Chaos detection and control in production systems (original) (raw)
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Production and inventory control with chaotic demands
Omega, 2005
This study explores an e cient approach for identifying chaotic phenomena in demands and develops a production lot-sizing method for chaotic demands. Owing to the butter y e ect of chaotic demands, precise prediction of long-term demands is di cult. The experiments conducted in this study reveal that the maximal Lyapunov exponent is very e ective in classifying chaotic and non-chaotic demands. A computational procedure of the Lyapunov exponent for production systems has been developed and some real world chaotic demands have been identiÿed using the proposed chaos-probing index. This study proposes a modiÿed Wagner-Whitin method that uses a forward focused perspective to make production lot-sizing decision under chaos demands for a single echelon system. The proposed method has been empirically demonstrated to achieve lower total production costs than three commonly used lot-sizing models, namely: lot-for-lot method, periodic ordering quantity, and Silver-Meal discrete lot-size heuristic under a ÿxed production horizon, and the conventional Wagner-Whitin algorithm under chaotic demands. Sensitivity analysis is conducted to compare changes in total cost with variations in look-ahead period, initial demand, setup cost and holding costs.
Chaotic behavior in manufacturing systems
International Journal of Production Economics, 2006
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.
Robust controlling of chaotic behavior in supply chain networks
Journal of the Operational Research Society, 2016
The supply chain network is a complex nonlinear system that may have a chaotic behavior. This network involves multiple entities that cooperate to meet customers demand and control network inventory. Although there is a large body of research on measurement of chaos in the supply chain, no proper method has been proposed to control its chaotic behavior. Moreover, the dynamic equations used in the supply chain ignore many factors that affect this chaotic behavior. This paper offers a more comprehensive modeling, analysis, and control of chaotic behavior in the supply chain. A supply chain network with a centralized decision-making structure is modeled. This model has a control center that determines the order of entities and controls their inventories based on customer demand. There is a time-varying delay in the supply chain network, which is equal to the maximum delay between entities. Robust control method with linear matrix inequality technique is used to control the chaotic behavior. Using this technique, decision parameters are determined in such a way as to stabilize network behavior.
A new method to control chaos in an economic system
Applied Mathematics and Computation, 2010
In this paper, the method to control chaos by using phase space compression is applied to economic systems. Because of economic significance of state variable in economic dynamical systems, the values of state variables are positive due to capacity constraints and financial constraints, we can control chaos by adding upper bound or lower bound to state variables in economic dynamical systems, which is different from the chaos stabilization in engineering or physics systems. The knowledge about system dynamics and the exact variety of parameters are not needed in the application of this control method, so it is very convenient to apply this method. Two kinds of chaos in the dynamic duopoly output systems are stabilized in a neighborhood of an unstable fixed point by using the chaos controlling method. The results show that performance of the system is improved by controlling chaos. In practice, owing to capacity constraints, financial constraints and cautious responses to uncertainty in the world, the firm often restrains the output, advertisement expenses, research cost etc. to confine the range of these variables' fluctuation. This shows that the decision maker uses this method unconsciously in practice.
International Journal of Computers Communications & Control, 2012
Currently, it is recognized that manufacturing systems are complex in their structure and dynamics. Management, control and forecasting of such systems are very difficult tasks due to complexity. Numerous variables and signals vary in time with different patterns so that decision makers must be able to predict the behavior of the system. This is a necessary capability in order to keep the system under a safe operation. This also helps to prevent emergencies and the occurrence of critical events that may put in danger human beings and capital resources, such as expensive equipment and valuable production. When dealing with chaotic systems, the management, control, and forecasting are very difficult tasks. In this article an application of neural networks and vector support machines for the forecasting of the time varying average number of parts in a waiting line of a manufacturing system having a chaotic behavior, is presented. The best results were obtained with least square support vector machines and for the neural networks case, the best forecasts, are those with models employing the invariants characterizing the system's dynamics.
Observations of Chaotic Behaviour in Nonlinear Inventory Models
International Journal of Applied Industrial Engineering, 2019
This article describes the use of simulation to investigate incipient chaotic behaviour in inventory models. Model structures investigated were either capacity limited or of variable delay time, implemented in discrete and continuous transform algebras. Results indicate the absence of chaos for a continuous time model but gave limited evidence for chaos in both unrestricted discrete models and those with a positive orders only limit. The responses where interaction with the capacity limit occurred did not confirm chaotic behaviour at odds with published results. Using the Liapunov exponent as a measure of chaotic behaviour, the results indicated, where the delay varies in proportion to order rate, a larger fixed delay reduced the Liapunov exponent as did increasing the dependence of delay on order rate. The effect of the model structures showed that the IOBPCS model, produced the largest Liapunov exponent. Reducing the discrete model update time reduced the Liapunov exponent.
Analysis of decision-making in economic chaos control
Nonlinear Analysis: Real World Applications, 2009
In some economic chaotic systems, players are concerned about whether their performance is improved besides taking some methods to control chaos. In the face of chaos occurring in competition, whether one player takes controlling measures or not affects not only their own earning but also other opponents' income. An output duopoly competing evolution model with bounded rationality is introduced in this paper. Using modern game theory, decision-making analyses about chaos control of the model are taken by taking aggregate profits as players' payoff. It is found that the speed of players' response to the market and whether the decisive parameters are in the stable region of the Nash equilibrium or not have a distinct influence on the results of the game. The impact of cost function' type on results of the game is also found. The mechanism of influences is discovered by using numerical simulation.
The nature and origin of chaos in manufacturing systems
Proceedings of 1994 IEEE/SEMI Advanced Semiconductor Manufacturing Conference and Workshop (ASMC)
In an informal manner, the word chaos frequently comes to the lips of engineers trying to operate manufacturing facilities. From a formal perspective, the discovery and application of the theory of deterministic chaos to natural systems has revolutionized work in many branches of physics, chemistry, and biology. This paper presents initial efforts to demonstrate chaotic behavior in manufacturing systems, and to explore its origins. We characterize chaotic behavior operationally as small changes bringing about large effects.
In 21. centuries' modern enterprises, system engineers have started to investigate the chaotic situations in the light of chaos theory by considering them in the earlier stages of the formation of manufacturing information systems. The purpose of this paper is to review chaos theory in order to motivate innovations in manufacturing enterprises and to examine the role that it may have in the discipline of the manufacturing information system and the management of an enterprise. In manufacturing information systems, data driven models based on alternative scenarios are developed according to chaos theory. The use of the chaos theory will contribute to the knowledge enhancement in manufacturing information systems' development and accelerate the transformation from complexity to incomplexity. The application of the chaos theory eases the controlling of the system, shorten manufacturing times, causes positive effect on the decreasing the cost and increasing the quality of the sy...
Modelling and Control of Production Systems based on Nonlinear Dynamics Theory
CIRP Annals - Manufacturing Technology, 2002
Today's highly dynamic market with its rapid changing demand requires highly dynamic order processing in very flexible production systems. Most conventional production planning and control methods do not support such fast-moving activities. A dynamical approach is introduced for modelling and control of production systems. It was developed from concepts of the Nonlinear Dynamics Theory. Manufacturing processes as well as planning and control mechanisms are seen as one unit toward the establishment of a dynamical system. The dynamical approach includes an analysis of the dynamic behaviour of the production system as well as the control of the manufacturing process by a continuous adjustment because of changes or disturbances in the environment or in the production system itself.