Inefficient Decision Making Units Research Articles

Allocating Benefits Due to Shared Resources Using Shapley Value and Nucleolus in Dynamic Network Data Envelopment Analysis

Shared resources are common among supply chain partners and also occur in multiple linked stages of an internal network. The sharing of these resources impacts the organization’s profits. This study is focused on the potential benefits of resource sharing on a three-stage network system and on the profit improvement allocation. Previous treatments concentrate on defining optimal proportions to allocate resources and disregard the impacts of allocations to promote cooperation and are limited to static evaluations. Data Envelopment Analysis performs the decision-making units (DMUs) efficiency measurement. Methodological advances have resulted in models that analyze their internal structure and temporal impacts on efficiency. We propose an integrated cooperative game and dynamic network DEA that considers known quantities of resources used in each stage and the time effects to optimize the system’s profit. Each DMU stage is a player, and we investigate performance before and after resource sharing. Using Shapley value and Nucleolus, it is possible to allocate the benefits obtained based on the marginal contributions of each stage, providing incentives to motivate and maintain cooperation. A numerical example is used to illustrate the method. The results confirm the identification of inefficient DMUs and that sharing resources allows for profit increase for all of them.

Congestion: relation between traditional DEA congestion and two-stage processes congestion

Congestion is a kind of inefficiency because it causes the decision-making units (DMUs) to be inefficient and reduces their output. Identifying inefficient DMUs and determining the cause of their inefficiencies has been one of the most important reasons for referring to the internal structure of DMUs and analyzing the effect of intermediate products on subDMUs (or stages) performance. In this paper, to characterize the cause of the DMU’s congestion, we refer to its internal structure as a two-stage network data envelopment analysis (DEA) and decompose the DMU’s congestion into black-box (BB) and two-stage structure congestion. Also, inputs have two separate and simultaneous roles; the black-box’s inputs role and the stage1’s input role, so three congestion types occur. Thus, we sought to analyze the relation between two types of initial inputs congestion, and intermediate products congestion, and express their effects on BB congestion. Finally, we define three congestion definitions and model the relation between two types of input congestion, intermediate products congestion and BB inputs congestion. Finally, a practical example illustrates the proposed method.

Maximum slacks-based measure of efficiency in network data envelopment analysis: A case of garment manufacturing

The conventional slacks-based measure (SBM) model is widely applied to measure the relative efficiency of a set of decision making units (DMUs) because the measured efficiency is not affected by weakly efficient frontiers. This model seeks the target point on the production frontier that is farthest to the assessed DMU to calculate efficiency, which requires more effort for the DMU to reach to become efficient. This paper develops a model to calculate the maximum SBM efficiency for general network production systems. Different from the conventional minimum SBM efficiency that is always less than the radial efficiency for inefficient DMUs, the maximum SBM efficiency can be greater than the radial efficiency. The measured efficiency satisfies the monotonicity property. The efficiencies of the component divisions of the network system can also be calculated at the same time. A garment manufacturing company whose major operations comprise cutting and sewing is studied using the developed model. The results show that the average maximum SBM efficiency is 35 % higher than the average minimum SBM efficiency and the sewing operation contributes more to the system efficiency than the cutting operation does.

Program evaluation and review technique – Data envelopment analysis in benchmarking sustainable supply chain management of the potato chips industry

Supply chain benchmarking of agroindustry can be done by emphasizing the perspective of sustainability. This paper aimed to analyze the efficiency of Sustainable Supply Chain Management (SSCM) in Micro, Small, and Medium Enterprises (MSMEs) and provided a prospective benchmark with the potato chips industry as a study case. Program Evaluation and Review Technique (PERT) estimated future input and output values to obtain prospective benchmarks and be added to the DEA formula later. Analytical Hierarchy Process (AHP) and Data Envelopment Analysis (DEA) methods were used to measure SSCM performance. The results showed that 17 of 20 Decision-Making Units (DMUs) were efficient (score 1). The other 3 DMUs were classified and got an efficiency score of 0.965, 0.955, and 0.995. In future estimates calculation, the efficiency score of one of the inefficient DMUs has changed to 1, while the other two got the scores of 0.996 and 0.980. The limitation of this research mainly comes from the scope of assessment, which is limited to the supply chain’s downstream sector and assesses only a limited number of MSMEs in a particular region. SSCM efficiency measurement variables were adjusted to be assessed and applied to MSMEs. PERT was also beneficial to gain future estimates of the assessment scope.

