PROC CLP: Constraint Data Set :: SAS/OR(R) 9.22 User's Guide: Constraint Programming

The CLP Procedure

Constraint Data Set

The Constraint data set defines linear constraints, variable types, and bounds on variable domains. You can use a Constraint data set in lieu of, or in combination with, a LINCON or a VARIABLE statement (or both) in order to define linear constraints, variable types, and variable bounds. The Constraint data set is specified by using the CONDATA= option in the PROC CLP statement.

The Constraint data set must be in dense input format. In this format, a model’s columns appear as variables in the input data set and the data set must contain the _TYPE_ variable, at least one numeric variable, and any reserved variables. Currently, the only reserved variable is the _RHS_ variable. If this requirement is not met, the CLP procedure terminates. The _TYPE_ variable is a character variable that tells the CLP procedure how to interpret each observation. The CLP procedure recognizes the following keywords as valid values for the _TYPE_ variable: EQ, LE, GE, NE, LT, GT, LOWERBD, UPPERBD, BINARY, and FIXED. An optional character variable, _ID_, can be used to name each row in the Constraint data set.

Linear Constraints

For the _TYPE_ values EQ, LE, GE, NE, LT, and GT, the corresponding observation is interpreted as a linear constraint. The _RHS_ variable is a numeric variable that contains the right-hand-side coefficient of the linear constraint. Any numeric variable other than _RHS_ that appears in a VARIABLE statement is interpreted as a structural variable for the linear constraint.
The _TYPE_ values are defined as follows:

EQ (=)

defines a linear equality of the form

$\text{[math]}$

LE (<=)

defines a linear inequality of the form

$\text{[math]}$

GE (>=)

defines a linear inequality of the form

$\text{[math]}$

NE (<>)

defines a linear disequation of the form

$\text{[math]}$

LT (<)

defines a linear inequality of the form

$\text{[math]}$

GT (>)

defines a linear inequality of the form

$\text{[math]}$

Domain Bounds

The keywords LOWERBD and UPPERBD specify additional lower bounds and upper bounds, respectively, on the variable domains. In an observation where the _TYPE_ variable is equal to LOWERBD, a nonmissing value for a decision variable is considered to be a lower bound for that variable. Similarly, in an observation where the _TYPE_ variable is equal to UPPERBD, a nonmissing value for a decision variable is considered to be an upper bound for that variable. Note that lower and upper bounds defined in the Constraint data set are overridden by lower and upper bounds that are defined by using a VARIABLE statement.

Variable Types

The keywords BINARY and FIXED specify numeric variable types. If the value of _TYPE_ is BINARY for an observation, then any decision variable with a nonmissing entry for the observation is interpreted as being a binary variable with domain {0,1}. If the value of _TYPE_ is FIXED for an observation, then any decision variable with a nonmissing entry for the observation is interpreted as being assigned to that nonmissing value. In other words, if the value of the variable X is $\text{[math]}$ in an observation for which _TYPE_ is FIXED, then the domain of X is considered to be the singleton { $\text{[math]}$ }. The value $\text{[math]}$ should belong to the domain of X, or the problem is deemed infeasible.

Variables in the CONDATA= Data Set

Table 3.2 lists all the variables that are associated with the Constraint data set and their interpretations by the CLP procedure. For each variable, the table also lists its type (C for character, N for numeric), the possible values it can assume, and its default value.

Table 3.2 Constraint Data Set Variables
Name	Type	Description	Allowed Values	Default
_TYPE_	C	Observation type	EQ, LE, GE, NE, LT, GT, LOWERBD, UPPERBD, BINARY, FIXED
_RHS_	N	Right-hand-side coefficient		0
_ID_	C	Observation name (optional)
Any numeric variable other than _RHS_	N	Structural variable

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