基于大语言模型的整数规划教学案例辅助生成

Case-Based Teaching Support for Integer Programming with Large Language Models

摘要: 随着大语言模型技术的迅猛发展，其在教育领域中的应用潜力日益凸显。本文聚焦于整数规划这一运筹学核心教学内容，针对当前教学实践中存在的答疑机制薄弱、教学案例资源匮乏及课程内容滞后等问题，系统探讨了大语言模型在教学中的三重辅助作用：智能答疑、教学设计与编程求解。本文通过具体示例展示了学生如何利用大语言模型辅助完成模型生成、模型检验和编程求解等任务，以及教师如何借助大语言模型高效生成多样化教学案例和材料。进一步地，本文指出，大语言模型的引入不仅优化了教学流程，更潜移默化地促进了学生的问题分解、模式识别、抽象和算法设计等计算思维能力发展。最后，本文呼吁在推进技术应用的同时，仍应坚持“教师主导、技术辅助”的教学原则，以实现智能化与规范化教学的良性融合。

Abstract: With the rapid development of large language model (LLM) technologies, their application potential in the field of education has become increasingly evident. This paper focuses on integer programming, a core subject in operations research, and addresses current challenges in teaching practice such as weak question-answering mechanisms, insufficient teaching case resources, and outdated course content. It systematically explores the threefold auxiliary role of LLMs in teaching: intelligent question and answering, instructional design, and programming-based problem solving. Through concrete examples, the paper demonstrates how students can use LLMs to assist with model generation, validation, and code-based solution processes, and how instructors can efficiently generate diverse teaching cases and materials with the help of LLMs. Moreover, this paper points out that the incorporation of LLMs not only optimizes the teaching process but also implicitly fosters the development of students’ computational thinking skills, including problem decomposition, pattern recognition, abstraction, and algorithmic design. The paper concludes by emphasizing the importance of maintaining the teaching principle of “teacher-led, technology-assisted” in order to achieve a healthy integration of intelligent and standardized instruction.