pso

Have you looked at the Modelling Schema Guide, RAM_Data_Update (delete_row)? 

PSO accepts object deletions for Scheduling Data, Modelling Data as Alex pointed out, and some System Data too (Like User deletions). If you are referring the external application, it depends on how the integration is written. 

Is It possible to delete location data alone completely in PSO without affecting its child rows?

I’m not sure what you meant by child rows. Locations do not have a hierarchical structure like divisions or skills. In PSO Standalone perspective, it is possible to delete location data if you configure the object deletion properly. Integration is another story. As an example, in FSM integration, deleting a Location in FSM when ARP is used will not automatically trigger an object deletion to PSO.

In Modelling if I delete any location by RAM_Data_Update it is deleting resources belonging to those locations.

If deleting a location will delete the Resource record(s) which Location is connected, this would be a bug. Please raise a support ticket with necessary test steps and sample data you are using.