Complexity of Single Machine HierarchicalSchedulingD

In this paper we deal with the dual criteria optimization, explore the complexity status of hierarchical scheduling on a single machine. Hierarchical optimization is a special case of dual criteria optimization, where the most important criterion is at its optimal value. We'll assume the complexity of hierarchical scheduling on a single machine. While doing this, we'll use the case of two criteria where the second criterion is optimized subject to the constraint that the rst meets its minimum value. For every problem we either provide an NP-completeness proof or else a polynomial time algorithm. I tried to show the results surveyed by the researchers about the existing results in the literature and new results. Besides, I discuss the applications of these problems to real life issues.