181 research outputs found

    Operational Research in Education

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    Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

    Examination timetabling at the University of Cape Town: a tabu search approach to automation

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    With the rise of schedules and scheduling problems, solutions proposed in literature have expanded yet the disconnect between research and reality remains. The University of Cape Town's (UCT) Examinations Office currently produces their schedules manually with software relegated to error-checking status. While they have requested automation, this study is the first attempt to integrate optimisation techniques into the examination timetabling process. Tabu search and Nelder-Mead methodologies were tested on the UCT November 2014 examination timetabling data with tabu search proving to be more effective, capable of producing feasible solutions from randomised initial solutions. To make this research more accessible, a user-friendly app was developed which showcased the optimisation techniques in a more digestible format. The app includes data cleaning specific to UCT's data management system and was presented to the UCT Examinations Office where they expressed support for further development: in its current form, the app would be used as a secondary tool after an initial solution has been manually obtained

    Transformation of the university examination timetabling problem space through data pre-processing

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    This research investigates Examination Timetabling or Scheduling, with the aim of producing good quality, feasible timetables that satisfy hard constraints and various soft constraints. A novel approach to scheduling, that of transformation of the problem space, has been developed and evaluated for its effectiveness. The examination scheduling problem involves many constraints due to many relationships between students and exams, making it complex and expensive in terms of time and resources. Despite the extensive research in this area, it has been observed that most of the published methods do not produce good quality timetables consistently due to the utilisation of random-search. In this research we have avoided random-search and instead have proposed a systematic, deterministic approach to solving the examination scheduling problem. We pre-process data and constraints to generate more meaningful aggregated data constructs with better expressive power that minimise the need for cross-referencing original student and exam data at a later stage. Using such aggregated data and custom-designed mechanisms, the timetable construction is done systematically, while assuring its feasibility. Later, the timetable is optimized to improve the quality, focusing on maximizing the gap between consecutive exams. Our solution is always reproducible and displays a deterministic optimization pattern on all benchmark datasets. Transformation of the problem space into new aggregated data constructs through pre-processing represents the key novel contribution of this research

    Transformation of the university examination timetabling problem space through data pre-processing

    Get PDF
    This research investigates Examination Timetabling or Scheduling, with the aim of producing good quality, feasible timetables that satisfy hard constraints and various soft constraints. A novel approach to scheduling, that of transformation of the problem space, has been developed and evaluated for its effectiveness. The examination scheduling problem involves many constraints due to many relationships between students and exams, making it complex and expensive in terms of time and resources. Despite the extensive research in this area, it has been observed that most of the published methods do not produce good quality timetables consistently due to the utilisation of random-search. In this research we have avoided random-search and instead have proposed a systematic, deterministic approach to solving the examination scheduling problem. We pre-process data and constraints to generate more meaningful aggregated data constructs with better expressive power that minimise the need for cross-referencing original student and exam data at a later stage. Using such aggregated data and custom-designed mechanisms, the timetable construction is done systematically, while assuring its feasibility. Later, the timetable is optimized to improve the quality, focusing on maximizing the gap between consecutive exams. Our solution is always reproducible and displays a deterministic optimization pattern on all benchmark datasets. Transformation of the problem space into new aggregated data constructs through pre-processing represents the key novel contribution of this research

    Evolutionary algorithms : concepts and applications

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    Evolutionary algorithms are a family of stochastic problem-solving techniques, within the broader category of what we might call \u201cnatural-metaphor models\u201d, together with neural networks, ant systems, etc. They find their inspiration in biology and, in particular, they are based on mimicking the mechanisms of what we know as \u201cnatural evolution\u201d. During the last twenty-five years these techniques have been applied to a large number of problems of great practical and economic importance with excellent results. This paper presents a survey of these techniques and a few sample applications

    Fuzzy methodologies for automated University timetabling solution construction and evaluation

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    This thesis presents an investigation into the use of fuzzy methodologies for University timetabling problems. The first area of investigation is the use of fuzzy techniques to combine multiple heuristic orderings within the construction of timetables. Different combinations of multiple heuristic ordering were examined, considering five graph-based heuristic orderings - Largest Degree, Saturation Degree, Largest Enrolment, Largest Coloured Degree and Weighted Largest Degree. The initial development utilised only two heuristic orderings simultaneously and subsequent development went on to incorporate three heuristic orderings simultaneously. A central hypothesis of this thesis is that this approach provides a more realistic scheme for measuring the difficulty of assigning events to time slots than the use of a single heuristic alone. Experimental results demonstrated that the fuzzy multiple heuristic orderings (with parameter tuning) outperformed all of the single heuristic orderings and non-fuzzy linear weighting factors. Comprehensive analysis has provided some key insights regarding the implementation of multiple heuristic orderings. Producing examination timetables automatically has been the subject of much research. It is generally the case that a number of alternative solutions that satisfy all the hard criteria are possible. Indeed, there are usually a very large number of such feasible solutions. Some method is required to permit the overall quality of different solutions to be quantified, in order to allow them to be compared, so that the best may be selected. In response to that demand, the second area of investigation of this thesis is concerned with a new evaluation function for examination timetabling problems. A novel approach, in which fuzzy methods are used to evaluate the end solution quality, separate from the objective functions used in solution generation, represents a significant addition to the literature. The proposed fuzzy evaluation function provides a mechanism to allow an overall decision in evaluating the quality of a timetable solution to be made based on common sense rules that encapsulate the notion that the timetable solution quality increases as both the average penalty and the highest penalty decrease. New algorithms to calculate what is loosely termed the lower limits and upper limits of the proximity cost function for any problem instance are also presented. These limits may be used to provide a good indication of how good any timetable solution is. Furthermore, there may be an association between the proposed lower limit and the formal lower bound. This is the first time that lower limits (other than zero) have been established for proximity cost evaluation of timetable solutions

    A domain transformation approach for addressing staff scheduling problems

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    Staff scheduling is a complex combinatorial optimisation problem concerning allocation of staff to duty rosters in a wide range of industries and settings. This thesis presents a novel approach to solving staff scheduling problems, and in particular nurse scheduling, by simplifying the problem space through information granulation. The complexity of the problem is due to a large solution space and the many constraints that need to be satisfied. Published research indicates that methods based on random searches of the solution space did not produce good-quality results consistently. In this study, we have avoided random searching and proposed a systematic hierarchical method of granulation of the problem domain through pre-processing of constraints. The approach is general and can be applied to a wide range of staff scheduling problems. The novel approach proposed here involves a simplification of the original problem by a judicious grouping of shift types and a grouping of individual shifts into weekly sequences. The schedule construction is done systematically, while assuring its feasibility and minimising the cost of the solution in the reduced problem space of weekly sequences. Subsequently, the schedules from the reduced problem space are translated into the original problem space by taking into account the constraints that could not be represented in the reduced space. This two-stage approach to solving the scheduling problem is referred to here as a domain-transformation approach. The thesis reports computational results on both standard benchmark problems and a specific scheduling problem from Kajang Hospital in Malaysia. The results confirm that the proposed method delivers high-quality results consistently and is computationally efficient
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