Setting Up CCP Models

Setting up a CCP model requires four steps.  Three of the steps are identical to those used in setting up an SP.  The one step found in SPs that's not found in CCPs is identifying initial decision and recourse variables, and this is because in a CCP all decision variables are considered to be in stage 0, i.e., they are all initial decision variables.  This contrasts with an SP, which may have any number of recourse stages in addition to the initial decision stage.  The fourth (and new) step in setting up CCPs is identifying the chance-constraint sets.  These four steps are summarized in the table below and are illustrated in detail in the example CCP model that follows.

Step

Task

Description

How

1

Defining core model

The core model is built just like any other deterministic LINGO model.  The random variables are used directly in the core model's expressions as if they were determinate.

Entered like any other deterministic LINGO model.

2

Identifying the random variables

Each random variable must be identified along with the stage of the model where it becomes known.  In a CCP, random variables must always belong to stage 1.

@SPSTGRNDV

3

Declaring distributions

The probability distributions of the random variables must be declared.  The techniques for doing so will depend on whether the variable of interest has a distribution defined by either a) a discrete outcome table, or b) a parametric distribution.

An outcome table is a finite set of all possible outcomes, their probabilities and values for the random variable(s).   Outcome tables may be constructed using either scalar values or attribute vectors.

A parametric distribution, on the other hand, is defined by a particular type of probability density function, e.g., the normal distribution.  Parametric distributions may have a finite or infinite number of possible outcomes, depending on the distribution type.

Outcome Tables:

  Scalar-based:

  @SPTABLESHAPE

  @SPTABLEOUTC

  @SPTABLEINST

  @SPTABLERNDV

 Vector-based:

  @SPDISTTABLE

 

4

Identify chance-constraint sets.

One or more sets of constraints are classified as being chance-constrained.  An individual constraint may appear in no more than one chance-constraint set.

@SPCHANCE