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A new perspective on measuring entropic complexity in manufacturing systems

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Abstract

The reopening of business systems caused by the effects of the pandemic has forced decision-makers to look for quick and efficient mechanisms to achieve adequate levels of production and sales. For this reason, it is necessary to promote improvements from the processes and operations that allow agile and less complex systems.The objective of this research is to propose a new entropic metric for measuring complexity in manufacturing systems, providing its validation at each stage for a better procedural understanding. Methodologically, a literature review was carried out, followed by a detailed proposal of the new metric and finally a case study comparing it with classical and extended metrics. The results allow to solve the shortcomings found in these methods and show a better performance in the measurement.

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References

  1. Deshmukh, A.V., Talavage, J.J., Barash, M.M.: Complexity in manufacturing systems, part 1: analysis of static complexity. IIE Trans. 30(7), 645–655 (1998). https://doi.org/10.1080/07408179808966508

    Article  Google Scholar 

  2. Calinescu, A., Efstathiou, J., Bermejo, J., Schirn, J.: Assessing decision-making and process complexity in a manufacturer through simulation. IFAC Proc. Vol. 30(24), 149–152 (1997). https://doi.org/10.1016/S1474-6670(17)42245-2

    Article  Google Scholar 

  3. Sivadasan, S., Efstathiou, J., Calinescu, A., Huatuco, L.H.: Advances on measuring the operational complexity of supplier–customer systems. Eur. J. Oper. Res. 171(1), 208–226 (2006). https://doi.org/10.1016/j.ejor.2004.08.032

    Article  MathSciNet  Google Scholar 

  4. Kochan, T.A., Lansbury, R.D., MacDuffie, J.P. (eds.): After lean production: evolving employment practices in the world auto industry. Cornell University Press (2018)

    Google Scholar 

  5. Companys, R.: Decision theory. Cpda-ETSEIB. Intangible capital. Barcelona, Spain, 3, 369 (2003)

  6. Salum, L.: The cellular manufacturing layout problem. Int. J. Prod. Res. 38(5), 1053–1069 (2000). https://doi.org/10.1080/002075400189013

    Article  Google Scholar 

  7. Boisot, M., Child, J.: Organizations as adaptive systems in complex environments: the case of China. Organ. Sci. 10(3), 237–252 (1999). https://doi.org/10.1287/orsc.10.3.237

    Article  Google Scholar 

  8. Schlick, C., Demissie, B. Validity analysis of selected closed-form solutions for effective measure complexity. In: Product development projects (pp. 283–351). Springer, Cham. (2016). https://doi.org/10.1007/978-3-319-21717-8_5

  9. Modrak, V., Marton, D.: Approaches to defining and measuring assembly supply chain complexity. In: Discontinuity and complexity in nonlinear physical systems (pp. 193–213). Springer, Cham. (2014). https://doi.org/10.1007/978-3-319-01411-1_11

  10. Andersson, C., Bellgran, M.: On the complexity of using performance measures: enhancing sustained production improvement capability by combining OEE and productivity. J. Manuf. Syst. 35, 144–154 (2015). https://doi.org/10.1016/j.jmsy.2014.12.003

    Article  Google Scholar 

  11. Ashby, W.: Ross: An Introduction to Cybernetics. New YorN (1963)

  12. Simon, H.A.: The architecture of complexity. In Facets of systems science (pp. 457–476). Springer, Boston, MA (1991)

  13. de Rosnay, J.: Il macroscopio: verso una visione globale (Vol. 60). Edızıonı Dedalo (1977)

  14. Yates, F.E.: Complexity and the limits to knowledge. Am. J. Physiol. Regul. Integr. Comp. Physiol. 235(5), R201–R204 (1978). https://doi.org/10.1152/ajpregu.1978.235.5.R201

    Article  Google Scholar 

  15. Schuh, G.: Lean innovation. Springer-Verlag (2013)

    Book  Google Scholar 

  16. Gaio, L., Gino, F., Zaninotto, E.: I sistemi di produzione. Edizioni Carocci, Roma, (2002)

  17. Garbie, I.H., Shikdar, A.: Analysis and estimation of complexity level in industrial firms. Int. J. Ind. Syst. Eng. 8(2), 175–197 (2011). https://doi.org/10.1504/IJISE.2011.041368

