., & Dounias, G. (2018). Acquisition of approximate throughput formulas for serial production lines with parallel machines using intelligent techniques. In Proceedings of the 10th Hellenic conference on artificial intelligence (pp. 18:1–18:7). Presented .at the SETN ’18, Rio Patras, Greece. ACM Press. https://doi.org/10.1145/3200947.3201028

  16. Bourisli, R. I., Altarakma, M. A., & AlAnzi, A. A. (2018). General correlation of building energy use via hybrid genetic programming/genetic algorithm. Journal of Solar Energy Engineering. https://doi.org/10.1115/1.4039447

    Article  Google Scholar 

  17. Brezocnik, M., Balic, J., & Kuzman, K. (2002). Genetic programming approach to determining of metal materials properties. Journal of Intelligent Manufacturing, 13(1), 5–17. https://doi.org/10.1023/A:1013693828052.

    Article  Google Scholar 

  18. Buzacott, J. A., & Shanthikumar, J. G. (1992). Design of manufacturing systems using queueing models. Queueing Systems, 12(1), 135–213. https://doi.org/10.1007/BF01158638

    Article  Google Scholar 

  19. Buzacott, J. A., & Shanthikumar, J. G. (1993). Stochastic models of manufacturing systems (Vol. 4). Prentice Hall.

    Google Scholar 

  20. Can, B., & Heavey, C. (2012). A comparison of genetic programming and artificial neural networks in metamodeling of discrete-event simulation models. Computers & Operations Research, 39(2), 424–436. https://doi.org/10.1016/j.cor.2011.05.004

    Article  Google Scholar 

  21. Chamnanlor, C., Sethanan, K., Gen, M., & Chien, C.-F. (2017). Embedding ant system in genetic algorithm for re-entrant hybrid flow shop scheduling problems with time window constraints. Journal of Intelligent Manufacturing, 28(8), 1915–1931. https://doi.org/10.1007/s10845-015-1078-9.

    Article  Google Scholar 

  22. Chang, H.-C., & Liu, T.-K. (2017). Optimisation of distributed manufacturing flexible job shop scheduling by using hybrid genetic algorithms. Journal of Intelligent Manufacturing, 28(8), 1973–1986. https://doi.org/10.1007/s10845-015-1084-y.

    Article  Google Scholar 

  23. Cheng, J. R., & Gen, M. (2019). Accelerating genetic algorithms with GPU computing: A selective overview. Computers & Industrial Engineering, 128, 514–525. https://doi.org/10.1016/j.cie.2018.12.067

    Article  Google Scholar 

  24. Cheng, R., Gen, M., & Tsujimura, Y. (1996). A tutorial survey of job-shop scheduling problems using genetic algorithms—I. representation. Computers & Industrial Engineering, 30(4), 983–997. https://doi.org/10.1016/0360-8352(96)00047-2

    Article  Google Scholar 

  25. Cheng, R., Gen, M., & Tsujimura, Y. (1999). A tutorial survey of job-shop scheduling problems using genetic algorithms, part II: Hybrid genetic search strategies. Computers & Industrial Engineering, 36(2), 343–364. https://doi.org/10.1016/S0360-8352(99)00136-9

    Article  Google Scholar 

  26. Costa, A., Cappadonna, F. A., & Fichera, S. (2017). A hybrid genetic algorithm for minimizing makespan in a flow-shop sequence-dependent group scheduling problem. Journal of Intelligent Manufacturing, 28(6), 1269–1283. https://doi.org/10.1007/s10845-015-1049-1.

    Article  Google Scholar 

  27. Curry, G. L., & Feldman, R. M. (2011). Manufacturing systems modeling and analysis (2nd ed.). Springer. https://doi.org/10.1007/978-3-642-16618-1

    Book  Google Scholar 

  28. Dallery, Y., David, R., & Xie, X.-L. (1988). An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers. IIE Transactions, 20(3), 280–283. https://doi.org/10.1080/07408178808966181

    Article  Google Scholar 

  29. Dallery, Y., David, R., & Xie, X. L. (1989). Approximate analysis of transfer lines with unreliable machines and finite buffers. IEEE Transactions on Automatic Control, 34(9), 943–953. https://doi.org/10.1109/9.35807

    Article  Google Scholar 

  30. Dallery, Y., & Gershwin, S. B. (1992). Manufacturing flow line systems: A review of models and analytical results. Queueing Systems, 12(1), 3–94. https://doi.org/10.1007/BF01158636

    Article  Google Scholar 

  31. Dar-El, E. M., & Mazer, A. (1989). Predicting the performance of unpaced assembly lines where one station variability may be smaller than the others. International Journal of Production Research, 27(12), 2105–2116. https://doi.org/10.1080/00207548908942678

    Article  Google Scholar 

  32. De Jong, K. A. (1975). An analysis of the behavior of a class of genetic adaptive systems (PhD Thesis). University of Michigan.

