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A Column Generation Mathematical Model for a Teaching Assistant Workload Assignment Problem
Volume 28, Issue 4 (2017), pp. 583–608
Pub. online: 1 January 2017      Type: Research Article      Open accessOpen Access
Received
1 January 2017
Accepted
1 September 2017
Published
1 January 2017

Abstract

This paper presents a column generation-based modelling and solution approach for a teaching assistant workload scheduling problem that arises at academic institutions. A typical weekly workload schedule involves teaching deficiency classes, instructing problem-solving tutorial sessions, and allocating help-hours for students. For this purpose, a mixed-integer programming model that selects valid combinations of weekly schedules from the set of all feasible schedules is formulated. Due to the overwhelming number of variables in this model, an effective column generation procedure is developed. To illustrate the proof-of-concept along with modelling and algorithmic constructs, a case study related to the Department of Mathematics at Kuwait University is addressed. Computational results based on real data indicate that the generated schedules using the proposed model and solution procedure yield improved weekly workloads for teaching assistants in terms of fairness, and achieve enhanced satisfaction levels among assistants, as compared to schedules obtained using ad-hoc manual approaches.

References

 
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Biographies

Al-Yakoob Salem M.
salem@al-yakoob.com

S.M. Al-Yakoob is an associate professor at the Department of Mathematics at Kuwait University. His research interests include mathematical programming and optimization with applications to real world problems such as location, transportation, scheduling, and timetabling problems.

Sherali Hanif D.
hanifs@vt.edu

H.D. Sherali is a university distinguished professor and the W. Thomas Rice endowed chaired professor of engineering, Emeritus in the Industrial and Systems Engineering Department at Virginia Polytechnic Institute and State University. His areas of research interest are in analysing problems and designing algorithms for specially structured linear, nonlinear, and integer programs arising in various applications, global optimization methods for non-convex programming problems, location and transportation theory and applications, economic and energy mathematical modelling and analysis. He has published over 345 refereed articles in various operations research journals, has (co-)authored eight books in this area, and serves on the editorial board of ten journals. He is an elected member of the National Academy of Engineering.


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© 2017 Vilnius University
Open access article under the CC BY license.

Keywords
academic timetabling scheduling mathematical programming column generation

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