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

Optimizing the location of weather monitoring stations using estimation uncertainty

In this article, we address the problem of planning a network of weather monitoring stations observing average air temperature (AAT). Assuming the network planning scenario as a location problem, an optimization model and an operative methodology are proposed. The model uses the geostatistical uncertainty of estimation and the indicator formalism to consider in the location process a variable demand surface, depending on the spatial arrangement of the stations. This surface is also used to express a spatial representativeness value for each element in the network. It is then possible to locate such a network using optimization techniques, such as the used methods of simulated annealing (SA) and construction heuristics. This new approach was applied in the optimization of the Portuguese network of weather stations monitoring the AAT variable. In this case study, scenarios of reduction in the number of stations were generated and analysed: the uncertainty of estimation was computed, interpreted and applied to model the varying demand surface that is used in the optimization process. Along with the determination of spatial representativeness value of individual stations, SA was used to detect redundancies on the existing network and establish the base for its expansion. Using a greedy algorithm, a new network for monitoring average temperature in the selected study area is proposed and its effectiveness is compared with the current distribution of stations. For this proposed network distribution maps of the uncertainty of estimation and the temperature distribution were created. Copyright (c) 2011 Royal Meteorological Societyinfo:eu-repo/semantics/publishedVersio

Heuristic Optimisation in Financial Modelling

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well- behaved’ in other ways (eg, discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. This paper argues that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable to handle non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, the paper presents several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, the paper describes in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. It is shown, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.Optimisation heuristics, Financial Optimisation, Portfolio Optimisation

State of the Art in the Optimisation of Wind Turbine Performance Using CFD

Wind energy has received increasing attention in recent years due to its sustainability and geographically wide availability. The efficiency of wind energy utilisation highly depends on the performance of wind turbines, which convert the kinetic energy in wind into electrical energy. In order to optimise wind turbine performance and reduce the cost of next-generation wind turbines, it is crucial to have a view of the state of the art in the key aspects on the performance optimisation of wind turbines using Computational Fluid Dynamics (CFD), which has attracted enormous interest in the development of next-generation wind turbines in recent years. This paper presents a comprehensive review of the state-of-the-art progress on optimisation of wind turbine performance using CFD, reviewing the objective functions to judge the performance of wind turbine, CFD approaches applied in the simulation of wind turbines and optimisation algorithms for wind turbine performance. This paper has been written for both researchers new to this research area by summarising underlying theory whilst presenting a comprehensive review on the up-to-date studies, and experts in the field of study by collecting a comprehensive list of related references where the details of computational methods that have been employed lately can be obtained

A review of portfolio planning: Models and systems

In this chapter, we first provide an overview of a number of portfolio planning models which have been proposed and investigated over the last forty years. We revisit the mean-variance (M-V) model of Markowitz and the construction of the risk-return efficient frontier. A piecewise linear approximation of the problem through a reformulation involving diagonalisation of the quadratic form into a variable separable function is also considered. A few other models, such as, the Mean Absolute Deviation (MAD), the Weighted Goal Programming (WGP) and the Minimax (MM) model which use alternative metrics for risk are also introduced, compared and contrasted. Recently asymmetric measures of risk have gained in importance; we consider a generic representation and a number of alternative symmetric and asymmetric measures of risk which find use in the evaluation of portfolios. There are a number of modelling and computational considerations which have been introduced into practical portfolio planning problems. These include: (a) buy-in thresholds for assets, (b) restriction on the number of assets (cardinality constraints), (c) transaction roundlot restrictions. Practical portfolio models may also include (d) dedication of cashflow streams, and, (e) immunization which involves duration matching and convexity constraints. The modelling issues in respect of these features are discussed. Many of these features lead to discrete restrictions involving zero-one and general integer variables which make the resulting model a quadratic mixed-integer programming model (QMIP). The QMIP is a NP-hard problem; the algorithms and solution methods for this class of problems are also discussed. The issues of preparing the analytic data (financial datamarts) for this family of portfolio planning problems are examined. We finally present computational results which provide some indication of the state-of-the-art in the solution of portfolio optimisation problems

The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem

Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations. --Heuristic optimization,Threshold Accepting,Stochastic analysis of heuristics