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<p>The university course scheduling problem is sub-problem of an educational timetabling problem, aims to allot courses to faculty members so that the faculty members, administrator and students will be satisfied. The satisfaction level is measured by means of preferences. However, due to incomplete or vague nature of data, mostly preferences will be in fuzzy nature. This paper presents a zero–one integer mathematical model of the multi-objective university course scheduling problem based on the double parametric form of fuzzy preferences. In this work, the fuzzy preferences are computed utilizing an analysis of faculty feedback provided by students and an analysis of the results of the previous year’s examination of students. The proposed mathematical fuzzy model is developed using faculty members preferences, the preferences of an administrator for faculty members to courses, and fuzzy preferences computed utilizing faculty members feedback and students result analysis. To deal with this proposed fuzzy model, the double parametric scheme is applied to transform it into crisp model. To validate model, the hypothetical numerical data of university considered to generate allocation plan with better degree of satisfaction of stakeholders. The exponential membership function based fuzzy programming technique is used to generate efficient and non-dominated allocations with better optimal values and degree of satisfaction of respective objective functions of faculty members, administrator and students for different values of parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> for fuzzy preferences and shape parameter ‘s’ of exponential membership function. Results are found using LINGO19.0 software. The model provides the alternative allocation schedule with different levels of degree of satisfaction which can be easily implemented by decision maker.</p>

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Double parametric scheme based multi-objective university course scheduling problem by fuzzy programming technique with exponential membership function

  • 期刊论文

  • 发表日期：

    2025年2月8日

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  • Sunil B. Bhoi,
  • Jayesh M. Dhodiya

摘要

The university course scheduling problem is sub-problem of an educational timetabling problem, aims to allot courses to faculty members so that the faculty members, administrator and students will be satisfied. The satisfaction level is measured by means of preferences. However, due to incomplete or vague nature of data, mostly preferences will be in fuzzy nature. This paper presents a zero–one integer mathematical model of the multi-objective university course scheduling problem based on the double parametric form of fuzzy preferences. In this work, the fuzzy preferences are computed utilizing an analysis of faculty feedback provided by students and an analysis of the results of the previous year’s examination of students. The proposed mathematical fuzzy model is developed using faculty members preferences, the preferences of an administrator for faculty members to courses, and fuzzy preferences computed utilizing faculty members feedback and students result analysis. To deal with this proposed fuzzy model, the double parametric scheme is applied to transform it into crisp model. To validate model, the hypothetical numerical data of university considered to generate allocation plan with better degree of satisfaction of stakeholders. The exponential membership function based fuzzy programming technique is used to generate efficient and non-dominated allocations with better optimal values and degree of satisfaction of respective objective functions of faculty members, administrator and students for different values of parameters \(\alpha\) α and \(\beta\) β for fuzzy preferences and shape parameter ‘s’ of exponential membership function. Results are found using LINGO19.0 software. The model provides the alternative allocation schedule with different levels of degree of satisfaction which can be easily implemented by decision maker.