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Cornell University Uses Integer Programming to Optimize Final Exam Scheduling

Tinghan Ye, Adam S. Jovine, Willem van Osselaer, Qihan Zhu, David B. Shmoys

TL;DR

This work develops a scalable MIP-based framework for final-exam scheduling at Cornell, integrating a multi-stage Group-then-Sequence (GtS) model with a Layer-Cake heuristic and a hybrid variant to balance direct conflicts, higher-order conflicts, and practical constraints. Core contributions include the Min_Conflict_IP and Zero_Conflict_IP block-assignment formulations, a cyclic-block sequencing approach with virtual blocks, a post-processing local search, and a Layer-Cake matheuristic that delivers fast, high-quality schedules. The framework demonstrates dominance over the historical baseline across five semesters, and extensive analyses reveal trade-offs among block counts, slot exclusions, and front-loading, with notable generalizability evidenced by Nottingham benchmarks. The approach enables flexible constraint handling (e.g., front-loading large exams, excluding slots) and robust performance through hybridization, making it a practical, adaptable tool for university exam timetabling with concrete reductions in student stress and administrative effort.

Abstract

This paper presents an integer programming-based optimization framework designed to effectively address the complex final exam scheduling challenges encountered at Cornell University. With high flexibility, the framework is specifically tailored to accommodate a variety of different constraints, including the front-loading of large courses and the exclusion of specific time slots during the exam period. By generating multiple scheduling model variants and incorporating heuristic approaches, our framework enables comprehensive comparisons of different schedules. This empowers the University Registrar to make informed decisions, considering trade-offs in terms of schedule comfort measured by different levels of exam conflicts. Our results demonstrate significant advantage over the historical lecture time-based approach, providing time and effort savings for the university administration while enhancing student and faculty satisfaction.

Cornell University Uses Integer Programming to Optimize Final Exam Scheduling

TL;DR

This work develops a scalable MIP-based framework for final-exam scheduling at Cornell, integrating a multi-stage Group-then-Sequence (GtS) model with a Layer-Cake heuristic and a hybrid variant to balance direct conflicts, higher-order conflicts, and practical constraints. Core contributions include the Min_Conflict_IP and Zero_Conflict_IP block-assignment formulations, a cyclic-block sequencing approach with virtual blocks, a post-processing local search, and a Layer-Cake matheuristic that delivers fast, high-quality schedules. The framework demonstrates dominance over the historical baseline across five semesters, and extensive analyses reveal trade-offs among block counts, slot exclusions, and front-loading, with notable generalizability evidenced by Nottingham benchmarks. The approach enables flexible constraint handling (e.g., front-loading large exams, excluding slots) and robust performance through hybridization, making it a practical, adaptable tool for university exam timetabling with concrete reductions in student stress and administrative effort.

Abstract

This paper presents an integer programming-based optimization framework designed to effectively address the complex final exam scheduling challenges encountered at Cornell University. With high flexibility, the framework is specifically tailored to accommodate a variety of different constraints, including the front-loading of large courses and the exclusion of specific time slots during the exam period. By generating multiple scheduling model variants and incorporating heuristic approaches, our framework enables comprehensive comparisons of different schedules. This empowers the University Registrar to make informed decisions, considering trade-offs in terms of schedule comfort measured by different levels of exam conflicts. Our results demonstrate significant advantage over the historical lecture time-based approach, providing time and effort savings for the university administration while enhancing student and faculty satisfaction.
Paper Structure (42 sections, 10 equations, 9 figures, 10 tables, 2 algorithms)

This paper contains 42 sections, 10 equations, 9 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Organization
  4. Problem Description
  5. Related Literature
  6. Educational Timetabling
  7. University Examination Timetabling: Problems and Formulations
  8. University Examination Timetabling: Solution Techniques
  9. Modeling Approach
  10. Multi-Stage Group-then-Sequence (GtS) Model
  11. Block Assignment
  12. Block Sequencing
  13. Post-Processing Local Search Algorithm
  14. Layer-Cake Heuristic Algorithm
  15. The Hybrid Model
  16. ...and 27 more sections

Figures (9)

  • Figure 1: Workflow of the Proposed Final Exam Scheduling Framework
  • Figure 2: This is an example of a zero-conflict block assignment. The value on each edge represents the number of co-enrollments. Blocks 0 and 1, as well as Blocks 1 and 2, are considered neighboring blocks. Consequently, the path-objective value can be calculated as the sum of the highlighted values.
  • Figure 3: Illustration of the $x_{ij\ell s}$ Variables and the Cyclic Self-Consistent Property
  • Figure 4: An Example Usage of Virtual Blocks
  • Figure 5: Visualization of the Layer-Cake Algorithm with Partial Overlaps in Consecutive Layers
  • ...and 4 more figures