—In this paper, we study new single machine scheduling problems where the objective functions are based on jobs positions. The original idea is to characterize easily a huge set of optimal solutions, without enumerating them. The (polynomially solvable) scheduling problems that can be addressed by this approach are such that a simple rule exists, giving a priority between two consecutive jobs. Assuming that the solution obtained by applying the rule is sequence Id = (J1, J2, ..., Jn) (correct after a renumbering of jobs), we search for a feasible solution (i.e. also optimal), at a maximum distance from sequence Id. Such considerations are also usefull for some robustness considerations. We identify some new objective functions and present first theoretical results and first computational experiments. Some new problems remain open.