In Amazon XML terminology, processing time is called FulfillmentLatency:
FulfillmentLatency - the number of days between the date of order and the date of the vessel (integer from 1 to 30).
The following XML snippet shows where this information fits.
<Inventory> <SKU>MyProductCode</SKU> <Quantity>100</Quantity> <FulfillmentLatency>3</FulfillmentLatency> </Inventory>
Assuming you already have the rest of the feed working and you are not getting any errors, adding a FulfillmentLatency to your XML feed should take care of your problem.
This and more information on Amazon MWS XML API formats can be found in Amazon Selling XML Guide
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