A MILP model for the teacher assignment problem considering teachers’ preferences

The Teacher Assignment Problem is part of the University Timetabling Problem and involves assigning teachers to courses, taking their preferences into consideration. This is a complex problem, usually solved by means of heuristic algorithms. In this paper a Mixed Integer Linear Programing model is developed to balance teachers’ teaching load (first optimization criterion), while maximizing teachers’ preferences for courses according to their category (second optimization criterion). The model is used to solve the teachers-courses assignment in the Department of Management at the School of Industrial Engineering of Barcelona, in the Universitat Politècnica de Catalunya. Results are discussed regarding the importance given to the optimization criteria. Moreover, to test the model's performance a computational experiment is carried out using randomly generated instances based on real patterns. Results show that the model is proven to be suitable for many situations (number of teachers-courses and weight of the criteria), being useful for departments with similar requests.Peer ReviewedPostprint (author's final draft

Solving an application of university course timetabling problem by using genetic algorithm

Generating timetables for academic institutions is a complex problem. This is due to many constraints involved whether they are vital or desirable, which are known as hard and soft constraints. The problem becomes more complicated and difficult to solve as the number of courses increase. Moreover, generating manual timetables is challenging and time-consuming, particularly to meet lecturers’ preferences. Thus, it is crucial to establish an automated course timetable system. Many efforts have been made using various computational heuristic methods to acquire the best solutions. Among the approaches, genetic algorithm (GA), constructed based on Darwin's theory of evolution, becomes the renowned approach to solve various types of timetabling problems. Therefore, this study produces the best timetable using GA to solve clashed courses, optimize room utilization and maximize lecturers’ preferences. Data of 41 course sections from 17 courses offered in semester A172 were taken from Decision Science Department, School of Quantitative Sciences (SQS). The phases in GA involves a number of main operators which are population initialization, crossover and mutation. The best parameter setting for GA was determined through combination of different mutation rate, population and iteration. The simulation results of GA show that this method is able to produce the best fitness value that satisfied all hard and soft constraints. There are no clashes either between lecturers or lecture rooms, and lecturers’ preferences were satisfied. The system can help SQS or any other academic schools or institutions to easily develop course timetabling in the coming semesters

Essays in Market Design:

Thesis advisor: Utku UnverThesis advisor: Bumin YenmezThis dissertation consists of two chapters. Both are centered around the theory and design of markets, in which the use of money is prohibited and/or strongly undesirable. In my first chapter, I study multi-object assignment problems. Here, the assignment of graduate students to teaching assistant positions over the course of two semesters, serves as an illustrative application. In my second chapter, I propose an alternative way to distribute asylum seekers among European member states based on the preferences of both sides. Chapter 1: Multi-Object Assignment: Booster Draft In my first chapter, I ask the question of how to divide among a set of n individuals a set of n × m indivisible objects without using monetary transfers, in a way that is efficient, incentive compatible, and ex-post fair. A well known impossibility result shows that the only mechanisms that are both incentive compatible and efficient are dictatorship mechanisms. I fill a gap in the literature by describing a novel mechanism that is both incentive compatible and fair in the responsive preference domain. The mechanism is inspired by booster drafts used in competitive card game tournaments. The idea is to arbitrarily divide the set n × m objects into m \boosters" (sets) of size n and specify a priority order for each such booster. Afterwards the individuals pick objects from the boosters in order of priority. The outcome of the booster draft mechanism can be improved if additional knowledge about a particular market is incorporated into the creation of boosters. I point out a special case of multi-object assignment problems, motivated by the allocation of teaching assignments among graduate students. In this domain the creation of the boosters is straightforward. Indeed, at the Boston College economics department, graduate students are assigned exactly one fall and one spring semester task over the academic year. Here the optimal way of creating boosters is to group up all spring teaching assignments in one booster and all fall semester assignments in the other. In this case the balanced booster draft is not only strategyproof and fair, but also weakly efficient (dominance efficient). Moreover, for this restricted assignment domain I characterize the set of all booster drafts as any (strongly) strategyproof, neutral and non-bossy mechanism. In the final part of the paper I take a closer look at the teaching assistant assignment problem, using date on the submitted rankings over semester-tasks by graduate students. The simulation exercise provides additional evidence that the proposed mechanism is a sensible practical solution. In particular, I show that for a simple measure of welfare students prefer a balanced booster draft to a serial dictatorship mechanism if they are mildly risk averse. Chapter 2: An Alternative Asylum Assignment The 2015 refugee crisis has demonstrated the necessity of revising the current European asylum system. As an alternative, I propose to take into account preferences of asylum seekers as well as preferences of member states. Asylum seekers indicate how long they are willing to wait for their asylum application for any given member state, allowing them to avoid overburdened member states by opting for \less popular" member states. Within the market design literature, this is the first paper proposing to match asylum seekers as opposed to refugees. In other words, its stays much closer to the template of the Common European Asylum System. From a theoretical perspective, it turns out that the asylum seeker framework can be formulated as an application of the well-known matching with contracts model by Hatfield and Milgrom (2005a). This simplifies the analysis a great deal, as matching with contracts is a well studied framework within the matching/market design literature. I show that the standard cumulative offer mechanism (Gale and Shapley, 1962a; Hatfield and Kojima, 2010a) is asylum seeker incentive compatible and leads to stable outcomes, using the fact that the proposed choice functions have a completion satisfying substitutability and the law of aggregate demand Hatfield and Kominers (2016). Moreover, stability implies two sided Pareto efficiency, giving consideration to both preferences of member states and asylum seekers.Thesis (PhD) — Boston College, 2020.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Economics

The Application of Genetic Algorithm in Teaching Assignment Problem

Genetic Algorithm is a search and optimization technique that is based on the principle of natural selection. In this thesis, a genetic algorithm is used to solve the teacher assignment problem. The result shows that the genetic algorithm is an efficient method to solve teacher assignment problem