Data envelopment analysis of two‐stage processes: an alternative (non‐conventional) approach

AbstractNetwork data envelopment analysis (NDEA) is an extension of standard DEA that models the efficiency assessment of decision‐making units (DMUs) by considering their internal structure. While in standard DEA, the DMU is regarded as a single process, in NDEA, the DMU is viewed as a network of interconnected sub‐processes (stages, divisions), where the flow of the intermediate products (measures) is essential in the efficiency assessment. In the prevalent conventional methodological approach to NDEA, the sub‐processes are assumed as distinct entities with distinct inputs and outputs. Thus, each sub‐process has its own production possibility set (PPS), which can be derived axiomatically from a set of assumptions using the minimum extrapolation principle. The PPS of the overall system is defined as the composition of the individual PPSs. The conventional approach comprises all the methods, in which the system and the divisional efficiencies are computed jointly in a single mathematical program. A fundamental property connecting the system with the divisional efficiencies is that a system is overall efficient if and only if its divisions are all efficient. In NDEA, regardless of the method used, there are cases where none of the observed DMUs is rendered overall efficient as corroborated by real‐world case studies. This is the main issue we discuss in this paper and the motivation to propose an alternative, non‐conventional, approach to address it in the frame of two‐stage processes. We consider the two‐stage process as a system that can be viewed from two perspectives depending on the role of the intermediate measures: the system as producer and as consumer of the intermediates. As our approach is based on standard DEA, it satisfies the basic desirable properties. The fundamental NDEA property, that the overall system is efficient if and only if both perspectives are efficient, is met. The efficient frontier of the system is explicitly defined by the overall efficient observed DMUs, and the inefficient DMUs are projected on the efficient frontier of the system. A convergent procedure is presented for this purpose. The proposed models are equivalently expressed in both the multiplier and the envelopment forms due to strict primal‐dual correspondence and can operate under both constant and variable returns‐to‐scale assumptions. We use the case of 22 automotive manufacturers for the fiscal year 2019 as an example to illustrate our approach. Comparison with other NDEA methods is also provided.

Stepwise benchmarking based on production function: Selecting path towards closest target

Data Envelopment Analysis (DEA) is used for not only assessing the performance of a set of homogeneous decision-making units (DMUs), but finding the target operating points to improve inefficient DMUs. When inefficient DMUs are far from their target, it will be impossible to reach those in a single move, therefore, a strategy of gradual improvements with intermediate targets has been proposed. In this study, we propose a method to determine benchmarking paths, which consider the improvement steps as the learning of the production functions, not the learning of inputs and outputs. Under the constant returns-to-scale (CRS) assumption, the paper, for each inefficient DMU, sets the ultimate target as the closest target and determines the shortest improvement path with existing DMUs by Dijkstra’s algorithm, and this is illustrated with a numerical experiment. As a real-world example, the method is introduced to the irons and steel enterprises in China, so that the specific steps to make efficient ones has been pointed out. The proposed method is the first study to discuss stepwise benchmarking path from the perspective of the production function.

Port environmental efficiency assessment using the one-stage and two-stage model DEA: comparison of Koper and Dublin ports

Ports are important and central hubs for logistical activities in transportation chains that contribute to economic growth. Nevertheless, port activities are associated with undesirable impacts such as energy consumption and air pollutant emissions. Various policy instruments and measures have been developed and adopted to reduce energy consumption and emissions from ports. In an effort to manage all undesirable impacts of port operations, the search for best practices has proven to be an effective approach. This study examines one- and two-stage Data Envelopment Analysis (DEA) models for measuring port environmental efficiency. The adequacy of the models was analyzed using two case studies, i.e., the port of Koper and port of Dublin. The results of the study provided the best practices and the main differences between one-stage and two-stage models. Distance metrics were used to identify the necessary improvements of inefficient decision-making units (DMUs) to achieve the best practices.

