Integer programming techniques for educational timetabling

Educational timetabling problems require the assignment of times and resources to events, while sets of required and desirable constraints must be considered. The XHSTT format was adopted in this work because it models the main features of educational timetabling and it is the most used format in recent studies in the field. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed cuts improved hugely the linear relaxation of the formulation, leading to an average gap reduction of 32%. Applied to XHSTT-2014 instance set, the alternative formulation pro- vided four new best known lower bounds and, used in a matheuristic framework, improved eleven best known solutions. The computational experiments also show that the resulting integer programming mod- els from the proposed formulation are more effectively solved for most of the instances

Model Zero-One Linear Programming untuk Penjadwalan Raw Mill dan Cement Mill

The scheduling of electrical energy usage during Peak Load Period (PLP) is a complicated problem that has been faced by PT Semen Padang after Indonesian Power Company (PLN) implemented the demarcation regulation of electrical energy usage during PLP (6:00 – 10:00 p.m.) which may not exceed 44.100 kWH. This regulation forces Production Department of PT Semen Padang to arrange the “on (1) or off (0)” schedule for the Raw Mills and Cement Mills during PLP. A Raw Mill or Cement Mill can be switched-off if the specified criteria are satisfied. Those criteria refer to the achievement of daily production targets, silo content at PLP, and the requirement for particular Raw Mill or Cement Mill to be off during those 4 hours of PLP. Meanwhile, the constraints are related to the length of machining hours of Raw Mill, Kiln or Cement Mill before preventive maintenance takes place. To solve this problem, a scheduling model for Raw Mills and Cement Mills on-off during PLP is then developed using a linear programming approach. The decision variables are the “on-off” state of Raw Mills and Cement Mills during PLP, while the objective function is to minimize the penalty expense of energy used during PLP. The developed scheduling model has the ability to solve the problem of the “on-off” assignment for Raw Mills and Cement Mills from Indarung II to Indarung V. This scheduling model can decrease the penalty of electrical energy expense during PLP from Rp. 3.07 billion to Rp. 1.79 billion

Optimal Decision Trees for the Algorithm Selection Problem: Integer Programming Based Approaches

Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic configuration based on aggregate results such as the average. In this paper, we propose Integer Programming based approaches to build decision trees for the Algorithm Selection Problem. These techniques allow automate three crucial decisions: (i) discerning the most important problem features to determine problem classes; (ii) grouping the problems into classes and (iii) select the best algorithm configuration for each class. To evaluate this new approach, extensive computational experiments were executed using the linear programming algorithms implemented in the COIN-OR Branch & Cut solver across a comprehensive set of instances, including all MIPLIB benchmark instances. The results exceeded our expectations. While selecting the single best parameter setting across all instances decreased the total running time by 22%, our approach decreased the total running time by 40% on average across 10-fold cross validation experiments. These results indicate that our method generalizes quite well and does not overfit.Comment: International Transactions in Operational Research. 201

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

Reatribuição de salas em horários escolares no ISEG

Mestrado em Métodos Quantitativos para a Decisão Económica e EmpresarialO presente trabalho tem como objetivo colmatar a necessidade de otimizar os horários dos alunos de licenciatura do ISEG, para que estes realizem o mínimo de deslocações de salas no mesmo dia. Assim, o desafio proposto consiste em resolver este problema utilizando o conhecimento adquirido ao longo do mestrado. Apesar de a Secretaria das Licenciaturas utilizar um programa para a elaboração dos horários das licenciaturas, o Bullet Education Scheduling and Timetabling, este não otimiza as deslocações dos alunos da mesma turma entre as várias salas de aula. Espera-se que a implementação computacional desenvolvida no âmbito do presente TFM auxilie a Secretaria das Licenciaturas na elaboração dos horários. Desta forma, a secretaria não necessitará de despender tempo a fazer alterações de salas, processo esse que atualmente é feito manualmente. Assim, será facilitado não só o trabalho da secretaria, como melhorado o dia-a-dia dos alunos e também o dos funcionários desta instituição. Através do Excel e de programação em VBA procede-se à leitura dos dados fornecidos pela Secretaria das Licenciaturas. Após a leitura dos dados, é aplicada uma Heurística de Trocas sobre os mesmos que permite a criação de horários de melhor qualidade, no que a deslocações dos alunos das várias licenciaturas do ISEG diz respeito. Assim, após a aplicação da heurística, obtêm-se alterações em 14 dos 79 horários analisados, sendo que o tempo de execução do programa comparado com o processo manual é relativamente baixo, demorando menos de cinco minutos.This work aims at filling the need of optimize the timetables of ISEG?s bachelor students, so that students make less movements from room to room on the same day. Therefore, the challenge that was proposed to me consists in solving this issue using the knowledge acquired during the master. Although the bachelors' secretariat uses a program for the preparation of undergraduate timetables, the Bullet Education Scheduling and Timetabling (BEST), it does not optimize the movement of students of the same class between their successive classrooms. It is expected that the computational implementation developed in the scope of the present masters degree work will assist the secretariat in the preparation of the schedules. As a result, the secretariat will not need to spend time making room changes, a process that is currently done manually. Not only the work of the bachelor's degree secretariat, but also the day-to-day work of the students, staff and teachers of this institution will be improved. Through Excel and VBA programming, the data provided by the bachelor's degree secretariat is read. After reading the data, a heuristic is applied to produce timetables of better quality, regarding the movements of the undergraduate students of ISEG. After the application of the heuristic, we obtain changes in 14 of the 79 timetables analyzed, and the execution time of the program is significantly low, comparing with the manual process, taking less than five minutes.info:eu-repo/semantics/publishedVersio