    Article  Google Scholar 

  18. Frizelle, G., Woodcock, E.: Measuring complexity as an aid to developing operational strategy. Int. J. Oper. Prod. Manag. (1995). https://doi.org/10.1108/01443579510083640

    Article  Google Scholar 

  19. Frizelle, G.: Getting the measure of complexity. Manuf. Eng. 75(6), 268–270 (1996)

    Article  Google Scholar 

  20. Efthymiou, K., Pagoropoulos, A., Papakostas, N., Mourtzis, D., Chryssolouris, G.: Manufacturing systems complexity: an assessment of manufacturing performance indicators unpredictability. CIRP J. Manuf. Sci. Technol. 7(4), 324–334 (2014). https://doi.org/10.1016/j.cirpj.2014.07.003

    Article  Google Scholar 

  21. Vidal, G.H., Hernández, J.R.C.: Complexity in manufacturing systems: a literature review. Prod. Eng. (2021). https://doi.org/10.1007/s10845-022-01974-5

    Article  Google Scholar 

  22. Calinescu, A.: Complexity in manufacturing: an information theoretic approach. In Conference on complexity and complex systems in industry, 19–20 Sept 2000 (pp. 19–20). University of Warwick (2000)

  23. Shannon, C.E.: A mathematical theory of communication. The Bell system technical journal 27(3), 379–423 (1948). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x

    Article  MathSciNet  Google Scholar 

  24. Vidal, G.H., Hernández, J.R.C.: Study of the effects of complexity on the manufacturing sector. Prod. Eng. Res. Devel. 15(1), 69–78 (2021). https://doi.org/10.1007/s11740-020-01014-2

    Article  Google Scholar 

  25. Vidal, G.H., Hernández, J.R.C., Minnaard, C.: Modeling and statistical analysis of complexity in manufacturing systems under flow shop and hybrid environments. The International Journal of Advanced Manufacturing Technology 118(9), 3049–3058 (2022). https://doi.org/10.1007/s00170-021-08028-9

    Article  Google Scholar 

  26. Abad, R. C. (2002). Introducción a la simulación ya la teoría de colas. Netbiblo.

  27. Suh, N.P.: A theory of complexity and applications. Massachusetts Institute of Technology Cambridge (2005)

  28. Papakostas, N., Efthymiou, K., Mourtzis, D., Chryssolouris, G.: Modelling the complexity of manufacturing systems using nonlinear dynamics approaches. CIRP Ann. 58(1), 437–440 (2009). https://doi.org/10.1016/j.cirp.2009.03.032

    Article  Google Scholar 

  29. Fan, G., Li, A., Xie, N., Xu, L., Liu, X.: Production line layout planning based on complexity measurement. Int. J. Ind. Manuf. Eng. 11(10), 1626–1629 (2017)

    Google Scholar 

  30. Youn, S.J.: Measuring syntactic complexity in L2 pragmatic production: Investigating relationships among pragmatics, grammar, and proficiency. System 42, 270–287 (2014). https://doi.org/10.1016/j.system.2013.12.008

    Article  Google Scholar 

  31. Zhang, G., Li, C.: Measuring method of system complexity. In: Wang, Y., Li, T. (eds.) Knowledge engineering and management. Advances in ıntelligent and soft computing. Springer, Berlin, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25661-5_77

    Chapter  Google Scholar 

  32. Smart, J., Calinescu, A., Huatuco, L.H.: Extending the information-theoretic measures of the dynamic complexity of manufacturing systems. Int. J. Prod. Res. 51(2), 362–379 (2013). https://doi.org/10.1080/00207543.2011.638677

    Article  Google Scholar 

  33. Malone, P., Wolfarth, L.: Measuring system complexity to support development cost estimates. In 2013 IEEE Aerospace Conference (pp. 1–13). IEEE. (2013). https://doi.org/10.1109/AERO.2013.6496853

