The CLP Procedure

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

LE (<=)

defines a linear inequality of the form

GE (>=)

defines a linear inequality of the form

NE (<>)

defines a linear disequation of the form

LT (<)

defines a linear inequality of the form

GT (>)

defines a linear inequality of the form

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 in an observation for which _TYPE_ is FIXED, then the domain of X is considered to be the singleton {}. The value should belong to the domain of X, or the problem is deemed infeasible.

Objective Function

The keywords MAX and MIN specify the objective function of a maximization or a minimization problem, respectively. In an observation where the _TYPE_ variable is equal to MAX or MIN, a nonmissing value for a decision variable is the coefficient of this variable in the objective function. The value specified for _RHS_ is ignored in this case.

The bisection method is used to find the optimal objective value within the specified or derived lower and upper bounds. A solution is considered optimal if the difference between consecutive objective values is less than or equal to the tolerance. You can use the OBJ statement to specify the tolerance in addition to upper and lower bounds on the objective value.

When an optimal solution is found, the solution is stored in the output data set and the resulting objective value is stored in the macro variable _ORCLP_. The objective value is not necessarily optimal when it is computed within a time limit specified by the MAXTIME= option. In this case, the last valid solution computed within the time limit appears in the output data set. See the macro variable _ORCLP_ for more information about solution status.

The CLP procedure does not support multiple solutions for an objective function, so the EVALVARSEL=, ALLSOLNS, and MAXSOLNS= options are ignored when an objective function is specified.

The MAX and MIN functions are defined as follows:

MAX

defines an objective function of the form

MIN

defines an objective function of the form

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.