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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Vydané v:Computational management science Ročník 12; číslo 2; s. 297 - 318
Hlavní autori: Al-Yakoob, Salem M., Sherali, Hanif D.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2015
Springer Nature B.V
Predmet:
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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Shrnutí: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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ISSN:1619-697X
1619-6988
DOI:10.1007/s10287-013-0163-9