Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.