The problem is that of scheduling jobs with diverse routings on the productive facilities in a shop such that the respective due dates are met, or failing this, the sum of lateness times is minimized. The approach is simulative in that the operation of the shop is simulated in a Fortran program, but in addition to the straightforward use of priority rules for determining sequences of jobs on the machines, a number of heuristics or rules of thumb are incorporated. Both the static and dynamic problems are investigated. The efficacy of a small number of heuristics in combination with certain priority rules is demonstrated.