The branch and bound method is used to obtain exact solutions of the single machine scheduling problem with the objective function of maximum lateness minimization. Lower bounds are estimated by solving dual problems. A machine-independent value, namely the number of branching points in the search tree, is used as the complexity index of instances. The instances are presented as points in 3n-dimensional space. Known and newly developed ways of instances generation (with a large number of branching points) are presented, and the advantages and disadvantages of each of them are described.