Can "supply chain management" be described as a business of a company?

I would like to answer your question--can you tell me why you ask?

I asked the question because I want to describe the business of a
company which has in place a supply chain management. I thought supply
chain management is a kind of a process managing the business activity
of a company. Can it then be described as a business in itself?

Supply chain management can include many things.  For example, UPS
considers itself a provider of supply chain management.  Many
companies outsource their purchasing function to other companies which
in turn source and purchase their parts, tools, packaging supplies,
paperclips, etc, then bill the company for all charges related to the
procurement.  This is also a form of supply chain management.  Another
example would be a company using a logistics business to route their
incoming freight, deciding which freight company will be sent to pick
up shipments, how the shipments will be routed, etc.  Anything that
involves the processes which get an item from a vendor to a customer
could be considered supply chain management.

I don't believe supply chain management includes such functions as
payroll, benefits, or other "business activity", so I'm not sure what
else the company you are trying to describe performs outside of
procurement, routing, etc.

Hope this info is helpful.

of course you can.  

e.g. Q: "What does your business do?"  Q: "Supply chain management -
we manage supply-chains".