Optimizing School Operations

Abstract

Educational institutions in the United States such as public schools and universities face difficult operational problems in order to keep the lights on and the doors open. These challenges must often be solved on a shoestring budget, and tend to intersect with complex policy questions. For instance, school transportation is both a complex combinatorial problem, and has served as a vector of racial and socioeconomic integration since the 1970s. This thesis seeks to develop practical, scalable optimization methodologies to address key challenges in educational operations.

Foremost among these challenges is school transportation. In the first chapter, we develop a novel algorithm to solve school bus routing problems at scale. We rely on a novel decomposition approach called bi-objective routing decomposition (BiRD). Instead of building routes for each school in isolation, we consider several solutions, allowing locally suboptimal routes for certain schools if it improves overall cost. The approach has led to $5 million annual savings at Boston Public Schools. In the second chapter, we design an algorithm to estimate travel times in a network given travel times (but not paths) observed between many pairs of locations.

We also focus on challenges that intersect with and arise from the peculiarities of school transportation. School districts often stagger start times across the morning (and correspondingly end times across the afternoon) to maximize bus re-use and reduce costs. However, setting school start times is a problem with many stakeholders, from students to staff. In the second part of the first chapter, we develop a multi-objective optimization approach to evaluate the tradeoffs between different objectives in selecting school start times, including the cost of transportation. Our approach was used by Boston Public Schools to propose new start times, though they were not implemented due to community concerns. Building on this work, we consider in the third chapter the interplay between transportation, start times, and student-to-school assignment.

Finally, in the fourth chapter, we consider the problem of scheduling courses in time and space, in the particular context of sudden capacity reduction caused by the COVID-19 pandemic. Using a simple two-stage optimization framework, we explore the implications of hybrid in-person and online education on campus density and faculty teaching load. Our approach was used to create a new course schedule for the Sloan School of Management in the Fall of 2020, affording students significant in-person learning opportunities in compliance with public health and safety regulations.