I use Amazon FBA for automatic fulfillment, here's my exact setup: https://speedboostr.com/automate-order-fulfillment-on-shopify.
I've talked to a few people recently that use and like Deliverr.com.
If you're doing 10+ orders a day, check out Shopify's own fulfillment network: https://www.shopify.com/fulfillment
I believe all 3 of these are capable of closest location, inventory management, shipping notifications.
Update on this (I couldn't edit post), I can't recommend Deliverr - I was working with 2 clients recently that like it but were having problems customizing the setup.
So I contacted Deliverr support to try and help these clients, but have been ignored for 6 days so far. That means they don't care about their customers. Amazon FBA works great for me, and I trust Shopify Fulfillment Network, so those 2 are my top recommendations.
For Shopify Fulfillment Network, I heard that it is required for every shipping plan to distribute the small portion of the shipment to different warehouse, right? If in that case, it would cost lot to dispatched to different location since I usually ship a whole container from China to US. Should I rent a warehouse as a hub first? But if I rent a warehouse, do I still need Shopify Fulfillment Network as fulfillment center?
Looking forward to your reply.
Thanks in advance.