IDEA-Based Malmquist Productivity Index

The purpose of this paper is to develop an output oriented methodology with both constant return to scale (CRS) and variable return to scale (VRS) assumptions for measuring productivity growth using data envelopment analysis (DEA) and malmquist productivity index (MPI). In this regard, we have used the double frontier (optimistic and pessimistic points of view) DEA simultaneously for two-stage processes. The MPIs measured from the two different DEA points of view reflects the productivity growth of decision making units (DMUs) over time more truly and more comprehensively than the traditional optimistic DEA-based MPI. This approach considers not only the optimistic technical efficiency changes of DMUs but also their pessimistic technical efficiency changes, and not only the shifts of efficiency frontiers but also the movements of inefficiency frontiers. Hence, it is more comprehensive and realistic than the traditional optimistic DEA-based MPI. The MPI values measured from the pessimistic DEA point of view, together with those from the optimistic DEA point of view, provide a panoramic view of the productivity changes over time. The proposed DEA-based MPI can be easily extended to the global MPI and measures the optimistic efficiencies with a unified efficiency frontier and the pessimistic efficiencies with a unified inefficiency frontier for time periods t and t + 1.

2013

The Malmquist index is one of the most significant indices for the economists in evaluating the efficiency growth of all the units. Up to now, lots of models have been introduced to develop the productivity index based on DEA (Data Envelopment Analysis). All these models have their own advantages and disadvantages. One of the most famous models is the Malmquist productivity index. One of the most important objections of this model is the mathematical complexity of it. For example, four different models should be solved to evaluate productivity progress of one Decision Making Unit (DMU) in two different years. So, if the DMUs or the evaluating years are increased, the mathematical complexity would increase, as well. In this study, it is tried to introduce a model with less complexity, which can also make possible to compute productivity and technology changes in a simpler way. Therefore, a more acceptable analysis would come up, too.

The Malmquist productivity index can be decomposed in two components: one measures the technical change and other measures the frontier shift. In the current study, we propose an extension to the DEA-based Malmquist by further analyzing these two Malmquist components. We use Russell measure model to obtain more accurate measurements.

2017

Malmquist Productivity Index (MPI) is one of the most famous indices, which is used for estimating the productivity change of a Decision Making Unit (DMU) during the time. Virtually any empirical study that uses MPI, reports average of the productivity indices they estimate to represent the overall tendency in productivity changes. In such a case, productivity indices of a DMU are considered with equal value. In this paper, we propose using the entropy of productivity indices of all DMUs at a specific part of time as the weight of indices of that in aggregating the indices during the under study time section. Then, we use the proposed method for an empirical study of 18 Iranian companies manufacturing automobiles and automobile parts, which have been accepted in Tehran Stock Exchange.

Journal of Applied Mathematics, 2013

Data envelopment analysis (DEA) models can calculate the Malmquist Productivity Index (MPI). Classic Malmquist Productivity Index shows regress and progress of a DMU in different periods with efficiency and technology variations without considering the present value of money. This issue is of major importance since while a currency of in previous year is not equal to that of now this would yield bias results which can affect the correct interpretation. The index developed here is defined in terms of Modified Malmquist Productivity Index model, which can calculate progress and regress by using the factor of present time value of money. The incorporation of present time value of money is also calculated within the framework of data envelopment analysis. This factor is fundamental and should be considered in DEA Malmquist Productivity Index. Moreover, here, differences between presented models are compared to those of previous ones indeed, biased results will be shown in the case study in banks, and problem and solution have been investigated in the literature.

Management science letters, 2013

Measuring relative efficiency of various universities has been a subject for years. In fact, when there is a growing competition among educational units, it is important to find facts on each university for making managerial decisions. In this paper, we present an empirical study to measure the relative efficiencies among different private universities in Iran. The proposed study of this paper uses data envelopment analysis along with Malmquist productivity index to measure the relative efficiencies of these units over the period 2004-2007. The method uses three inputs including number of students, number of university professors and the number of employees. The model also includes the number of educated people as well as research outputs for outputs of the DEA model. The results indicate that there are some big gaps among various units in terms of the number of research products and the number of graduated students.

International Journal of Contemporary Mathematical Sciences, 2007

DEA-based Malmquist productivity index measures the productivity change over time. Cost Malmquist index is defined in terms of input cost rather than input quantity distance functions. Hence, productivity change is decomposed into overall efficiency and cost technical change.

Measurement and Control

Data envelopment analysis is a nonparametric method for measuring of the performance of decision-making units—which do not need to have or compute a firm’s production function, which is often difficult to calculate. For any manager, the progress or setback of the thing they manage is important because it makes planning and adoption of future policies for the organization or decision-making unit more rational and scientific. Different methods have been used to calculate the improvements and regressions using Malmquist Index. In this article, we evaluate the units under review in terms of economic efficiency, and the units in terms of spending, production, revenue and profit over several periods, and the rate of improvement or regression of each of these units. Considering the minimal use of resources and consuming less money, generating more revenue, and maximizing profits, the improvement or retreat of the recipient’s decision unit in terms of cost, revenue, and profit was examined ...

2020

Measuring relative efficiency of various universities has been a subject for years. In fact, when there is a growing competition among educational units, it is important to find facts on each university for making managerial decisions. In this paper, we present an empirical study to measure the relative efficiencies among different private universities in Iran. The proposed study of this paper uses data envelopment analysis along with Malmquist productivity index to measure the relative efficiencies of these units over the period [2004][2005][2006][2007]. The method uses three inputs including number of students, number of university professors and the number of employees. The model also includes the number of educated people as well as research outputs for outputs of the DEA model. The results indicate that there are some big gaps among various units in terms of the number of research products and the number of graduated students.

International Journal of Applied Operational Research - An Open Access Journal, 2014

The productivity change of a decision making unit (DMU) between two time periods can be evaluated by the Malmquist productivity index. In this study, we propose a method to compute the Malmquist productivity index in several time periods (from the first to the last periods) on interval data in data envelopment analysis (DEA). Then, the obtained Malmquist productivity index is compared with Malmquist productivity index between two time periods (the first and last time periods) on interval data. The aim of this paper is to investigate the progress and regress of decision making units (DMUs) in several time periods by considering all time periods between the first and the last one, on interval data. Consequently when the Malmquist productivity index is computed in several time periods, progress and regress of decision making units can be evaluated more carefully than before. What is more, one can judge with greater accuracy whether or not such strategy are favorable and promising. Last...