One thing that you can do that will greatly simplify dishwasher management, is to have two dishwashers.
There is one clean dishwasher and one dirty dishwasher. You take plates from the clean dishwasher, use them, and put them in the dirty dishwasher. Once the clean dishwasher is empty, the dirty dishwasher is run, and then becomes the clean dishwasher, and the empty one now becomes the dirty dishwasher.
There are analogous situations in system design as well.
There is one clean dishwasher and one dirty dishwasher. You take plates from the clean dishwasher, use them, and put them in the dirty dishwasher. Once the clean dishwasher is empty, the dirty dishwasher is run, and then becomes the clean dishwasher, and the empty one now becomes the dirty dishwasher.
There are analogous situations in system design as well.