Class Timetable Optimizer
Optimize class schedules with room utilization, teacher workload, and constraint satisfaction. Enter values for instant results with step-by-step formulas.
Formula
Utilization = (Total Course Hours) / (Rooms × Hours/Day × Days/Week) × 100
Room utilization is calculated by dividing total weekly course hours by available room-hours. Teacher utilization follows similarly. Constraint satisfaction scores penalize overutilization, conflicts, and insufficient breaks to assess schedule feasibility.
Worked Examples
Example 1: Small Private School
Problem:A private school has 20 courses, 10 teachers, 6 rooms, operates 7 hours/day for 5 days. Each course meets 4 hours/week. Calculate capacity and feasibility.
Solution:Step 1: Calculate total capacity\nTotal slots = 7 hours × 5 days = 35 slots\nRoom capacity = 35 × 6 rooms = 210 room-hours\nTeacher capacity = 35 × 10 teachers = 350 teacher-hours\n\nStep 2: Calculate demand\nCourse hours = 20 courses × 4 hours = 80 hours/week\n\nStep 3: Utilization\nRoom utilization = 80 / 210 = 38.1%\nTeacher utilization = 80 / 350 = 22.9%\n\nStep 4: Feasibility assessment\n- Room utilization well under 80% ✓\n- Teacher utilization under 70% ✓\n- Average 2 hours/day per room\n- Average 8 hours/week per teacher\n\nConstraint score: 95/100 (Highly feasible)
Result:Feasible | 38% room utilization | 23% teacher load | Ample scheduling flexibility
Example 2: University Department
Problem:A CS department offers 45 courses, has 15 faculty, 8 classrooms (2 labs), 10-hour days, 5 days. Courses average 3 hours/week. Labs need specialized rooms.
Solution:Step 1: Capacity calculation\nRegular room capacity = 50 × 6 = 300 hours\nLab capacity = 50 × 2 = 100 hours (specialized)\nTotal capacity = 400 room-hours\nFaculty capacity = 50 × 15 = 750 hours\n\nStep 2: Demand (assuming 10 courses need labs)\nRegular courses = 35 × 3 = 105 hours\nLab courses = 10 × 3 = 30 hours\n\nStep 3: Utilization\nRegular room: 105 / 300 = 35%\nLab rooms: 30 / 100 = 30%\nFaculty: 135 / 750 = 18%\n\nStep 4: Constraints\n- Labs not oversubscribed ✓\n- Faculty load reasonable ✓\n- Consider peak hours (10am-2pm)\n\nConstraint score: 88/100
Result:Feasible | Lab constraint satisfied | Consider peak-hour distribution
Example 3: High-Demand High School
Problem:A high school has 60 courses, 25 teachers, 12 rooms, 8 hours/day, 5 days. Each course meets 5 hours/week. Maximum 4 consecutive hours allowed.
Solution:Step 1: Capacity\nRoom capacity = 40 × 12 = 480 hours\nTeacher capacity = 40 × 25 = 1000 hours\n\nStep 2: Demand\nTotal course hours = 60 × 5 = 300 hours\n\nStep 3: Utilization\nRoom: 300 / 480 = 62.5%\nTeacher: 300 / 1000 = 30%\n\nStep 4: Constraint analysis\n- Average 12 hours/week per teacher\n- Average 3 hours/day per teacher\n- 4 consecutive max = ~2 sessions/day\n- Need 2-3 breaks per day\n\nStep 5: Peak analysis\nIf all courses want 9am-1pm slots:\nPeak demand = 300 × 0.5 = 150 hours\nPeak capacity = 4 hrs × 5 days × 12 rooms = 240\nPeak utilization = 62.5% (acceptable)\n\nConstraint score: 82/100
Result:Feasible | 62.5% utilization | Monitor peak hours | Good teacher balance
Frequently Asked Questions
What is class timetable optimization?
Class timetable optimization is the process of creating schedules that assign courses, teachers, and rooms to time slots while satisfying multiple constraints. These constraints include: teacher availability, room capacity, no double-booking, consecutive class limits, break requirements, and student course combinations. It's a classic constraint satisfaction problem (CSP) that becomes exponentially complex as variables increase. Modern solutions use algorithms like genetic algorithms, simulated annealing, or constraint propagation.
What is the optimal class duration and break pattern?
Research suggests: 50-minute classes with 10-minute breaks for standard courses. 75-90 minute blocks for lab/seminar courses. Maximum 3 consecutive hours before a longer break. 15-20 minute mid-morning and mid-afternoon breaks. Attention spans decline after 45-50 minutes, making block scheduling with active learning more effective than longer passive lectures.
What algorithms are used for timetable optimization?
Common approaches include: Constraint Propagation: Reduces search space by eliminating impossible combinations. Genetic Algorithms: Evolves schedules through selection, crossover, and mutation. Simulated Annealing: Probabilistically accepts worse solutions to escape local optima. Integer Linear Programming: Formulates scheduling as mathematical optimization. Graph Coloring: Models conflicts as graph edges to find valid colorings. Hybrid approaches combining multiple techniques often perform best.
What metrics measure timetable quality?
Key metrics include: Constraint satisfaction rate (hard/soft). Room utilization percentage. Teacher workload balance (variance in hours). Student gap minimization (idle time between classes). Preference satisfaction score. Schedule compactness (concentrated vs spread schedule). Conflict-free rate. Travel time between consecutive classes. These metrics help compare different schedule options and identify improvement areas.