  33. De Jong, K. A. (1993). Genetic algorithms are NOT function optimizers. In D. Whitley (Ed.), Foundations of genetic algorithms (Vol. 2, pp. 5–17). Elsevier. https://doi.org/10.1016/B978-0-08-094832-4.50006-4

  34. Demir, L., Tunali, S., & Eliiyi, D. T. (2014). The state of the art on buffer allocation problem: A comprehensive survey. Journal of Intelligent Manufacturing, 25(3), 371–392. https://doi.org/10.1007/s10845-012-0687-9

    Article  Google Scholar 

  35. Derigent, W., Cardin, O., & Trentesaux, D. (2020). Industry 4.0: Contributions of holonic manufacturing control architectures and future challenges. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01532-x

    Article  Google Scholar 

  36. Dhouib, K., Gharbi, A., & Mejri, M. (2010). Throughput variability of homogeneous transfer lines subject to operation-dependant failures. In 8th international conference on modeling and simulation (MOSIM’10) (pp. 1290–1299). Presented at the 8th ENIM IFAC International Conference of Modeling and Simulation : Evaluation and optimization of innovative production systems of goods and services MOSIM’10, Hammamet, Tunisia: Lavoisier.

  37. Diamantidis, C. A., & Papadopoulos, T. C. (2009). Exact analysis of a two-workstation one-buffer flow line with parallel unreliable machines. European Journal of Operational Research, 197(2), 572–580. https://doi.org/10.1016/j.ejor.2008.07.004

    Article  Google Scholar 

  38. Diamantidis, A. C., Papadopoulos, C. T., & Heavey, C. (2007). Approximate analysis of serial flow lines with multiple parallel-machine stations. IIE Transactions, 39(4), 361–375. https://doi.org/10.1080/07408170600838423

    Article  Google Scholar 

  39. Dimopoulos, C., & Zalzala, A. M. S. (2001). Investigating the use of genetic programming for a classic one-machine scheduling problem. Advances in Engineering Software, 32(6), 489–498. https://doi.org/10.1016/S0965-9978(00)00109-5

    Article  Google Scholar 

  40. Duerden, C., Shark, L.-K., Hall, G., & Howe, J. (2015). Genetic algorithm for energy consumption variance minimisation in manufacturing production lines through schedule manipulation. In H. K. Kim, M. A. Amouzegar, & S. Ao (Eds.), Transactions on engineering technologies (pp. 1–13). Springer. https://doi.org/10.1007/978-94-017-7236-5_1

  41. Fernandes, Paulo, O’Kelly, M. E., Papadopoulos, C. T., & Sales, A. (2013). Analysis of exponential unreliable production lines using Kronecker descriptors (pp. 1–9). Presented at the IXth International Conference on Stochastic Models of Manufacturing and Service Operations (SMMSO 2013), Kloster Seeon, Germany.

  42. Falih, A., & Shammari, A. Z. M. (2020). Hybrid constrained permutation algorithm and genetic algorithm for process planning problem. Journal of Intelligent Manufacturing, 31(5), 1079–1099. https://doi.org/10.1007/s10845-019-01496-7.

    Article  Google Scholar 

  43. Fernandes, P., O’Kelly, M. E. J., Papadopoulos, C. T., & Sales, A. (2013a). Analysis of exponential reliable production lines using Kronecker descriptors. International Journal of Production Research, 51(14), 4240–4257. https://doi.org/10.1080/00207543.2012.754550

    Article  Google Scholar 

  44. Freitag, M., & Hildebrandt, T. (2016). Automatic design of scheduling rules for complex manufacturing systems by multi-objective simulation-based optimization. CIRP Annals, 65(1), 433–436. https://doi.org/10.1016/j.cirp.2016.04.066

    Article  Google Scholar 

  45. Garces-Perez, J., Schoenefeld, D. A., & Wainwright, R. L. (1996). Solving facility layout problems using genetic programming. In J. R. Koza, D. E. Goldberg, D. B. Fogel, & R. L. Riolo (Eds.), Genetic programming 1996: Proceedings of the first annual conference (pp. 182–190). MIT Press.

