What is the exact functionality of replacement path in Variable reporting.  What exactly it replaces?

Replacement path processing type is used in a variable when you wish to get a value from attributes of another character or from a query. 
  
Example:- if you wish to display the age of a customer in your report which will not be in the cube. I mean Age is attribute of customer and not part of the cube. But each transaction record in the cube is assigned with a customer field. So ..if we want to get this value into our report .. we create a variable on customer with replacement path and use its attribute AGE . So when you use this variable in your query for any thing you get the age of the customer associated with that transaction data
   
You can find one more example:
   
Lets assume we are using a text variable in the Query description (-->Query properties) description is : 'Sales Qty report'

Suppose we have Fiscal year/Period in our Query and variable on it(characteristic).

Now your requirement is to display Fiscal year/period along with description of the Query.  For that you need to create a text variable and use it...

While creating text variable, you have to choose processing type as 'replacement path' and characteristic as 'fiscal year/period' and replace variable with as 'key or text'....

and place this text variable into Query description (from Query properties)...

Suppose user selects some value for fiscal year period, same period will be displayed along with description.

*--  Soujanya

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