title: Scheduling algorithm which minimizes maximum lateness is optimal (it finds a feasible schedule, if one exists)
body: <p>I need to understand why if a scheduling algorithm A minimizes maximum lateness, then A is optimal (it finds a feasible schedule, if one exists).</p>
  <p>I searched on the web for a long time, but without any success.
  Can you tell me which ingredients I need to prove that please?</p>
  <hr />
  <p>EDIT
  The viceversa is not true: if A is optimal, it can happen that A is not able to minimize the maximum lateness.</p>