Minimizing the total weighted tardiness of overlapping jobs on parallel machines with a learning effect

The influence of learning effects on job scheduling has been studied for years. By considering learning effects, an operator can schedule jobs in a more precise way and improve on the original schedules. In fact, jobs with duplicate contents (i.e., overlapping jobs) do not require as much processing time as do disjoint jobs. However, this phenomenon is seldom discussed in traditional scheduling models. In this study, a parallel-machine scheduling problem with a learning effect and an overlap effect is introduced. The objective is to minimise the total weighted tardiness of jobs whose processing times are influenced by both effects. A branch-and-bound algorithm comprising a lower bound algorithm is developed to generate the optimal schedules. Compared with past research, two main contributions are made. First, a model considering simultaneously both the learning effect and the overlap effect is proposed. Second, an efficient lower bound algorithm accelerating the execution speed is developed. At the end, computational experiments are conducted to show the execution efficiency and cost effectiveness.