Course timetabling in medical universities given physicians' educational and clinical tasks

Document Type : Article


1 Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

2 Department of infectious disease, Kurdistan University of Medical Sciences, Sanandaj, Iran


The physician assignment and course timetabling problem at medical universities is a generalized version of the academic timetabling problem. This problem entails assigning courses, educational and clinical tasks to physician faculty members over a semester or academic year. The problem of timetabling academic courses and scheduling physicians in a hospital has been investigated independently in previous studies in this field. These two fields of research are brought together in this article through the presentation of a multi-objective mixed-integer linear programming (MILP) model. The proposed model is based on two optimization criteria: minimizing workload imbalance and maximizing physician preferences. The model is applied to a case study involving the assignment of physicians to courses, educational and clinical tasks at Kurdistan University of Medical Sciences' Department of Infectious Diseases. Pareto solutions are obtained using an enhanced version of the augmented epsilon constraint implemented in the GAMS optimization software; one is selected as the most desirable solution using the TOPSIS method. The proposed model is generic and could be adapted for use in other departments or medical schools.


  1. References

    1. Mousavipoor, S., Farughi, H., AhmadiZar, F. “A novel bi-objective model for a job shop scheduling problem with consideration of Fuzzy parameters, modified learning effects and multiple preventive maintenance activities”, Scientia Iranica, (), pp. -. doi: 10.24200/sci.2021.54614.3839 (2021).
    2. Rabbani, M., Sadeghsa, S., Vaez-Alaei, M., & Farrokhi-Asl, H. “Robust and sustainable full-shipload routing and scheduling problem considering variable speed: A real case study”, Scientia Iranica, 26(3), pp. 1881-1897 (2019).
    3. Ataeian, S., Solimanpur, M., Amiripour, S., Shankar, R. “Synchronized timetables for bus rapid transit networks in small and large cities”, Scientia Iranica, 28(1), pp. 477-491. doi: 10.24200/sci.2019.51501.2220 (2021).
    4. Babaei, H., Karimpour, J., & Hadidi, A. “A survey of approaches for university course timetabling problem”, Computers & Industrial Engineering, 86, pp. 43-59 (2015).
    5. Behmanesh, R., Zandieh, M., Hadji Molana, S. “The surgical case scheduling problem with fuzzy duration time: An ant system algorithm”, Scientia Iranica, 26(3), pp. 1824-1841. doi: 10.24200/sci.2018.20602 (2019).
    6. Yazdi, M., Zandieh, M., Haleh, H., Pasandideh, S. “Efficient scheduling of emergency surgeries by adjusting the schedule of elective surgeries”Scientia Iranica, (), pp. -. doi: 10.24200/sci.2021.53630.3339 (2021).
    7. Van Bulck, D., Goossens, D., Schönberger, J., & Guajardo, M. “RobinX: A three-field classification and unified data format for round-robin sports timetabling”,European Journal of Operational Research, 280(2), pp. 568-580 (2020).
    8. Kayanda, A., Busagala, L., Tedre, M., & Oyelere, S. “Towards the Development of Timetabling Software for improving Decision-Making in Tanzanian Higher Education Context”, In 2020 15th Iberian Conference on Information Systems and Technologies (CISTI), IEEE , pp. 1-6, (2020).
    9. Leung, J. Y. (Ed.). “Handbook of scheduling: algorithms, models, and performance analysis”, CRC Press (2004).
    10. Garey, M. R. “Computers and intractability: A guide to the theory of np-completeness”, Revista Da Escola De Enfermagem Da USP, 44(2), p. 340 (1979).
    11. Schaerf, A. “A survey of automated timetabling”, Artificial intelligence review, 13(2), pp. 87-127 (1999).
    12. Erhard, M., Schoenfelder, J., Fügener, A., & Brunner, J. O. “State of the art in physician scheduling”, European Journal of Operational Research, 265(1), pp. 1-18 (2018).
    13. Tillett, P. I. “An operations research approach to the assignment of teachers to courses”, Socio-Economic Planning Sciences, 9(3-4), pp. 101-104 (1975).
    14. Tripathy, A. “Computerised decision aid for timetabling—a case analysis”, Discrete applied mathematics, 35(3), pp. 313-323 (1992).
    15. Hultberg, T. H., & Cardoso, D. M. “The teacher assignment problem: A special case of the fixed charge transportation problem”, European Journal of Operational Research, 101(3), pp. 463-473 (1997).
    16. Dimpoulou, M., & Miliotis, P. “Implementation of a university course and examination timetabling system”, European Journal of Operational Research, 130(1), pp. 202-213 (2001).
