Scheduling identical parallel machines involving flexible maintenance activities

Motivated by a practical situation in chip manufacturing process, for the first time in the literature, this paper considers an identical parallel-machine scheduling problem with new flexible maintenance activities to minimize makespan where a maintenance activity is needed if and only if the machine capability has deteriorated by a critical value. To address the proposed problem, a mixed integer linear programming model and a lower bound are established. Since this problem is NP-hard, a combined constructive heuristic algorithm with six priority rules is developed. In order to improve the solution obtained by the proposed combined heuristic algorithm, an embedded learning mechanism is combined with the existing artificial immune system (AIS) algorithm to help self-adjust and modify the search direction. The effectiveness of the proposed combined constructive heuristic and the AIS algorithms is empirically tested on the randomly generated problem instances. These computational results show that the proposed AIS algorithm can generate better near-optimal solutions than several adaptations of the existing algorithms.