Free Disposal Hull Model Research Articles

Maintenance groups evaluation under uncertainties: a novel stochastic free disposal hull in the presence of lognormally distributed data

Maintenance groups play an essential role in the successful operation of large companies and factories. Additionally, data envelopment analysis (DEA) is known as a valuable tool for monitoring the performance of maintenance groups. Especially, in contrast to the conventional DEA models that impose the convexity assumption into the technology, the free disposal hull (FDH) model provides a method for assessing the efficiency without the assumption of convexity and can be considered a valuable tool for determining one of the observed groups as the benchmark for each maintenance group. Meanwhile, because of the stochastic structure of data with lognormal distribution in the maintenance groups, this paper extends the FDH model in stochastic data with the lognormal distribution. Moreover, the method’s capabilities are confirmed based on some theorems, and a simulation study that illustrated the properties of the developed procedure is also performed. The developed methodology is applied to assess the performance of 21 maintenance groups of AZCO under uncertainty conditions.

An inverse multi-period FDH model with undesirable outputs

In some examinations, the changes in performance measures and the efficiency of entities should be addressed over a span of time despite the undesirable outputs and unsatisfactory convexity property. In this study, the performance of processes is analyzed over several periods of time by presenting a multi-period model based on the free disposal hull (FDH) approach, incorporating undesirable outputs. Using the product of availability, performance (efficiency) and quality, the overall equipment effectiveness (OEE) is calculated which shows the level of productivity. After estimating the performance and OEE, an inverse multi-period FDH model is introduced to measure the input changes for the changes made to outputs in different time periods. The proposed approaches are used in the automotive industry to analyze the performance and changes in input measures over multiple periods of time. The results show that the proposed technique is reasonable for assessing the multi-period efficiency, the period and overall OEE of the systems, and the input changes related to several periods while the convexity assumption is violated.

A Novel Machine Learning Approach Combined with Optimization Models for Eco-efficiency Evaluation

Machine learning approaches have been developed rapidly and also they have been involved in many academic findings and discoveries. Additionally, they are widely assessed in numerous industries such as cement companies. Cement companies in developing countries, despite many profits such as valuable mines, face many challenges. Optimization, as a key part of machine learning, has attracted more attention. The main purpose of this paper is to combine a novel Data Envelopment Analysis (DEA) approach in optimization at the first step to find the Decision-Making Unit (DMU) with innovative clustering algorithms in machine learning at the second step introduce the model and algorithm with higher accuracy. At the optimization section with converting two-stage to a simple standard single-stage model, 24 cement companies from five developing countries over 2014–2019 are compared. Window-DEA analysis is used since it leads to increase judgment on the consequences, mainly when applied to small samples followed by allowing year-by-year comparisons of the results. Applying window analysis can be beneficial for managers to expand their comparison and evaluation. To find the most accurate model CCR (Charnes, Cooper and Rhodes model), BBC (Banker, Charnes and Cooper model) and Free Disposal Hull (FDH) DEA model for measuring the efficiency of decision processes are used. FDH model allows the free disposability to construct the production possibility set. At the machine learning section, a novel three-layers data mining filtering pre-processes proposed by expert judgment for clustering algorithms to increase the accuracy and to eliminate unrelated attributes and data. Finally, the most efficient company, best performance model and the most accurate algorithm are introduced. The results indicate that the 22nd company has the highest efficiency score with an efficiency score of 1 for all years. FDH model has the highest efficiency scores during all periods compared with other suggested models. K-means algorithm receives the highest accuracy in all three suggested filtering layers. The BCC and CCR models have the second and third places, respectively. The hierarchical clustering and density-based clustering algorithms have the second and third places, correspondingly.

La eficiencia de los puertos en el sureste de Asia, 2005-2015: una medición no paramétrica a través del modelo Free Disposal Hull (FDH)

The objective of the study is to determine the technical efficiency of the 12 most representative ports in the countries of Southeast Asia during the period 2005-2015, through Free Disposal Hull (FDH) model with output orientation. To have greater robustness in the results, bootstrap statistic is applied. In a second moment, the FDH model is compared with DEA model. In FDH model it was found that on average, no year was efficient. The year in which the highest level of efficiency was presented was 2007, with an average of 0.82, while the least efficient year was 2013, where an average of 0.58 was reached. In the comparison of the FDH with the DEA model, the port of Singapur was the most efficient while Yangon in Burma and Sihanoukville in Cambodia were the ports with the lowest efficiency index.

