Development and validation of an integer linear programming model for the lecturer-to-course assignment problem
الموضوعات :Lone Seboni 1 , Kgalalelo Rakgomo 2 , Botshelo Mhalapitsa 3
1 - Mechanical Engineering Department, University of Botswana, Faculty of Engineering and Technology, Gaborone, Botswana
2 - Mechanical Engineering Department, University of Botswana, Faculty of Engineering and Technology, Gaborone, Botswana
3 - Mechanical Engineering Department, University of Botswana, Faculty of Engineering and Technology, Gaborone, Botswana
الکلمات المفتاحية: Optimization, Integer linear programming, Delphi, Assignment, Workload,
ملخص المقالة :
This study developed and validated a formalized and robust integer linear programming (ILP) model to optimize the lecturer-to-course assignment problem (concerning balancing workload) for a university department that offers engineering programs. Questionnaire surveys with 4 groups of a total of 159 informants (10 lecturers, 1 head of department, 1 program coordinator, and 147 mechanical engineering students) were conducted. Enumeration was used for lecturers, the head of the department, and the program coordinator, whilst convenience sampling was used for students, with a response rate of 60%. A binary integer linear programming (ILP) model was developed by considering workload-related constraints such as class capacity, course contact hours, course credits, and the number of courses per lecturer. The ILP model was implemented in optimization software and the results were validated using the Delphi method. The results demonstrate the robustness and efficiency of the model in balancing workload by objectively (reducing biases) assigning under-utilized lecturers to more courses and over-utilized lecturers to fewer courses, in terms of simultaneously considering other workload-related variables, unlike existing studies. These results were used to instill a timely, formal, and consistent assignment approach that is fair and free from biases. The proposed model contributes to enhancing fairness and hence collective satisfaction of lecturers, program coordinators, and students, given a formalized, consistent, and timesaving assignment approach that considers other workload-related variables other than the number of courses per lecturer. Another contribution lies in a deeper understanding of a comprehensive range of factors that play a role in lecturer-to-course assignments for higher education institutions. Moreover, this study has implications for practice, given that other academic institutions may benefit from this work, in terms of policy considerations.
Algethami, H., & Laesanklang, W. (2021). "A Mathematical Model for Course Timetabling Problem With Faculty-Course Assignment Constraints," in IEEE Access, 9(1), 111666-111682.
Akpan, N. P., & Abraham, U. P. (2016). A Critique of the Hungarian Method of Solving Assignment Problem to the Alternate Method of Assignment Problem by Mansi. International Journal of Sciences: Basic and Applied Research (IJSBAR), 29(1), 43-56.
Arratia-Martinez, N. M., Maya-Padron, C., & Avila-Torres, P. A. (2021). University Course Timetabling Problem with Professor Assignment. Mathematical Problems in Engineering, 2021(1), 1-9.
Arinze, V., & Partovi, F. Y. (2000). A knowledge based approach to the faculty-course assignment problem. Socio-Economic Planning Sciences, 29(3), 245-256.
Awang, N., Jamian, N. H., & Saleh, S. S. (2020). The department team teaching assignment problem using zero-one integer programming. Journal of computing research and innovation, 5(1), 1-6.
Babad, E., Avni-Babad, D. & Rosenthal, R. (2004). Prediction of Students' Evaluations from Brief Instances of Professors' Nonverbal Behavior in Defined Instructional Situations. Social Psychology of Education, 7(1), 3–33.
Baruch, Y. (1999). Response Rate in Academic Studies – A Comparative Analysis. Human Relations, 52(4), 421–438.
Belding, J., Loanzon, E., Millward, H. et al. (2009). A Decision Model for Purchasing the Highest Value Printer for Home use for the Least Cost. In: Proceedings of PICMET '09, - Technology management in the age of fundamental change, Volume 1-5, 2-6 Aug 2009, Portland, Oregon, USA, 484–502.
Bhoi, S. B., & Dhodiya, J. M. (2021). Multi-Objective Faculty Course Assignment Problem with Result and Feedback Based Uncertain Preferences. International Journal of Mathematical, Engineering and Management Sciences, 6(4), 1055-1075.
