<p>In response to global environmental challenges, green manufacturing has emerged as a critical development trend. While existing research has primarily focused on internal workshop scheduling, the impact of external carbon policies has been largely overlooked. This study addresses this gap by investigating a variable-speed flexible job-shop, where machine processing speeds can be adjusted to align with carbon policies. We develop a multi-objective optimization model aimed at minimizing makespan, carbon emissions during manufacturing, and total processing costs. To solve this multi-objective optimization problem, we propose an enhanced Non-dominated Sorting Genetic Algorithm II (NSGA-II) that integrates a variable neighborhood search mechanism to improve optimization performance. Comparative experiments with comparison algorithms demonstrate the superior performance of our proposed approach. Furthermore, we compare the model that incorporates carbon policies with conventional scheduling models, highlighting the necessity of considering carbon policies in scheduling decisions. The study also explores the specific effects of carbon policies across three distinct scheduling scenarios and identifies the optimal benefit point of carbon reward policies, offering valuable insights for sustainable manufacturing practices.</p>