I applied online and was contacted by a recruiter within a couple of days. I spoke with a recruiter initially, and then had another interview with a hiring manager. That conversation went well, and I was asked to do a case study.
The case study asked you to analyze three different warehouse options with various size constraints and costs, and determine which, given a number of customers, which warehouses you'd choose, why, and what your staff build out would look like.
So I ran with it. I ran my approach by a couple of MBA friends, and got the thumbs up that I was using the standard method by which businesses calculate such things. I put together a presentation, suggested staff members based on how long I thought it would take to pack things, explained my logic, and sent them all the calculations, worksheets, and a preso. It took between 35-40 hours to put everything together.
The next day I got a "thanks but no thanks" form letter. I asked, and was told, essentially, that my entire analysis was wrong.
I decided against invoicing them for my time, but I would definitely suggest that anyone who is interviewing with them be cautious about spending any amount of time on the case study, since they don't seem to appreciate the amount of time their case study requires.