  34. Zuzana, S., Slavomir, B., Annamaria, B.: Measuring production process complexity. In Smart Technology Trends in Industrial and Business Management (pp. 71–83). Springer, Cham. (2019). https://doi.org/10.1007/978-3-319-76998-1_6

  35. Zhang, Z., Zhang, Z., Ma, W., Zhou, H.: Research on shortest paths-based entropy of weighted complex networks. In: International Conference on Electrical and Information Technologies for Rail Transportation (pp. 793–800). Springer, Singapore. (2017). https://doi.org/10.1007/978-981-10-7986-3_79

  36. Manns, M., Otto, M., Mauer, M.: Measuring motion capture data quality for data driven human motion synthesis. Procedia CIRP 41, 945–950 (2016). https://doi.org/10.1016/j.procir.2015.12.068

    Article  Google Scholar 

  37. Sharma, A., Amarnath, M., Kankar, P.K.: Feature extraction and fault severity classification in ball bearings. J. Vib. Control 22(1), 176–192 (2016). https://doi.org/10.1177/1077546314528021

    Article  Google Scholar 

  38. Modrak, V., Marton, D., Bednar, S.: Modeling and determining product variety for mass-customized manufacturing. Procedia CIRP 23, 258–263 (2014). https://doi.org/10.1016/j.procir.2014.10.090

    Article  Google Scholar 

  39. Vanmali, A.V., Deshmukh, S.S., Gadre, V.M.: Low complexity detail preserving multi-exposure image fusion for images with balanced exposure. In: 2013 National Conference on Communications (NCC) (pp. 1–5). IEEE. (2013). https://doi.org/10.1109/NCC.2013.6488013

  40. Modrak, V., Marton, D.: Complexity metrics for assembly supply chains: A comparative study. In Advanced Materials Research (Vol. 629, pp. 757–762). Trans Tech Publications Ltd. (2013) https://doi.org/10.4028/www.scientific.net/AMR.629.757

  41. Modrak, V., Semanco, P.: Structural complexity assessment: a design and management tool for supply chain optimization. Proc. CIRP 3, 227–232 (2012). https://doi.org/10.1016/j.procir.2012.07.040

    Article  Google Scholar 

  42. Modrak, V., Marton, D.: Modelling and complexity assessment of assembly supply chain systems. Proc. Eng. 48, 428–435 (2012). https://doi.org/10.1016/j.proeng.2012.09.536

    Article  Google Scholar 

  43. Isik, F.: An entropy-based approach for measuring complexity in supply chains. Int. J. Prod. Res. 48(12), 3681–3696 (2010). https://doi.org/10.1080/00207540902810593

    Article  Google Scholar 

  44. Bone, M. A., Cloutier, R., Korfiatis, P., Carrigy, A.: System architecture: Complexities role in architecture entropy. In: 2010 5th International Conference on System of Systems Engineering (pp. 1–6). IEEE. (2010) https://doi.org/10.1109/SYSOSE.2010.5544089

  45. Efstathiou, J., Calinescu, A., Blackburn, G.: A web-based expert system to assess the complexity of manufacturing organizations. Robot. Comput. Integr. Manuf. 18(3–4), 305–311 (2002). https://doi.org/10.1016/S0736-5845(02)00022-4

    Article  Google Scholar 

  46. Frizelle, G.: The management of complexity in manufacturing: a strategic route map to competitive advantage through the control and measurement of complexity. Business Intelligence (1998)

  47. Sivadasan, S., Efstathiou, J., Frizelle, G., Shirazi, R., Calinescu, A.: An information-theoretic methodology for measuring the operational complexity of supplier-customer systems. Int. J. Oper. Prod. Manag. (2002). https://doi.org/10.1108/01443570210412088

    Article  Google Scholar 

  48. Zhang, Z.: Manufacturing complexity and its measurement based on entropy models. Int. J. Adv. Manuf. Technol. 62(9), 867–873 (2012). https://doi.org/10.1007/s00170-011-3872-7

