Eur. Phys. J. Special Topics 164, 85-104 (2008)
DOI: 10.1140/epjst/e2008-00836-2

Symbolic recurrence plots: A new quantitative framework for performance analysis of manufacturing networks

R. Donner¹, U. Hinrichs² and B. Scholz-Reiter<sup>2

1</sup>  Institute for Transport and Economics, Dresden University of Technology, Andreas-Schubert-Str. 23, 01062 Dresden, Germany
²  BIBA, University of Bremen, Hochschulring 20, 28359 Bremen, Germany

donner@vwi.tu-dresden.de

Abstract
During the last years, the concept of recurrence plots has received considerable interest as a tool for analysing nonlinear and non-stationary time series. However, in the case of discrete-valued observables or variations on very different time scales, problems may occur in direct interpretations of the results of recurrence quantification analysis (RQA). As a potential solution, we suggest combining this approach with ideas from symbolic time series analysis, which allows an arbitrary static or dynamic coarse-graining of the dynamics that goes beyond recent recurrence plot based methods. As an illustrative application, we discuss how the resulting symbolic recurrence plots may be used for a quantitative investigation of the dynamics of discrete-valued inventory levels of cooperating firms in a manufacturing network. Based on discrete-event simulations, measures from traditional RQA are used to evaluate the performance of the individual firms under different production strategies as well as order policies. The results of our investigations are an important step towards an anticipative knowledge about the performance of manufacturing systems under different conditions, which is of major importance for the planning and control of both production and logistics.

© EDP Sciences, Springer-Verlag 2008