Canady, R. L., & Rettig, M. D. (Eds.). (1996). Teaching in the block: Strategies for engaging active learners. Eye on Education, (1st edition), London: Routledge.
Carbonetto, T. (2022). Optimization of Student Learning Outcomes Using an Hours of Instructional Activity Tool. In 2022 Spring ASEE Middle Atlantic Section Conference, Newark, New Jersey, 22 April 2022.
Caselli, G., Delorme, M., Iori, M. (2022). Integer Linear Programming for the Tutor Allocation Problem: A practical case in a British University, Expert Systems with Applications, 187(1), 115967.
Chang, C-T. (2008). Revised multi-choice goal programming, Applied Mathematical Modelling, 32(12), https://doi.org/10.1016/j.apm.2007.09.008.
Conway, D. G. and Ragsdale, C. T. (1997). Modeling optimization problems in the unstructured world of spreadsheets. Omega International Journal of Management Science. 25(3), 313-322.
da Cunha, J.J., and de Souza, M.C. (2018). A linearized model for academic staff assignment in a Brazilian university focusing on performance gain in quality indicators, International Journal of Production Economics, 197(1), 43-51.
Dobela, J., and Seboni, L. (2023). Attitudes and Academic Performance of Engineering Students in both Prerequisite Courses to Final Year Project and Final Year Project, International Journal of Higher Education, 12(1), 45-69.
Domenech, B., & Lusa, A. (2016). A MILP model for the Teacher Assignment Problem Considering Teachers’ Preferences. European Journal of Operations Research, 249(3), 1153-1160.
Ekhosuehi, V. U. (2016). University Course Allocation In A Department Using Linear Programming Techniques, The Journal of the Mathematical Association of Nigeria, 43(1), 403-413.
Esfahani, A. A., Ershadi, M. J., & Azizi, A. (2020). Monitoring indicators of research data using I-MR control charts, Iranian Journal of Information Processing and Management, 35(4), 953-978.
Faudzi, S., Rahman, S. A., & Rahman, R. A. (2018). An Assignment Problem and its application in education domain: A review and potential path. Advances in Operations Research, Vol 2018.
Faudzi, S., Abdul-Rahman, S., Rahman, R.A., Zulkepli, J., and Bargiela, A. (2020). Optimizing the preference of student-lecturer allocation problem using analytical hierarchy process and integer programming. Journal of Engineering Science and Technology, 15(1), 261-275.
Ferland, J.A., Berrada, I., Nabli, I. et al. (2001). Generalized Assignment Type Goal Programming Problem: Application to Nurse Scheduling. Journal of Heuristics, 7(1), 391–413.
Fico. (2012). Xpress Optimization Suite, Fico. https://www.fico.com/en/products/fico-xpress-optimization.
Gillian F., and Sigrid S. (2018). Design, implementation, and evaluation of an inverted (flipped) classroom model economics for a sustainable education course, Journal of Cleaner Production, 183(1), 1323-1336.
Gueret, C., Prins, C. and Sevaux, M. (2002). Applications of Optimization with Xpress-MP. Northants: United Kingdom; Dash Optimization Limited.
Güler, M.G., Keskin, M.E., Döyen, A., and Akyer, H. (2015). On teaching assistant-task assignment problem: A case study, Computers & Industrial Engineering, 79(1), 18-26.
Gunawan, A., & Ng, K. M. (2011). Solving the teacher assignment problem by two Metaheuristics. International Journal of Information and Management Sciences, 22(1), 73-86.
Jensen, P. A. and Bard, J. F. (2003). Operations Research Models and Methods. Wiley.
Johnson R., Kgomotso, M., and Seboni, L. (2022). An Optimization Model for the Student-to-Project Supervisor Assignment Problem-The Case of an Engineering Department, Journal of Optimization, vol. 2022.
