Need Help with Shipping!!

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We are working with multiple warehouses across the country. Currently, we have an app that splits the US into two zones. East/West Coast. It has been ok. However, as we grow and shipping costs increase, customers are abandoning their carts due to high shipping costs.

Is there an app or solution which can house multiple warehouse locations across the US and determine by the customer's zip code which one warehouse to ship from?

That would be a huge step... Then if an app can do that as well as have an inventory count per warehouse and determine if can

A) Find the closest warehouse by customers zip
B} Check if products are in stock at said location. If not, then second closest, and so on.

Any insight would help us greatly! Thanks!!