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A column generation mathematical programming approach for a class-faculty assignment problem with preferences

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Abstract

This paper presents a column generation approach for assigning faculty members to sections of offered classes (class-sections) in a case study related to Kuwait University. For a given class, the total number of class-sections to be offered is known; however, the distribution of these class-sections into available time-slots is determined via a mixed-integer programming model that takes into consideration faculty members’ aggregate preferences for specific offered classes and the time-slots of the corresponding sections, as well as other restrictions imposed by the Office of the Registrar. Subsequently, upon fixing the time-slot assignments of the class-sections, another mixed-integer programming model is formulated and solved to select weekly schedules for faculty members, while considering their preferences for specific classes and time-slots. In this latter model, each variable corresponds to a feasible schedule of a faculty member, and by exploiting its special structure, we demonstrate that its continuous relaxation can be solved very efficiently via a column generation method in order to heuristically derive a good quality feasible solution. Computational results are provided for a number of test instances, including 10 real cases pertaining to the Department of Mathematics at Kuwait University.

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Acknowledgments

This research has been supported by the Kuwait University under Grant No. [SM02/06] and partially supported by the National Science Foundation under Grant No. [DMI-0094462]. The authors also gratefully acknowledge the assistance of Ms. Renju Lekshmi in implementing the developed procedures.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Kuwait University, P.O. Box: 5969, 13060 , Safat, State of Kuwait

    Salem M. Al-Yakoob

  2. Grado Department of Industrial and Systems Engineering (0118), Virginia Tech, Blacksburg, VA, 24061, USA

    Hanif D. Sherali

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  1. Salem M. Al-Yakoob
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  2. Hanif D. Sherali
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Correspondence to Salem M. Al-Yakoob.

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Al-Yakoob, S.M., Sherali, H.D. A column generation mathematical programming approach for a class-faculty assignment problem with preferences. Comput Manag Sci 12, 297–318 (2015). https://doi.org/10.1007/s10287-013-0163-9

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