    Article  Google Scholar 

  49. Modrak, V., Soltysova, Z.: Novel complexity indicator of manufacturing process chains and its relations to indirect complexity indicators. Complexity (2017). https://doi.org/10.1155/2017/9102824

    Article  MathSciNet  Google Scholar 

  50. Isik, F.: Complexity in supply chains: a new approach to quantitative measurement of the supply-chain-complexity. Supply Chain Manag. 21(4), 417–432 (2011)

    Google Scholar 

  51. Samy, S.N., ElMaraghy, H.: A model for measuring complexity of automated and hybrid assembly systems. Int. J. Adv. Manuf. Technol. 62, 813–833 (2012). https://doi.org/10.1007/s00170-011-3844-y

    Article  Google Scholar 

  52. Gomes, V.M., Paiva, J.R., Reis, M.R., Wainer, G.A., Calixto, W.P.: Mechanism for measuring system complexity applying sensitivity analysis. Complexity (2019). https://doi.org/10.1155/2019/1303241

    Article  Google Scholar 

  53. Kavilal, E.G., Venkatesan, S.P., Sanket, J.: An integrated interpretive structural modeling and a graph-theoretic approach for measuring the supply chain complexity in the Indian automotive industry. J. Manuf. Technol. Manag. (2018). https://doi.org/10.1108/JMTM-03-2017-0032

    Article  Google Scholar 

  54. Hamta, N., Shirazi, M.A., Behdad, S., Ghomi, S.F.: Modeling and measuring the structural complexity in assembly supply chain networks. J. Intell. Manuf. 29(2), 259–275 (2018). https://doi.org/10.1007/s10845-015-1106-9

    Article  Google Scholar 

  55. De Paiva, J.R.B., Gomes, V.M., Rodrigues, B.A., Silva, L.F.A., Aniceto, B.C.M., Furriel, G.P., Calixto, W.P.: Metric for calculation of system complexity based on its connections. Trans. Environ. Electr. Eng. 2(1), 67–73 (2017). https://doi.org/10.22149/teee.v2i1.80

    Article  Google Scholar 

  56. Gravier, M.J., Kelly, B.P.: Measuring the cost of complexity in supply chains: Comparison of weighted entropy and the bullwhip effect index. In Modelling Value: Selected Papers of the 1st International Conference on Value Chain Management (pp. 257–271). Physica-Verlag HD. (2012). https://doi.org/10.1007/978-3-7908-2747-7_13

  57. Hofman, J., Lukáš, L.: Quantitative measuring of operational complexity of supplier-customer system with control thresholds. In: Proceedings of the 30th International Conference on Mathematical Methods in Economics, Karvina, Czech Republic (pp. 11–13) (2012)

  58. Sivadasan, S., Efstathiou, J., Frizelle, G., Shirazi, R., Calinescu, A.: An information-theoretic methodology for measuring the operational complexity of supplier-customer systems. Int. J. Oper. Prod. Manag. 22(1), 80–102 (2002). https://doi.org/10.1108/01443570210412088

    Article  Google Scholar 

  59. Modrak, V., Soltysova, Z.: Development of operational complexity measure for selection of optimal layout design alternative. Int. J. Prod. Res. 56(24), 7280–7295 (2018). https://doi.org/10.1080/00207543.2018.1456696

    Article  Google Scholar 

  60. Guoliang, F., Aiping, L., Giovanni, M., Liyun, X., Xuemei, L.: Operation-based configuration complexity measurement for manufacturing system. Procedia CIRP 63, 645–650 (2017). https://doi.org/10.1016/j.procir.2017.03.136

    Article  Google Scholar 

  61. Modrak, V., Marton, D.: Approaches to defining and measuring assembly supply chain complexity. Discontinuity and Complexity in Nonlinear Physical Systems, 193–213. (2014). https://doi.org/10.1007/978-3-319-01411-1_11

  62. Marton, D.: Complexity measuring approaches to assessing of assembly supply chain structures. J. Eng. Appl. Sci 8(10), 811–816 (2013)

