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

Planning, Scheduling, and Timetabling in a University Setting

Methods and procedures for modeling university student populations, predicting course enrollment, allocating course seats, and timetabling final examinations are studied and proposed. The university enrollment model presented uses a multi-dimensional state space based on student demographics and the Markov property, rather than longitudinal data to model student movement. The procedure for creating adaptive course prediction models uses student characteristics to identify groups of undergraduates whose specific course enrollment rates are significantly different than the rest of the university population. Historical enrollment rates and current semester information complete the model for predicting enrollment for the coming semester. The course prediction model aids in the system for reserving course seats for new students during summer registration sessions. The seat release model addresses how to estimate seat need each session, how to release seats among multiple course sections, and how to predict seat shortages and surpluses. Finally, procedures for creating reusable university final examination timetables are developed and compared. Course times, rather than individual courses, are used as the assignment elements because the demand for course times remains relatively constant despite changes in course schedules. Our heuristic procedures split the problem into two phases: a clustering phase--to minimize conflicts--and a sequencing phase--to distribute exams throughout finals week while minimizing the occurrence of consecutive exams. Results for all methods are compared using enrollment data from Clemson University

A mathematical programming tool for an efficient decision-making on teaching assignment under non-regular time schedules

[EN] In this paper, an optimization tool based on a MILP model to support the teaching assignment process is proposed. It considers not only hierarchical issues among lecturers but also their preferences to teach a particular subject, the non-regular time schedules throughout the academic year, different type of credits, number of groups and other specific characteristics. Besides, it adds restrictions based on the time compatibility among the different subjects, the lecturers' availability, the maximum number of subjects per lecturer, the maximum number of lecturers per subject as well as the maximum and minimum saturation level for each lecturer, all of them in order to increase the teaching quality. Schedules heterogeneity and other features regarding the operation of some universities justify the usefulness of this model since no study that deals with all of them has been found in the literature review. Model validation has been performed with two real data sets collected from one academic year schedule at the Spanish University Universitat Politecnica de Valencia.Solano Cutillas, P.; Pérez Perales, D.; Alemany Díaz, MDM. (2022). A mathematical programming tool for an efficient decision-making on teaching assignment under non-regular time schedules. Operational Research. 22(3):2899-2942. https://doi.org/10.1007/s12351-021-00638-12899294222

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

Grammatical evolution hyper-heuristic for combinatorial optimization problems

Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves templates of perturbation heuristics. The evolved templates are improvement heuristics, which represent a complete search method to solve the problem at hand. To test the generality and the performance of the proposed method, we consider two well-known combinatorial optimization problems: exam timetabling (Carter and ITC 2007 instances) and the capacitated vehicle routing problem (Christofides and Golden instances). We demonstrate that the proposed method is competitive, if not superior, when compared to state-of-the-art hyper-heuristics, as well as bespoke methods for these different problem domains. In order to further improve the performance of the proposed framework we utilize an adaptive memory mechanism, which contains a collection of both high quality and diverse solutions and is updated during the problem solving process. Experimental results show that the grammatical evolution hyper-heuristic, with an adaptive memory, performs better than the grammatical evolution hyper-heuristic without a memory. The improved framework also outperforms some bespoke methodologies, which have reported best known results for some instances in both problem domains

Decision support tool for Operations Management course and instructor scheduling

The goal of this project is develop a decision support tool that will assist the Operations Management Department at the University of Arkansas with scheduling courses and instructors for the upcoming academic year. The staff of the department dreads this time each year because it takes countless hours to complete the daunting task. Creating an abstract mathematical model will assist the department in scheduling the courses. The model will have the ability to optimize the schedule of the courses and instructors from a large number of variables and constraints that the department requires. An optimization software package can solve the problem based on the data for the upcoming year. The staff will be able to use a decision support tool to input the relevant data with ease, and run the optimization software package with little knowledge of how mathematical models work. The focus of this project will be creating an abstract class-scheduling mathematical model that will be easily solved through the creation of a decision support tool. The tool will optimize the schedule, and save the staff precious time that could be spent elsewhere

A Set Union Based Formulation for Course Scheduling and Timetabling

The Course Timetabling Problem is a widely studied optimization problem where a number of sections are scheduled in concert with the assignment of students to sections in order to maximize the desirability of the resulting schedule for all stakeholders. This problem is commonly solved as a linear program with variables for each student or group of students with identical schedules. In this paper we explore an alternative formulation that aggregates binary student variables into integer variables denoting the number of students enrolled in a course. Our solution method assumes decomposition of the general schedule into time blocks, and applies a unique set theory based, integer linear programming formulation that seeks to maximize the total number of students enrolled in their desired sections across the time blocks. Once the problem has been solved, the simpler problem of disaggregating the solution is resolved. This approach can be used to find exact solutions, given sufficient computing power, or simplified to quickly find solutions within calculable bounds of optimality. Case studies with a local elementary school and a local high school show that the new formulation is significantly faster and can be made to be reasonably accurate