Multi-channel, multi-source inventory, order dispatcher?

Is there a solution that allows you to setup rules and then decides to dispatch certain orders from certain sources?

For example, we want to store some inventory at Amazon FBA, some inventory at our own warehouse. If we receive an order in which all the items are located at Amazon, then we ship from Amazon.

If the order contains items that are not at Amazon, then we will fulfill it from our own warehouse.

So the solution would follow all these rules and automatically direct Amazon to ship.

Also, it would be ideal if this solution would also allow us to sync up products to Amazon, eBay, etc