The document presents a novel Reliable and Efficient Webserver Management (REWM) framework designed for task scheduling in heterogeneous edge-cloud environments, aimed at improving performance while minimizing energy consumption and task failure rates. It highlights that existing workflow scheduling methods struggle to achieve an effective trade-off between reliability, cost, and energy efficiency, which the proposed framework addresses. Experimental results demonstrate significant reductions in costs and energy consumption compared to traditional webserver management methodologies, particularly for complex bioinformatic workflows.