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

Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem

We consider the university course timetabling problem, which is one of the most studied problems in educational timetabling. In particular, we focus our attention on the formulation known as the curriculum-based course timetabling problem, which has been tackled by many researchers and for which there are many available benchmarks. The contribution of this paper is twofold. First, we propose an effective and robust single-stage simulated annealing method for solving the problem. Secondly, we design and apply an extensive and statistically-principled methodology for the parameter tuning procedure. The outcome of this analysis is a methodology for modeling the relationship between search method parameters and instance features that allows us to set the parameters for unseen instances on the basis of a simple inspection of the instance itself. Using this methodology, our algorithm, despite its apparent simplicity, has been able to achieve high quality results on a set of popular benchmarks. A final contribution of the paper is a novel set of real-world instances, which could be used as a benchmark for future comparison

Local search: A guide for the information retrieval practitioner

There are a number of combinatorial optimisation problems in information retrieval in which the use of local search methods are worthwhile. The purpose of this paper is to show how local search can be used to solve some well known tasks in information retrieval (IR), how previous research in the field is piecemeal, bereft of a structure and methodologically flawed, and to suggest more rigorous ways of applying local search methods to solve IR problems. We provide a query based taxonomy for analysing the use of local search in IR tasks and an overview of issues such as fitness functions, statistical significance and test collections when conducting experiments on combinatorial optimisation problems. The paper gives a guide on the pitfalls and problems for IR practitioners who wish to use local search to solve their research issues, and gives practical advice on the use of such methods. The query based taxonomy is a novel structure which can be used by the IR practitioner in order to examine the use of local search in IR

Enhanced genetic algorithm-based fuzzy multiobjective strategy to multiproduct batch plant design

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessary involves how equipment may be utilized, which means that plant scheduling and production must constitute a basic part of the design problem. Rather than resorting to a traditional probabilistic approach for modeling the imprecision on product demands, this work proposes an alternative treatment by using fuzzy concepts. The design problem is tackled by introducing a new approach based on a multiobjective genetic algorithm, combined wit the fuzzy set theory for computing the objectives as fuzzy quantities. The problem takes into account simultaneous maximization of the fuzzy net present value and of two other performance criteria, i.e. the production delay/advance and a flexibility index. The delay/advance objective is computed by comparing the fuzzy production time for the products to a given fuzzy time horizon, and the flexibility index represents the additional fuzzy production that the plant would be able to produce. The multiobjective optimization provides the Pareto's front which is a set of scenarios that are helpful for guiding the decision's maker in its final choices. About the solution procedure, a genetic algorithm was implemented since it is particularly well-suited to take into account the arithmetic of fuzzy numbers. Furthermore because a genetic algorithm is working on populations of potential solutions, this type of procedure is well adapted for multiobjective optimization

Two Phase Heuristic Algorithm for the University Course Timetabling Problem: The Case of University of Dar Es Salaam

University course timetabling is the problem of scheduling resources such as lecturers, courses, and rooms to a number of timeslots over a planning horizon, normally a week, while satisfying a number of problem-specific constraints. Since timetabling problems differ from one institution to another, this paper investigated the case of the University of Dar Es salaam, based on the combination of Simulated Annealing (SA), and steepest descent in a two-phase approach. Solutions have been generated which greatly outperform the manually generated ones. Furthermore, the method compares well with previous work on Tabu Search but with faster execution time and higher quality on rooms allocation. It is concluded that the approach gives good results given a careful selection of parameters.Keywords: Timetabling Problem, Simulated Annealing, Combinatorial Optimization, Steepest DescentTanz. J. Sci. Vol. 37 201

Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management

We present the mapping of a class of simplified air traffic management (ATM) problems (strategic conflict resolution) to quadratic unconstrained boolean optimization (QUBO) problems. The mapping is performed through an original representation of the conflict-resolution problem in terms of a conflict graph, where nodes of the graph represent flights and edges represent a potential conflict between flights. The representation allows a natural decomposition of a real world instance related to wind-optimal trajectories over the Atlantic ocean into smaller subproblems, that can be discretized and are amenable to be programmed in quantum annealers. In the study, we tested the new programming techniques and we benchmark the hardness of the instances using both classical solvers and the D-Wave 2X and D-Wave 2000Q quantum chip. The preliminary results show that for reasonable modeling choices the most challenging subproblems which are programmable in the current devices are solved to optimality with 99% of probability within a second of annealing time.Comment: Paper accepted for publication on: IEEE Transactions on Intelligent Transportation System

An application of Soft System Methodology

AbstractThe typical course timetabling problem is assigning Classes of students to appropriate faculty members, suitable classrooms and available timeslots. Hence, it involves a large number of stakeholders including students, teachers and institutional administrators. Different kinds of Hard Operational Research techniques have been employed over the years to address such problems. Due to the computational difficulties of this NP complete problem as well as the size and the complexity of the real world instances, an efficient optimal solution cannot be found easily.As an alternative strategy, this paper investigates the application of Checkland‘s Soft System Methodology (SSM) to the course timetabling problem. Besides giving an ideal course timetable, even to large and complex real problems, application of SSM, generates debate, learning, and understanding; enables key changes; facilitates negotiating the actions to be taken and makes possible the meaningful collaboration among concerned stakeholders. This paper also provides an appropriate course timetable for the management faculty at University of Tehran to show the potential of this application to real problems