An MPS basis file, known as a BAS file, contains the information needed by ILOG CPLEX to define an advanced basis. Like an MPS file, the BAS file begins with a NAME indicator record and ends with an ENDATA record.

A basis defines a list of basic structural variables and row variables. A structural variable is one of the variables (columns) defined in the MPS problem file. A row variable is actually the slack, surplus, or artificial variable associated with a row.

For linear programs, the total number of basic variables—both structural and row—is equal to the number of rows in the constraint matrix. Additionally, the number of basic structural variables is equal to the number of nonbasic row variables. By convention, an MPS basis file is built on the assumption that all row variables are basic and that all structural variables are nonbasic with values at their lower bound. The data records in a BAS file list structural and row variables that violate this assumption. This convention minimizes the size of the BAS file.

For quadratic programs, the total number of basic variables can exceed the number of rows and so not all basic variables can be paired with a nonbasic row variable.

Variable 1 specifies a structural variable identifier which has entered the basis. By convention, this structural variable must displace one of the row variables. Variable 2 is a row variable that has left the basis. No relationship between structural variables entering the basis and row variables leaving the basis is implied within the BAS file.