The Imaging Satellite Task Scheduling (ISTS) problem is a complex combinatorial optimization challenge critical to improving the efficiency of Earth observation data acquisition. Traditional methods rely on manual design of optimization models and algorithms—such as Integer Programming (IP), Constraint Satisfaction Problem (CSP), and Vehicle Routing Problem (VRP)—which is often time-consuming and requires domain expertise. To address this limitation, this paper investigates the application of Large Language Models (LLMs) to automatically generate both mathematical models and solution algorithms for ISTS. We propose a structured prompt framework that guides LLMs in constructing models and corresponding greedy algorithms tailored to various ISTS scenarios. Through systematic experiments, we automatically generated five types of optimization models—IP, CSP, VRP, Knapsack Problem (KP), and Job Shop Scheduling (JSP)—along with executable greedy algorithms. Experimental results demonstrate that LLMs are capable of producing functionally correct and effective scheduling models. Notably, the VRP model consistently achieved superior performance across multiple task scales, outperforming not only other LLM-generated models but also classical algorithms in the field (Single-layer Optimization and Double-layer Optimization), especially in large-scale settings. This work confirms the potential of LLMs to automate the end-to-end modeling and algorithm design process, significantly reducing manual effort while maintaining competitive solution quality. Our findings offer a new pathway for rapidly developing adaptive scheduling systems in satellite operations and other complex scheduling domains.