ارائۀ یک مدل برنامه‌ریزی خطی عدد صحیح دومرحله‌ای برای مسئلۀ زمان‌بندی دروس دانشگاهی

نوع مقاله : مقاله علمی پژوهشی

نویسندگان

1 استادیار گروه مدیریت، دانشکدۀ علوم اداری و اقتصاد، دانشگاه اصفهان، اصفهان، ایران

2 کارشناس ارشد مدیریت صنعتی، دانشکدۀ علوم اداری و اقتصاد، دانشگاه اصفهان، اصفهان، ایران

چکیده

در این پژوهش، یک مدل برنامه‌ریزی عدد صحیح برای مسئلۀ زمان‌بندی دروس دانشگاهی ارائه شده است. برای کاهش تعداد متغیرهای تصمیم، ترکیب درس و استاد و گروه دانشجو به‌عنوان فعالیت معرفی ‎شد و دو مدل برنامه‌ریزی عدد صحیح با عنوان مدل مبتنی بر فعالیت و مدل دومرحله‌ای مبتنی بر فعالیت به­دست آمد. در مرحلۀ اول برمبنای تعداد جلسات لازم در هفته در بازه‌های زمانی روزهای مختلف هفته، تمام فعالیت‌ها زمان‌بندی ‌شد و در مرحلۀ دوم با درنظرگرفتن محدودیت‌های خاص، کلاس‌ها و فضاهای آموزشی به جلسات برنامه‌ریزی­شده تخصیص یافت. این مدل‌ها برای یک نیمسال تحصیلی برمبنای فرایند تخصیص دروس به بازه‌های زمانی خاص در روزهای هفته با محدودیت‌های سخت در دانشکدۀ علوم اداری و اقتصاد دانشگاه اصفهان فرموله شده است. در این مطالعه، ضمن فرموله­کردن تمام قواعد تعریف جدول زمان‌بندی دروس یک نیمسال در نرم‌افزار، با استفاده از مدل دومرحله‌ای مبتنی بر فعالیت، تعداد 239 درس در زمان 556 ثانیه (9 دقیقه و 16 ثانیه) زمان‌بندی‌شده است.

کلیدواژه‌ها


عنوان مقاله [English]

Proposing a Two-Phase Integer Linear Programming for University-Course Timetabling

نویسندگان [English]

  • Majid Esmaelian 1
  • Sayedeh Maryam Abdollahi 2
1 Assistant Prof. in Management, Faculty of Administrative Sciences and Economics, Isfahan University, Isfahan, Iran
2 MSc of Industrial Management, Faculty of Administrative Sciences and Economics, Isfahan University, , Iran
چکیده [English]

An integer linear programming model for university courses timetabling is proposed here. In order to reduce the number of decisive variables, a combination of a course, a professor schedule and the students ‘group was defined as an activity. In this context, the two integer programming models namely the activity-based model and a two-phase activity-based model were proposed. In the first model, all activities were scheduled based on the number of required weekly sessions in the weekdays intervals; however, in the second model, classes and training courses were determined according to the planned sessions considering their special restrictions. These models were formulated based on the process of assigning the university courses within specific intervals throughout the week considering fierce constraints for a given semester in the department of Economics at University of Isfahan. All regulation concerning the courses timetable of a semester were formulated in GAMS software. Then, 239 courses were successfully scheduled using the two-phase activity-based model in only 9 minutes and 16 seconds

کلیدواژه‌ها [English]

  • Bi-level model
  • Hard constraint
  • Integer linear programming
  • Mathematical modeling
  • University course timetabling
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