In this thesis, single machin scheduling problems with availability constraint have been considered. At first, a general division of these problems are explained and based on this framework the literature on deterministic single machine scheduling problems with one and multiple fixed non-availability periods is reviewd. First, the single machine scheduling problem with one fixed unavailability period and non-resumable jobs with the aim of minimizing the number of tardy jobs is studied. By proving a number of theorems, a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes efficient upper and lower bounds and dominance rules. Computational results for 2400 problem instances show that the branch-and-bound approach is capable of optimally solving 97.4% of the instances, bearing witness to the efficiency of the proposed procedure. The proposed heuristic procedure is then evaluated for the problems with large sizes and it is observed that this procedure has a good performance to silve these problems. Results also indicate that the proposed approaches are more efficient when compared to other methods. Next, the single machine scheduling problem with one fixed unavailability period, non-resumable jobs, with the aim of minimizing maximum earliness is considered. Because no previous study has been reported on the problem in the literature, complexity of the problem is first studied and this problem is proved to be NP-hard. an exact branch and bound approach is proposed for the problem. By proving a number of theorems and lemmas, a lower bound and some efficient dominance rules are developed. A heuristic algorithm with O(nlogn) is presented which additionally used to calculate the upper bound. Computational results for 2400 instances show that the branch and bound procedure is capable of optimally solving 98.79% of the instances. Finally, the single machine scheduling with a fixed non-availability period, non-resumable jobs and bicriteria target function of maximum earliness and number of tardy jobs is studied. Mathematical model of the problem is proposed and complexity of the problem is studied. A set of lower and upper bounds for both certerions of the problem is then stated. A branch and bound procedure, along with efficient dominance rules and lower and upper bounds is also proposed in which the lower and upper bounds of criterions are used. In order to evaluate the branch and bound approach, a total of 1440 instances are solved by this procedure and their results are analyzed. These results show that the branch and bound approach is capable of optimally solving 97.22% of instances