Operational Research in Education

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

DEM Timetabling Project ? Development/implementation of an algorithm to support the creation of timetables

This work presents the development of an algorithm to support the process of creating academic timetables, specifically aimed at solving the University Course Timetabling Problem. To date, this problem is solved manually in Instituto Superior de Engenharia do Porto, where professors and engineers face the complex task of creating timetables based on schedules from previous years. The proposed solution aimed to support the process of creating timetables at ISEP, reducing the time and human resources required for this task. The developed algorithm uses an integer programming approach and can consider a variety of constraints and preferences of both faculty and students. It was designed to adapt and optimize the timetable creation process as needs evolve, ensuring future demands can be easily accommodated. The algorithm implementation was based on the Python programming language and the Pyomo library, offering a flexible and efficient approach to optimizing resource allocation. Additionally, the system is designed to import data from real-world sources, simplifying the integration of crucial information. The result assigned all the 128 one-hour classes among the week, presenting the faculty member, the classroom assigned and the type of class according to each course. This research presents feasible solutions that need improvement on the demanding conditions and restrictions imposed by ISEP. The computational results obtained offered a significantly decrease in the time resource used, compared to the manual work previously done

Genetic Algorithm For University Course Timetabling Problem

Creating timetables for institutes which deal with transport, sport, workforce, courses, examination schedules, and healthcare scheduling is a complex problem. It is difficult and time consuming to solve due to many constraints. Depending on whether the constraints are essential or desirable they are categorized as ‘hard’ and ‘soft’, respectively. Two types of timetables, namely, course and examination are designed for academic institutes. A feasible course timetable could be described as a plan for the movement of students and staff from one classroom to another, without conflicts. Being an NP-complete problem, many attempts have been made using varying computational methods to obtain optimal solutions to the timetabling problem. Genetic algorithms, based on Darwin\u27s theory of evolution is one such method. The aim of this study is to optimize a general university course scheduling process based on genetic algorithms using some defined constraints

Aspects of computerised timetabling

This research considers the problem of constructing high school timetables using a computer. In the majority of high schools, termly or yearly timetables are still being produced manually. Constructing a timetable is a hard and time consuming task which is carried out repeatedly thus a computer program for assisting with this problem would be of great value. This study is in three parts. First. an overall analysis of the problem is undertaken to provide background knowledge and to identify basic principles in the construction of a school timetable. The characteristics of timetabling problems are identified and the necessary data for the construction of a timetable is identified. The first part ends with the production of a heuristic model for generating an initial solution that satisfies all the hard constraints embodied in the curriculum requirements. The second stage of the research is devoted to designing a heuristic model for solving a timetable problem with hard and medium constraints. These include constraints like the various numbers of common periods, double periods and reducing the repeated allocation of a subject within any day. The approaches taken are based on two recently developed techniques, namely tabu search and simulated annealing. Both of these are used and comparisons of their efficiency are provided. The comparison is based on the percentage fulfilment of the hard and medium requirements. The third part is devoted to one of the most difficult areas in timetable construction, that is the softer requirements which are specific to particular schools and whose satisfaction is not seen as essential. This section describes the development of an expert system based on heuristic production rules to satisfy a range of soft requirements. The soft requirements are studied and recorded as rules and a heuristic solution is produced for each of the general requirements. Different levels of rule are developed, from which the best possible solution to a particular timetable problem is expertly produced. Finally, possible extensions of the proposed method and its application to other types of the timetabling problem are discussed

Term-End Exam Scheduling at United States Military Academy/West Point

Scheduling term-end exams (TEE) at the United States Military Academy in West Point is unlike any other exam timetabling problem we know of. Exam timetabling normally produces a conflict-free timetable covering a reasonably long exam period, where every exam is scheduled exactly once for all the students enrolled in the corresponding class. The situation is quite different at West Point. There are hundreds of exams to schedule over such a short time period that there is simply no feasible solution. The challenge is then to allow something that is not even considered elsewhere, that is, creating multiple sessions of some exams, scheduled at different times within the exam period, to allow each student to take all exams he/she must take. The overall objective is to find a feasible exam schedule with a minimum number of such duplicate exams. The paper describes a system that has been developed at GAMS Development Corp. in close cooperation with the scheduling staff at West Point, and that has been used successfully since 2001. It uses mathematical optimization in several modules, and some of the techniques proposed are new. It is fast and flexible, and allows for human interaction, such as adding initially unexpected constraints, coming for instance from instructors’ preferences and dislikes, as well as their hierarchical rankings. It is robust and can be used by people familiar with the organization at West Point, without the need for them to be technically-trained. Overall, using the course and student information databases, it is an effective decision support system that calls optimization tools in an unobtrusive way

