Using Enhanced Russell Model to Solve Inverse Data Envelopment Analysis Problems

This paper studies the inverse data envelopment analysis using the nonradial enhanced Russell model. Necessary and sufficient conditions for inputs/outputs determination are introduced based on Pareto solutions of multiple-objective linear programming. In addition, an approach is investigated to identify extra input/lack output in each of input/output components (maximum/minimum reduction/increase amounts in each a of input/output components). In addition, the following question is addressed: if among a group of DMUs, it is required to increase inputs and outputs to a particular unit and assume that the DMU maintains its current efficiency level with respect to other DMUs, how much should the inputs and outputs of the DMU increase? This question is discussed as inverse data envelopment analysis problems, and a technique is suggested to answer this question. Necessary and sufficient conditions are established by employing Pareto solutions of multiple-objective linear programming as well

Using interactive multiobjective methods to solve DEA problems with value judgements,”

Abstract Data envelopment analysis (DEA) is a performance measurement tool that was initially developed without consideration of the decision maker (DM)'s preference structures. Ever since, there has been a wide literature incorporating DEA with value judgements such as the goal and target setting models. However, most of these models require prior judgements on target or weight setting. This paper will establish an equivalence model between DEA and multiple objective linear programming (MOLP) and show how a DEA problem can be solved interactively without any prior judgements by transforming it into an MOLP formulation. Various interactive multiobjective models would be used to solve DEA problems with the aid of PROMOIN, an interactive multiobjective programming software tool. The DM can then search along the efficient frontier to locate the most preferred solution where resource allocation and target levels based on the DM's value judgements can be set. An application on the efficiency analysis of retail banks in the UK is examined. Comparisons of the results among the interactive MOLP methods are investigated and recommendations on which method may best fit the data set and the DM's preferences will be made

Robustness analysis based on weight restrictions in data envelopment analysis

Includes bibliographical references.Evaluating the performance of organisations is essential to good planning and control. Part of this process is monitoring the performance of organisations against their goals. The comparative efficiency of organizations using common inputs and outputs makes it possible for organizations to improve their performance so that can operate as the most efficient organizations. Resources and outputs can be very diversified in nature and it is complex to assess organizations using such resources and outputs. Data Envelopment Analysis models are designed to facilitate this of assessment and aim to evaluate the relative efficiency of organisations. Chapter 2 is dedicated to the basic Data Envelopment Analysis. We present the following: * A review of the Data Envelopment Analysis models; * The properties and particularities of each model. In chapter 3, we present our literature survey on restrictions. Data Envelopment Analysis is a value-free frontier which has the of yielding more objective efficiency measures. However, the complete freedom in the determination of weights for the factors and products) relevant to the assessment of organisations has led to some problems such as: zero-weights and lack of discrimination between efficient organizations. Weight restriction methods were introduced in order to tackle these problems. The first part of chapter 3 in detail the motivations for weight restrictions while the second part presents the actual weight restriction rnethods