Just today i went for the workpermit medical. I think the process works as follows:
1. Your company applies online for WP and you get a piece of paper that it is issued. - Max 1 week.
2. They get a medical date - another week max.
3. Finger printing - another 3-4 days.
4. WP card - another 2-3 days.

above days are just from my personal experience and may vary.