An approach multiple criteria network data envelopment analysis model

A conic relaxation model for searching for the global optimum of network data envelopment analysis

Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures

How to evaluate the carbon emission efficiency of multimodal transport is an important issue of public concern, and this article attempts to solve it with a network data envelopment analysis (DEA) model. DEA is a method to evaluate the efficiency of homogeneous decision-making units (DMUs). First, this article studies the efficiency decomposition and efficiency aggregation of the general network structure for DEA model. In efficiency decomposition, the relationship between system efficiency and division efficiency is discussed; whereas in efficiency aggregation, the division tendency brought about by the definition of weights is analyzed. Then, a reasonable and single compromise solution to division efficiency scores is investigated while the system efficiency remains optimal. Finally, a two-stage network DEA model of rail-water intermodal transport is established with carbon dioxide (CO2) emissions as an undesirable output. Based on this model, the rail-water intermodal transport efficiencies of 14 ports in China in 2015 are evaluated by the methods of efficiency decomposition, efficiency aggregation, and non-cooperation. The results show that Rizhao Port, Tangshan Port, Nanjing Port, and Zhuhai Port have set an example to other ports. Qinhuangdao Port, Ningbo-Zhoushan Port, Guangzhou Port, and Beiliang Port need to improve the efficiency of railway transportation. Beibu Gulf port, Zhanjiang Port, Dalian Port, Lianyungang Port, Yantai Port, and Yichang Port should optimize their intermodal system. In addition, Yantai Port and Yichang Port urgently need to improve the port efficiency in low-carbon operation. The network DEA model constructed in this article can be further applied to the efficiency evaluation of multi-link supply chains, and the empirical results can provide a reference for the efficiency evaluation of ports in China.

Assessing the sustainability of high-, middle-, and low-income countries: A network DEA model in the presence of both zero data and undesirable outputs

Food security is a global challenge. With rising world population and demand for food being compounded by resource and arable land constraints, raising the efficiency of food production and use has become increasingly important. While much of the research on food security is focused on farm efficiency and productivity, most neglect post-harvest (PH) handling which is critical in determining the availability of food. In this study, we employ the network Data Envelopment Analysis (DEA) model to evaluate the PH efficiency of milling, using data from Kenya’s rice processing industry. The results show lower efficiency scores when using a network DEA model, which reflects its greater discriminatory power when compared to the standard DEA approach. The study also quantified sources of productive efficiency using a fractional regression model and identified storage space and distance to market as having an impact on drying efficiency; while experience, age of mill, servicing and energy type influenced milling efficiency. The results suggest that policy makers should focus on investing in drying technologies and storage facilities to improve drying efficiency. To improve milling efficiency, policy recommendations include enhancing millers’ access to better technologies, investing in reliable sources of energy and providing PH handling workshops to reduce PH losses.

Traditional Data Envelopment Analysis (DEA) models take Decision-Making Unit (DMU) as a 'black box' without considering the inputs/outputs of its intermediate production processes. To provide efficiency enhancing information regarding the sources of DMUs' inefficiencies, researchers investigate network DEA models. This paper proposes a network DEA model in the presence of undesirable factors. In the network DEA model, a DMU is composed of a set of interdependent sub-DMUs, that is, input of a sub-DMU may be an undesirable output of another sub-DMU. We develop a method of estimating efficiency of such DMU, and analyses efficiency relationship between a DMU and its sub-DMUs. Our model provides a way of improving performance of a DMU through identifying its inefficient sub-DMUs. Numerical examples are used to show our results.

The production process may have internal or network structure, for example, a company may have several production lines which use different inputs to produce the outputs, and there may be connection activities (or intermediate products) among the production lines. The traditional data envelopment analysis (DEA) models cannot be directly employed to measure the performance of this kind of decision making unit (DMU) as they treat the production system as a whole, disregarding the internal production process when calculating the efficiency. Depending on the characteristics of the DMU's inputs and outputs, this paper first classifies the network structure of DEA models. Then, a network DEA model is proposed to evaluate the airport's efficiency, and 20 major airports' system efficiencies, ground service efficiencies, passenger transport efficiencies, and freight transport efficiencies are analyzed systematically.

One of the new concepts that have found a considerable position in many countries of the world is organizing EFQM organizational excellence models. Different organizations and institutions have been evaluated and compared on its basis, and the move towards improvement and promotion is strengthened in them due to creation of competitive space. The EFQM organizational excellence model cannot remove the managers’ and users’ need for the levels of quantitative goals’ operation solely. Thus, requirement for a tool which considers quantitative goals and present environment was felt, and in this manner, various assessment processes were created to be used in different organizations; one of the most important ones is the technique for Data Envelopment Analysis. Evaluating organization efficiency based on the EFQM model is one of the strategic managerial tools in many organizations. The classic DEA models were designed to work with deterministic data and cannot deal with uncertainties in their inputs. The techniques developed so far for fuzzy performance evaluation are also very limited. Given that the inputs and outputs of a real system are not always definite and accurate and that some data can only be expressed in vague verbal and subjective terms, the use of fuzzy sets in modeling is inevitable (Ali et al., 2019). In this paper, a Network Data Envelopment Analysis Model is proposed in fuzzy conditions for assessing units of an organization based on an organizational excellence model. The suggestive model utilizes the privileges of both Fuzzy Network Data Envelopment Analysis and EFQM organizational excellence models simultaneously in order to assess organization’s efficiency. The Fuzzy Network Data Envelopment Analysis model is able to calculate the whole organization’s efficiency as well as organization’s efficiency separately for various phases of the organizational excellence model. Another privilege of the suggested model is that it utilizes fuzzy theory and concepts for modeling and observance of existing noncertainties in the experts’ views while assessing organization’s excellence criteria. The EFQM-fuzzy network DEA model is applied for assessing a holding’s organizational units within the discipline of “project management.”