    Google Scholar 

  63. Hamou-Lhadj, A.: Measuring the complexity of traces using Shannon entropy. In: Fifth International Conference on Information Technology: New Generations (ITNG 2008) (pp. 489–494). IEEE. (2008) https://doi.org/10.1109/ITNG.2008.169

  64. Xiaoxiao, Y.A.N.G., Zikui, L.I.N.: Supply chain complexity meaning and quantitative research. In: 2019 Chinese Control And Decision Conference (CCDC) (pp. 971–976). IEEE. (2019). https://doi.org/10.1109/CCDC.2019.8832976

  65. Ucenic, C.I., RAȚIU, C.I.: Evaluation of supply chain complexity at material flow level for a Romanian company. Acta Techn. Napoc. Series Appl. Math, Mech. Eng., 61(3_Spe) (2018)

  66. Rebout, N., Lone, J.C., De Marco, A., Cozzolino, R., Lemasson, A., Thierry, B.: Measuring complexity in organisms and organizations. R. Soc. Open Sci. 8(3), 200895 (2021). https://doi.org/10.1098/rsos.200895

    Article  Google Scholar 

  67. Guo, R., Wang, B.Y.: Measuring complexity of modern sea-warfare system. In: 2010 International Conference of Information Science and Management Engineering (Vol. 2, pp. 539–542). IEEE. (2010). https://doi.org/10.1109/ISME.2010.224

  68. Sinha, S., Kumar, B., Thomson, A.: Measuring project complexity: a project manager’s tool. Archit. Eng. Des. Manag. 2(3), 187–202 (2006). https://doi.org/10.1080/17452007.2006.9684615

    Article  Google Scholar 

  69. Thomsona, A., Kumarb, B., Chasec, S., Duffyd, A., Street, M.: Measuring complexity in a design environment. Embracing Complexity in Design, 67 (2005)

  70. Sinha, S., Thomson, A. I., Kumar, B.: Measurıng complexıty of a sub task of a project actıvıty. Postgraduate Researchers, 493 (2003)

  71. Perona, M., Miragliotta, G.: Complexity management and supply chain performance assessment. A field study and a conceptual framework. Int. J. Prod. Econ. 90(1), 103–115 (2004). https://doi.org/10.1016/S0925-5273(02)00482-6

    Article  Google Scholar 

  72. Wu, Y., Frizelle, G., Ayral, L., Marsein, J., Van de Merwe, E., Zhou, D.: A simulation study on supply chain complexity in manufacturing industry. In Proceedings of the Conference of the Manufacturing Complexity Network. University of Cambridge (2002)

  73. Jacobs, M.A.: Product complexity: a definition and impacts on operations. Decision Line, 38(5) (2007)

  74. Efthymiou, K., Mourtzis, D., Pagoropoulos, A., Papakostas, N., Chryssolouris, G.: Manufacturing systems complexity analysis methods review. Int. J. Comput. Integr. Manuf. 29(9), 1025–1044 (2016). https://doi.org/10.1080/0951192X.2015.1130245

    Article  Google Scholar 

  75. Coronado Hernández, J.R.: Analysis of the effect of some complexity and uncertainty factors on the performance of Supply Chains. Proposal for a simulation-based assessment tool (Doctoral dissertation). (2016). http://hdl.handle.net/10251/61467

  76. Flynn, B.B., Flynn, E.J.: Information-processing alternatives for coping with manufacturing environment complexity. Decis. Sci. 30(4), 1021–1052 (1999). https://doi.org/10.1111/j.1540-5915.1999.tb00917.x

    Article  Google Scholar 

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Acknowledgements

Thank you to the Fundación Universitaria Tecnológico Comfenalco (FUTC), Research Group Ciptec, Universidad de la Costa (CUC)—Colombia and to the Universidad Nacional Lomas de Zamora (UNLZ)—Argentina, for the support of their academic and scientific group.

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Vidal, G.H., Hernández, J.R.C. & Minnaard, C. A new perspective on measuring entropic complexity in manufacturing systems. Int J Interact Des Manuf 18, 191–201 (2024). https://doi.org/10.1007/s12008-023-01462-x

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