    17. Socha, K., Knowles, J., & Sampels, M. “A max-min ant system for the university course timetabling problem”, Springer, Berlin, Heidelberg, In International Workshop on Ant Algorithms , pp. 1-13 (2002).
    18. Yang, S., & Jat, S. N. “Genetic algorithms with guided and local search strategies for university course timetabling”, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 41(1), pp. 93-106 (2011).
    19. Daskalaki, S., Birbas, T., & Housos, E. “An integer programming formulation for a case study in university timetabling”, European Journal of Operational Research, 153(1), pp. 117-135 (2004).
    20. Rezaeipanah, A., Matoori, S. S., & Ahmadi, G. “A hybrid algorithm for the university course timetabling problem using the improved parallel genetic algorithm and local search”, Applied Intelligence, 51(1), pp. 467-492 (2021).
    21. Deb, K. “Multi-objective optimization”, In Search methodologies ,Springer, Boston, MA, pp. 403-449 (2014).
    22. Domenech, B., & Lusa, A. “A MILP model for the teacher assignment problem considering teachers' preferences”, European Journal of Operational Research, 249(3), pp. 1153-1160 (2016).
    23. Immonen, E., & Putkonen, A. “An heuristic genetic algorithm for strategic university tuition planning and workload balancing”, International Journal of Management Science and Engineering Management, 13(2), pp. 118-128 (2018).
    24. Jamili, A., Hamid, M., Gharoun, H., & Khoshnoudi, R. “Developing a comprehensive and multi-objective mathematical model for university course timetabling problem: a real case study”, In Conference: proceedings of the international conference on industrial engineering and operations management, Paris, France, p. 2108 (2018).
    25. Lindahl, M., Mason, A. J., Stidsen, T., & Sørensen, M. “A strategic view of University timetabling”, European Journal of Operational Research, 266(1), pp. 35-45 (2018).
    26. da Cunha Jr, J. J., & de Souza, M. C. “A linearized model for academic staff assignment in a Brazilian university focusing on performance gain in quality indicators”, International Journal of Production Economics, 197, pp. 43-51 (2018).
    27. Yasari, P., Ranjbar, M., Jamili, N., & Shaelaie, M. H. “A two-stage stochastic programming approach for a multi-objective course timetabling problem with courses cancelation risk”, Computers & Industrial Engineering, 130, pp. 650-660 (2019).
    28. Zaerpour, F., Bischak, D. P., & Menezes, M. B. “Coordinated lab-clinics: A tactical assignment problem in healthcare”, European Journal of Operational Research, 263(1), pp. 283-294 (2017).
    29. Castaño, F., & Velasco, N. “Exact and heuristic approaches for the automated design of medical trainees rotation schedules”, Omega, 97, p. 102107 (2020).
    30. Bard, J. F., Shu, Z., Morrice, D. J., & Leykum, L. K. “Constructing block schedules for internal medicine residents”, IISE Transactions on Healthcare Systems Engineering, 7(1), pp. 1-14 (2017).
    31. Ağralı, S., Taşkın, Z. C., & Ünal, A. T. “Employee scheduling in service industries with flexible employee availability and demand”, Omega, 66, pp. 159-169 (2017).
    32. Hong, Y. C., Cohn, A., Gorga, S., O'Brien, E., Pozehl, W., & Zank, J. “Using Optimization Techniques and Multidisciplinary Collaboration to Solve a Challenging Real-World Residency Scheduling Problem”, INFORMS Journal on Applied Analytics, 49(3), pp. 201-212 (2019).
    33. Selim, S. M. “An algorithm for constructing a university faculty timetable”, Computers & Education, 6(4), pp. 323-332 (1982).
    34. Entezari, Z., Mahootchi, M. “Developing a mathematical model for staff routing and scheduling in home health care industries: Genetic Algorithm based solution scheme”, Scientia Iranica, (), pp. -. doi: 10.24200/sci.2020.54116.3600 (2020).
    35. Hosseinpour-Sarkarizi, A., Davari-Ardakani, H., Izadbakhsh, H. “Home Health Care Routing and Scheduling Problem under Uncertainty Considering Patient Preferences and Service Desirability”, Scientia Iranica, (),pp. -. doi: 10.24200/sci.2020.54313.3694 (2020).
    36. Akbarzadeh, B., & Maenhout, B. “An exact branch-and-price approach for the medical student scheduling problem”, Computers & Operations Research, 129, p. 105209 (2021).
    37. Mavrotas, G., & Florios, K. “An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems”, Applied Mathematics and Computation, 219(18), pp. 9652-9669 (2013).
    38. Mavrotas, G. “Effective implementation of the ε-constraint method in multi-objective mathematical programming problems”, Applied mathematics and computation, 213(2), pp. 455-465 (2009).
    39. Hwang, C. L., & Yoon, K. “Multiple Attribute Decision Making: Methods and Applications”, Springer Verlag. New York (1981).