  46. García-Martínez, C., Rodriguez, F. J., & Lozano, M. (2018). Genetic algorithms. In R. Martí, P. M. Pardalos, & M. G. C. Resende (Eds.), Handbook of heuristics (pp. 431–464). Springer. https://doi.org/10.1007/978-3-319-07124-4_28

  47. Gen, M., & Lin, L. (2014). Multiobjective evolutionary algorithm for manufacturing scheduling problems: State-of-the-art survey. Journal of Intelligent Manufacturing, 25(5), 849–866. https://doi.org/10.1007/s10845-013-0804-4

    Article  Google Scholar 

  48. Gershwin, S. B. (1987). An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking. Operations Research, 35(2), 291–305. https://doi.org/10.1287/opre.35.2.291

    Article  Google Scholar 

  49. Gershwin, S. B. (1994). Manufacturing systems engineering. PTR Prentice Hall.

    Google Scholar 

  50. Goldberg, D. E. (1989). Genetic algorithms in search optimization and machine learning. Addison-Wesley.

    Google Scholar 

  51. Gong, Y.-J., Chen, W.-N., Zhan, Z.-H., Zhang, J., Li, Y., Zhang, Q., & Li, J.-J. (2015). Distributed evolutionary algorithms and their models: A survey of the state-of-the-art. Applied Soft Computing, 34, 286–300. https://doi.org/10.1016/j.asoc.2015.04.061

    Article  Google Scholar 

  52. Han, K.-H., & Kim, J.-H. (2002). Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Transactions on Evolutionary Computation, 6(6), 580–593. https://doi.org/10.1109/TEVC.2002.804320

    Article  Google Scholar 

  53. Hardier, G., Roos, C., & Seren, C. (2013). Creating sparse rational approximations for linear fractional representations using surrogate modeling. In 3rd IFAC conference on intelligent control and automation science ICONS 2013, 46(20) (pp. 399–404). https://doi.org/10.3182/20130902-3-CN-3020.00066

  54. Hatcher, J. M. (1969). The effect of internal storage on the production rate of a series of stages having exponential service times. AIIE Transactions, 1(2), 150–156. https://doi.org/10.1080/05695556908974427

    Article  Google Scholar 

  55. Haydon, B. J. (1973). The behaviour of systems of finite queues (Ph.D. Thesis). The University of New South Wales, Kensington.

  56. Heavey, C., Papadopoulos, H. T., & Browne, J. (1993). The throughput rate of multistation unreliable production lines. European Journal of Operational Research, 68(1), 69–89. https://doi.org/10.1016/0377-2217(93)90077-Z

    Article  Google Scholar 

  57. Helber, S. (1999). Performance analysis of flow lines with non-linear flow of material (Vol. 473). Springer. https://doi.org/10.1007/978-3-642-95863-2

    Book  Google Scholar 

  58. Hillier, F. S., & Boling, R. W. (1966). The effects of some design factors on the efficiency of production lines with variable operation times. Journal of Industrial Engineering, 17(12), 651–658.

    Google Scholar 

  59. Hillier, F. S., & Boling, R. W. (1967). Finite queues in series with exponential or Erlang service times—a numerical approach. Operations Research, 15(2), 286–303. https://doi.org/10.1287/opre.15.2.286

    Article  Google Scholar 

  60. Hira, D. S., & Pandey, P. C. (1987). Efficiency of manual flow line systems—predictive equations. International Journal of Production Research, 25(4), 603–614. https://doi.org/10.1080/00207548708919864

    Article  Google Scholar 

  61. Holland, J. H. (1992). Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence (1st MIT Press ed.). MIT Press. https://doi.org/10.7551/mitpress/1090.001.0001

  62. Hopp, W. J., & Spearman, M. L. (2008). Factory physics (3rd ed., international edition.). McGraw-Hill/Irwin.

  63. Howard, L. M., & D’Angelo, D. J. (1995). The GA-P: A genetic algorithm and genetic programming hybrid. IEEE Expert, 10(3), 11–15. https://doi.org/10.1109/64.393137

    Article  Google Scholar 

  64. Hunt, E. B., Marin, J., & Stone, P. J. (1966). Experiments in induction. Academic Press.

    Google Scholar 

  65. Hunt, G. C. (1956). Sequential arrays of waiting lines. Operations Research, 4(6), 674–683. https://doi.org/10.1287/opre.4.6.674

