Loss and Gain are random linear functions of decision variables with random coefficients.  If random coefficients of these functions have  finite joint discrete distribution, then these functions are Scenario Functions.  Output of these functions are scenarios. Scenario Functions are used in PSG only as arguments of risk functions. Scenario Functions  may be used separately from risk functions only for calculation of scenarios. 

 

PSG includes also Loss and Gain Functions with random coefficients, having multivariate normal distribution.  These types of Loss and Gain Functions are not Scenario Functions.

 

Syntax

For calculation of scenarios of Loss function:

 

 

For calculation of scenarios of Gain function:

 

 

Parameters

matrix        is a Matrix of Scenarios:

       

 

where the header row contains names of variables (except scenario_probability, and scenario_benchmark). Other rows contain numerical data. The scenario_probability, and scenario_benchmark columns are optional.

 

 

Mathematical Definition

Loss Function is the following random linear function of decision variables with random coefficients:

, 

where

  is a decision vector;

random vector has components and vector scenarios, ;

random value , which is the -th component of the random vector, , has  discrete scenarios .

 

Output of the Loss Function are scenarios ,

where .

 

Gain Function is the following random linear function of decision variables with random coefficients:

. 

Output of the Gain Function are scenarios .

 

Remarks

Scenario Functions pass to risk functions scenarios as well as probabilities of these scenarios.

 

Example

 

See also

Difference of two Losses, Recourse, Sum of Splines Operator