Integer Programming entities supported in Xpress

• Binary variables (BV) – decision variables that must take either the value 0 or the value 1, sometimes called 0/1 variables;
• Integer variables (UI) – decision variables that must take on integer values. Some upper limit must be specified;
• Partial integer variables (PI) – decision variables that must take integer values below a specified limit but can take any value above that limit;
• Semi-continuous variables (SC) – decision variables that must take on either the value 0, or any value in a range whose lower an upper limits are specified. SCs help model situations where, if a variable is to be used at all, it has to be at some minimum level;
• Semi-continuous integer variables (SI) – decision variables that must take either the value 0, or any integer value in a range whose lower and upper limits are specified;
• Special ordered sets of type one (SOS1) – an ordered set of variables of which at most one can take a nonzero value;
• Special ordered sets of type two (SOS2) – an ordered set of variables of which at most two can be nonzero, and if two are nonzero, they must be consecutive in their ordering.

Remarks

• The solution values of binary and integer variables are real valued, not integer valued.
• At an optimal MIP solution, the actual values of the binary and integer variables will be integer – to within a certain tolerance.