System-theoretical Approach to Fundamental Limits of Controllability in Complex Organization Networks

Abstract

Organisation is fundamentally based on elaborating the equilibrium of two contradicting forces. An increasing degree of separation of work leads to specialisation and therefore significant increase of productivity in terms of time and cost. This advantage is compensated for by the therewith rising effort required to define, shape and delegate the subtasks to the different players and have them well-informed, coordinated and motivated to successfully contribute to the overall project. The well-known and common approaches to optimize division of work are mainly based on strict hierarchical structures like work breakdown structures in order to perfectly identify work-packages and their respective interfaces. Control loops are then established maintaining the certainty to achieve the previously defined results of the subtasks so that they will perfectly fit and will be ready to flawlessly form the total product. However, this traditional approach presupposes perfectly defined stable and separable systems as well as perfectly operating controlling mechanisms. As soon as some imperfection of either of these is given, which can be safely assumed in reality, the method is bound to fail principally. With this paper, we propose a system-theoretical framework modelling in particular a local imperfect however controlled situation and providing the principal limits on a mathematical basis as well as allowing for means for a practical approach. Organisations are represented by slightly contradicting systems while interactions as well as controlling mechanisms are given by first and second order differential equations according to the Theory of Systems. The resulting long-term behavior of the model, optimally avoiding oscillating and probably escalating development, indicates the principal limits of controllability. We find that the concepts of Lean Construction mainly address exactly these requirements and therefore find their formal justification including some quantitative framework.