Justaguy,
For what ever reason, you believe that your question about shape is a good way to begin to understand barge performance. It isn't.
You think it has an easy answer. It doesn't.
You think the answer will be the same for most barges. It isn't.
You don't think highly specialized math is needed to get an approximate answer or understand why. It is. It is harder than most of what NASA engineers actually do. I was a missile guy and did missile math. Now I'm retired and struggle with boat math.
You think "how hard can it be - one moving part, steady speed, steady direction, whats the problem". The problem is that you have to calculate the path taken by millions of water droplets as they flow around the boat. You have to define the entire flow around the whole boat and far into the wake. And the pressure everywhere around the boat. And the wavy surface created by the boat. And the waves that are already on the water. Do that and we can start making some generalities. With out that, you've got zip. And we still aren't very good at calculating that stuff for arbitrary shapes. Nobody would promise you an answer within 10%, even if you paid them thousands of dollars. Ok, Yobarnacle probably could. He drove tugs for half a century.
Boat shape is a very hard nut to crack. Until recently, it was done by building a few million boats over 6000 years and seeing what worked. Naval battles and hurricanes kept it a lively business. And finding a new continent every now and then encouraged investment. Lots of investment. Like we spend billion dollars a year now a days to answer the same question - what should it look like.
I suggest you begin by learning boat speak. A dictionary is pinned near the top of the "all things boating" sub forum. The odds of getting an answer improve if we speak the same language. And regarding this, it is you that have to come to us since you haven't posted your boat dictionary for us to read. Think of it as meeting us half way.
The first thing you need to do is stop thinking in 2D. There aren't any 2D best shape answers. Everything is 3D. Water flows in 3D.
If you wanted to build a barge, you would need to comply with the building regulations just like a house. So you take courses to learn the regulations. Your barge has to fit on the body of water - more regulations. Your barge has to play well with other barges - additional requirements. It has to be loaded and unloaded without flipping over. It has to protect the product. This is where you begin. Shape in the water comes later. There are no general shape answers because in the real world, their aren't any general shape questions, only a great many very particular ones. You look for a shape which retains dozens of performance characteristics, economic, physical, and regulatory.
If you want to study a good shape, study traditional sharpies. There were five shops side by side each building 1 per week for fifty years in New Haven. They launched on Saturday and raced on Sunday and then went clamming until they sank. Go figure out WHY they ended up like they did after 12,000 were built by the same people. The things that contribute to shape are mostly not what you think they are. Boats that always come home remain popular. Cheap boats remain popular. Fast boats remain popular. You need to learn what constrains the shape of each boat before worrying about blue sky optimization.
Real world optimal shape solution.