# Data Mining

**Topics:**Complexity, Information theory, Computational complexity theory

**Pages:**25 (7962 words)

**Published:**February 22, 2013

Alberto F. De Toni, Alessio Nardini, Fabio Nonino, Gianluca Zanutto Laboratory of Management Engineering, Department of Electrical, Management and Mechanical Engineering, University of Udine, Via delle Scienze 208 33100 Udine (UD), Italy

Corresponding Author: Gianluca Zanutto Office: (+39) 0432 55 82 96 Fax: (+39) 0432 55 82 51 e-mail: zanutto@uniud.it

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Abstract This study analyzes the most widewpread methodologies available in literature used to measure complexity. The research moves from a theoretical physic perspective, through the Complexity Theory, to a manufacturing system. On these subjects, two classification frameworks are proposed in order to categorize the most widespread measures. In particular, the second classification framework regards entropic measures widely used to measure complexity in manufacturing systems. With reference to this second framework, two indexes were selected (static and dynamic complexity index) and a Business Dynamic model was developed. This model was used with empirical data collected in a job shop manufacturing system in order to test the usefulness and validity of the dynamic complex index. The Business Dynamic model analyzed the trend of the index in function of different inputs in a selected work center. The results showed that the maximum value of the dynamic complexity index represents the so called “edge of chaos”, where the amount of information needed to manage the system is maximum and where there is the trade off between flexibility and efficiency of the production system. In conclusion, the main result reached in this study regards the “edge of chaos” that is the target configuration for a company, in a particular system and under the same external conditions. Key Words Complexity Measures, Entropic Measures, Manufacturing Systems, Job-shop, Business Dynamics

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1. Introduction The origins of the studies of the Complexity Theory come from the researches about far from equilibrium thermodynamical phenomenon carried out by Nobel Prize Ilya Prigogine [1,2]. The following studies about complexity took very different directions and their development has been rushing and untidy because of their extreme multidisciplinary. A system is a whole of linked parts which interact each other. Therefore, the complexity of a system refers to the number of connections or influences between the same parts of the system [3]. A “simple” system may assume a limited number of conditions, while a chaotic one may assume an enormous number of conditions because its parts are dispersed and they interact freely; in this way his behavior is absolutely not predictable. But a complex system is not a chaotic system. Particularly, a complex system [4] is made of a number of different parts, which possess specialized functions. The elements of the system are hierarchically organized and they are linked by many non-linear connections but the hierarchical structures guarantees to keep a kind of control. These non-linear connections make impossible an analytical approach for the description of every part of the system, while it is necessary a synthetic approach for the comprehension of the whole system. Therefore, a complex system places itself between systems whose behavior is simply predictable and the chaotic systems. A particular kind of complex system is a complex adaptive system (CAS) [5]. This kind of system has another important characteristic: it changes, learns and evolves passing through “almost equilibrium” configurations. Complex adaptive systems are characterized by an emergent behavior of its elements, whose behavior stands between predictability and unpredictability. Classical economic theory describes firms as entities whose target is optimizing resources utilization and maximizing earning [6]. Moreover, a company: − Knows all available techniques, e.g. all possible combinations of input and output; − Knows its own production...

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