Centralised resource allocation using Lexicographic Goal Programming. Application to the Spanish public university system

Identificador de proyecto: FEDER-UPO UPO-1380624This paper deals with Data Envelopment Analysis (DEA) in centralised settings in which the operating units belong to the same organisation. In such a scenario, a global system-wide perspective may be adopted as regards resource allocation and target setting. In this paper, a new Lexicographic Goal Programming (lexGP) approach is proposed using three priority levels: the aggregated input consumption and output production goals; the input and output goals of the individual operating units; and the technical efficiency of the computed targets. It is assumed that the goals for the overall organisation are established by the Central Decision-Maker (CDM) and that they are consistent with those of the individual operating units. The proposed approach has been applied to the Spanish public university system, comprising 47 institutions. Given the CDM preferences in terms of input and output aggregate goals and relative importance weights, specific technical efficient targets have been computed for each university. The results show that the proposed approach is more suitable than the non-centralised DEA approach and produces targets that are more effective than other centralised resource allocation approaches in the sense that they are much closer to both the aggregate goals of the CDM and the specific goals of each university.Universidad de Sevill

A classification of DEA models when the internal structure of the Decision Making Units is considered

We classify the contributions of DEA literature assessing Decision Making Units (DMUs) whose internal structure is known. Starting from an elementary framework, we define the main research areas as shared flow, multilevel and network models, depending on the assumptions they are subject to. For each model category, the principal mathematical formulations are introduced along with their main variants, extensions and applications. We also discuss the results of aggregating efficiency measures and of considering DMUs as submitted to a central authority that imposes constraints or targets on them. A common feature among the several models is that the efficiency evaluation of the DMU depends on the efficiency values of its subunits thereby increasing the discrimination power of DEA methodology with respect to the black box approach

The effect of ICT on schools’ efficiency: Empirical evidence on 23 European countries

In the last two decades, ICT use in schools grew exponentially. In this paper, the relationship between ICT and school’s efficiency and the mechanisms through which ICT can enhance schools’ productivity are investigated, using PISA 2018 data for about 5400 schools. Empirically, we analyze school’s efficiency in producing ICT-mediated instructional time as well as final educational output, by implementing a network Data Envelopment Analysis (DEA) model. The analysis is complemented by a conditional DEA to account for the presence of possible external drivers of schools’ efficiency. Results show that the average schools’ efficiency in using ICT is relatively low, and that it is mainly driven by the ability of translating ICT-mediated instructional time into learning, rather than by the amount of ICT and human resources. This evidence is consistent across countries. By investigating the role of ICT in schools’ efficiency the paper provides insights to guide the transition of digital technology into learning

Centralized DEA approach to assess efficiency scores of bank branches with foreign exchange transactions

