A Unified Mathematical Model for Stochastic Data Envelopment Analysis

2021 ◽  
Vol 12 (1) ◽  
pp. 127-141
Author(s):  
Basma E. El-Demerdash ◽  
Assem A. Tharwat ◽  
Ihab A. A. El-Khodary
Keyword(s):  
Data Envelopment Analysis ◽  
Organizational Performance ◽  
Real Life ◽  
Efficiency Measurement ◽  
Data Envelopment ◽  
Stochastic Dea ◽  
Chance Constrained Approach ◽  
Dea Efficiency ◽  
Stochastic Data ◽  
And Performance

Efficiency measurement is one aspect of organizational performance that managers are usually interested in determining. Data envelopment analysis (DEA) is a powerful quantitative tool that provides a means to obtain useful information about the efficiency and performance of organizations and all sorts of functionally similar, relatively autonomous operating units. DEA models are either with a constant rate of return (CRS) or variable return to scale (VRS). Furthermore, the models could be input-oriented or output-oriented. In many real-life applications, observations are usually random in nature; as a result, DEA efficiency measurement may be sensitive to such variations. The purpose of this study was to develop a unified stochastic DEA model that handles different natures of variables independently (random and deterministic) and can be adapted to model both input/output-oriented problems, whether it is CRS or VRS. The chance-constrained approach was adopted to handle the stochastic variables that exist in the model. The developed model is implemented through an illustrative example.

Fuzzy stochastic Data Envelopment Analysis with application to NATO enlargement problem

2019 ◽  
Vol 53 (2) ◽  
pp. 705-721 ◽  
Author(s):  
Ali Ebrahimnejad ◽  
Seyed Hadi Nasseri ◽  
Omid Gholami
Keyword(s):  
Data Envelopment Analysis ◽  
Data Envelopment ◽  
Threshold Values ◽  
Discrimination Power ◽  
Dea Model ◽  
Nato Enlargement ◽  
Proposed Model ◽  
Stochastic Dea ◽  
Dea Models ◽  
Stochastic Data

Data Envelopment Analysis (DEA) is a widely used technique for measuring the relative efficiencies of Decision Making Units (DMUs) with multiple deterministic inputs and multiple outputs. However, in real-world problems, the observed values of the input and output data are often vague or random. Indeed, Decision Makers (DMs) may encounter a hybrid uncertain environment where fuzziness and randomness coexist in a problem. Hence, we formulate a new DEA model to deal with fuzzy stochastic DEA models. The contributions of the present study are fivefold: (1) We formulate a deterministic linear model according to the probability–possibility approach for solving input-oriented fuzzy stochastic DEA model, (2) In contrast to the existing approach, which is infeasible for some threshold values; the proposed approach is feasible for all threshold values, (3) We apply the cross-efficiency technique to increase the discrimination power of the proposed fuzzy stochastic DEA model and to rank the efficient DMUs, (4) We solve two numerical examples to illustrate the proposed approach and to describe the effects of threshold values on the efficiency results, and (5) We present a pilot study for the NATO enlargement problem to demonstrate the applicability of the proposed model.

scholarly journals Inverse data envelopment analysis with stochastic data

2021 ◽  
Vol 55 (5) ◽  
pp. 2739-2762
Author(s):  
Ali Ghomi ◽  
Saeid Ghobadi ◽  
Mohammad Hassan Behzadi ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Data Envelopment Analysis ◽  
Banking Sector ◽  
Uncertain Data ◽  
Sufficient Conditions ◽  
Real Life ◽  
Efficiency Score ◽  
Data Envelopment ◽  
Stochastic Data ◽  
Level Of Significance ◽  
Necessary And Sufficient

The inverse Data Envelopment Analysis (InvDEA) is an exciting and significant topic in the DEA area. Also, uncertain data in various real-life applications can degrade the efficiency results. The current work addresses the InvDEA in the presence of stochastic data. Under maintaining the efficiency score, the inputs/outputs-estimation problem is investigated when some or all of its outputs/inputs increase. A novel optimality concept for multiple-objective programming problems, stochastic (weak) Pareto optimality in the level of significance α ∈[0,1], is introduced to derive necessary and sufficient conditions for input/output estimation. Furthermore, the performance of the developed theory in a banking sector application is verified.

Randomizing DEA Efficiency Scores with Beta Distribution

2014 ◽  
pp. 1977-1985
Author(s):  
P. Sunil Dharmapala
Keyword(s):  
Data Envelopment Analysis ◽  
Order Statistic ◽  
Beta Distribution ◽  
Data Envelopment ◽  
Random Errors ◽  
Input Output ◽  
Stochastic Dea ◽  
Dea Models ◽  
Dea Efficiency ◽  
Statistical Results

A criticism leveled against Data Envelopment Analysis (DEA) is that it is incapable of handling input/output data contaminated with random errors, and therefore, efficiency scores reported by DEA do not reflect reality. Several researchers have addressed this issue by incorporating statistical noise into DEA modeling, thus giving birth to Stochastic DEA. In this chapter, utilizing well known DEA models, we propose a method to randomize efficiency scores by treating each score as an order statistic of an underlying Beta distribution. In an application to a set of banks, we demonstrate how to do this randomization and derive some statistical results.

scholarly journals Efficiency in the Worst Production Situation Using Data Envelopment Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Md. Kamrul Hossain ◽  
Anton Abdulbasah Kamil ◽  
Adli Mustafa ◽  
Md. Azizul Baten
Keyword(s):  
Data Envelopment Analysis ◽  
Shape Parameter ◽  
Pareto Distribution ◽  
Maximum Output ◽  
Data Envelopment ◽  
Dea Efficiency ◽  
Dea Method ◽  
Stochastic Data ◽  
Using Data ◽  
Decision Making Units

Data envelopment analysis (DEA) measures relative efficiency among the decision making units (DMU) without considering noise in data. The least efficient DMU indicates that it is in the worst situation. In this paper, we measure efficiency of individual DMU whenever it losses the maximum output, and the efficiency of other DMUs is measured in the observed situation. This efficiency is the minimum efficiency of a DMU. The concept of stochastic data envelopment analysis (SDEA) is a DEA method which considers the noise in data which is proposed in this study. Using bounded Pareto distribution, we estimate the DEA efficiency from efficiency interval. Small value of shape parameter can estimate the efficiency more accurately using the Pareto distribution. Rank correlations were estimated between observed efficiencies and minimum efficiency as well as between observed and estimated efficiency. The correlations are indicating the effectiveness of this SDEA model.