Hybrid genetic algorithm for university examination timetabling problem

This paper considers a Hybrid Genetic Algorithm (HGA) for University Examination Timetabling Problem (UETP). UETP is defined as the assignment of a given number of exams and their candidates to a number of available timeslots while satisfying a given set of constraints. Solutions for uncapacitated UETP are presented where five domain-specific knowledge in the form of low-level heuristics are used to guide the construction of the timetable in the initial population. The main components of the genetic operators in a GA will be tested and the best combination of the genetic operators will be adopted to construct a Pure Genetic Algorithm (PGA). The PGA will then hybridised with three new local optimisation techniques, which will make up the HGA; to improve the solutions found. These new local optimisation techniques will arrange the timeslots and exams using new explicit equations, if and only if, the modification will reduce the penalty cost function. The performance of the proposed HGA is compared with other metaheuristics from literature using the Carter’s benchmark dataset which comprises of real-world timetabling problem from various universities. The computational results show that the proposed HGA outperformed some of the metaheuristic approaches and is comparable to most of the well-known metaheuristic approaches

Examination timetabling automation using hybrid meta-heuristics

Trabalho de projeto realizado para obtenção do grau de Mestre em Engenharia Informática e de ComputadoresNos últimos anos, o tema da geração automática de horários tem sido alvo de muito estudo. Em muitas instituições, a elaboração de horários ainda é feita manualmente, constituindo-se uma tarefa demorada e penosa para instâncias de grande dimensão. Outro problema recorrente na abordagem manual é a existência de falhas dada a dificuldade do processo de verificação, e também a qualidade final do horário produzido. Se este fosse criado por computador, o horário seria válido e seriam de esperar horários com qualidade superior dada a capacidade do computador para pesquisar o espaço de soluções. A elaboração de horários não é uma tarefa fácil, mesmo para uma máquina. Por exemplo, horários escolares necessitam de seguir certas regras para que seja possível a criação de um horário válido. Mas como o espaço de estados (soluções) válidas é tão vasto, é impraticável criar um algoritmo que faça a enumeração completa de soluções a fim de escolher a melhor solução possível. Por outro lado, a utilização de algoritmos que realizam a enumeração implícita de soluções (por exemplo, branch and bound), não é viável para problemas de grande dimensão. A utilização de heurísticas que percorrem de uma forma guiada o espaço de estados, conseguindo assim uma solução razoável em tempo útil, constituem uma abordagem adequada para este tipo de problemas. Um dos objetivos do projeto consiste na criação duma abordagem que siga as regras do International Timetabling Competition (ITC) 2007 incidindo na criação de horários de exames em universidades (Examination timetabling track). Este projeto utiliza uma abordagem de heurísticas híbridas. Isto significa que utiliza múltiplas heurísticas para obter a melhor solução possível. Utiliza uma variação da heurística de Graph Coloring para obter uma solução válida e as meta-heurísticas Simulated Annealing e Hill Climbing para melhorar a solução obtida. Os resultados finais são satisfatórios, pois em algumas instâncias os resultados são melhores do que alguns dos cinco finalistas do concurso ITC 2007.Abstract: In the last few years the automatic creation of timetables is being a well-studied subject. In many institutions, the elaboration of timetables is still manual, thus being a time-consuming and difficulty task for large instances. Another current problem in the manual approach is the existence of failures given the difficulty in the process verification, and so the quality of the produced timetable. If this timetable had been created by a computer, the timetable would be valid and timetables with better quality should be obtained, given the computer’s capacity to search the solution space. It is not easy to elaborate timetables, even for a machine. For example, scholar/university timetables need to follow certain type of constraints or rules for them to be considered valid. But since the solution space is so vast, it is highly unlikely to create an algorithm that completely enumerates the solutions in order to choose the best solution possible, considering the problem structure. The use of algorithms that perform implicit enumeration solutions (for example, an branch bound), is not feasible for large problems. Hence the use of heuristics which navigate through the solution space in a guided way, obtaining then a reasonable solution in acceptable time. One main objective of this project consists in creating an approach that follows the International Timetabling Competition (ITC) 2007 rules, focusing on creating examination timetables. This project will use a hybrid approach. This means it will use an approach that includes multiple heuristics in order to find the best possible solution. This approach uses a variant of the Graph Coloring heuristic to find an initial valid solution, and the metaheuristics Simulated Annealing and Hill Climbing to improve that solution. The final results are satisfactory, as in some instances the obtained results beat the results of some of the five finalists from ITC 2007