Bottleneck Identification of Extended Flexible Job Shop Scheduling Problem

In the Extended Flexible Job Shop Scheduling Problem (EFJSP), the temporal constraints among the tasks could be very complex including serial, parallel and flexible relations. This paper presents a method for identifying the critical tasks that affect the makespan most remarkably, which we call the "bottleneck tasks". To this end, we first transfer the solution of the EFJSP, which corresponds to a schedule plan, into an AOE Network (Activity On Edge Network), and then propose a bottleneck identification index based on the critical paths of the AOE Network. The tasks with the biggest bottleneck identification index value are identified as bottleneck tasks. The experimental results show that the bottleneck identification index as well as its computing method proposed in this paper are effective for identifying critical tasks. Moreover, it is proved that the time complexity of the bottleneck identification method is O((NJ * NT)^2), where NJ denotes the number of jobs and NT denotes the number of tasks in each job, respectively.