Class Scheduling Algorithm + Basic Software

Warning: This is a math intensive problem, not a software problem. We are looking for someone to make a quick and dirty software / use an existing software and send us code,with highly functional algorithm that can handle the following complex scheduling problem. The problem: 1. 83 students 2. At least 13 courses with 2 sections of each course – i.e. 26 sections - each capped at different sizes, but usually 10, 30, and 45. 3. 10 classrooms of different sizes. 4. Around 10-15 faculty members 5. 8 periods per day – some courses occupy multiple periods. Most courses meet 3 times a week. Saturday course not preferred, but can be scheduled worst case. 6. Students usually choose between 5 to 6 courses as long as they do not conflict. 7. Faculty members have day and time constraints. 8. Certain courses need certain specific classrooms. 9. Classrooms are of various sizes. Our optimization goal is: 1. Students need to have maximum flexibility in choosing their courses. (i.e. We need to maximize the number of combinations of courses possible). 2. Once the best schedule is outputted in some format, all the possible combinations must be listed. Please mention the code word: AlgoProb in your bid.