    Article  Google Scholar 

  66. Jeong, W., & Nof, S. Y. (2008). Performance evaluation of wireless sensor network protocols for industrial applications. Journal of Intelligent Manufacturing, 19(3), 335–345. https://doi.org/10.1007/s10845-008-0086-4

    Article  Google Scholar 

  67. Kelisky, R. P., & Rivlin, T. J. (1968). A rational approximation to the logarithm. Mathematics of Computation, 22(101), 128–136. https://doi.org/10.2307/2004770

    Article  Google Scholar 

  68. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of ICNN’95—international conference on neural networks (Vol. 4, pp. 1942–1948). Presented at the Proceedings of ICNN’95—International Conference on Neural Networks. https://doi.org/10.1109/icnn.1995.488968

  69. Kovačič, M., & Šarler, B. (2009). Application of the genetic programming for increasing the soft annealing productivity in steel industry. Materials and Manufacturing Processes, 24(3), 369–374. https://doi.org/10.1080/10426910802679634

    Article  Google Scholar 

  70. Koza, J. R. (1995). Survey of genetic algorithms and genetic programming. In Proceedings of 1995 WESCON conference (pp. 589–594). IEEE. https://doi.org/10.1109/WESCON.1995.485447

  71. Koza, J. R. (1992). Genetic programming: On the programming of computers by means of natural selection. MIT Press.

    Google Scholar 

  72. Koza, J. R. (1994). Genetic programming II: Automatic discovery of reusable programs. MIT Press.

    Google Scholar 

  73. Kusiak, A. (1990). Intelligent Manufacturing Systems. NJ, USA: Prentice Hall.

    Google Scholar 

  74. Kuhnle, A., Kaiser, J.-P., Theiß, F., Stricker, N., & Lanza, G. (2021). Designing an adaptive production control system using reinforcement learning. Journal of Intelligent Manufacturing, 32(3), 855–876. https://doi.org/10.1007/s10845-020-01612-y

    Article  Google Scholar 

  75. Kuo, Y., Yang, T., Peters, B. A., & Chang, I. (2007). Simulation metamodel development using uniform design and neural networks for automated material handling systems in semiconductor wafer fabrication. Simulation Modelling Practice and Theory, 15(8), 1002–1015. https://doi.org/10.1016/j.simpat.2007.05.006

    Article  Google Scholar 

  76. Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied linear statistical models. McGraw-Hill.

    Google Scholar 

  77. Lahoz-Beltra, R. (2016). Quantum genetic algorithms for computer scientists. Computers, 5(4), 24. https://doi.org/10.3390/computers5040024

    Article  Google Scholar 

  78. Langdon, W. B. (2000). Genetic programming and evolvable machines: Books and other resources. Genetic Programming and Evolvable Machines, 1(1/2), 165–169. https://doi.org/10.1023/A:1010028616099

    Article  Google Scholar 

  79. Langdon, W. B. (2020). Genetic programming and evolvable machines at 20. Genetic Programming and Evolvable Machines, 21(1–2), 205–217. https://doi.org/10.1007/s10710-019-09344-6

    Article  Google Scholar 

  80. Langdon, W. B., & Gustafson, S. (2005). Genetic programming and evolvable machines: Five years of reviews. Genetic Programming and Evolvable Machines, 6(2), 221–228. https://doi.org/10.1007/s10710-005-6165-9

    Article  Google Scholar 

  81. Langdon, W. B., & Gustafson, S. M. (2010). Genetic programming and evolvable machines: Ten years of reviews. Genetic Programming and Evolvable Machines, 11(3/4), 321–338. https://doi.org/10.1007/s10710-010-9111-4

    Article  Google Scholar 

  82. Li, L., Huang, G. Q., & Newman, S. T. (2007). Interweaving genetic programming and genetic algorithm for structural and parametric optimization in adaptive platform product customization. In 16th international conference on flexible automation and intelligent manufacturing (Vol. 23(6), pp. 650–658). https://doi.org/10.1016/j.rcim.2007.02.014

  83. Li, J., Blumenfeld, D. E., & Alden, J. M. (2006). Comparisons of two-machine line models in throughput analysis. International Journal of Production Research, 44(7), 1375–1398. https://doi.org/10.1080/00207540500371980

    Article  Google Scholar 

  84. Li, J., Blumenfeld, D. E., Huang, N., & Alden, J. M. (2009). Throughput analysis of production systems: Recent advances and future topics. International Journal of Production Research, 47(14), 3823–3851. https://doi.org/10.1080/00207540701829752