Construction of three-dimensional sections of the efficient frontier for non-convex models

Non-convex Free Disposal Hull (FDH) model was proposed in the scientific literature in the end of 20-th century for performance measurement of complex multidimensional production units. FDH model was proposed almost simultaneously with DEA (Data Envelopment Analysis) model. However, as distinct from the DEA models, production possibility set of FDH models are non-convex ones, what significantly refrained the development of these models. As far as we know, the necessity for such approach has been noted in the world scientific literature for a long time. In this paper, an approach is proposed for three-dimensional visualization of FDH models. An approach was tested using real-life data sets from different areas. Computational experiments confirm reliability and effectiveness of the proposed approach.

Frontier Visualization and Estimation of Returns to Scale in Free Disposal Hull Models

The free disposal hull (FDH) model of production technology assumes free disposability of all inputs and outputs, but does not make any convexity assumptions. In this paper, we develop an algorithm for the reconstruction of the frontier of the FDH technology that corresponds to its sections by different two-dimensional planes. From a practical perspective, the suggested algorithm is useful for the visualization and exploration of the efficient frontier of the FDH technology. Furthermore, based on the suggested algorithm, we develop a new procedure for the evaluation of returns to scale in the FDH technology. Compared to the existing methods, our approach does not require assessing the efficiency of productive units in the reference technologies, which is known to be a computationally intensive task. Our theoretical results are confirmed by computational experiments in applications with real-life data sets from different industries.

Frontier Visualization for Nonconvex Models with Increasing and Decreasing Returns to Scale with the Use of Enumeration Methods

A lot of scientific literature in the world is devoted to the returns-to-scale (RTS) evaluation of production units. Kerstens and Vanden Eeckaut were the first who considered the notion and evaluation of RTS for nonconvex Free Disposal Hull (FDH) models. Their methods are based on the comparison of the radial efficiency scores of a production unit in the FDH model and the corresponding non-increasing and non-decreasing RTS reference models. At the same time Cesaroni, Kerstens and Van de Woestyne noted the absence of papers in the world literature devoted to methods of frontier visualization in nonconvex models. In this paper, we developed methods for visualization of production function of nonconvex models and of the corresponding non-increasing and non-decreasing models. Our approach of frontier visualization can be used for decision making based on nonconvex models, it allows us to evaluate RTS for FDH models. Our results are confirmed by computational experiments in applications with real-life data sets.

Proposing a new approach to the selection of material portfolio using a combination of data mining and optimisation methods

The present paper aims to provide a new framework for the selection of a portfolio of materials. This paper shows that, compared with the traditional methods in the selection of materials, how the new materials are analysed based on new ideas. The case study is materials required for production of tile glaze in both traditional and modern methods. Modelling in this study was done based on mathematical description approach. The results of execution of feature selection algorithm revealed that important factors in the selection of glaze for production of tile in both traditional and modern methods include cracking, self-cleaning, uniformity, water absorption, and market potential. In addition, the results of K-means algorithm showed that all the materials of choice for production of tile glaze are not placed in a single cluster. Therefore, each cluster should be evaluated separately. Unlike the classical approaches to the selection of materials, in the new approach, candidates for the selection of tile glaze are firstly clustered by K-means algorithm. Each cluster is independently ranked using free disposal hull model. Free disposal hull is a mathematical programming model based on data envelopment analysis. The final optimised portfolio of materials was determined using the genetic algorithm.

Frontier visualization for nonconvex models with the use of purposeful enumeration methods

Free Disposal Hull (FDH) model was proposed in the end of 20-th century for performance measurement and management of complex units. Production possibility set of FDH model is a nonconvex set. For this reason, nonlinear integer programming methods and enumeration methods have been used for computations of various characteristics of units’ performance. However, as Cesaroni, Kerstens and Van de Woestyne noted, there are no methods in the world scientific literature for frontier visualization in nonconvex FDH models. In this paper, an approach is proposed for frontier visualization with the use of methods of purposeful enumeration. Computational experiments, conducted with the use of real-life data sets, confirm reliability and effectiveness of proposed algorithms.

Bargaining powers of buyers and sellers on the online diamond market: a double perspective non-parametric analysis

This paper investigates the relative efficiency of buyers and sellers on the online diamond market using a non-parametric double-frontier setting. Our data consists in a sample of more than 100,000 round cut diamonds offered for sale online. For a given quality defined by a combination of color and clarity grades, we turn to the free disposal hull model to estimate the sets of efficient diamonds respectively for buyers and sellers in the price-weight space. We find that the average bargaining power of buyers is lower than that of sellers. Regression estimates show that the relative efficiency of buyers is reduced for heavier diamonds and when there are many diamonds of the same quality offered for sale.