Measuring Efficiencies of Dairy Buffalo Farms in the Philippines Using Data Envelopment Analysis

This study aimed to measure the efficiency scores of 75 dairy buffalo farms in the province of Nueva Ecija, Central Luzon, Philippines, using an input-oriented, variable-return-to-scale Data Envelopment Analysis (DEA) model. The farmer-informants or decision-making units (DMUs) were categorized as smallholders, family modules, and semi-commercial in operations. Personal interviews using structured questionnaires were done to gather various information on the socio-economic and management practices of the DMUs. Output in the form of volume and value of milk produced and inputs such as quantities and costs of biologics, feeds, forage, and labor were also collected and evaluated among individual DMUs. The efficiency scores were computed using PIM-DEA software, which identified fully efficient DMUs lying on the frontier line (scores of 1.0) and those enveloped by it (inefficient DMUs with scores of less than 1.0). The overall mean Technical Efficiency (TE), Allocative Efficiency (AE), and Economic Efficiency (EE) scores among the DMUs were 0.80, 0.81, and 0.65, respectively. Most of the inefficient DMUs were in the smallholder category. In sum, smallholder DMUs classified under low and moderate TE clusters should reduce their inputs by 53.31% and 40.01%, respectively, to become fully efficient. Likewise, higher lambda values among efficient peer DMUs indicate the best practice frontiers that the inefficient peer DMUs can benchmark with. Extension and advisory services can help promote the best management practices of the frontiers to improve the TE, AE, and EE of the inefficient DMUs.

How to improve the future efficiency of Covid-19 treatment centers? A hybrid framework combining artificial neural network and congestion approach of data envelopment analysis

Covid-19 virus (severe acute respiratory syndrome coronavirus 2, SARS-CoV-2) threatens the health of human beings worldwide, imposing a concern for the world and prompting governments to control the contagion. Although vaccination is a proper tool to control the transmission, the efficient allocation of limited health-care resources to massive patients can improve the effectiveness of medical services. Relying on the Artificial Neural Network (ANN), the aim of this research is to enhance the future efficiency of Covid-19 treatment centers by forecasting their efficiency and providing benchmarks. To do this, we use the congestion approach of data envelopment analysis (DEA) based on the theory of economies of scale principles. In the traditional input-oriented DEA, inefficient decision-making units (DMUs) can become efficient merely by reducing the inputs. However, this may not always be true in real-world applications such as improving the efficiency of COVID-19 treatment centers (DMUs). Meaning that the treatment centers with less congested inputs (e.g., ventilators, test equipment, pulmonologists, and nurses, etc.) normally have higher mortality rates. For this reason, in this study, we take the congested inputs approach into account to provide proper benchmarks for the inefficient treatment centers. According to the congestion approach of DEA, an optimum increase in congested inputs can lead to a greater than a proportional increment in outputs. In other words, if more respiratory equipment, pulmonologists, patient rooms, nurses and beds, etc. are allocated to Covid-19 treatment centers, not only the number of deaths (undesirable outputs) are decreased, but also the number of recoveries (desirable outputs) are increased. Such an optimal rise in the congested inputs is determined in pairwise comparisons derived from the model. Accordingly, in this study, first, considering the congestion approach of DEA and historical data of five periods, we identify the initial efficiency of Iranian Covid-19 treatment centers. Then, by running ANN, we forecast the future inputs and outputs, the overall efficiency, and rank of the treatment centers. By doing this, the prospective efficient and inefficient DMUs are identified, and appropriate benchmarks are determined.

