The Detection and Quantification of Chaos in Supply Chains.

In recent years it has become accepted that Logistics and Supply Chain systems are susceptible to uncertainty by the generation of deterministic chaos [Wilding, 1998a; Levy, 1994; Mosekilde & Larsen, 1988]. In this paper an explanation of a methodology for detecting and quantifying deterministic chaos within measured supply chain data is discussed. The paper describes the use of Lyapunov exponents [Peitgen, Jurgens, & Saupe, 1992; Wolf, 1986] and how these can be used to determine the average predictability horizon of a chaotic system [Wilding, 1997b]. This can then be used as a method of quantifying the amount of uncertainty from chaos within a system. The magnitude of the Lyapunov exponent gives a reflection of the time scale over which the dynamics of the system are predictable, so the exponent can be used to approximate the average prediction horizon of a system [Wolf et al., 1985; Shaw, 1981]. After this prediction horizon has been reached the future dynamics of the system become unforecastable. This occurs because any cause and effect relationship between current data and previous data becomes increasingly blurred and is eventually lost.