Group scheduling with deteriorating jobs to minimize the total weighted number of late jobs

Deteriorating jobs scheduling has received tremendous attention in the past two decades. However, the group technology has seldom been discussed. With the current emphasis on customer service and meeting the promised delivery dates, we consider a single-machine scheduling problem of minimizing the total weighted number of late jobs with deteriorating jobs and setup times. A branch-and-bound with several dominance properties and a lower bound is developed to solve this problem optimally. Computational results show that the proposed algorithm can solve instances up to 1500 jobs. In addition, statistical tests are conducted to investigate the impact of the parameters.