Wood harvesting efficiency analysis of regional forest directorates in Turkey: k-means clustering and data envelopment analysis approach

ABSTRACT Wood harvesting is a crucial element of sustainable forest management. Harvesting of wood and non-wood forest products has gained importance for increasing environmental services, economic development and sustainability of forests. The aim of this study was to reveal the efficiency values of regional forest directorates (RFD) for wood harvesting between 2015 and 2020 in Turkey using six input and two output variables. Data envelopment analysis (DEA) and k-means clustering analysis were used. From the results obtained, 35.7% of the 28 RFDs were efficient using the results of the input- and output-oriented Charnes, Cooper, and Rhodes (CCR) model. In the input-oriented CCR model, for inefficient decision-making units (DMUs) to become efficient, on average the variable that needs to be reduced the most is forest area, and the variable that needs to be reduced the least is allowable cutting. Conversely, in the output-oriented CCR model, an average potential increase of 23.84% in the harvest of industrial wood, and of 29.48% for fuelwood, was determined for the inefficient DMUs. In addition, according to the results of the k-means cluster analysis, it was found that the DMUs in the cluster distribution of inefficient DMUs were similar to each other in terms of location. It will make a positive contribution for inefficient DMUs to consider the efficient DMUs shown as references to reach the targeted input/output values to become efficient. In addition, the results of this study are important for enabling forest managers to make performance evaluations based on efficiency analyses.

Stability analysis with general fuzzy measure: An application to social security organizations.

An effective method for evaluating the efficiency of peer decision-making units (DMUs) is data envelope analysis (DEA). In engineering sciences and real-world management problems, uncertainty in input and output data always exists. To achieve reliable results, uncertainties must be taken into account. In this research, a General Fuzzy (GF) approach is designed to cope with uncertainty in the presence of fuzzy observations for categorizing and specifying stability radius and alterations ranges of efficient and inefficient DMUs, which is applicable to real-world decision-making problems. For this purpose, a DEA sensitivity analysis model is presented, which will be modeled by fuzzy sets. Then, by applying the General Fuzzy (GF) approach, the fuzzy DEA sensitivity analysis model is transformed into the equivalent crisp form of fuzzy chance constraints according to specific confidence levels. Finally, a numerical example and a case study of branches of the social security organization are presented to illustrate sensitivity and stability analysis in the presence of fuzzy data. The obtained results provide the input and output changes of the evaluated units according to the attitude and preference of the decision maker with different confidence levels so that the data changes in the fuzzy environment do not change the units’ classification from efficient to inefficient and vice versa.

Performance Analysis in Production Systems with Uncertain Data: A Stochastic Data Envelopment Analysis Approach

The problem of determining an optimal benchmark to inefficient decision-making units (DMUs) is an important issue in the field of performance analysis. Previous methods for determining the projection points of inefficient DMUs have only focused on one objective and other features have been ignored. This paper attempts to determine the best projection point for each DMU when the inputs and outputs data are in stochastic form and presents an alternative definition for the best projection by considering three main aspects: technical efficient, minimal cost, and maximal revenue as much as possible. Considering the important role of the electricity industry in the economic growth of each country, a practical example has been implemented on 16 regional electricity companies in Iran in 9 consecutive periods. The efficiency score along with the projection points of the three technical models (BCC model of Banker et al. (1984)), cost, and stochastic revenue are compared with the projection point obtained from the model presented in this article, which simultaneously meets these three objectives, showing the improvement of companies’ performance.

Integrated one-stage models considering undesirable outputs and weighting preference in slacks-based measure of efficiency and superefficiency

In the evaluation scenario with undesirable outputs, the SBM-Undesirable model is usually used together with the SuperSBM-Undesirable model to fully differentiate efficient and inefficient decision-making units (DMUs). The existing SuperSBM-Undesirable model has two main forms, but both have problems in implementation. One form may be infeasible under the variable returns to scale (VRS); Another form has an inappropriate definition for undesirable output efficiency. These two problems are seriously ignored in the existing applications. In this paper, we first propose an improved SuperSBM-Undesirable model with strongly efficient projections, which is feasible under the constant returns to scale (CRS) or VRS technology. Then, by integrating the SBM-Undesirable and the improved SuperSBM-Undesirable models, we focus on proposing a concise, precise and practical one-stage model considering undesirable outputs to differentiate all DMUs and determine their strongly efficient projections simultaneously. The proposed one-stage model only contains essential decision variables and constraints, thereby effectively conserving computational time for large-scale practical applications. Further, by introducing the weighting preference of inputs and outputs, we construct the one-stage model with weighting preference to differentiate the importance of different indicators. Finally, through several data experiments, the superiority of our models in computational results and computational scale are verified.

