Abstract
We consider complex dynamical behavior in a simple model of production dynamics, based on the Wiendahl’s funnel approach. In the case of continuous order flow a model of three parallel funnels reduces to the one‐dimensional Bernoulli‐type map, and demonstrates strong chaotic properties. The optimization of production costs is possible with the OGY method of chaos control. The dynamics changes drastically in the case of discrete order flow. We discuss different dynamical behaviors, the complexity and the stability of this discrete system.
Highlights
A production system consists of a number of work units, in which sets of different parts are produced corresponding to customer orders
We address the problem of minimizing the cost function, by controlling chaos
We have considered a simple balanced threefunnel model of production dynamics, both for continuous and discrete order flow
Summary
A production system consists of a number of work units, in which sets of different parts are produced corresponding to customer orders. Our aim in this work is to discuss the optimization of the production costs of a simple three-funnel model with continuous flow and chaotic behavior described by Chase et al (1993); Schtirmann and Hoffmann (1995). Because the Bernoulli map has a natural Markov partition, the invariant probability distribution can be found analytically According to this distribution, shown, we can find different statistical characteristics of the work process, in particular the cost function. According to Ott et al (1990), it is possible to stabilize periodic orbits inside chaotic regions by using the so-called OGY method of chaos control If these orbits have a larger mean switching time, the cost function will have a lower value than for the chaotic regime. The minimum of the cost function is reached on the simplest period-3 periodic orbit when all three funnels are filled in a cyclic manner: 2 ---, 3
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