Variable iterated greedy for energy-efficient hybrid flow shop scheduling problem with blocking constraint

This study addresses the hybrid flow-shop scheduling problem with blocking constraint (BHFSP), a critical challenge in modern manufacturing, with an emphasis on minimizing energy consumption during job sequencing. Unique to BHFSP, this research considers essential factors such as machine standby and setup modes, along with the absence of intermediate buffers between processing stages. We propose a novel mixed-integer linear programming (MILP) model that incorporates machine turn-on/off strategies, significantly enhancing operational efficiency and sustainability. To tackle this complex issue, we develop a problem-specific variable neighborhood search iterated greedy (VIG) algorithm. The distinctiveness of our approach lies in its tailored variable neighborhood search strategies aimed at minimizing setup and blocking times while improving solution diversity through random perturbations in job sequencing. Simulation experiments on 480 benchmark instances demonstrate that the proposed VIG algorithm achieves the lowest average objective value (106729.07), outperforming seven state-of-the-art algorithms by up to 13.3%. Compared to representative methods such as DPSO and IGS, VIG yields 2.1%–5.0% lower costs and achieves the best ARPI (0.00 vs. 0.01–0.13), confirming its superior efficiency and energy-saving potential.