I think that usually when a conflict occurs, the supervisors usually handle the conflict. If the problem gets worse, then the issue is handled by the manager. The problem may rarely get escalated and the owner may get involved if the matter is serious.
Whenever the business have the structure of supervisors playing a role in the management of the business, I believe that they are the ones that are going to be reported to directly in order to look into the conflict. But in a situation whereby there is no office of supervisor, it is going to fall on the table of the business owner to take care of the conflict.