I had an assessment day at Simon & Kucher recently. The day consisted of a firm presentation, a math test (half an hour, multiple choice, nothing fancy) and 5 one on one interviews. One of the interviews was during the lunch in a restaurant. I had to speak to different employees in the corporate ladder.
One of the interviews consisted of a case; first testing my quantitive skills (I had to guess the rice consumption in Japan every year) and subsequently more business sense/qualitative skills (solutions to upgrade rice sales).
Oh, and don't be surprised of not getting feedback afterwards. I got a letter simply stating they could not offer me a job. I think that's a bit harsh considering the fact that I was there the whole day.
Word of advice: show that you are interested in Simon & Kucher during all of your interviews. Ask them questions about employee training, internal rotation, formation of project groups etc. I forgot to do this durring ALL of the interviews. Some interviewers thus thought I was not much interested in the firm itself.
Good luck at the assessment centre!
All the best,