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A Fuzzy Logic and Binary-Goal Programming-Based Approach for Solving the Exam Timetabling Problem to Create a Balanced-Exam Schedule

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Abstract

This study presents a fuzzy logic and binary-goal programming-based approach for solving the exam timetabling problem to create a balanced-exam schedule. To be able to address the practical challenges of the exam timetabling problem, the model is developed with and verified by a human expert for exam scheduling. We propose a fuzzy-criticality level identification methodology to assign the criticality levels of exams for the students using three pieces of information, namely, credits, success ratios, and types of the classes. It is noted that the computed criticality levels are close approximates for those of the human expert. We then present a goal programming model to schedule exams using these criticality levels as well as other general problem data. The result of the goal program is a balanced-exam schedule in terms of exam criticality levels. Final step includes room assignments using a simple algorithm. The significance of the study is the consideration of the exam criticalities, for not only the students of the same year but also the students with different levels of seniority, as well as an even distribution of exams for professors which make the problem more challenging for the human expert in practice. Using a real-life problem, we show that our approach creates an exam schedule that is more preferable than the one prepared by the human expert. Additionally, computational results show the potential of our model to be used in real-life problems of larger-size.

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References

  1. Johnes, J.: Operations research in education. Eur. J. Oper. Res. 243(3), 683–696 (2015)

    Article  Google Scholar 

  2. Al-Yakoob, S.M., Sherali, H.D.: Mathematical programming models and algorithms for a class-faculty assignment problem. Eur. J. Oper. Res. 173, 488–507 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Daskalaki, S., Birbas, T., Housos, E.: An integer programming formulation for a case study in university timetabling. Eur. J. Oper. Res. 153, 117–135 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Daskalaki, S., Birbas, T.: Efficient solutions for a university timetabling problem through integer programming. Eur. J. Oper. Res. 160, 106–120 (2005)

    Article  MATH  Google Scholar 

  5. Philips, A.E., Waterer, H., Ehrgott, M., Ryan, D.M.: Integer programming methods for large-scale practical classroom assignment problems. Comput. Oper. Res. 53, 42–53 (2015)

    Article  MathSciNet  Google Scholar 

  6. Al-Yakoob, S.M., Sherali, H.D.: Mathematical models and algorithms for a high school timetabling problem. Comput. Oper. Res. 61, 56 (2015)

    Article  MathSciNet  Google Scholar 

  7. Alzaqebah, M., Abdullah, S.: Hybrid bee colony optimization for examination timetabling problems. Comput. Oper. Res. 54, 142–154 (2015)

    Article  MathSciNet  Google Scholar 

  8. Burke, E.K., Newall, J.P.: Solving examination timetabling problems through adaption of heuristic orderings. Ann. Oper. Res. 129, 107–134 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Carter, M.W., Laporte, G., Lee, S.Y.: Examination timetabling: algorithmic strategies and applications. J. Oper. Res. Soc. 47(3), 373–383 (1996)

    Article  Google Scholar 

  10. Babaei, H., Karimpour, J., Hadidi, A.: A survey of approaches for university course timetabling problem. Comput. Ind. Eng. (2014). doi:10.1016/j.cie.2014.11.010

  11. Burke, E.K., Jackson, K., Kingston, J.H., Weare, R.F.: Automated university timetabling: the state of the art. Comput. J. 40(9), 565–571 (1997)

    Article  Google Scholar 

  12. Burke, E.K., Petrovic, S.: Recent research directions in automated timetabling. Eur. J. Oper. Res. 140, 266–280 (2002)

    Article  MATH  Google Scholar 

  13. Schaerf, A.: A survey of automated timetabling. Artif. Intell. Rev. 13, 87–127 (1999)

    Article  Google Scholar 

  14. Schmidt, G., Strohlein, T.: Timetable construction an annotated bibliography. Comput. J. 23(4), 307–316 (1980)

    Article  MathSciNet  Google Scholar 

  15. Burke, E.K., Elliman, D.G., Ford, P.H., Weare, R.F.: Examination Timetabling in British Universities: A Survey. Practice and Theory of Automated Timetabling I, pp. 76–90. Springer, Berlin (1996)

    Google Scholar 

  16. Carter, M.W.: OR practice—a survey of practical applications of examination timetabling algorithms. Oper. Res. 34(2), 193–202 (1986)

    Article  MathSciNet  Google Scholar 

  17. Carter, M.W., Laporte, G.: Recent Developments in Practical Examination Timetabling. Practice and Theory of Automated Timetabling I, pp. 3–21. Springer, Berlin (1996)

    Google Scholar 

  18. Qu, R., Burke, E.K., McCollum, B., Merlot, L.T.G., Lee, S.Y.: A survey of search methodologies and automated system development for examination timetabling. J. Sched. 12, 55–89 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Carter, M.W., Laporte, G., Chinneck, J.W.: A general examination scheduling system. Interfaces 24, 109–120 (1994)

