Genetic Algorithm for a Two-Agent Scheduling Problem with Truncated Learning Consideration

Scheduling with learning effects has received lots of research attention lately. However, the multiple-agent setting with learning consideration is relatively limited. On the other hand, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of the jobs already processed increases. This is rather absurd in reality. Based on these observations, this paper considers a single-machine two-agent scheduling problem in which the actual processing time of a job depends not only on the job's scheduled position, but also on a control parameter. The objective is to minimize the total weighted completion time of jobs from the first agent with the restriction that no tardy job is allowed for the second agent. A branch-and-bound algorithm incorporated with several dominance properties and lower bounds is proposed to derive the optimal solution for the problem. In addition, genetic algorithms (GAs) are also provided to obtain the near-optimal solution. Finally, a computational experiment is conducted to evaluate the performance of the proposed algorithms.