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

Families of Linear Efficiency Programs based on Debreu's Loss Function

Gerard Debreu introduced a well known radial efficiency measure which he called a “coefficient of resource utilization.†He derived this scalar from a much less well known “dead loss†function that characterizes the monetary value sacrificed to inefficiency, and which is to be minimized subject to a normalization condition. We use Debreu’s loss function, together with a variety of normalization conditions, to generate several popular families of linear efficiency programs. Our methodology also can be employed to generate entirely new families of linear efficiency programs.

Extended Topics in the Integration of Data Envelopment Analysis and the Analytic Hierarchy Process in Decision Making.

The Analytic Hierarchy Process (AHP) is a procedure, which can only consider relative priorities as estimated by decision-makers. A Data Envelopment Analysis (DEA) model is a data-oriented approach for evaluating the relative efficiency of a group of entities referred to as Decision Making Units (DMUs). This research work integrates and combines positive aspects of AHP\u27s estimated qualitative data and DEA\u27s quantitative data. This combination is accomplished by specifying two variants of the DEA methodology for selection of the best DMU. Initially the priority weights of AHP are integrated with the DEA methodology to provide results that are logic based. Next, a method is developed to work backwards through the DEA model to provide values that would be the required results from an AHP formulation to give the same result in DEA. The objective of the research is to propose variants of DEA that would possibly improve the results and also integrate subjective data. Through the application of the methods developed in this research, it is believed that the acceptability of the results obtained from DEA analysis can be improved

Allocating the fixed cost:an approach based on data envelopment analysis and cooperative game

Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res 235(1): 206–214, 2014) proposed a novel approach for allocating the fixed cost based on the game cross-efficiency method by taking the game relations among users in efficiency evaluation. This paper proves that the novel approach of Du et al. (Eur J Oper Res 235(1): 206–214, 2014) is equivalent to the efficiency maximization approach of Li et al. (Omega 41(1): 55–60, 2013), and may exist multiple optimal cost allocation plans. Taking into account the game relations in the allocation process, this paper proposes a cooperative game approach, and uses the nucleolus as a solution to the proposed cooperative game. The proposed approach in this paper is illustrated with a dataset from the prior literature and a real dataset of a steel and iron enterprise in China

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Efficiency in Bulgaria's schools : a nonparametric study

In Eastern European countries in large social sectors such as education, inefficiency and technical deficiencies are the legacy of the old command economy. The authors examine the technical efficiency of classroom use (defined as the number of classes per classroom in one transitional economy -- Bulgaria. They examine the concept of efficiency in 199 urban and rural municipalities, using data envelopment analysis to generate efficiency scores. Those scores -- discussed in terms of frequency and regional distribution -- are then regressed on several socioeconomic variables. The researchers find significant relationships between the efficiency scores, on the one hand, and, on the other, the proportion of students in the population under age 20 (demand indicator), the number of teachers (variable input), the percentage of the municipal budget spent on education, and the degree of urbanization. Efficiency in the use of classrooms (in terms of classes) varies considerably among municipalities, and the efficiency is highest in the capital city of Sofia. To the extent that some variation in efficiency reflects demand or demographic factos, there is little that policy can do to change the pattern. But some changes in municipal policy could increase the efficiency of classroom use without jeopardizing the fundamental learning objective. In some rural areas, for example, where there are few students and classroom utilization is low, it may be possible to consolidate several grades into multigrade classes and reduce the size of the teaching (and nonteaching) staff, while maintaining the quality of learning and maximizing the use of such fixed inputs as classrooms. To the extent that it is possible to use such classrooms more efficiently, savings could be generated in the municipalities that need them most: in demographically sparse, poor municipalities with a weak economic base. Those savings could then be reallocated to other educational essentials, such as equipment and materials.Teaching and Learning,Primary Education,Public Health Promotion,Health Monitoring&Evaluation,Environmental Economics&Policies,Environmental Economics&Policies,Teaching and Learning,Health Monitoring&Evaluation,Primary Education,Curriculum&Instruction

The state of the art development of AHP (1979-2017): a literature review with a social network analysis

Although many papers describe the evolution of the analytic hierarchy process (AHP), most adopt a subjective approach. This paper examines the pattern of development of the AHP research field using social network analysis and scientometrics, and identifies its intellectual structure. The objectives are: (i) to trace the pattern of development of AHP research; (ii) to identify the patterns of collaboration among authors; (iii) to identify the most important papers underpinning the development of AHP; and (iv) to discover recent areas of interest. We analyse two types of networks: social networks, that is, co-authorship networks, and cognitive mapping or the network of disciplines affected by AHP. Our analyses are based on 8441 papers published between 1979 and 2017, retrieved from the ISI Web of Science database. To provide a longitudinal perspective on the pattern of evolution of AHP, we analyse these two types of networks during the three periods 1979–1990, 1991–2001 and 2002–2017. We provide some basic statistics on AHP journals and researchers, review the main topics and applications of integrated AHPs and provide direction for future research by highlighting some open questions

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order