Mathematical Programming Models and Algorithms for Academic Class Scheduling at Kuwait University

يتعلق هذا البحث أساساً في استنباط وتطوير نماذج رياضية مبرمجة ومبنية على الأمثلة وذلك للحصول بقدر الامكان على جداول دراسية ذات كفاءة عالية، آخذين بعين الاعتبار محدودية المصادر (أعضاء هيئة التدريس) بأفضلية في الأداء بالنسبة للقاعات والوقت، واحتياجات الطلاب.
وكنتيجة للصعوبات المصاحبة لعمل الجداول للأعداد الكبيرة فقد تم القيام بتطوير النماذج الرياضية لهذا المشروع والتي يمكن وضعها في نطاق نظام لاتخاذ ودعم القرار تلقائيا والذي يعمل على عمل جداول ذات كفاءة وبنمط وقتي. ولذا فإن أهمية البحث لا تكمن فقط بالجوانب النظرية، بل تمتد لتغطي الجوانب التطبيقية لأنه يحوي ابتكاراً لطرق حل ذات كفاءة عالية والتي تؤدي إلى تحسين كفاءة الطرق التقليدية لعمل الجداول الدراسية.

Many universities throughout the world encounter the problem of assigning classes to faculty members, available time-slots and suitable classrooms. The task of providing conflict-free class schedules and satisfying faculty members’ preferences in terms of classes and lecture time-slots is a complex problem. These problems are more apparent in colleges of relatively large universities. For example, the College of Science at Kuwait University (KU), which is the subject of our present study, is composed of six departments and offers more than 300 classes, some of which are associated with tutorials and/or lab sessions. It is imperative for the decision-makers at KU to efficiently utilize available facility and human resources in order to deal with the increasing number of accepted students and offered classes, the increasing aggravated parking and traffic congestion and the newly imposed gender segregation policy. Most of the shortcomings that often accompany generated timetables basically result from: 1) the manual scheduling approaches that are being adopted by individual departments to assign classes to time-slots and faculty members; 2) the preferences of individual faculty members for time-slots and specific classes; and 3) the lack of coordination between departments that share certain facility resources. Based on this, we propose a two-stage approach for the Comprehensive Class Scheduling Problem (CCSP) at KU. In stage I, time-slots for the various (male, female and joint) sections of offered classes are determined and in stage II, faculty members are assigned to classes given that the time-slots for classes are obtained from stage I. This approach emphasizes first and foremost to provide good class offering patterns for students and efficient facility resource utilization, and, second, the satisfaction of faculty members’ preferences with respect to time-slots and specific classes. In addition the Office of Registration is now imposing a new policy that restric