A range filter adds a constraint over a linear expression, like this:

lower bound <= linear expression <= upper bound

where the linear expression is a sum of weights multiplied by the value of a variable. That is,

sum{weights[i]*x[varind[i]]}

Range filters can be defined by any type of variables (binary, integer, continuous, semi-integer, semi-continuous).

In the sample filter file, the range filter corresponds to this constraint that the transportation cost must be no more than the fixed cost:

1.0 * transport - 1.0 * fixed <= 0

In a formatted FLT file, a range filter is specified by the keyword RNGFILTER.

The name of the filter (in this example, f2) follows the keyword RNGFILTER on the same line.

The lower and upper bounds on the linear expression follow the name of the filter on the same line as the keyword RNGFILTER. In this example, the lower bound on the expression is negative infinity (that is, no lower limit) and the upper bound is 0 (zero).

Each successive line shows the name of the variable and its coefficient in the linear expression.