A multi-objective Immune Balancing Algorithm for Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling

Driven by economic globalization, global supply chain collaboration has gained significant importance, fostering the emergence of distributed manufacturing. This paper addresses the Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling (DHBIAHFS) problem within the pharmaceutical industry. Jobs are allocated to factories for processing, batched within defined lot sizes for transportation, and subsequently assembled into products to minimize the maximum completion time and tardy product count. Effective lot sizing during transport is emphasized between factories and assembly machines. Drawing inspiration from the biological immune system's balancing mechanisms, we propose a Multi-objective Immune Balancing Algorithm (MOIBA) equipped with learning and repairing mechanisms. Each solution is structured with three nested sequences, and composite heuristic evaluations are employed to generate high-quality initial solutions. The performance of each solution is assessed based on both fitness and diversity metrics. Customized crossover and mutation operators are introduced with dynamically adjusted probabilities reflective of immune response dynamics. Quantitative analysis validates our mathematical model and the distinct components of MOIBA. We compare MOIBA's efficiency against six other effective multi-objective strategies using three performance metrics. Stability and robustness assessments, conducted through variance examination and statistical testing, offer insights into MOIBA's consistency and reliability across diverse problem instances.