An entropic measurement of queueing behaviour in a class of manufacturing operations

This paper is motivated by a view that there is practical value in being able to measure aspects of complexity in industrial, particularly manufacturing, systems. We address, at a decreasing level of generality, the following questions. What is required from a measure that might reflect some aspects of complexity in a large dynamical system? What is the appropriate measure? How do the main characteristics of this measure show themselves in the systems of interest? Does the proposed measurement process lead to useful theoretical and practical insights? In answer to questions (i) and (ii), we suggest that in general one measures the rate of variety of behaviour the system can exhibit, and propose the Kolmogorov–Sinai (KS) entropy of the corresponding random process as a convenient measure. We then consider input–output processes as models for manufacturing systems and discuss some simple mathematical observations on how the KS entropy can be assessed in terms of random queues and a state of the server. Next, we take into account some basic features of a manufacturing process and propose formulae for its operational and structural complexity, thus answering (iii). Finally, to answer (iv), a case study is given demonstrating how the proposed measure can be used in a manufacturing plant, and we discuss practical insights for the company involved.