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

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...

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Published in:	Computational management science Vol. 12; no. 2; pp. 297 - 318
Main Authors:	Al-Yakoob, Salem M., Sherali, Hanif D.
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2015 Springer Nature B.V
Subjects:	Aggregates Assignment problem Business and Management Classrooms Colleges & universities Columnar structure Columns (structural) Computation Computer science Integer programming International Logic programming Management science Mathematical analysis Mathematical models Mathematical programming Mathematics Offices Operations Research/Decision Theory Optimization Original Paper Programming Schedules Scheduling Students Studies Teaching Kuwait Column generation Mixed-integer programming Class scheduling
ISSN:	1619-697X, 1619-6988
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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.
AbstractList	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.
Author	Sherali, Hanif D. Al-Yakoob, Salem M.
Author_xml	– sequence: 1 givenname: Salem M. surname: Al-Yakoob fullname: Al-Yakoob, Salem M. email: salem@al-yakoob.com organization: Department of Mathematics, College of Science, Kuwait University – sequence: 2 givenname: Hanif D. surname: Sherali fullname: Sherali, Hanif D. organization: Grado Department of Industrial and Systems Engineering , Virginia Tech
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Snippet	This paper presents a column generation approach for assigning faculty members to sections of offered classes (class-sections) in a case study related to...
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SubjectTerms	Aggregates Assignment problem Business and Management Classrooms Colleges & universities Columnar structure Columns (structural) Computation Computer science Integer programming International Logic programming Management science Mathematical analysis Mathematical models Mathematical programming Mathematics Offices Operations Research/Decision Theory Optimization Original Paper Programming Schedules Scheduling Students Studies Teaching
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Title	A column generation mathematical programming approach for a class-faculty assignment problem with preferences
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