Cloud services have become indispensable in critical sectors such as healthcare, drones, digital twins, and autonomous vehicles, providing essential infrastructure for data processing and real-time analytics. These systems operate across multiple layers, including edge, fog, and cloud, requiring efficient resource management to ensure reliability and energy efficiency. However, increasing computational demands have led to rising energy consumption and frequent faults in cloud data centers. Inefficient task scheduling exacerbates these issues, causing resource overutilization, execution delays, and redundant processing. Current approaches struggle to optimize energy consumption, execution time, and fault tolerance simultaneously. While some methods offer partial solutions, they suffer from high computational complexity and fail to effectively balance the workloads or manage redundancy. Therefore, a comprehensive task scheduling solution is needed for mission-critical applications. In this article, we introduce a novel scheduling algorithm based on Mixed Integer Linear Programming (MILP) that optimizes task allocation across edge, fog, and cloud environments. Our solution reduces energy consumption, execution time, and failure rates while ensuring balanced distribution of computational loads across virtual machines. Additionally, it incorporates a fault tolerance mechanism that reduces the overlap between primary and backup tasks by distributing them across multiple availability zones. The scheduler's efficiency is further enhanced by a custom-designed heuristic, ensuring scalability and practical applicability. The proposed MILP-based scheduler demonstrates significant average improvements over the best state-of-the-art algorithms evaluated. It achieves a 9.63% increase in task throughput, reduces energy consumption by 18.20%, shortens execution times by 9.35%, and lowers failure probabilities by 11.50% across all layers of the distributed cloud system. These results highlight the scheduler's effectiveness in addressing key challenges in energy-efficient and reliable cloud computing for mission-critical applications. © 2024 Elsevier Inc.