In my opinion Asset ID would be a good alternative to an actual serial number.  In our ACQuipedia article concerning Item Unique Identification (IUID) we provide the following based upon DoD instructions:

DoD requires IUID for all new item acquisitions meeting one or more of these criteria:

• Line item acquisition cost in its contract of $5,000 or more
• Serially managed by the DoD
• Controlled or mission essential
• Government wants permanent identification for any other reason

Some manufacturers mark nearly all parts regardless of the above criteria because they use IUID internally for pedigree (parent/children) tracking and error proofing of manufacturing and factory maintenance. The IUID Registry (described below) readily accepts the records of these additionally marked parts.

Serially-managed legacy items may also be IUID relevant according to the decision tree in DoD Instruction (DoDI) 8320.04, Item Unique Identification Standards for Tangible Personal Property. Legacy means that the item is already in the government’s inventory.

For embedded items, the only criteria for IUID are whether the item is or will be DoD serially managed or if the government wants permanent identification for any reason. Embedded items are parts or components delivered under contract without their own line item specifying their explicit cost.

Follow the link for the ACQuipedia article on IUID, it has additional references that may assist you and your company:

Item Unique Identification (IUID) (dau.edu)