Timetable Optimizer: Automated University Schedule Generation Using CP-SAT Constraint Solving and Large Language Model Intelligence

Abstract

This paper presents Timetable Optimizer, a production-grade automated scheduling system that addresses both the generation and operational maintenance of university course timetables through a hybrid architecture combining con- straint satisfaction solving and large language model intelligence. University timetable scheduling is a well-established NP-hard combinatorial optimization problem requiring simultaneous sat- isfaction of hundreds of hard constraints—faculty availability, room capacity, laboratory batch splitting, and room-type match- ing—alongside soft preferences for workload fairness and session continuity. In practice, manual scheduling through spreadsheets consumes days of administrative effort and produces schedules with latent conflicts discovered only after the semester begins. The proposed system is built on a three-service architecture: a Next.js frontend providing role-differentiated interfaces for four user types; an Express.js backend serving as API gate- way, data orchestrator, and job dispatcher; and a Python CP- SAT solver worker using Google OR-Tools, connected via a Redis job queue. The scheduling model is formulated as a 5- dimensional binary decision variable problem over a space of
6 days and 8 time slots per day, enforcing seven categories of hard constraints with pre-pruning eliminating 70–80% of decision variables before solving. Natural language constraints entered by faculty are parsed to structured JSON using the Google Gemini API, eliminating the formal specification barrier. Asynchronous job processing with Server-Sent Events delivers real-time progress feedback throughout solver execution. Daily operational overrides are managed through an append-only log applying greedy substitute matching without requiring solver re- execution. The system additionally supports PDF and iCal export, academic year rollover, comprehensive audit logging, and role- based access control. Evaluation demonstrates solver execution within 10–120 seconds for realistic institutional instances, sub- 50ms authorization latency, and correct constraint enforcement across all hard constraint categories.