Microsoft SQL Server reported SQL message 547, severity 16:

Object Replication errors after a ConfigMgr 2012 R2 SP1 upgrade.

After a ConfigMgr 2012 R2 SP1 upgrade, I experienced a lot of Object Replication errors in the SMS_Object_Replication_Manager.

These errors looked like this:
Microsoft SQL Server reported SQL message 547, severity 16: [23000][547][Microsoft][SQL Server Native Client 11.0][SQL Server]The DELETE statement conflicted with the REFERENCE constraint "CI_CurrentRuleDetail_CIID_FK". The conflict occurred in database "CM_***", table "dbo.CI_CurrentRuleDetail", column 'Setting_
Please refer to your Configuration Manager documentation, SQL Server documentation, or the Microsoft Knowledge Base for further troubleshooting information.

After a Little Google'ing, I found that Henk Hoogendoorn had the same problem, and he had described how he solved this.

Look here:
http://henkhoogendoorn.blogspot.dk/2015/06/object-replication-errors-after.html