    Article  Google Scholar 

  85. Li, J., & Meerkov, S. M. (2009). Production systems engineering. Springer. https://doi.org/10.1007/978-0-387-75579-3

    Book  Google Scholar 

  86. Li, L., Qian, Y., Du, K., & Yang, Y. (2016). Analysis of approximately balanced production lines. International Journal of Production Research, 54(3), 647–664. https://doi.org/10.1080/00207543.2015.1015750

    Article  Google Scholar 

  87. Li, M., Zhong, R. Y., Qu, T., & Huang, G. Q. (2021). Spatial–temporal out-of-order execution for advanced planning and scheduling in cyber-physical factories. Journal of Intelligent Manufacturing. https://doi.org/10.1007/s10845-020-01727-2

    Article  Google Scholar 

  88. Lim, J., Meerkov, S. M., & Top, F. (1990). Homogeneous, asymptotically reliable serial production lines: Theory and a case study. IEEE Transactions on Automatic Control, 35(5), 524–534. https://doi.org/10.1109/9.53518

    Article  Google Scholar 

  89. Lin, J. T., & Chiu, C.-C. (2018). A hybrid particle swarm optimization with local search for stochastic resource allocation problem. Journal of Intelligent Manufacturing, 29(3), 481–495. https://doi.org/10.1007/s10845-015-1124-7

    Article  Google Scholar 

  90. Liu, J., Yang, S., Wu, A., & Hu, S. J. (2012). Multi-state throughput analysis of a two-stage manufacturing system with parallel unreliable machines and a finite buffer. European Journal of Operational Research, 219(2), 296–304. https://doi.org/10.1016/j.ejor.2011.12.025

    Article  Google Scholar 

  91. Magazine, M. J., & Stecke, K. E. (1996). Throughput for production lines with serial work stations and parallel service facilities. Performance Evaluation, 25(3), 211–232. https://doi.org/10.1016/0166-5316(95)00005-4

    Article  Google Scholar 

  92. Martin, G. E. (1993). Predictive formulae for unpaced line efficiency. International Journal of Production Research, 31(8), 1981–1990. https://doi.org/10.1080/00207549308956835

    Article  Google Scholar 

  93. Meurer, A., Smith, C. P., Paprocki, M., Čertík, O., Kirpichev, S. B., Rocklin, M., et al. (2017). SymPy: Symbolic computing in Python. PeerJ Computer Science, 3, e103. https://doi.org/10.7717/peerj-cs.103

    Article  Google Scholar 

  94. Michalski, R. S., & Chilausky, R. L. (1980). Knowledge acquisition by encoding expert rules versus computer induction from examples: A case study involving soybean pathology. International Journal of Man-Machine Studies, 12(1), 63–87. https://doi.org/10.1016/S0020-7373(80)80054-X

    Article  Google Scholar 

  95. Minsky, M., & Papert, S. (1969). Perceptrons: An introduction to computational geometry (1st ed.). The MIT Press.

    Google Scholar 

  96. Mishra, A., Acharya, D., Rao, N. P., & Sastry, G. P. (1985). Composite stage effects in unbalancing of series production systems. International Journal of Production Research, 23(1), 1–20. https://doi.org/10.1080/00207548508904687

    Article  Google Scholar 

  97. Mitchell, M. (1996). An introduction to genetic algorithms. MIT Press.

    Google Scholar 

  98. Mitchell, T. M. (1997). Machine learning. McGraw-Hill.

    Google Scholar 

  99. Muth, E. J. (1977). Numerical methods applicable to a production line with stochastic servers. In M. F. Neuts (Ed.), Algorithmic methods in probability (Vol. 7, pp. 143–159). North-Holland.

    Google Scholar 

  100. Muth, E. J. (1987). An update on analytical models of serial transfer lines (No. Research Report No 87–15). Department of Industrial and Systems Engineering, University of Florida Gainesville FL.