It is inevitable for a manager to consider the performance effects of each component of a multi-stage financial equity capital. These components serve as inputs in the first stage to raise investments. The investments, as outputs of the first stage, become inputs for the second stage and are used in bank services, such as bank facilities, which are outputs of the second stage. Therefore, when evaluating bank performance, the connectivity between the stages must be considered; otherwise, efficiency may not be calculated correctly. Traditional methods often assess multi-stage systems as black boxes, neglecting the potential connectivity that may exist among the stages. We delve into the system and propose models to improve overall efficiency and the efficiency of each stage. Additionally, the continuity and relationships among stages introduce numerous variables and constraints to linear programming for evaluating the entire system. A centralized approach calculates the efficiency score of units simultaneously by solving only one linear programming problem, significantly reducing computational complexity. This approach, especially in large organizations, is commonly employed by central managers. In this paper, we introduce a centralized method for evaluating units with a multi-stage structure. We apply the proposed models to evaluate the efficiencies of bank branches and insurance companies, demonstrating the superiority of the improved network approach and centralized method in enhancing overall system efficiency. Bank branches typically have a two-stage structure, involving labor, physical capital, and other factors.IntroductionBank branches operate under the supervision of a central management team. The central manager, acting as the decision-maker, allocates resources such as labor and financial equity capital as inputs for these branches. The goal is to optimize the overall efficiency of the branches by minimizing the total consumption of resources while maximizing the desired outputs, such as security investments. A common approach to enhancing the performance of banks involves evaluating each branch separately. However, this method does not guarantee the minimization of total resource consumption and can be time-consuming. Since all bank branches are under the control of central management, the decision-maker can optimize the efficiency scores of branches by allocating resources to them simultaneously. This approach, known as centralized Data Envelopment Analysis (DEA), is particularly relevant when certain variables are controlled by a central authority, such as a Head Office, rather than individual unit managers. DEA is a mathematical programming technique used to assess the performance of homogeneous Decision Making Units (DMUs). However, in cases where DMUs have a network structure, such as banks, where the outputs of one division or sub-process serve as inputs for the next sub-process, traditional DEA models treat two-stage DMUs as black boxes and overlook potential connectivity among the stages. In our approach, we consider the internal activities within the system and propose a non-radial model to optimize multi-stage DMUs by taking into account the connectivity among the stages. Furthermore, in previous network DEA models, constraints related to intermediate activities were treated as inequalities, which, as we will demonstrate in this paper, can lead to contradictions in optimality. We address this issue by carefully considering the connectivity among stages. The presence of connectivity among stages introduces numerous variables and constraints to the corresponding model. This model, when used to measure the overall efficiency scores of all DMUs, would traditionally require solving as many problems as there are DMUs, which can be highly time-consuming. In our paper, we introduce a centralized approach that measures the efficiency scores of multi-stage structure DMUs by solving only one linear programming problem. We have applied these proposed models to evaluate bank branches and insurance companies. This approach provides a more comprehensive and efficient way to assess and improve the performance of multi-stage organizations like banks, taking into account the interconnected nature of their operations.MethodologyWe employ the Data Envelopment Analysis approach to evaluate systems with a multi-stage structure, often referred to as a network structure. Traditional DEA models treat two-stage DMUs as black boxes and overlook the potential for connectivity among these stages. In contrast, we delve into the internal activities of the system and propose a model that optimizes multi-stage DMUs by considering the interconnections among the stages. Moreover, in previous models designed to assess network systems, constraints related to intermediate activities were typically treated as inequalities, which could lead to inconsistencies in optimization. In our approach, we enhance these constraints associated with intermediate activities to ensure more robust optimization. Additionally, we apply a centralized approach to allocate resources to DMUs, allowing for the simultaneous optimization of the efficiency scores of all DMUs through the solution of a single linear programming problem. This centralized method streamlines resource allocation and improves the overall efficiency of the DMUs.ResultsWe evaluated 20 bank branches, treating them as 20 DMUs with a two-stage structure. In the first stage, inputs included paid interest, personnel costs, paid interest related to foreign currency transactions, and personnel costs related to foreign currency transactions. The first stage produced intermediate outputs in the form of raised funds and raised funds related to foreign currency transactions. In the second stage, the outputs consisted of loans and common incomes. Notably, some loans in the second stage might become non-performing, where borrowers are unable to make full or even partial repayments. To address this, we considered non-performing loans as undesirable or bad outputs and transformed them into inverse values to treat them as good outputs. To calculate the efficiency scores of the bank branches, we employed both our improved network model and the traditional DEA approach. Our network-based method revealed that many of the bank branches under evaluation were inefficient, in contrast to the traditional method, which inaccurately identified many of the bank branches as efficient. Subsequently, we extended our network method to a centralized case, significantly reducing computation time. The network-based assessment of bank branches took nearly 5 seconds, whereas solving the centralized model required only 0.1 second. In addition to evaluating bank branches, we applied our methods to assess insurance companies. The results demonstrated that our model provided more accurate efficiency scores compared to previous network-based approaches.ConclusionIn multi-stage production systems, the production process comprises several stages. Banks, for example, operate with a network structure in which labor, physical capital, and financial equity capital serve as inputs in the first stage to generate deposits as intermediate outputs. In the second stage, these banks utilize the deposits obtained from the first stage to create loans and security investments. We have introduced models to assess the efficiency of each stage, whether it's the first, intermediate, or final stage, individually. Additionally, we have developed a non-radial SBM model designed for evaluating DMUs with multi-stage structures. The Centralized DEA approach is a valuable method for central managers, particularly in large organizations like bank branches, to allocate resources effectively. We have extended our network-based method to a centralized approach, allowing us to calculate efficiency scores by solving just one linear programming problem. The results obtained from applying our proposed models to evaluate bank branches and insurance companies, both exhibiting network structures as DMUs, demonstrate the superiority of the network centralized approach over previous models

