HETEROJEN ZAMAN ARALIKLARI VE İŞ YÜKÜ ADALETİNE DAYALI SINAV ZAMAN ÇİZELGELEMESİ İÇİN ÜÇ AŞAMALI BİR MIP MODELİ ÖNERİSİ

Öz

Bu çalışma, bir fakülteye bağlı 12 bölümün sınav çizelgeleme problemini çözmek üzere üç aşamalı bir karma tamsayılı programlama (MIP) modeli önermektedir. Modelin ilk aşaması sınavların gün ve saat atamasına, ikinci aşaması derslik tahsisine, üçüncü aşaması ise gözetmen atamasına odaklanmaktadır. Geleneksel sabit süreli sınav dilimlerinden farklı olarak, gün ve saat atama modeli 30, 60 ve 90 dakikalık heterojen zaman dilimlerini kullanmaktadır. Bu yaklaşım, her sınava en uygun süreyi atamayı mümkün kılarak zaman verimliliğini artırmakta ve boşta kalan süreleri azaltmaktadır. Ayrıca model, sınav dönemi boyunca bölümlere ait iş yükünün dengeli bir biçimde dağılmasını sağlayarak bölümler arasında adaletsiz sınav yoğunlaşmalarını önlemektedir. Derslik atama modeli, tahsis edilen salonlardaki boş koltuk sayısını en aza indirerek salon kullanımını optimize etmeyi ve kapasite planlamasını iyileştirmeyi hedeflemektedir. Gözetmen atama aşamasında ise iş yükünün gözetmenler arasında dengeli bir şekilde paylaştırılması önceliklendirilmiştir. Problemin NP-zor yapısı nedeniyle çözüm için genetik algoritma (GA) kullanılmıştır. Elde edilen çizelgeler, manuel olarak oluşturulan çizelgelerle karşılaştırılmış ve sonuçlar; adalet, verimlilik ve kaynak kullanımında belirgin iyileşmeler ortaya koyarak önerilen MIP modelinin pratik değerini göstermiştir.

Anahtar Kelimeler

• Sınav Zaman Çizelgeleme
• Gözetmen Atama
• Karma Tamsayılı Programlama
• Genetik Algoritma

A PROPOSAL FOR A THREE-STAGE MIP MODEL FOR EXAMINATION TIMETABLING BASED ON HETEROGENEOUS TIME SLOTS AND WORKLOAD FAIRNESS

Öz

This paper presents a three-stage mixed-integer programming (MIP) model for addressing the complex examination timetabling problem faced by 12 departments within a faculty. The first stage focuses on assigning days and time slots, the second stage allocates rooms, and the third stage assigns invigilators. Unlike traditional approaches that rely on fixed-length periods, the day and time slot assignment model incorporates heterogeneous slots of 30, 60, and 90 minutes. This design enables assigning the most appropriate time duration to each exam, thereby improving time efficiency and reducing idle periods. Furthermore, the model ensures an even distribution of departmental workload throughout the examination period, preventing unfair clustering of exams across departments. The room allocation model is formulated to minimize the number of empty seats in assigned rooms, which enhances room utilization and overall capacity planning. In the invigilator assignment stage, workload balancing is emphasized to distribute responsibilities equitably among available staff members. Due to the NP-hard complexity of the problem, a genetic algorithm (GA) was utilized to produce feasible and high-quality solutions. The generated schedules were evaluated by comparing them to manually prepared timetables, and the results demonstrated significant improvements in fairness, efficiency, and resource utilization, highlighting the practical value of the proposed MIP model.

Anahtar Kelimeler

• Examination Timetabling
• Invigilator Assignment
• Mixed-integer Programming
• Genetic Algorithm

Kaynakça

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