ANALİTİK AĞ SÜRECİ VE VERİ ZARFLAMA ANALİZİ İLE İŞLETMELERİN ETKİNLİK ÖLÇÜMLERİ ÜZERİNE BİR UYGULAMA

In this study, the financial efficiency of enterprises registered in the BIST Food, Beverage and Tobacco index was measured using Data Envelopment Analysis and Analytical Network Process Methods. Within the scope of the analysis, 18 enterprises were considered as decision-making units, and efficiency measurements were made on 6 input and 3 output variables. CCR, BCC and Assurance Region models of Data Envelopment Analysis were used in the application phase. Analytical Network Process method was used to obtain the weight constraints required by the Assurance Region model. As a result of the application, it was observed that the lower and upper limits used in the Assurance Region model decreased the number of decision making units (DMU) that were evaluated and hence gave more realistic results by discriminating the efficient and inefficient DMUs.

Ranking Decision Making for Eco-Efficiency Using Operational, Energy, and Environmental Efficiency

The objective of this paper is to propose a method for evaluating the eco-efficiency of business organizations. In order to adequately capture the inherent properties of eco-efficiency, we present a decision support model that can evaluate an organization based on ranking the derived efficiencies at the operational, energy, and environmental dimensions and taking these factors into account comprehensively. The proposed model was designed in the form of a combination of data envelopment analysis (DEA) and TOPSIS, and we tried to make use of the advantages of each method and offset the disadvantages. Specifically, the operational, energy, and environmental efficiencies were derived through DEA. Then, each efficiency was set as the criteria, and the eco-efficiency ranking was determined through TOPSIS. This study shows that it has the advantage of not requiring preference information from the decision maker and, at the same time, can improve the discriminatory power between efficient and inefficient decision-making units. To apply the proposed model, the analysis results are presented through an illustrative example, and the theoretical significance is described. It is also explained that the proposed model can provide a more realistic and convincing evaluation.

Least-Distance Range Adjusted Measure in DEA: Efficiency Evaluation and Benchmarking for Japanese Banks

This study aims to formulate the least-distance range adjusted measure (LRAM) in data envelopment analysis (DEA) and apply it to evaluate the relative efficiency and provide the benchmarking information for Japanese banks. In DEA, the conventional range adjusted measure (RAM) acts as a well-defined model that satisfies a set of desirable properties. However, because of the practicality of the least-distance measure, we formulate the LRAM and propose the use of an effective mixed integer programming (MIP) approach to compute it in this study. The formulated LRAM (1) satisfies the same desirable properties as the conventional RAM, (2) provides the least-distance benchmarking information for inefficient decision-making units (DMUs), and (3) can be computed easily by using the proposed MIP approach. Here, we apply the LRAM to a Japanese banking data set corresponding to the period 2017–2019. Based on the results, the LRAM generates higher efficiency scores and allows inefficient banks to improve their efficiency with a smaller extent of input–output modification than that required by the RAM, thereby indicating that the LRAM can provide more easy-to-achieve benchmarking information for inefficient banks. Therefore, from the perspective of the managers of DMUs, this study provides a valuable LRAM for efficiency evaluation and benchmarking analysis.

Theory of binary-valued data envelopment analysis: an application in assessing the sustainability of suppliers

PurposeThe objective of this study is to present a binary-valued data envelopment analysis (DEA) theory. The authors’ proposed approach, for the first time, combines binary-valued and integer-valued theories concurrently in the DEA context. To do so, new production possibility sets (PPSs) with some distinguished features are developed.Design/methodology/approachThe authors address integer inputs and outputs in the proposed approach by introducing a new PPS.FindingsTo take into account the binary data, the authors develop axiomatic DEA principles. The binary production principles guarantee any combination of convexity and feasibility. Furthermore, the authors develop a new DEA model to consider integer and real data. A case study is presented to show the usefulness of the developed models. Using the proposed models, the authors obtained benchmarks to solve the sustainable supplier selection problems.Originality/value(1) For the first time, binary-valued and integer-valued theories are presented in an integrated DEA model. (2) To deal with the pure binary data, a new PPS is proposed. (3) To consider real, integer and binary data, a new PPS is introduced. (4) New technologies are developed to propose feasible solutions. (5) The proposed models can project inefficient decision-making units (DMUs) on efficiency frontier given binary, integer and real data. (6) A case study is given for the performance evaluation of sustainable suppliers.

