Matrix Method for Higher 3M&I-Management

  • Masayuki MatsuiEmail author
Part of the SpringerBriefs in Business book series (BRIEFSBUSINESS)


In modern enterprises, the traditional management style may encounter many complex problems, and the static/statistical method needs to be developed by incorporating a stochastic/intelligence approach. For higher productivity and better management, two subjects or classes that have been discussed since 2009 are faster and more systematic decision-making. There has been some progress with the former, which has been developed by Matsui (2013). With regard to the problem of the latter class, our matrix (white-box) approach has been more effective than management by feeling and experience. The advantage of the matrix approach is the visualization and bird’s-eye view of the black-box object, and the operability of any settings of resolution and shortcut pass (compression of causal cascade) at any stages of objects. First, the table (structured matrix) versus compact (Matsui’s matrix equations or ME) matrix approaches are discussed and unified (generalized) as the matrix model in the (finite) fractal form. Next, the case of interindustry relations table and its decision-making is formulated and up-circulated in the generalized (fractal) form of the matrix approach. To achieve a higher level of management, we also recall and rewrite an original means of integrating such intelligence using a matrix approach to the “Product (materials) × Enterprise (things)” strategy in 2009. Finally, the unified and dual problems of Matsui’s ME and the structured matrix are discussed to achieve higher systemization and management. The purpose of this chapter is to present and consider a frame matrix, along with a case study of enterprise systems to achieve systematic and visual sustainability.


Matrix approach Matsui’s ME Structured matrix Fractal-like form Interindustry relations Materials × things 


  1. 1.
    Matsui, M., Suzuki, H., Tsubaki, H., Ohba, M., & Irohara, T. (2016). Toward the integration of intelligence for higher management. OUKAN Journal, 4(1), 1–4. (in Japanese).Google Scholar
  2. 2.
    Matsui, M. (2012). A foundation and development of performance indexing and decision method for the next generation. In Pre-print of OUKAN symposium, Japan University, Tokyo, 47–50. (in Japanese).Google Scholar
  3. 3.
    Matsui, M. (2013). An enterprise-aided theory and logic for real-time management. International Journal of Production Research, 51(23–24), 7308–7312.CrossRefGoogle Scholar
  4. 4.
    Toyama, T. (2000). Business structure modeling based on structured matrix. Doctoral paper. Tokyo: Tokyo Institute of Technology.Google Scholar
  5. 5.
    Toyama, T. (2011). Integration theory of activity and costing: From paired costing to triplet costing. The Journal of Cost Accounting Research, 35(1), 23–38.Google Scholar
  6. 6.
    Matsui, M. (2013). Product × enterprise strategy: A matrix approach to enterprise systems for sustainability management. In Proceedings of 14th Asia pacific industrial engineering and management systems conference, Cebu, Philippines.Google Scholar
  7. 7.
    Matsui, M. (2016). Fundamentals and principles of artifacts science: 3M&I-body system. Berlin: Springer.CrossRefGoogle Scholar
  8. 8.
    Matsui, M. (2011). Conveyor-like network and balancing. In. A. B. Savarese (Ed.), Manufacturing engineering (pp. 65–87). New York: NOVA.Google Scholar
  9. 9.
    Leontief, W. (1996). Input-output economics. Cambridge University Press, 2004.Google Scholar
  10. 10.
    Matsui, M. (2017). Artifacts formulation & realization: Matsui’s matrix method, Riccati equation and enterprise robot. In Proceedings of 24th international conference on production research. Poznan, Poland.Google Scholar
  11. 11.
    Toyama, T., & Nakajima, N. (2018) Proposal of expression 4.0 toward pilling out collective intelligence and harmony at the progressing diversification and complexity. In OUKAN conference. UEC Tokyo. (in Japanese).Google Scholar
  12. 12.
    Toyama, T., & Stainer, A. (1999). Strategic productivity management-a business structure-based system. International Journal of Computer Applications in Technology, 12(2–5), 102–109.CrossRefGoogle Scholar
  13. 13.
    Comon, P. (2008). Structure matrices and inverses. In A. Bojanczyk, & G. Cybenko (Eds.), Linear algebra for signal processing. Springer.Google Scholar
  14. 14.
    Arcidiacono, G., Calabrese, C., & Yang, K. (2012). Leading processes to lead companies: Lean six sigma. Kaizen Leader & Green Handbook: Springer.CrossRefGoogle Scholar
  15. 15.
    Matsui, M. (2008). Manufacturing and service enterprise with risks: A stochastic management approach. In International series in OR&MS (p. 125). Springer.Google Scholar
  16. 16.
    Matsui, M., & Oogawara, T. (2009). On product × enterprise strategy and sustainability. In Reprints of Japan industrial management association (pp. 148–149). Fall, Tokyo. 2010 Master’s thesis of Oogawara at UEC Tokyo. (in Japanese).Google Scholar
  17. 17.
    Matsui, M. (2012). A foundation and development of performance indexing and decision method for the next generation. In Proceedings of the 4th Oukan symposium (pp. 47–50). Chiba, Japan. (in Japanese).Google Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Research Institute for EngineeringKanagawa UniversityYokohamaJapan
  2. 2.The University of Electro-CommunicationsTokyoJapan

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