Kabiru, S., Saidu, B.M., Abdul, A.Z. and Ali, U.A. (2017) An Optimal Assignment Schedule of Staff-Subject Allocation. Journal of Mathematical Finance, 7(1), 805-820. https://doi.org/10.4236/jmf.2017.74042
Malik, B. B., & Nordin, S. Z. (2018). Mathematical model for timetabling problem in maximizing the preference level. AIP Conference Proceedings, AIP Publishing, 1-7. https://doi.org/10.1063/1.5041568.
Mallick, C., Kumar , B. S., Jena, K. K., Sahoo, K. S., Humayn, M., & Shahd, M. H. (2021). Course and Lecturer Assignment problem solver for Educational Institution using Hungarian Method. Turkish Journal of Computer and Mathematics Education, 12(10), 3085-3092.
Martinez, N. A., Padron, C. M., & Torres, P. A. (2021). University course timetabling problem with professor assignment. Mathematical problems in Engineering, 2021(1), 1-9, https://doi.org/10.1155/2021/6617177.
Mason, A. J. (2011). OpenSolver – An Open Source Add-in to Solve Linear and Integer Programmes in Excel. In: Operations Research Proceedings 2011, Berlin Heidelberg. Springer, 401–406.
Mason, A. J. (2013). SolverStudio: A New Tool for Better Optimisation and Simulation Modelling in Excel. INFORMS Transactions on Education. 14(1), 45-52.
McClure, R. & Wells, C. (2007). A mathematical programming model for faculty course assignment, Decision Sciences, 15(1), 409 - 420.
Meerschaert, M. M. (2007). Mathematical modeling. 3rd ed. London: Elsevier/Academic Press.
Meindl, B. and Templ, M. (2013). Analysis of Commercial and Free and Open Source Solvers for the Cell Suppression Problem. Transactions on Data Privacy. 6(2), 147-159.
MirHassani, S. (2006). Improving paper spread in examination timetables using integer programming, Applied Mathematics and Computation, 179(2), 702-706, https://doi.org/10.1016/j.amc.2005.11.125.
Murthy, D. N. P., Page, N. W. and Rodin, E. Y. (1990). Mathematical modelling: a tool for problem solving in engineering, physical, biological and social sciences. Oxford: Pergamon.
Na, L. A., & Hussin, M. S. (2021). Course Allocation Among Lecturers Using Python, Journal of Undergraduate Research, 3(4), 127–136.
Ngo, S. T., Jaafar, J., Aziz, I. A., & Anh, B. N. (2021). A Compromise Programming for Multi-objective Task Assignment Problem. Computers, 10(2), 1-16.
Nulty, D. D. (2008). The adequacy of response rates to online and paper surveys: what can be done? Assessment & Evaluation in Higher Education, 33(3), 301-314.
Ongy, E. (2017). Optimizing student learning: A Faculty-Course Assignment Problem Using Linear Programming. Journal of Science, Engineering and Technology, 5(1), 1-14.
Patanakul, P., and Milosevic, D. (2006). Assigning new product projects to multiple-project managers: What market leaders do. The Journal of High Technology Management Research, 17(1), 53-69.
Patanakul, P., Milosevic, D. and Anderson, T. R. (2007). A Decision Support Model for Project Manager Assignments, IEEE Transactions on Engineering Management, 54(3), 548-564.
Ragsdale, C. T. (2021). Spredsheet Modeling and Decision Analysis: A Practical Introduction to Business Analytics. (9th edition), Stamford: USA; Cengage Learning.
Ramotsisi, J., Kgomotso, M. and Seboni, L. (2022). An Optimization Model for the Student-to-Project Supervisor Assignment Problem-The Case of an Engineering Department, Journal of Optimization, vol. 2022, Article ID 9415210.
Rocco, T. S., and Plakhotnik, M. S. (2009). Literature reviews, conceptual frameworks, and theoretical frameworks: Terms, functions, and distinctions. Human Resource Development Review, 8(1), 120-130.
Russell, J. (2000). Stress free teaching: A practical guide to tackling stress in teaching, lecturing and tutoring. (1st edition), London; Routledge.
Saleh, S. S., Awang, N., & Jamian, N. H. (2020). The Department Team Teaching Assignment Problem Using Zero-One Integer Programming. Journal of Computing Research and Innovation, 5(1), 1-6.
