An Efficient Job Insertion Algorithm for Hybrid Human–Machine Collaborative Flexible Job Shop Scheduling with Random Job Arrivals

Human–machine collaborative scheduling has been widely applied in the modern manufacturing industry. Traditional scheduling algorithms often rely on frequent rescheduling when new jobs arrive, resulting in low responsiveness and difficulty in meeting the demands of high-paced production scenarios. Aiming at the hybrid human–machine collaborative flexible job shop scheduling problem (HHCFJSP) with random job arrivals, this paper proposes a hybrid algorithm based on improved job insertion strategy (HAIJI) dedicated to coping with sudden job insertion demands during the scheduling process. The algorithm constructs a two-dimensional evaluation vector based on minimum scheduling delay and residual scheduling flexibility to jointly assess potential insertion positions for each operation. A non-dominated sorting mechanism is employed to identify a set of promising insertion candidates, which are further evaluated using a tailored evaluation function. During the construction of the insertion plan, an A*-inspired greedy search strategy is adopted to guide the search process, followed by a backtracking mechanism to recover the globally optimal insertion sequence. Finally, the proposed algorithm is applied to the pre-scheduling phase and the dynamic rescheduling phase of a hybrid human–machine collaborative flexible job shop. Experimental results demonstrate that the proposed method achieves higher scheduling efficiency and stability in both stages and outperforms benchmark algorithms in terms of makespan and response time.