Cities versus agriculture: revisiting intersectoral water transfers, potential gains and conflicts

Water scarcity / Water demand / Water transfer / Water use / Water supply / Water allocation / Environmental effects / Water market

Ein DEA-basierter Ansatz zur Messung der Performance bei zentralisierten Managementstrukturen

Traditional performance measurement approaches are usually characterized by a number of different limitations. Among other things, these approaches require the subjective determination of weights to aggregate a set of indicators to an overall performance score. Furthermore, traditional approaches are usually not able to incorporate additional improvement potentials that can be received from a centralized management. A performance measurement framework which can overcome these limitations is called data envelopment analysis (DEA). Against this background, this thesis provides a thorough overview of how different degrees of centralization are modeled in the current DEA literature. The systematic literature review identified 135 different approaches that assume a centralized or partially centralized management structure. A concluding discussion of the respective DEA approaches showed two fundamental research gaps. In response to this, this thesis has two fundamental objectives: The first objective is to propose a DEA-based performance measurement approach for measuring performance changes over time. The second objective is to develop another DEA-based approach for comparing the performance of management groups. In contrast to so far developed DEA-models, the here proposed approaches explicitly incorporate the respective management structure. Both DEA approaches thus developed are based on the combination of the metafrontier concept and the Malmquist index. The first approach evaluates productivity changes of operating entities over time and, hence, may indicate potential sources for performance changes. Thereby, the proposed approach preserves the individual characteristics of each local group technology. The second DEA approach proposed here uses the Malmquist index for comparing the performance of management groups. This index accounts for the existence of a central decision maker who can, e.g., undertake resource reallocations to improve the overall performance of its managed group. The applicability and usefulness of both proposed approaches is empirically shown with real-world data from KONE Corporation.Traditionelle Performance Measurement Ansätze gehen mit einer Reihe von Herausforderungen einher. So erfordert die Aggregation unterschiedlicher Kennzahlen zu einem einzelnen Performancemaß die Verwendung von subjektiven Gewichtungen. Darüber hinaus lassen sich in traditionellen Ansätzen nur schwer etwaige Verbesserungspotentiale modellieren, die aus zentralisierten Managementstrukturen resultieren. Eine betriebswirtschaftliche Methode, welche die genannten Limitationen nicht aufweist, ist die Data Envelopment Analysis (DEA). Aufgrund dieser Vorteile wird in dieser Arbeit zunächst ein umfassender Literaturüberblick erarbeitet, wie unterschiedliche Managementstrukturen in einer DEA modelliert werden können. Mithilfe der Literaturrecherche wurden insgesamt 135 unterschiedliche Ansätze ermittelt, die entweder ein vollkommen zentralisiertes oder teilweise zentralisiertes Managementmodell unterstellen. Eine abschließende Diskussion der verschiedenen DEA-Ansätze zeigte allerdings eine Forschungslücke, woraus die beiden folgenden Forschungsziele für diese Arbeit abgeleitet wurden: Einerseits soll ein DEA-basierter Ansatz erarbeitet werden, der zur Messung von Effizienzveränderungen einzelner Produktiveinheiten über die Zeit geeignet ist. Andererseits soll eine DEA-basierte Methode entwickelt werden, welche bei Performancevergleichen zwischen Managementgruppen anwendbar ist. Im Gegensatz zu den bisher in der Literatur diskutierten Ansätzen sollten die entwickelten Methoden dabei die jeweils vorliegende Managementstruktur berücksichtigen. Die entwickelten DEA-Ansätze basieren auf der Kombination des Metafrontier-Konzepts mit dem Malmquist-Index. Der erste Ansatz erlaubt es, Performanceveränderungen von einzelnen Produktiveinheiten über mehrere Zeitperioden zu messen. Im Gegensatz zu konventionellen Metafrontier-basierten Malmquist-Indizes berücksichtigt der vorgeschlagene Ansatz die individuellen Eigenschaften der lokalen Produktionstechnologien. Der zweite vorgeschlagene DEA-Ansatz nutzt den Malmquist-Index für den Vergleich der Performance von Managementgruppen. Der Index berücksichtigt dabei explizit, dass eine zentrale Entscheidungsinstanz existiert, welche Ressourcenumverteilungen durchführen kann. Beide Ansätze werden anhand eines Datensatzes des Unternehmens KONE illustriert