Saleh, S. S., Jamian, N. H., & Awang, N. (2019). Team Teaching Load using Linear Programming. Journal of Computing Research and Innovation, 4(1), 8-15.
Schniederjans, M.J. and Kim, G.C. (1987). A goal programming model to optimize departmental preference in course assignments, Computers & Operations Research, 14(2), 87-96.
Seboni, L. 2018. Development and Verification of an Industry Application to Improve the Project Manager-to-Project (PM2P) Allocation Practice. In: Proceedings of PICMET '18, 19-23 Aug 2018, Honolulu, Hawaii, USA.
Seboni, L. (2021). A Framework for Identifying and Validating Idea Screening Criteria—A Case of Research and Development Projects in the Computing and Automation Industry. IEEE Transactions on Engineering Management, 1-10.
Seboni, L., and Moreri, K. (2022). A Practical Application of the Analytic Hierarchy Process and Integer Linear Programming for Fuzzy Front-End Project Selection, Mathematical Problems in Engineering, vol. 2022.
Seboni, L., and Ssegawa, J. (2022). Does a Project Manager Assignment Process Affect Project Management Performance Indicators? An Empirical Study, Sustainability, 14(13), 7637-7654.
Seboni, L., and Tutesigensi, A. (2015a). A mathematical model for allocating project managers to projects. In: Raiden, A. (Ed.) and Aboagye-Nimo, E. (ed.), Proceedings of the 31th Annual ARCOM Conference, 7-9 September 2015, Lincoln, UK, Association of Researchers in Construction Management, 3-12.
Seboni, L. and Tutesigensi, A. (2015b). Project manager-to-project allocations in practice: an empirical study of the decision-making practices of a multi-project based organization. Construction Management and Economics, 33(5-6), pp. 428-443.
Sharma, S., & Tuli, R. (2020). Feasible Solution of the Course Assignment Problem to Faculty. AIP Conference Proceedings, Advances in Mathematics and its emerging areas, New Delhi: AIP Publishing. 2214(1), 1-10. https://doi.org/10.1063/5.0003705.
Shohaimay, F., Dasman, A., & Suparlan, A. (2016). Teaching Load Allocation using Linear Programming: A Case Study in Mathematics Department, Business Management and Computing Research Colloquium, Raub, Malaysia, 25-28.
Smith, B. C. (1994). Scholarship in the professoriate: A comparative study of official workloads and perceptions of workloads among faculty in six academic disciplines in selected state colleges and universities. PhD Thesis, Texas A & M University.
Solaja, O., Abiodun, J., Ekpudu, J., Abioro, M., & Akinbola, O. (2020). Assignment problem and its application in Nigerian institutions: Hungarian method approach. International Journal of Applied Operational Research, 10(1), 1-9.
Sze, S. N., Bong, C-L., Chiew, K. L, Tiong, W. K., & Bolhassan, N. A. (2017). Case study: University lecture timetabling without pre-registration data. Proceedings of the 2017 IEEE International conference on applied system innovation, Department of computational science and mathematics, Universiti Malaysia Sarawak, 2017, 735-735.
Taha, H. A. (2007). Operations research: An introduction. New Jersey: Pearson Education, Inc.
Triantaphyllou, E. (2000). Multi-Criteria Decision Making Methods: A Comparitive Study. Dordrecht: Kluwer Academic Publishers.
Wicaksono, E., & Wisesa, W. W. (2020). An Optimization Model for Teaching Assignment based on lecturer's capability using linear programming. Indonesian Journal of Artificial Intelligence and Data Mining, 3(2). 57-63.
Wilson, P.M., Petticrew, M., Calnan, M.W. et al. (2010). Disseminating research findings: what should researchers do? A systematic scoping review of conceptual frameworks. Implementation Science, 5(1), 91. https://doi.org/10.1186/1748-5908-5-91.
Zavadskas, E. K.Turskis, Z., Tamošaitienė, J. and Marina, V. (2008). Multicriteria selection of project managers by applying grey criteria, Technological and Economic Development of Economy, 14(4), 462-477.