    Article  Google Scholar 

  20. Al-Yakoob, S.M., Sherali, H.D., Al-Jazzaf, M.: A mixed-integer mathematical programming modeling approach to exam timetabling. Comput. Manag. Sci. 7, 19–46 (2010)

    Article  MATH  Google Scholar 

  21. Burke, E.K., Bykov, Y., Petrovic, S.: A Multicriteria Approach to Examination Timetabling. Practice and Theory of Automated Timetabling III, pp. 104–117. Springer, Berlin (2001)

    Google Scholar 

  22. Brailsford, S.C., Potts, C.N., Smith, B.M.: Constraint satisfaction problems: algorithms and applications. Eur. J. Oper. Res. 119, 557–581 (1999)

    Article  MATH  Google Scholar 

  23. MirHassani, S.A.: Improving paper spread in examination timetables using integer programming. Appl. Math. Comput. 179(2), 702–706 (2006)

    Article  MATH  Google Scholar 

  24. Anderson, J.M., Bernhard, R.H.: A university examination-scheduling model to minimize multiple-examination days for students. Decis. Sci. 12(2), 231–239 (1981)

    Article  Google Scholar 

  25. Ismayilova, N.A., Sagir, M., Gasimov, R.N.: A multiobjective faculty-course-time slot assignment problem with preferences. Math. Comput. Model. 46, 1017–1029 (2007)

    Article  MathSciNet  Google Scholar 

  26. Ozdemir, M.S., Gasimov, R.N.: The analytic hierarchy process and multiobjective 0–1 faculty course assignment. Eur. J. Oper. Res. 157, 398–408 (2004)

    Article  MathSciNet  Google Scholar 

  27. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  28. Nguyen, H.T.: On foundations of fuzzy theory for soft computing. Int. J. Fuzzy Syst. 8(1), 39–45 (2006)

    MathSciNet  Google Scholar 

  29. Azadegan, A., Porobic, L., Ghazinoory, S., Samouei, P., Kheirkhah, A.S.: Fuzzy logic in manufacturing: a review of literature and a specialized application. Int. J. Prod. Econ. 132(2), 258–270 (2011)

    Article  Google Scholar 

  30. Kar, S., Das, S., Ghosh, P.K.: Applications of neuro fuzzy systems: a brief review and future outline. Appl. Soft Comput. 15, 243–259 (2014)

    Article  Google Scholar 

  31. Kobbacy, K.A., Vadera, S., Rasmi, M.: AI and OR in management of operations: history and trends. J. Oper. Res. Soc. 58, 10–28 (2007)

    Article  MATH  Google Scholar 

  32. Melin, P., Castillo, O.: A review on type-2 fuzzy logic applications in clustering, classification and pattern recognition. Appl. Soft Comput. 21, 568–577 (2014)

    Article  Google Scholar 

  33. Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), B-141–B-164 (1970)

    Article  MathSciNet  Google Scholar 

  34. Carlsson, C., Fuller, R.: Fuzzy multiple criteria decision making: recent developments. Fuzzy Sets Syst. 78(2), 139–153 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  35. Tao, Z., Chen, H., Zhou, L., Liu, J.: A generalized multiple attributes group decision making approach based on intuitionistic fuzzy sets. Int. J. Fuzzy Syst. 16(2), 184–195 (2014)

    MathSciNet  Google Scholar 

  36. Yu, D.: Group decision making under multiplicative hesitant fuzzy environment. Int. J. Fuzzy Syst. 16(2), 233–241 (2014)

    MATH  Google Scholar 

  37. Tsai, C.M., Yeh, Z.M.: Classifying student’s attentiveness via spatial-temporal fuzzy logic classification. Int. J. Fuzzy Syst. 16(4), 541–553 (2014)

    Google Scholar 

  38. Asmuni, H., Burke, E.K., Garibaldi, J.M., McCollum, B.: An investigation of fuzzy multiple heuristics orderings in the construction of university exam timetables. Comput. Oper. Res. 36(4), 981–1001 (2009)

    Article  MATH  Google Scholar 

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Acknowledgments

We would like to thank to the staff of the Faculty of the Engineering and the Department of Industrial Engineering of Uludag University on behalf of Erdal Emel, the department head, for the support provided.

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Authors and Affiliations

  1. Department of Industrial Engineering, Uludag University, Nilufer, Bursa, Turkey

    Fatih Cavdur & Merve Kose

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  1. Fatih Cavdur
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  2. Merve Kose
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Correspondence to Fatih Cavdur.

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Cavdur, F., Kose, M. A Fuzzy Logic and Binary-Goal Programming-Based Approach for Solving the Exam Timetabling Problem to Create a Balanced-Exam Schedule. Int. J. Fuzzy Syst. 18, 119–129 (2016). https://doi.org/10.1007/s40815-015-0046-z

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  • DOI: https://doi.org/10.1007/s40815-015-0046-z

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