An inverse DEA model for intermediate and output target setting in serially linked general two-stage processes

Abstract In this paper, we formulate an inverse data envelopment analysis (DEA) model for a serially linked two-stage production process operating under constant returns to scale technology. The inverse DEA model determines a set of intermediate and output targets for an input augmented decision-making unit (DMU) to maintain its relative efficiency at a pre-specified level. We solve the inverse DEA model using the constraint method used in multi-objective optimization. The input augmented DMU with intermediate and output targets obtained in the inverse DEA model is a hypothetical DMU. Under our modelling framework, when such a hypothetical DMU established on an inefficient DMU is included in the observed DMU set, the frontier established with observed DMU set remains intact. This is important in practice as the intermediate and output targets of the hypothetical DMU would be feasible. When overall efficiency of the hypothetical DMU is decomposed, individual stages have the same efficiency level as that of the hypothetical DMU. This is important to DMU managers as sub-processes also maintain the desired overall efficiency level. We apply our inverse DEA model to a sample of Australian superannuation funds. We demonstrate that each unique Pareto optimal solution of the inverse DEA model obtained through the constraint method provides a specific set of intermediate and output targets and they may offer trade-off between intermediates and outputs. When fund managers anticipate expansion or growth in their funds, choice of targets allows comparison of different trade-off scenarios and makes informed decisions.

The Efficiency of Anganwadi Centers Located in Rural Field Practice Area of a Medical College in North India: Data Envelopment Analysis.

The Integrated Child Development Services (ICDS) scheme was launched in 1975 for the improvement in maternal and child health and nutrition. The services under ICDS are implemented through Anganwadi centers (AWCs) and are delivered by Anganwadi workers (AWWs) at grassroots level. To evaluate the efficiency of all AWCs located in the field practice area of the medical college in North India, using data envelopment analysis (DEA) technique. A cross-sectional study was conducted in the catchment area of rural health training center. Each of the 15 AWCs was considered a decision-making unit (DMU), and physical structure and logistics were included as input variables; and percentage of beneficiaries receiving supplementary nutrition and health checkups were included as output variables. DEA technique was used to calculate the efficiency score for each DMU with the help of DEAOS free online software. DMU 14th was found to be most efficient (100%) and DMU second was the least efficient (45%). DMU 13 and 14 demonstrated a level of performance that is superior to all other DMUs. DMU 13th and 14th were, therefore, considered 100% efficient. DEA analysis showed that total output increases and/or input reductions were required for making the inefficient DMUs efficient. Most of the AWCs were inefficient and an improvement in the infrastructure and logistics is likely to improve the efficiency of AWCs.

Measuring the Efficiency of Turkish State Universities Based on a Two-Stage DEA Model

According to the efficiency scores obtained by Data Envelopment Analysis (DEA), the main problem for inefficient decision-making units (DMU) is the factors that cause inefficiency. To deal with this problem, various studies have been handled, such as decomposing the total efficiency score, and two-stage DEA which can divide the whole process into two parts has been developed. In this study, independent models where the whole process is called a black box and related models where the series relationship is established in the whole process are discussed comparatively. These models are used to measure graduate education performances and scientific and technological research competency performances of state universities in Turkey. When the overall performances of universities are examined; Gebze Technical, Hacettepe, İstanbul Technical, İzmir Institute of Technology and Middle East Technical have been determined as efficient universities both in terms of overall performances of universities and in terms of independent model and related model. İstanbul, Ankara, Boğaziçi and Gazi, have beendetermined as efficient universities only in terms of independent model. Furthermore, this study is consistent with the research universities determined by the Council of Higher Education through certain criteria.