We have a requirement which can give solution for the following & It would be better if its open source software.
1.Revision control of documents
2.Structuring documents in folders grouped as per supplier or as per product/SKU (see graphic of current system).
3.Handling of multiple file formats e.g. word, excel, jpeg etc.
4.Sharing of documents through web interface.
5.Managing Engineering/Manufacturing Change Process (Change request, Change Order and Change History)
6.Digital Signatures for individuals.
7.Creation of product structures (BOM) linking parts, sub-assemblies and finished products with all applicable documents (Product Data Management system).
Alfresco is another big player in the (open source) document management picture, so make sure you also check them out to see what you can rig together.
You can get basic document management (folders, revision control) for free, but with the BOM request you might be moving beyond what out-of-the-box open source can give you.
If you're not averse to going down the Windows route, the basic Windows SharePoint Services (WSS) can do all of what you want (and more) and won't cost you anything.
Yes, Your requirement addresses some complex characteristics that gained by version control systems + management systems. So most probably you may need a custom application or a customized version of an existing applications.
I've used OpenDocMan. There were some of your needs but I am not sure whether it addresses all your requirements. So please have a look.
OpenDocMan
I work for an Engineering firm and we have to deal with many of the same issues. For now we are using Knowledge Tree for document management. It can handle 1-5 easily and 6 and 7 I would put down as a maybe.
1-4 are pretty straight forward. Number 5 can be handled with workflows which notifies the appropriate people and gives them choices to take actions with which sends the document along the appropriate direction in the workflow.
Numbers 6 I'm not sure exactly what you're looking for in a digital signature. You can certainly setup a workflow that's available on all documents to sign it. So you may be able to get that to work for that requirement.
Number 7 is a little tougher. Knowledge Tree does support linking files which could potentially be used for BOMs but realistically you'll need to write a plugin to do this efficiently and manage the links.
We tend to use Knowledge Tree to keep data sheets, do proposal and quotation workflows, and back office documents. For the engineering apps we are looking to move to a real engineering management solution as soon as finances allow. But they aren't cheap. But they properly manage BOMs and integrate into the engineering tools.
Edit:
Omnify is the engineering management tool that we are looking at to do revision control on the engineering files and BOMs.
These are pretty heavy requirements. You might have to look for custom application, as it would be hard to find open source application that satisfies all these requirements.
A custom website made using PHP/MySQL could help you with most of the requirements and can be built in few months. That might be better option in long run then trying to customize some application too much for your needs.
I know that Perforce can handle the first 4 of your requirements quite well. It's not cheap, but the support is excellent.
Caveat - It's been a while since I used it in a production environment.
Although I haven't used it myself, nuxeo seems like a very good solution. I do have used Alfresco extensively and the web interface is a pain.
Try Google Docs