From time to time, I come across a book which I would have liked to have read and had on my academic bookshelves years ago. Here is one. It is Neil Johnson's book on complexity theory, which is published under two titles: the copy that has come from a UK library has the title: Two's Company, Three is Complexity: a simple guide to the science of all sciences, but Amazon has a similar book:Simple Complexity.
There is comparatively little about Complexity Theory, as Johnson defines it, in the O.R. literature. Type "complexity" into International Abstracts in O.R. and you come up with analyses of the complexity of various algorithms, and a very few references to complexity theory in the sense of the book. But Johnson is writing about the complexity of large systems, and so it overlaps with systems theory in O.R., with knowledge management, and with agent-based simulation (among others).
Johnson comes from a background in physics, but his work links to the work of others in traffic modelling, conflict analysis, epidemiology, financial modelling, and much else.
In this book, Johnson defines the key components of complexity and complex systems as follows:
- The system contains a collection of many interacting objects or "agents"
- These objects' behaviour is affected by memory or "feedback"
- The objects can adapt their strategies according to their history
- The system is typically "open"
- The system exhibits emergent phenomena which are generally surprising, and may be extreme
- The emergent phenomena typically arise in the absence of any sort of "invisible hand" or central controller
- The system shows a complicated mix of ordered and disordered behaviour
Other entries in this blog have mentioned the need in O.R. for the analyst to define the extent of the system being considered in a project. Learning about complexity theory from the book has emphasised the importance of that. I thought of two linked studies that I did; the first involving the long-term strategy for managing some water resources, and the second with the hour-by-hour management of part of those resources. In the first part, we assumed that there were good rules for the hour-by-hour management, and for the latter we used the long-term results as a constraint on the control policies. But throughout these two studies, we were aware that the interaction of the two models needed much more refining - but we lacked the data and computing power to do it. One system had a time horizon of years, the other, used models with a horizon of a few hours. The two time scales differed by several orders of magnitude. We might have made progress by introducing some concepts and techniques from complexity theory.
In another study, we looked at the deployment of patrol vehicles along a motorway; there was a "basic" policy for assigning them. But as soon as those vehicles were being "used", their deployment needed active human intervention. Traffic on the motorway, and the patrols, created a complex system which matched the list of components above.
My recent blog about supermarket shopping in the run-up to Christmas touched on some aspects of the complexity of human beings going shopping!
Johnson's work on financial models overlaps with some models in O.R. What I found especially interesting was the discussion of time series analysis ... there was a lot of material which deserved a place in an O.R. module about forecasting.
The one gap in the book for me was how to use some of the models to do what O.R. people do - answer questions "What happens if?" The models work to describe real-life phenomena, but don't always offer opportunities for studying the effects of change through management decision-making. There's scope for a follow-up book. When I looked in the International Abstracts in O.R, one abstract was for a paper which covered some of this, and the abstract claimed that the paper would be the first of two papers. I can't find the second paper!
All in all, if you are doing O.R., and you want to learn a little about how complexity science is modelling systems which are of interest to O.R (and many of us ought to have done this a few years ago!), have a look at this introduction!