In recent studies of scheduling, a multi-agent scheduling problem has been recognized as an important issue, where multiple decision makers perform scheduling while considering their own objectives and competing for resources. Limited scheduling resources can be efficiently utilized by a suitable solution for the multi agent scheduling problem.
Meanwhile, there is another element that should be considered, namely learning and aging effect. The actual processing time in real industry can be increased or decreased by them. In recent years, multi-agent scheduling and learning/aging effect are considered simultaneously. However, they did not consider the due date. Although the due date is as important as cost, there are few studies considering the due date because of its high computational complexity.
Motivated by these remarks, we consider a single-machine two-agent scheduling problem with the aging effect based on sum-of-processing-times, where one agent wants to minimize total weighted tardiness, not allowing tardy job for the other agent. We develop a branch-and-bound (B&B) algorithm and a genetic algorithm (GA). We propose dominance properties and lower bound for an efficient B&B algorithm and consider four initial populations to improve the performance of the GA. We implemented the suggested algorithms using MATLAB and performed a numerical experiment to show the superiority of them.