Efficiency of fiscal allocations in site-based empowered schools

This study implemented a two phase concurrent mixed-methods design to generate a greater understanding of how elementary schools with increased autonomy in fiscal decision making allocated their money, how their site-based decisions affected allocative efficiency, and how increased autonomy affected site-based decision making when compared with a set of matched control schools within a large urban district. Phase I compared school site expenditure patterns of site-based empowered schools to demographically matched control schools and to all elementary schools within a large urban district over four years, 2004-05, 2005-06, 2006-07, and 2007-08. Expenditure data were collected from the In$ite data base using the categories set by Cooper‟s and Lybrand‟s Finance Analysis Model: a model that uses the downward accounting extension. Also explored was the relationship between fiscal decision making and allocative efficiency through the use of a data envelopment analysis (DEA) which used multiple outputs against multiple inputs to compare levels of efficiency among the four, site-based empowered schools and demographically matched control schools. Phase II consisted of a qualitative analysis of interview questions answered by empowerment and control school principals. If how dollars are spent is a critical factor in maximizing student outcomes, then a critical question becomes „who should make those decisions?‟. An empowerment school concept in a large urban district in the southwest was developed with the belief that involving those closest to the student in making decisions about the fiscal allocation of resources can improve student outcomes. However, the concept of making decisions closest to the client to affect productivity outcomes can only be effective if schools allocate money toward variables that are known to improve outcomes. By looking at schools in a large urban school district, this study provides insight into how schools deemed empowerment and control allocated their dollars, how site-based decision making affects efficiency, and the link between school improvement efforts and fiscal decisions. This study revealed there was little difference in how empowerment schools spent their money when compared with demographically matched control schools and the total number of elementary schools within the district. The empowerment and control schools both showed decreased efficiency when compared with themselves during base line years (2005 and 2006) and with all elementary schools in the district during the study years (2007 and 2008). In terms of site-level decision making, empowerment schools expressed a greater sense of empowerment than did control schools. However, being a site-based empowered school did not ensure that they would make decisions that improved efficiency. While these site-based schools were more aware of issues at the site level, principals did not show awareness of the growing body of literature that connects school based fiscal allocation decisions to educational outcomes

Cities versus agriculture : revisiting intersectoral water transfers, potential gains and conflicts

The report is anchored in an annex that examines how cities round the world have in practice acquired water. While direct conflicts between urban and rural interests characterize some of the case studies presented (Ta'iz in Yemen being an extreme example), the empirical evidence suggests that, by-and-large, cities have been able to obtain supplies, often at greater cost than is necessary but without significantly compromising their ability to expand and prosper, even in most inauspicious locations. Where citizens face shortages or any other water problem, the report argues that this is predominantly due to development and financing constraints rather than to water shortages as such. Under conditions of scarcity, any transfers to cities will probably have some adverse impact on agriculture. However, the volume transferred is typically small and, though important social and equity issues arise, it is argued that farmers can often adjust. And where the environment is adversely affected by human impacts, this is predominantly an issue between the environment and agriculture and not between the environment and cities, at least in regard to water quantity. The section titled "Urban Water Scarcity and Its Links to Irrigation" sets the scene by reviewing what is meant by urban water scarcity and its links to irrigation, investigating its physical, political and economic dimensions. The section titled "Intersectoral Transfers" categorizes different types of transfers and transfer mechanisms. In the light of this typology, the section titled "Intersectoral Water Transfers in Practice" discusses how transfers are effected in practice with reference to the empirical evidence in the annex. The section titled "Are Urban Uses Constrained by Agriculture?" seeks to answer the question: are urban uses in practice constrained by agriculture. And, finally, the section titled "Where Are We Heading?" discusses some ways ahead and the conclusion summarizes the report's main findings