رفتار آشفته در سیستم های تولید

In this article, we present a methodology derived from non-linear dynamic systems (NLDS) theory for analyzing the dynamic behavior of manufacturing systems. Some simple production systems are simulated, for which a chaotic behavior can be observed under certain dispatching rules and utilization levels. The dynamic behavior of a reactive system is studied; i.e., a system in which there is no previous schedule but jobs and operations are assigned to machines according to the state of the system. A discrete event model is used to represent the manufacturing system.

In recent years, an increasing interest in chaotic behavior in physical systems has arisen. During the last decade, several publications in different scientific and technological domains describe chaotic phenomena. In the domain of production systems, some researchers have studied this problem, particularly Horns (1989), Tönshoff and Glöckner (1992), Massotte (1993), Deshmukh and Talavage (1995), Alfaro et al. (1997), and Rousseau (2000) among others. These authors show that chaotic behavior can occur in manufacturing systems. In this article, we study the dynamic behavior of a reactive system. That is, a system where there is no previously determined schedule and the assignment of operations to machines is done according to the state of the system. We have chosen discrete event simulation to represent the system in first place, and secondly, we analyze its behavior by using non-linear dynamic systems (NLDS) theory. The article is divided into three sections: Section 2 presents the method used for analysis, which is based on Taken's theorem. Section 3 shows the method as applied to some simple manufacturing systems. Section 4 shows results for an actual FMS for assembly tasks. The results show that even in the case of simple systems under deterministic rules such as SPT (Shortest Processing Time), FIFO (First In First Out), or HPT (Highest Processing Time), a complex system's behavior can be obtained. For the real flexible manufacturing cell, several state and performance variables are analyzed by means of Fourier's spectrum and the Lyapounov's fractal dimension. It is shown that for the specific operating conditions, the cell's dynamics is chaotic.

In this work, we have presented a methodology for analyzing the dynamic behavior of some manufacturing systems. We tested the behavior of two hypothetical simple systems and also we showed the results for an actual flexible assembly cell that is operating under certain decision rules. From these results, we can conclude that flexible production systems may have chaotic behavior depending on the workload of the system and the decision rules used to assign jobs to machines. The main implications of our study to manufacturing system design are two-fold: (a) determining the chaotic behavior of a manufacturing system may be crucial in operational decisions such as planning and scheduling, since in this kind of systems a small change in operating conditions may lead to a large deviation in meeting due dates or performance goals, and, (b) that planners and production system designers must be careful when establishing operating rules, since, as seen in this work, a chaotic behavior may result from the chosen rule. Further research is needed to: (a) investigate other systems commonly found in manufacturing, and (b) how to control chaos in such systems.