SAP Functional, Basis and ABAP Programming Reference Books
PM - SM notifications

In 3.1f Notifications, there is option to create special Notification or Activity or Request.

The screen fields of Notification and request are different. 

Request displays all Catalogs codes,  Sales Organization, DC,  Division, Maintenance Plant etc. whereas Notification does not ask for these details.

So in general which is preferred to use and why?

Assuming you have 15 regions which will create Notification for customer calls. So will Request help in doing analysis of outstanding, completed Notifications region-wise etc.

Let me put it this way;

What will I not get if I use Notification?

What will I not get if I use Request as default? 

This is not from 3.0f client, it is from 4.5A but the concept is still the same.

There are 3 generic Notification types.

1. Reporting defects
2. Reporting previously carried out work
3. Requesting work.

In 4.5A these are called Problem Notification, Activity Report and Service Request.

They are all Notification "Types".

You can create your own types and mix and match the initial screens and defaulted catalog types, but these three are the ones from the menu path you quoted. Also, the initial screens and defaulted catalogs for these 3 types are also configurable.
If you don't use Notifications (in general) then you miss out on catalog reporting, breakdown reporting, downtime and most of the functionality in the SMIS. 

Recommendation, use Notifications.

The type to use? That depends on the industry and your company's needs. 

In SAP the order is the planning tool and the collector and distributor of costs.

SAP has created the functionality for Notification Tasks for the planning of work, but there is no cost planning or allocations.

Problem Notifications are just what they suggest. Reporting problems.

Depending upon the size of the job depends whether an order is created to plan the work and/or capture the costs.

Activity Reports are normally created to save the administration of an Order. i.e. No significant costs, but you wish to record some technical history after the event. They can also be created from a Preventive type maintenance Order (created automatically from a Maintenance Plan) for technical reporting.

Service request. Typically a Service is required, not a defect or problem. 

Typical examples are upgrade or improvements.

Recommendation: Use which is right for you, but you can report across all the Notification types.
 

Best regards,
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