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Tightening Bounds and Side Constraints

If any piece of data is furnished to PROC INTPOINT more than once, PROC INTPOINT checks for consistency so that no conflict exists concerning the data values. For example, if the cost of some arc is seen to be one value and as more data are read, the cost of the same arc is seen to be another value, PROC INTPOINT issues an error message on the SAS log and stops. There are two exceptions to this:

• The bounds of arcs and nonarc variables, or the bounds of LP variables, are made as tight as possible. If several different values are given for the lower flow bound of an arc, the greatest value is used. If several different values are given for the lower bound of a nonarc or LP variable, the greatest value is used. If several different values are given for the capacity of an arc, the smallest value is used. If several different values are given for the upper bound of a nonarc or LP variable, the smallest value is used.
• Several values can be given for inequality constraint right-hand sides. For a particular constraint, the lowest rhs value is used for the rhs if the constraint is of less than or equal to type. For a particular constraint, the greatest rhs value is used for the rhs if the constraint is of greater than or equal to type.