Often there is a need to drive the part number via an existing attribute on the Physical Product into the Enterprise Item Number.  The mapped attribute can also be used in combination with any of the other existing formula configurations available to enforce uniqueness or other business rules.

Open the Platform Management dashboard and navigate to Content -> Collaborative Spaces Configuration Center.  Open the Engineering Definition section.

Add a new Formula by selecting the plus icon. Enter a name and set the Type to Attribute and then select the Attribute you wish to map from the dropdown.  You can enter a default value if desired along with the checkbox to add a counter to ensure uniqueness.

Add any additional formula criteria to the definition and click the Apply button when done.

Find a Product and set the target mapped attribute value.  

Select the Set Enterprise Item Number on the Product and you will see the mapped attribute as the New EIN.  Select the checkbox to Update Existing Enterprise Item Number and then Set.  The Enterprise Item Number is now set on the Product.

For additional documentation of the formula options for the Enterprise Item Number please refer to the following link: https://help.3ds.com/2022x/english/dsdoc/spacecontrolmap/exp3dbasicsadmin-t-engineeringdefinition.htm?contextscope=onpremise

As noted by @MC, the best practice to delegate the EIN setting by an external system is to use the web services (dseng: Engineering corpus REST Services). In the future (date to be defined), we will provide the capability for the administrator to delegate the EIN setting to an external system. In this case, the users will have to indicate that a Physical Product requires an EIN, then a new dedicated Event will be triggered to inform the external system to set the EIN using the proper web service.