Fuzzy preference programming formulation in data envelopment analysis for university department evaluation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Dyanne Brendalyn Mirasol-Cavero ◽  
Lanndon Ocampo
Keyword(s):  
Data Envelopment Analysis ◽  
Real Life ◽  
The Philippines ◽  
Data Envelopment ◽  
Data Accessibility ◽  
Content Type ◽  
Proposed Model ◽  
University Department ◽  
Fuzzy Dea ◽  
Fuzzy Preference

Purpose University department efficiency evaluation is a performance assessment on how departments use their resources to attain their goals. The most widely used tool in measuring the efficiency of academic departments in data envelopment analysis (DEA) deals with crisp data, which may be, often, imprecise, vague, missing or predicted. Current literature offers various approaches to addressing these uncertainties by introducing fuzzy set theory within the basic DEA framework. However, current fuzzy DEA approaches fail to handle missing data, particularly in output values, which are prevalent in real-life evaluation. Thus, this study aims to augment these limitations by offering a fuzzy DEA variation. Design/methodology/approach This paper proposes a more flexible approach by introducing the fuzzy preference programming – DEA (FPP-DEA), where the outputs are expressed as fuzzy numbers and the inputs are conveyed in their actual crisp values. A case study in one of the top higher education institutions in the Philippines was conducted to elucidate the proposed FPP-DEA with fuzzy outputs. Findings Due to its high discriminating power, the proposed model is more constricted in reporting the efficiency scores such that there are lesser reported efficient departments. Although the proposed model can still calculate efficiency no matter how much missing and unavailable, and uncertain data, more comprehensive data accessibility would return an accurate and precise efficiency score. Originality/value This study offers a fuzzy DEA formulation via FPP, which can handle missing, unavailable and imprecise data for output values.

scholarly journals Can the Implementation of Sharia Banks’ Roadmap Increase Their Performance? (Evidence from Indonesia 2012-2017)

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Riko Hendrawan
Keyword(s):  
Data Envelopment Analysis ◽  
T Test ◽  
P Value ◽  
Islamic Banking ◽  
Data Envelopment ◽  
Average Efficiency ◽  
Road Map ◽  
Significant Difference ◽  
Dea Efficiency ◽  
Increase Efficiency

Abstract. The purpose of this research is to compare the efficiency of 11 Sharia Banks in Indonesia and its impact on their performance. This study relies on the quarterly data from 2012-2017 and applied Data Envelopment Analysis to measure their performance. The result of the T-test shows that the P-value for two tail = 0.706. So based on this trend the P-value is greater than α = 0.05 (P-value> α). In the condition of P-value> α, H1 is rejected, meaning that there is no change in the value of efficiency between the period 2012-2014 and the period 2015-2017. This research shows that the efficiency of Islamic banking has not occurred during the implementation of the 2012-2017 Indonesian Sharia Banking Roadmap. Furthermore, the highest efficiency value during the period before implementation was 0.92 with an average efficiency value of 0.57. This means that during this period there was room to increase efficiency by 0.35. Meanwhile the period after implementing the highest efficiency value was 0.87 with an average efficiency value of 0.59. This means that during this period there was room to increase efficiency by 0.28. This means that during the 2012-2017 period, there was no significant difference in efficiency levels during the 2012-2014 period (before the implementation) and the 2015-2017 period (after the implementation of the Islamic banking road map). Keywords: DEA, Efficiency, Sharia Bank Abstrak. Tujuan dari penelitian ini adalah untuk membandingkan efisiensi dari 11 Bank Syariah di Indonesia dan dampaknya terhadap kinerja bank tersebut. Penelitian ini menggunakan data setiap kuartal selama tahun 2012 hingga tahun 2017 dan menggunakan Data Envelopment Analysis untuk mengukur kinerja. Hasil penelitian ini menunjukan bahwa selama implementasi Roadmap, perbankan syariah belum menunjukan kenaikan efisiensi. Sementara itu, sebelum implementasi tersebut, nilai efisiensi tertinggi perbankan syariah sebesar 0,92, sedangkan rata-rata nilai efisiensinya sebesar 0,57. Ini berarti bahwa ada ruang untuk meningkatkan level efisiensi sebesar 0,35. Sedangkan pada periode implementasi, nilai efisiensi tertingi perbankan syariah sebesar 0,87, dan ratarata nilai efisiensinya sebesar 0,59. Ini berarti ada ruang untuk meningkatkan level efisiensi sebesar 0,28. Hasil penelitian juga menunjukan bahwa, secara keseluruhan periode tahun 2012 hingga tahun 2017, hasil t-test menunjukan nilai P-value for two tail = 0.706. Ini berarti P-value> α, dan menolak H1, sehingga tidak terdapat perbedaan level efisiensi selama periode 2012-2014 (sebelum implementasi) dan periode 2015 – 2017 (setelah implementasi) Kata kunci: DEA, Efisiensi, Bank Syariah

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