  101. Muth, E. J. (1973). The production rate of a series of work stations with variable service times. International Journal of Production Research, 11(2), 155–169. https://doi.org/10.1080/00207547308929957

    Article  Google Scholar 

  102. Muth, E. J. (1984). Stochastic processes and their network representations associated with a production line queuing model. European Journal of Operational Research, 15(1), 63–83. https://doi.org/10.1016/0377-2217(84)90049-3

    Article  Google Scholar 

  103. Muth, E. J., & Alkaff, A. (1987). The throughput rate of three-station production lines: A unifying solution. International Journal of Production Research, 25(10), 1405–1413. https://doi.org/10.1080/00207548708919922

    Article  Google Scholar 

  104. Nahas, N., & Nourelfath, M. (2015). Buffer allocation, machine selection and preventive maintenance optimization in unreliable production lines. In 2015 international conference on industrial engineering and systems management (IESM) (pp. 1028–1033). Presented at the 2015 International Conference on Industrial Engineering and Systems Management (IESM), Seville. https://doi.org/10.1109/IESM.2015.7380281

  105. Nguyen, S., Mei, Y., & Zhang, M. (2017). Genetic programming for production scheduling: A survey with a unified framework. Complex & Intelligent Systems, 3(1), 41–66. https://doi.org/10.1007/s40747-017-0036-x

    Article  Google Scholar 

  106. Nishi, T., Konishi, M., & Hasebe, S. (2005). An autonomous decentralized supply chain planning system for multi-stage production processes. Journal of Intelligent Manufacturing, 16(3), 259–275. https://doi.org/10.1007/s10845-005-7022-7

    Article  Google Scholar 

  107. Önüt, S., Soner Kara, S., & Efendigil, T. (2008). A hybrid fuzzy MCDM approach to machine tool selection. Journal of Intelligent Manufacturing, 19(4), 443–453. https://doi.org/10.1007/s10845-008-0095-3

    Article  Google Scholar 

  108. Panda, B., Shankhwar, K., Garg, A., & Savalani, M. M. (2019). Evaluation of genetic programming-based models for simulating bead dimensions in wire and arc additive manufacturing. Journal of Intelligent Manufacturing, 30(2), 809–820. https://doi.org/10.1007/s10845-016-1282-2

    Article  Google Scholar 

  109. Panwalkar, S. S., & Smith, M. L. (1979). A predictive equation for average output of K stage series systems with finite interstage queues. AIIE Transactions, 11(2), 136–139. https://doi.org/10.1080/05695557908974453

    Article  Google Scholar 

  110. Papadopoulos, C., Tsakonas, A., & Dounias, G. (2002). Combined use of genetic programming and decomposition techniques for the induction of generalized approximate throughput formulas in short exponential production lines with buffers. In C. Papadopoulos & E. Triantaphyllou (Eds.), Proceedings of the 30th international conference on computers & industrial engineering (p. 6). Tinos Island, Greece.

  111. Papadopoulos, C. T., Heavey, C., & Browne, J. (1993). Queueing theory in manufacturing systems analysis and design (1st ed.). Chapman & Hall.

    Google Scholar 

  112. Papadopoulos, C. T., & Karagiannis, T. I. (2001). A genetic algorithm approach for the buffer allocation problem in unreliable production lines. International Journal of Operations and Quantitative Management, 7(1), 1–13.

    Google Scholar 

  113. Papadopoulos, C. T., Li, J., & O’Kelly, M. E. J. (2019). A classification and review of timed Markov models of manufacturing systems. Computers & Industrial Engineering, 128, 219–244. https://doi.org/10.1016/j.cie.2018.12.019

    Article  Google Scholar 

  114. Papadopoulos, C. T., O’Kelly, M. E. J., Vidalis, M. J., & Spinellis, D. (2009). Analysis and design of discrete part production lines (Vol. 31). Springer. https://doi.org/10.1007/978-0-387-89494-2_1

    Book  Google Scholar 

  115. Papadopoulos, H. T. (1995). The throughput of multistation production lines with no intermediate buffers. Operations Research, 43(4), 712–715. https://doi.org/10.1287/opre.43.4.712

    Article  Google Scholar 

  116. Papadopoulos, H. T. (1996). An analytic formula for the mean throughput of K-station production lines with no intermediate buffers. European Journal of Operational Research, 91(3), 481–494. https://doi.org/10.1016/0377-2217(95)00113-1

    Article  Google Scholar 

  117. Papadopoulos, H. T., & Heavey, C. (1996). Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines. European Journal of Operational Research, 92(1), 1–27. https://doi.org/10.1016/0377-2217(95)00378-9

    Article  Google Scholar 

  118. Papadopoulos, H. T., Heavey, C., & O’Kelly, M. E. J. (1989). Throughput rate of multistation reliable production lines with inter station buffers: (I) Exponential Case. Computers in Industry, 13(3), 229–244. https://doi.org/10.1016/0166-3615(89)90113-9

    Article  Google Scholar 

  119. Papadopoulos, H. T., Heavey, C., & O’Kelly, M. E. J. (1990). Throughput rate of multistation reliable production lines with inter station buffers (II) Erlang case. Computers in Industry, 13(4), 317–335. https://doi.org/10.1016/0166-3615(90)90004-9

    Article  Google Scholar 

  120. Pasandideh, S. H. R., & Niaki, S. T. A. (2012). Genetic application in a facility location problem with random demand within queuing framework. Journal of Intelligent Manufacturing, 23(3), 651–659. https://doi.org/10.1007/s10845-010-0416-1.

