This is a huge legal liability and invasion of privacy. You would have to keep the presence of the GPS feature hidden from the patient. Alzheimer's patients that do run away often experience paranoia. If they knew about the tracking device, they'd deliberately take off the shoes. They're not stupid, they're brain damaged. My mother was quite crafty for a while there, and when she got mean-spirited, you really needed to watch your step. If she had run, we'd probably not have found her in time.
So, to be effective, this has to be involuntary. My mother is dead now, but there is no way I would ever "tag" her like this. What an indignity to have Alzheimer's in the first place. I'll be damned if I'm going to heap on another one with a wildlife tracking mechanism. We should just say no, with our lack of dollars for these jerks.