I have not written here for so long. There have been too many activities, in research and in people's network, all these movements, they are moving rapidly. Here I just record my mail to a new industry colleague I was recently introduced, explaining in general terms the role of the pi-calculus as a basis of systems building with distribution. I hope it is of some use for those who wish to know about the pi-calculus and its usage.
Your note is quite nice. I do not know much about the supply chain management: however I can see how each part will interact with each other from your description very clearly.
I think what you have done in this paper is to consider the systems design from the viewpoint of communication. That has been implicit in many (large) corporate systems, but only now this idea is getting explicit.
If you are serious in extending this idea, being informed by the pi-calculus, I think it may be useful to know a little bit about the different ways pi-calculus can be used. In fact already you used it, o model behaviours of systems through interaction. To proceed further, my modest experience with industry colleagues suggests some basic ideas about this calculus can be often useful. I do not wish to be long and bore you, so I will be very brief (for this vast subject!). I will be able to augment it in our later conversations.
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The pi-calculus has two aspects. One aspect is that it is a tool to understand computation in general, including sequential programming languages, thread-based (shared variable) concurrency, distributed systems, Turing machine, lambda-calculus, synchronous systems, asynchronous systems. For example we can embed various programming languages without losing their structures and properties in this tiny calculus. For this, if you have not read yet, the following address by Robin gives a good summary:
The other aspect of the pi-calculus is a fully expressive, but tiny, communication-based language with exact semantics, just as you used in your modelling of supply management. Thus it can offer a basis for various experiments on how we can model, program and validate software based on communication. As you may know, there is a general trend towards the use of communications in corporate systems. As an example, AMQP is an open standard for messaging (there are others). Messaging has been at the core of large corporate systems centring on e.g. IBM MQ, but we can now find its robust equivalent for free, changing the ways corporate applications are developed, enriched by so-called ESB. From the pi-calculus viewpoint, such a trend enables developers at large to think about software based on processes and messages.
In this context, we can think of the pi-calculus as a theoretical basis for experimenting various ideas, such as programming, modelling and testing software based on communications; validating such programs and models; and managing and controlling them. For example, the current development tools (starting from UML, to Java, to C++, taught all over the globe) often centre on classes and objects. Are they adequate for modelling, programming and validating software whose main mode of operation is communication of messages? If not, what alternative(s) can we provide to developers, from Chennai to London to Tokyo to New York to Paris? The pi-calculus, because it distills the full expressiveness of communication-based computing, including its richness and challenges, in its tiny syntax, offers a key tool upon which various efforts along this line can be based on, compared, and discussed.
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Since I wished to be brief I needed to be abstract. The second aspect of the pi-calculus discussed above is a rich source of dialogue between practice and theories: I will be glad to have further conversations.