    Article  Google Scholar 

  121. Park, J., Mei, Y., Nguyen, S., Chen, G., & Zhang, M. (2018). An investigation of ensemble combination schemes for genetic programming based hyper-heuristic approaches to dynamic job shop scheduling. Applied Soft Computing, 63, 72–86. https://doi.org/10.1016/j.asoc.2017.11.020

    Article  Google Scholar 

  122. Poli, R., Langdon, W. B., & McPhee, N. F. (2008). A field guide to genetic programming. Lulu Press.

    Google Scholar 

  123. Qin, W., Zhang, J., & Song, D. (2018). An improved ant colony algorithm for dynamic hybrid flow shop scheduling with uncertain processing time. Journal of Intelligent Manufacturing, 29(4), 891–904. https://doi.org/10.1007/s10845-015-1144-3

    Article  Google Scholar 

  124. Quinlan, J. R. (1986). Induction of decision trees. Machine Learning, 1(1), 81–106. https://doi.org/10.1007/BF00116251

    Article  Google Scholar 

  125. Rao, N. P. (1975a). On the mean production rate of a two-stage production system of the tandem type. International Journal of Production Research, 13(2), 207–217. https://doi.org/10.1080/00207547508942987

    Article  Google Scholar 

  126. Rao, N. P. (1975b). Two-stage production systems with intermediate storage. AIIE Transactions, 7(4), 414–421. https://doi.org/10.1080/05695557508975025

    Article  Google Scholar 

  127. Rao, N. P. (1976a). A generalization of the ‘bowl phenomenon’ in series production systems. International Journal of Production Research, 14(4), 437–443. https://doi.org/10.1080/00207547608956617

    Article  Google Scholar 

  128. Rao, N. P. (1976b). A viable alternative to the ‘method of stages’ solution of series production systems with Erlang service times. International Journal of Production Research, 14(6), 699–702. https://doi.org/10.1080/00207547608956388

    Article  Google Scholar 

  129. Rayno, J., Iskander, M. F., & Kobayashi, M. H. (2016). Hybrid genetic programming with accelerating genetic algorithm optimizer for 3-D metamaterial design. IEEE Antennas and Wireless Propagation Letters, 15, 1743–1746. https://doi.org/10.1109/LAWP.2016.2531721

    Article  Google Scholar 

  130. Rosenblatt, F. (1958). The perceptron: A probabilistic model for information storage and organization in the brain. Psychological Review, 65(6), 386–408. https://doi.org/10.1037/h0042519

    Article  Google Scholar 

  131. Scale, I. E. (1972). The analysis and design of multiple-parallel production lines with interaction and feedback (Ph.D. Thesis). University of Newcastle, Australia.

  132. Sellami, C., Miranda, C., Samet, A., Bach Tobji, M. A., & de Beuvron, F. (2020). On mining frequent chronicles for machine failure prediction. Journal of Intelligent Manufacturing, 31(4), 1019–1035. https://doi.org/10.1007/s10845-019-01492-x

    Article  Google Scholar 

  133. Shanthikumar, J. G. (1980). On the production capacity of automatic transfer lines with unlimited buffer space. AIIE Transactions, 12(3), 273–274. https://doi.org/10.1080/05695558008974517

    Article  Google Scholar 

  134. Simon, H. A. (1996). The sciences of the artificial (3rd ed.). MIT Press.

    Google Scholar 

  135. Sipper, M., & Moore, J. H. (2019). Genetic programming theory and practice: A fifteen-year trajectory. Genetic Programming and Evolvable Machines. https://doi.org/10.1007/s10710-019-09353-5

    Article  Google Scholar 

  136. Smith, J. M., & Tan, B. (Eds.). (2013). Handbook of stochastic models and analysis of manufacturing system operations (Vol. 192). Springer. https://doi.org/10.1007/978-1-4614-6777-9

    Book  Google Scholar 

  137. Spinellis, D. D., & Papadopoulos, C. T. (2000). Stochastic algorithms for buffer allocation in reliable production lines. Mathematical Problems in Engineering, 5(6), 441–458. https://doi.org/10.1155/S1024123X99001180