Another brick in the wall: a new ranking of academic journals in Economics using FDH

The academic journals rankings are widely used for academic purposes, especially in the field of Economics. There are many procedures to construct academic journals rankings. Some of them are based on citation analysis while other are based on expert opinion. In this study, we introduced a methodological innovation to aggregate different performance measures to build an alternative ranking of journals in Economics. Our approach is based on a pure output oriented Free Disposal Hull (FDH). We analyzed four indicators--Journal Impact Factor, Discounted Impact Factor, h-index, and Article Influence--for a set of 232 journals in Economics. The results allow us to reach two main conclusions. First, the ranking based on the FDH method seems to be consistent with other well-known reference rankings (i.e.: KMS, Invariant, Ambitious and Area Score). Second, the additional information that provides the FDH model may be used by the Editorial Board to formulate strategies to achieve goals. For instance, to improve a journal score by comparing it with the scores of similar journals.

An improved non-convex model for discriminating efficient units in free disposal hull

A number of methods, including data envelopment analysis (DEA), have been proposed for evaluating the performance of decision making units (DMUs) converting multiple inputs into multiple outputs. The free disposal hull (FDH) is an alternative non-parametric, deterministic production method useful to evaluate the technical efficiency of DMUs. Unlike DEA, the FDH imposes minimal assumptions on the production technology and it does not require convexity. The conventional FDH model assigns an efficiency score less than one to inefficient DMUs, from which a ranking can be derived. However, all efficient DMUs have an efficiency score of 1 and, hence, equal ranking. Several ranking methods have been proposed to discriminate among the efficient DMUs. These ranking methods are sometimes either break down or produce infeasible solution(s). The Mehrabian, Alirezae, Jahanshahloo (MAJ) (1999) method is usually used to discriminate among the efficient DMUs in convex DEA problems, while the MAJ-FDH method proposed by Sun and Hu (2009) has been used to discriminate among the efficient DMUs in non-convex DEA problems. In this paper: (1) we show that the MAJ-FDH model is not always feasible; (2) we propose a modified MAJ-FDH model, both input and output oriented, and mathematically prove that this model is always feasible; (3) we show that the proposed method can produce an optimal solution without the need to solve the integer programming problem; (4) we prove the validity of the proposed method through theorems; and (5) we provide two numerical examples to demonstrate the applicability and show the efficacy of the proposed method.

Non-convex value efficiency analysis and its application to bank branch sales evaluation

We have observed when applying Value Efficiency Analysis [21] that decision makers wish to provide preference information related to existing rather than virtual (efficient) units. This observation motivated us to develop an approach based on the preference comparisons of existing units. The Free Disposal Hull model provides the requisite framework. We assume that a Decision Maker compares units using an implicitly known value function that reaches its maximum at his/her most preferred (efficient) unit. The unknown value function is assumed to be quasi-concave in outputs and quasi-convex in inputs. The main purpose – as in the original Value Efficiency Analysis – is to approximate the distance of each unit from the contour of the value function passing through the most preferred unit. We use examples to illustrate the approach. Finally, we describe a real application in which Value Efficiency Analysis was used to produce information for bank managers wishing to evaluate the performance of bank branches.

Competitive benchmarking technique for “the followers”: a case of Ukrainian dairies

Purpose – The paper is devoted to develop the methodological technique for the implementation of competitive benchmarking in an industrial company in strategy of “the follower”. The paper aims to discuss these issues. Design/methodology/approach – In the research, a non-parametric methodology of efficiency analysis is used. To solve the problem of finding the best competitor, the author proposes to apply the method of free disposal hull (FDH). Findings – The proposed methodological technique for the implementation of competitive benchmarking in an industrial company in strategy of the follower enables to gradually develop and make informed strategic decisions that ensure the achievement of efficiency frontier and a leadership in its market segment. Research limitations/implications – The research is limited by a single industry (dairy products). This is explained by requirement of technology (product, service) homogeneity when using FDH model. Practical implications – By a case of 60 Ukrainian dairies, the paper demonstrates how the author can use the proposed technique in a practice and what steps the author should make to find company benchmark and improve the efficiency. It is possible to use the results of this research to make competitive benchmarking for the other industries. Originality/value – This paper adopts FDH model for competitive benchmarking and implementing the strategy of the followers. The proposed technique enables to improve the various activities of the analyzed dairies.

Nonparametric analysis of technology and productivity under non-convexity: a neighborhood-based approach

This paper investigates the nonparametric analysis of technology under non-convexity. The analysis extends two approaches now commonly used in efficiency and productivity analysis: data envelopment analysis where convexity is imposed; and free disposal hull (FDH) models. We argue that, while the FDH model allows for non-convexity, its representation of non-convexity is too extreme. We propose a new nonparametric model that relies on a neighborhood-based technology assessment which allows for less extreme forms of non-convexity. The distinctive feature of our approach is that it allows for non-convexity to arise in any part of the feasible set. We show how it can be implemented empirically by solving simple linear programming problems. And we illustrate the usefulness of the approach in an empirical application to the analysis of technical and scale efficiency on Korean farms.

