This paper introduces an approach based on the general variable neighborhood search algorithm to address the multi-objective online flexible job shop scheduling problem where new jobs arrive in batches at various times. We focus on minimizing two objectives, the maximum tardiness and the maximum workload. Additional objectives can be easily integrated if necessary. A penalty-based system is proposed to enhance schedule stability and minimize operator fatigue during the rescheduling process whenever a new batch of operations arrives in a workshop. Preliminary results showcase the effectiveness of this approach compared to the offline variant.