A batch scheduling model on unrelated parallel machines with resource constraints and sequence-dependent setup time to minimize total actual flow time

Findings: The proposed algorithm achieves an average efficiency of 99.32% compared to the enumeration algorithm, with minimal deviation (0.4%). The results validate the main proposition for efficient scheduling, including prioritizing jobs based on due dates, allocating job demands based on machine capacity, and sequencing batches based on size to minimize delays.Research limitations/implications: The model assumes static machine conditions and predefined job parameters, limiting its applicability in dynamic environments. Future research can extend this approach to incorporate real-time job arrivals or machine breakdown scenarios.Practical implications: This algorithm provides a practical tool for industries to optimize batch scheduling on unrelated parallel machines, improving production efficiency and reducing operational costs.Social implications: By improving production scheduling, this model indirectly supports sustainable manufacturing practices through optimal resource utilization.Originality/value: This study introduces a novel integration of backward scheduling with resource constraints and sequence-dependent setup times, addressing gaps in scheduling research for unrelated parallel machines.