DISCLAIMER: We have about 10x more computers than you do and we buy "Business" series devices
We have a procurement deal with HP. We buy HP Servers, Desktops, Workstations, Laptop and Tablets. I have no idea what this is worth in monetary terms, but I would project our spending well into a $million each year.
For that business-business relationship, we get a couple of useful things:
- Direct Ordering - our Business Systems generate orders direct with HP
- Standard Configurations - and standard OS images pre-installed
- Different Support Arrangements
(3) Seems to be your complaint, but my experience with HP is very different. One of our IT Support people will log a job in HP's "Support Case Manager - Professional Edition" web site, stating our organisations "ATS Customer Number" and we skip the rubbish troubleshooting questions and get parts in about 48hrs. I'm not sure which of those two ensures priority routing and it may be that neither is available to you, but it sure does work.
So I think my solution to your problem would be to find out what the cost, (to you) of establishing that kind of relationship with one or more of your Vendors is. It may be that it saves you time logging jobs, but the cost is prohibitive - only you and your colleagues can decide.