We are suggesting that the IT shop of a company should move from level 1 to level 3. They have all of the documents available to give the benefits of implementing CMMi, however, they did not take into account the resources required to move up the maturity level. My question is: how do we size the number of CMMi experts our client will need to transform its IT activities from level 1 to 3 (say for 800 people). I would appreciate any thoughts that you might have on this.
Wow, you have ALL the documents in place? Doesn't that make them Level Three already? I'm kidding of course.
There are two ways of looking at your situation. My preference is to say "no additional resources are required" to achieve CMMI Maturity Level Three.
How is this possible? It's because the CMMI isn't something you can "do" to a client. It's something only they can do to themselves. It isn't about documents, it's about culture. I have had appraisals where all of the documents were in place, but it was obvious the company was not performing any of the behaviors from the model, and they were not successful at achieving CMMI Level Two or Three.
If an external firm does this to a client, they will leave at the conclusion of the engagement with all of the knowledge of how to develop and sustain the process. Part of Level Three is knowing how to design, deploy, and sustain a process. This might be good for business and billing rates, but it's not the best thing for the client organization.
Here at the 'sword we normally recommend to have one person onsite part time helping to guide the client organization towards managing this themselves - but any more than one tends to muddy the waters and the organization starts to depend on us too much and won't change themselves.
Now, once in awhile we come across a client that wants to hire an outside firm to do this for them. This is not something we do, but if they insist on a recommendation of needed resources, we have learned that to kick off and sustain an effort to move from CMMI Maturity Level One to ML3 takes about 3% of the overall engineering staff, plus another 1.5% to perform "PPQA" responsibilities. Given that you've said your client has 800 practitioners, that would account for about 24 people plus 12 for QA. How many of those are client personnel would depend on their skills and availability.
I would implore you to consider alternate ways to accomplish this goal that involve the client taking on as much of the load as possible. Your chances of success (and theirs) are far greater if you do!