Turns out you can add putaway rules to consumables items and an internal transfer will be created showing the location.

Simple solution (smaller companies)

Use Product Tags, create one per location and tag each Product with the location.

More robust solution (larger companies)

When Consumable products are procured via a Purchase Order, an Inventory Receipt is generated which allows you to receive them into a specific location.

Validating the Receipt creates a Move History record that you can access via the Product:

To the Move History View, add the "Destination Location" field to see the child location it went to. Each time you receive and/or move this product, you will see another entry on this screen:

To keep this information accurate, your team has to transfer quantities of products OUT of this location when they consume (or transfer quantities TO another location if they move it), or scrap quantities when they are used, which ever works better for you. The Internal Transfer operation would be used for moving. A Scrap button can be accessed by opening any Move History record, or the Scrap Menu can be accessed from the Operations Menu.

All Inventory operations can be managed with the Barcode App - even if you don't have barcodes on your products (but that makes it easier).

If you don't use Purchase Orders, or if you already have Inventory you'd like to bring into specific locations, you can create the Inventory Receipt manually and validate it.