We want to install a dishwasher in our kitchen, however the cabinet box is only 23" deep and dishwashers are usually 24 inches deep (as I understand). This would pose a problem when opening a bank of drawers that are perpendicular to the dishwasher. The cabinets were built on-site/in-place and cannot be removed. We were considering "chipping away" part of the wall studs behind where the dishwasher would go in order to gain an additional inch. However, this method is a bit awkward. Does anyone have a clever idea on how to solve this problem?
You can definitely get dishwashers that are not as deep as the standard, though selection will be more limited.
One thing to consider is that the dishwasher needs a bit of clearance and wiggle room, so you'll likely need to accomodate more than 1" difference.
I would recommend against chipping away at the studs in you wall as this will reduce the strength of the studs and wall significantly. If this is an internal non-load bearing wall this might be OK but this would be a big problem if it were a load bearing wall.
I think the best/easiest solution is just to find a different dishwasher that will fit your space.
I am having this exact problem (also in the vertical dimension) right now. I didn't get to choose my dishwasher. I did discover that some of the Bosch dishwashers are slightly less than 24" across and some less than 24" deep as well. There are the half size (16") ones as well but those tend to be really expensive for whatever reason (less demand and less competition I guess) and I don't remember if they tend to have less depth as well, or make up for their small width by being the full 24" deep.
My plan to get the dishwasher I already happen to have in is to cut out the back of the cabinet (just enough for the back parts of the dishwasher to go through, perhaps adding some horizontal and vertical strips around the hole to reinforce the cabinet) and maybe even the plaster wall, then cover the cracks between lath pieces with drywall tape and put on a coat or two of join compound, and paint. I will be careful NOT to damage either the framing or the lath. The dishwasher will still stick out about 1/2" so I will have to add trim to join it to the existing cabinet faces. (For the vertical dimension I need to cut and route a thin slice off the bottom of the countertop.) I don't have any drawers or cabinets at right angles though so it's ok if it sticks out a bit.
I have no idea if this is a good plan or if it will work but can post here the results (hopefully after this weekend.)