How do you keep up an exercise routine with a varied schedule, such as shift work?

A routine doesn't have to be rigid or happen at certain times each day, it's not linear it's cyclical. It's an order to do things in not a schedule and it is always okay to adapt it to the things you HAVE to do like work, so if you have varied shifts you can push back excercise or move it forward depending on the time you have available, if you wake up late so what? Just do everything late, it won't hurt anyone. Nor is it a problem to skip a day because you don't have time or energy, nothing is set in stone, do what you can when you can and don't beat yourself up if you don't accomplish everything you wanted to, focus more on what you have achieved rather than what you want to achieve x

I personally do a just 5 minutes total of core exercises every day—resting as needed. Many core exercises also work either the arms or legs, and by doing it every day, it sets a routine. I either do this when I wake up, or right before bed.