Schedule a task for all users on a computer

Question

What I am trying to accomplish here is to shutdown a shared machine when it has been idle for 3 hours. I'm in a domain environment with partial admin privileges.

I logged on that machine with account A, and created a scheduled task to do that. After 3 hours, the machine is shutdown automatically, which is perfect. But if I log on with account B, the machine cannot get shutdown, I think the scheduled task just doesn't run.

So what should I do to make sure the scheduled task will run for all users logged on on that machine? I'm thinking we can try domain group policy, but unfortunately I don't have the access. Maybe local group policy? Or let's think out of the box a little box, is there any easier ways than scheduled task to accomplish my goal?