The measurement of complexity in production and other commercial systems

The paper gives a review of three case studies of complexity of production systems in manufacturing and commercial industry and develops mathematical methods stemming from these studies. We use as measures of complexity various (long term) entropy rates that naturally emerge in the analysis of systems under consideration; in our case, the main focus is on (physical or virtual) queues and related phenomena. Consequently, a system is considered 'more complex' when its entropy rates are higher. The same principle is applied when different subsystems of a given system are compared with each other, identifying a 'bottleneck'. The numerical values for entropy rates are determined in the course of observation and recording, subject to some simplifying assumptions. To enable us to make effective comparisons, we introduce various classifications of queue-related conditions in systems under investigation. We also discuss a number of practical issues that emerge here, including noise and data loss.