A predict-and-prescribe framework for dynamic course scheduling toward strategic university scaling
提出首个利用趋势预测指导长期动态课程排课的数学优化框架，帮助大学在扩招背景下高效分配教学空间资源，平衡教师偏好与资源利用率。
Universities play vital roles in educating current and future generations. Universities that intend to survive in competitive academic markets where there are evolving enrollment trends must responsibly manage resources. Planning processes for instructional spaces can benefit from optimization and lead to more effective resource utilization, yet the use of trends in major and course demands to inform long-term planning remains largely unexplored. We propose a novel mathematical optimization framework that appears to be the first to use trend predictions to guide long-term dynamic course scheduling decisions and effective resource allocation. We begin with a baseline formulation that assigns course sections to time patterns and classroom spaces while considering instructor preferences, as well as constraints related to conflicts and capacity. We then extend this to a dynamic formulation that addresses bottleneck courses while prioritizing classroom utilization and honoring instructor preferences. Our dynamic formulation optimizes instructional space allocation for an academic period over the entire university, and solving for sequential independent academic periods reveals valuable insights into the efficiency of physical resource utilization on the horizon. Our framework is flexible, accommodating the objectives of faculty, schedulers, and administrators through a hierarchical multi-objective approach that integrates these diverse priorities. Our formulation addresses 76% and 81% of bottleneck sections for back-to-back semesters, with a substantial number of unutilized locations that could potentially be repurposed to accommodate the remaining bottleneck sections or other purposes. Through extensive experiments with varying university enrollment scenarios, we examine the resulting tradeoffs among objectives and highlight a variety of implications.