Crew on ships seems to be of two classes (I know nothing about shipping be warned!)
1) Direct crew: captain, engineer, etc.
2) Support for the direct crew: Ship's doctor, cook etc.
To eliminate #2, you basically have to eliminate #1 (or get #1 so small and with so many free hours in the day that somebody can dual-hat and handle cooking for whoever's left or even for themselves. Getting rid of decent medical care might be tough though.
So let's look at the ship's engineer. Supposedly, there's a reason there's an engineer on board a ship, things break down and need maintenance on a voyage. So automated or no automation, it seems like he's still going to be needed. If he's not, why hasn't that role (and his team) already been eliminated as a labor cost? Not even Star Trek figured out a way to automate away the engineer on a large ship. Smaller vessels don't need an engineer aboard, but their voyage time at sea is shorter, so the "ship's engineer" role is relegated to a land-based job and split across several vessels - we call these guys mechanics when dealing with cars.
Here's a video of a container ship engine room https://www.youtube.com/watch?v=41priD5GJyY It looks pretty automated today, yet there's still a ship's engineer aboard. I bet that the equation is spend a few hundred dollars a day on a guy or risk losing hundreds of millions of dollars of cargo because the automated system had a fault on a fuel pump or something.
But I suppose you could start splitting duty across ships, have an engineer basically helicopter around to ships to do inspections and solve limited issues. But how many ships does an engineer have to fly around to to make up the cost difference of having him flown around vs just having guys on board?
What about the captain? Out at sea a ship can basically go on a kind of autopilot today. https://www.yokogawa.com/ydk/mr/marine/pilot/products/ydkmr-... Better integration with GPS, charts and real-time weather and piracy rerouting data I guess could make blue water sailing a reality. But coastal sailing, docking, berthing, towing, and other complex navigation functions are pretty complex operations. FTA it sounds like they intend a land-based captain to remote control the vessels, but I suppose a system where they navigate to an offshore location and are towed in or a docking captain in flown in to "park" the ship could work. I believe something like this happens with canal transit.
I'm assuming there's other direct crew on board, probably with similar issues. For the support crew, as soon as the numbers of the direct crew go to zero, they all disappear...fast. But suppose they don't then you'll need two 12 hour or three 8 hour shifts of people.
Let's minimize it and say there's a captain, first mate (backup guy), engineer. Then 3 shifts we'll have 9 people. We'll need a cook for each shift, so we're at 12 people. Add in a doctor and a laundry/room (steward) cleaning person and we're at 14 people. It turns out most container ships have between 15-24 crew, so it doesn't seem I'm too far off. https://answers.yahoo.com/question/index?qid=20100924203011A...
The Xin Los Angeles has 19 crew and it's the most heavily automated, largest container ship at the time of launch in 2006. http://www.gizmag.com/go/5853/
Not a container ship, but a bulk goods ship can have dozens of crew (I suppose the cargo handling is more complex) https://en.wikipedia.org/wiki/Bulk_carrier#Crew
1 - Captain
Deck Department:
1 - Chief Officer
1 - 2nd Officer
1 - 3rd Officer
1 - Boatswain
2-6 - Able Seamen
0-2 - Ordinary Seamen
Engines:
1 - Chief Engineer
1 - 1st Asst Eng.
1 - 2nd Asst Eng.
1-2 - 3rd Asst Engr.
0-2 - Jr. Eng.
1-3 - Oiler
0-3 - Greaser
1-3 - Entry Level
Steward:
1 - Chief Steward
1 - Cook
1 - Asst.