Each drop ship supplier has a different method of calculating shipping costs, and it would be best that you clarify this detail with them before you sell. Some set a fixed price no matter the amount or size of the package, and some ship by weight and so forth.
Some online stores use a built in shopping cart system called Zen Cart. Link hidden: Login to view
Zen Cart has a drop shipper purchase order module in its downloads. This will send emails to each vendor/supplier with products, customer details, shipping method, etc . It is not automatic but itâ€™s a very simple admin interface that can be handy. The problem with Zen Cart is that its setting is across the board, so it becomes difficult when you are offering items from different vendors. For example, there are drop ship suppliers that may charge a $5 drop ship fee on top of handling and shipping. Zen Cart by default can allow you to add this charge to UPS (and whatever shipping you intend to use) but this charge gets carried across and is reflected in other items from other vendors. So with this, for small items thereâ€™s a tendency for shipping rate to become higher than the cart value, and a tendency to lose potential sales.
I've read of commercial modules that will allow you to configure shipping by product, category or manufacturer so you can set up different rules for your different vendors. You can even set the zip/postal code for every vendor to get really accurate rates. One of this is the Advanced Shipper by Ceon Link hidden: Login to view
Hope this helps. :)