Estimation of congestion in free disposal hull models using data envelopment analysis.

This paper deals with evaluating congestion in free disposal hull (FDH) models. There are several approaches in data envelopment analysis (DEA) literatures which discuss the theory and application of congestion. However, almost all of these approaches considered convex DEA technologies. So, in the case of nonconvex technologies, including FDH technology, this field is almost nil. This paper makes an attempt to fill in this void. To do so, this study provides a pairwise comparisons-based algorithm to evaluate congestion in FDH model. This algorithm identifies the sources of congestion and estimates its amounts. It is also capable of detecting the losses amounts of output due to congestion. The validity of the proposed model is demonstrated using some numerical and empirical examples.

Container selection in the presence of partial dual‐role factors

PurposeThe purpose of this paper is to introduce an innovative data envelopment analysis (DEA) model entitled “Non‐binary Arithmetic Operator Dual‐role” (NAOD) under free disposability assumption for selecting the refrigerated containers in cold chain management (CCM).Design/methodology/approachIn classical DEA models, it is assumed that all of input and output variables play a certain role. However, in some cases, some variables play both input and output roles, simultaneously. These variables in DEA are called “dual‐role” factors. This study introduces a new approach to deal with these factors in the process of evaluating a set of homogeneous refrigerated containers, which is based on Free Disposal Hull (FDH) (one of the DEA models). However, in previous dual‐role models, this variable is considered as a binary variable. In this paper, a partial role for dual‐role factors is considered.FindingsThe main findings of this paper are: for the first time, the NAOD model is developed for the container selection problem in the context of CCM and the dual‐role factors are considered for the container selection problem. The NAOD model determines partial role of dual‐role factors and can consider multiple dual‐role factors. For the first time, the container selection problem is solved by an FDH model. The result of NAOD model is validated by genetic algorithm.Originality/valueThe paper makes a sufficient contribution to the practice of operations research. It is the first study which applies advanced DEA models for selecting the containers in the context of the CCM. To the best of the authors' knowledge, there is no other reference that deals with container selection in the context of CCM in the presence of dual‐role factors.

DEA 방법론을 이용한 온라인 판매자 추천 시스템의 구축

구매자와 판매자의 판매과정에서 '구매가치'는 구매자의 구매의사결정에 있어서 매우 중요한 가격대비 질의 중요한 측정치이다. 본 논문의 목적은 온라인 구매자들이 통일한 물건을 파는 판매자를 중에 최적 판매자를 선택하는 데 도움이 되는 방법론을 제안함에 있다. 이 방법론 수립을 위하여 DEA(data envelopment analysis) 방법론의 적용모형의 하나인 FDH(free disposal hull) 모형을 사용하고, 이 모형의 실효성을 질제 가격비교 사이트로부터 획득한 데이터를 이용하여 검증하였다. 모형 검증과정에서는 가격, 브랜드 배달 기간 등 거래 조건에 대하여 구매자들이 어떻게 반응하는지를 우선 분석하고, 이를 바탕으로 구매자의 구매 의사결정을 돕는 판매자 추천 시스템을 구축하였다. 본 연구를 통하여 검증된 FDH 모형은 구매자 측면에서 최적조건, 최저가로 좋은 제품과 서비스를 원하는 구매자에게 유용한 정보를 제공하고, 나아가 자동화된 소규모 거래에도 활용될 수 있을 것으로 기대된다. 판매자 측면에서는, 구매자의 선호도를 더욱 자세히 파악함으로써 타판매자 대비 경쟁력을 가지는 벤치마킹 전략을 수립하는 데에도 유용하게 이용될 수 있을 것으로 기대된다. In a buyer-seller transaction process, 'value for money,' a measure of quality-price-ratio, is one of the most important criteria for buyers' purchasing decisions. The purpose of this paper is to suggest a method which helps online shoppers choose the best of several sellers offering homogeneous goods. We suggest FDH (free disposal hull) model, an applied model of data envelopment analysis (DEA), for online buyer-seller transactions and verify it with the data from an Internet comparison shopping site. For this purpose, we analyze consumer choice behaviors by examining how consumers respond to different sale conditions such as price, brand, or delivery time. Then, we implement a seller recommendation system to support buyers' purchasing decisions. We expect our FDH model to provide valuable information for rational buyers who want to pay the least price for high quality products/services and to be used in implementing automated evaluation processes in micro transactions. Moreover, we expect that our results can be utilized for sellers' benchmarking strategies which help sellers be more competitive by showing them how to attract buyers.

Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we find the optimal scale to be situated around 7–10 million m3.

Big and Beautiful? On Non-Parametrically Measuring Scale Economies in Non-Convex Technologies

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we find the optimal scale to be situated around 7 to 10 million m3.