Section III
The Theory
4
The Lean Brain Theory
“The Lean Brain Theory” by Dr. H4.
Paraphrasing Immanuel Kant, a science is not a Science until there is a relation to mathematics. Although this characterization is provocative, and nowadays few would frame a discussion in such absolute terms, the main implicit question remains valid: can we find mathematical expressions that explain Lean as predictive and quantitative?“The Lean Brain Theory” by Dr. H4.
Or shall Lean practitioners keep on letting the consultant industry tell the tale? Can this scientific approach help Lean practitioners stop following Toyota and its soft narrators (Rother and Aulinger, 2017; Liker, 2004) and start leading their own way 道 with quantifiable metrics?
Can Lean become a Science that explains phenomena in complex socio-technical interdependent systems such as organizations and help Lean practitioners understand their own specific situations?
This chapter aims to contribute to this direction by introducing certain mathematical characterizations of complex networked Lean strategic organizational design configurations.
We will start by analyzing complex networks and their degree exponent, then we will follow by presenting the conditions for complex networked Lean strategic organizational design configurations to emerge, and we will finalize the chapter by providing a quantifiable explanation of how behavioral spreading phenomena can be analytically described in such organizational design architectures.
4.1ANALYTIC CHARACTERIZATION OF DEGREE EXPONENT
As seen before, complex networks present generally a degree distribution that has a power-law tail p(k )~ k–γ where γ is called degree exponent. The degree exponent γ is a parameter whose value has been experimentally shown to be in the range 2 < γ < 5 (Barabási, 2016).
How the evolution of the structural network has behaved in the past can be determined by understanding three time-dependent parameters (Albert and Barabási, 2000):
•p(t), or the quote of new (CPD)nA links created within already activated process owners
•q(t), or the quote of re-wired (CPD)nA linked to already existing process owners
•m(t), the growth rate of the complex organizational network or the number of new activated (CPD)nAs in the complex networked organizational design configuration
Albert and Barabási (2000) showed that the exponent γ can be expressed by Equation 4.1 at any point in time:
| (4.1) |
where time is discrete t = 1,…,n and is typically measured on a weekly or monthly basis
4.1.1Management Implications
It is important for organizational leaders to track the degree exponent as a vital parameter to avoid deviations in the desired development of the organizational design configuration.
This KPI becomes then a measurable relevant strategic KPI describing the organizational design architecture. The desired values of such KPIs are those that lie in the scale-free range 2 < γ < 3.
The degree exponent of the real case study shown in the previous chapter that was depicted in Figure 4.1A has been calculated with Equation 4.1.
FIGURE 4.1
Lean Brain Theory.
It can be observed how the threshold γ = 3 is approached by the curve when the small-world condition is reached APL~ln(N) and is expected to attain a value 2 < γ < 3 when the scale-free condition is reached APL~ln(ln(N)).
But how can the analytic description of the emergence of such a scale-free complex networked organizational design configuration be described?
4.2ANALYTIC CONDITIONS FOR EMERGENCE OF SCALE-FREE Complex NETWORKED ORGANIZATIONAL CONFIGURATIONS
Under the organizational network paradigm, there are two conditions for complex organizational evolving networks to adopt a scale-free network structure (Albert and Barábasi, 2000):
•Continuous growth
•Preferential attachment
The need to analytically describe an evolutional process of continuous growth and preferential attachment that describes such organizational design configurations is vital to understand and guide the emergent dynamics toward desired organizational configuration states.
4.2.1Continuous Growth Dynamics
Organizational networks are not static systems. They expand or con...