    Article  Google Scholar 

  138. Streeter, M., & Becker, L. A. (2003). Automated discovery of numerical approximation formulae via genetic programming. Genetic Programming and Evolvable Machines, 4(3), 255–286. https://doi.org/10.1023/A:1025176407779

    Article  Google Scholar 

  139. Tan, C. J., Neoh, S. C., Lim, C. P., Hanoun, S., Wong, W. P., Loo, C. K., et al. (2019). Application of an evolutionary algorithm-based ensemble model to job-shop scheduling. Journal of Intelligent Manufacturing, 30(2), 879–890. https://doi.org/10.1007/s10845-016-1291-1

    Article  Google Scholar 

  140. Ting, T. O., Yang, X.-S., Cheng, S., & Huang, K. (2015). Hybrid metaheuristic algorithms: Past, present, and future. In X.-S. Yang (Ed.), Recent advances in swarm intelligence and evolutionary computation (pp. 71–83). Springer. https://doi.org/10.1007/978-3-319-13826-8_4

  141. Tsakonas, A., Papadopoulos, C., & Dounias, G. (2001). The throughput rate of short exponential production lines with finite intermediate buffers using genetic programming approximation techniques. In MCCS—2001 (pp. 11–15). Presented at the 6th International Conference Measurement and Control in Complex Systems, Vinnitsa State Technical University, Ukraine.

  142. Tsakonas, A., & Dounias, G. (2002). Hybrid computational intelligence schemes in complex domains: An extended review. In I. P. Vlahavas & C. D. Spyropoulos (Eds.), Methods and applications of artificial intelligence (pp. 494–511). Springer. https://doi.org/10.1007/3-540-46014-4_44

  143. Tzanetos, A., & Dounias, G. (2017). A New metaheuristic method for optimization: Sonar inspired optimization. In G. Boracchi, L. Iliadis, C. Jayne, & A. Likas (Eds.), Engineering applications of neural networks (pp. 417–428). Springer. https://doi.org/10.1007/978-3-319-65172-9_35

  144. Vaissier, B., Pernot, J.-P., Chougrani, L., & Véron, P. (2019). Genetic-algorithm based framework for lattice support structure optimization in additive manufacturing. Computer-Aided Design, 110, 11–23. https://doi.org/10.1016/j.cad.2018.12.007

    Article  Google Scholar 

  145. Vijay Chakaravarthy, G., Marimuthu, S., & Naveen Sait, A. (2013). Performance evaluation of proposed Differential Evolution and Particle Swarm Optimization algorithms for scheduling m-machine flow shops with lot streaming. Journal of Intelligent Manufacturing, 24(1), 175–191. https://doi.org/10.1007/s10845-011-0552-2

    Article  Google Scholar 

  146. Viswanadham, N., & Narahari, Y. (1992). Performance modeling of automated manufacturing systems. Prentice Hall.

    Google Scholar 

  147. Wolpert, D. H., & Macready, W. G. (1997). No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation, 1(1), 67–82. https://doi.org/10.1109/4235.585893

    Article  Google Scholar 

  148. Yelkenci Kose, S., & Kilincci, O. (2020). A multi-objective hybrid evolutionary approach for buffer allocation in open serial production lines. Journal of Intelligent Manufacturing, 31(1), 33–51. https://doi.org/10.1007/s10845-018-1435-6.

    Article  Google Scholar 

  149. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

    Article  Google Scholar 

  150. Zhang, Y., Bernard, A., Harik, R., & Karunakaran, K. P. (2017). Build orientation optimization for multi-part production in additive manufacturing. Journal of Intelligent Manufacturing, 28(6), 1393–1407. https://doi.org/10.1007/s10845-015-1057-1

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Dr. Michael E.J. O’Kelly and Dr. Jan Jantzen for their valuable comments and suggestions for improving the paper. The first author would also like to acknowledge the Municipality of Chios for providing him a leave of absence to participate in this project (A∆A: 783XΩHN-ΛTT).

Funding

No funding was received for conducting this study.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chrissoleon T. Papadopoulos.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare that are relevant to the content of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Boulas, K.S., Dounias, G.D. & Papadopoulos, C.T. A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines. J Intell Manuf (2021). https://doi.org/10.1007/s10845-021-01828-6

Download citation

Keywords

  • Discrete part reliable production lines
  • Performance evaluation
  • Throughput
  • Hybrid evolutionary algorithms
  • Genetic programming
  • Genetic algorithms