The routine CPXmdleave assumes that there is a resident optimal simplex basis, and a resident LU-factorization associated with this basis. It takes as input a list of basic variables as specified by goodlist[] and goodlen, and returns values commonly known as Driebeek penalties in the two arrays downratio[] and upratio[].

For a given j = goodlist[i], downratio[i] has the following meaning. Let xj be the name of the basic variable with index j, and suppose that xj is fixed to some value t' < t. In a subsequent call to CPXdualopt, the leaving variable in the first iteration of this call is uniquely determined: It must be xj.

There are then two possibilities. Either an entering variable is determined, or it is concluded (in the first iteration) that the changed model is dual unbounded (primal infeasible). In the latter case, downratio[i] is set equal to a large positive value (this number is system dependent, but is usually 1.0E+75). In the former case, where r is the value of the objective function after this one iteration, downratio[i] is determined by |r| = (t - t') * downratio[i].