Minimizing the Number of Tardy Jobs on Single Machine Scheduling with Flexible Maintenance Time

In this study, single machine scheduling with exible maintenance is investigated with non-resumable jobs by minimizing the weighted number of tardy jobs. It is assumed that the machine stops for a constant interval time during the scheduling period to perform mainte- nance. In other words, the starting time of maintenance is the decision variable. By reviewing the literature, we noticed that this problem has not been studied yet. Ini- tially, it is proved that the problem is NP-hard. Then, a mathematical model is proposed and solved by the GAMS software. Because of the long time for solving the problem with an exact method, we develop a heuris- tic algorithm. To evaluate the effciency of theproposed algorithm, 696 test problems with different sizes of the problem in the range from 1 to 2000 jobs, are generated. The computational results demonstrate that the average error of solution is 10.93%.