Data envelopment analysis (DEA) is a broadly used non-parametric technique for performance evaluation and data analytics. While conventional single-stage DEA models overlook the internal interactions of decision making units (DMUs), network DEA opens this black box to investigate the internal structure of DMUs. Practically, many network DEA models involve shared performance measures that are not easily divisible among individual components of a network. Based upon a two-stage network DEA model, the current study treats such performance measures as inseparable links, implying that no proportions are optimized and allocated to the two stages of the network. The shared and unsplittable links in the proposed two-stage DEA model manifest integrality while both ends of the link are maximized or minimized simultaneously, and this setting has not been modeled in any existing DEA studies. The shared and unsplittable links in our model can be considered intermediate measures, but they are different from the two existing types of dual-role intermediate measures, which are traditional intermediate measures and feedback measures. Our performance link is a new type of intermediate measure that is minimized or maximized in both stages of the network. The resulting network DEA model is highly non-linear. To address the non-linearity, a parametric linear model is adopted. The proposed approach is construed in four variants, and then illustrated using a set of 100 banks in the United States.

Evaluation of the sustainability of supply chains is a complex decision-making problem. One of the techniques, which are used for assessing the sustainability of supply chains is data envelopment analysis (DEA). Conventional DEA models consider decision making units (DMUs) as black boxes that consume a set of inputs to produce a set of outputs and do not take into consideration the internal interactions of DMUs. Also, they assume inputs and outputs are crisp. In this research, the network DEA (NDEA) model for assessing the sustainability of supply chains in the presence of fuzzy rough data is developed. The main contribution of this paper is to develop a novel NDEA model in the existence of internal and external uncertainties. To validate the proposed model, a case study for evaluating the sustainability of the supply chain in the pasta industry is presented.

Data envelopment analysis (DEA) is a linear programming method for assessing the efficiency and productivity of organizational units called decision-making units (DMUs). We propose a new network DEA (NDEA) model for measuring the performance of agility in supply chains. The uncertainty of the input and output data is modeled with linguistic terms parameterized with fuzzy sets. The proposed fuzzy NDEA model is linear and independent of the α-cut variables. The linear feature allows for a quick identification of the global optimum solution and the α-cut independency feature allows for a significant reduction in the computational efforts. We show that our model always generate solutions within a bounded feasible region. Our model also eliminates the potential for conflict by producing unique interval efficiency scores for each DMU. The proposed model is used to measure the performance of agility in a real-life case study in the dairy industry.

This thesis focuses on the modeling of non-parametric production functions in two stages without assuming any specific functional form. Data Envelopment Analysis (DEA) is an approach based on linear programming and is used to assess the relative efficiency among a set of Decision Making Units (DMUs) while offering a number of advantages. However, conventional DEA models make no assumption regarding the procedures taking place inside the DMU. On the contrary, DEA treats a DMU as a “black box” which uses inputs to produce outputs without considering the internal procedures, a usually sufficient assumption. However in some cases, such as supply chain systems, DEA models consist of two or more stages and these internal procedures may be important for evaluating the efficiency. The stages are connected with intermediate variables which are considered as outputs in one stage and inputs in another stage. Network DEA models are used to accommodate such cases. This thesis classifies network DEA models into four categories which are independent, connected, relational and game theoretic models. Inside this framework this thesis constructs two-stage DEA models and use them create novel indices which evaluate the efficiency in various economic applications. Specifically, the most significant research contribution of this thesis is the incorporation of a priori information such as expert opinions and value judgements into the modeling process. This objective is achieved with the construction of the Weight Assurance Region (WAR) model which modifies the original additive model in order to incorporate a priori information using assurance region-based weights in the two-stages. Furthermore, WAR model solves the infeasibility problem of the original model. Another research contribution is the mathematical framework for the extension of the original additive model into a time-dependent window-based approach. This approach allows the handling of panel data in a two-stage network DEA framework and provides robust efficiency measures. A third research contribution is the incorporation of metafrontier framework into two-stage DEA analysis in order to treat the heterogeneity of DMUs in different groups (such as firms in different groups or regions in different countries) which experience different technologies. DMUs from different groups face different production opportunities; therefore feasible input-output combination in one group may not be feasible in another. These differences among groups may refer to physical, human and financial capital, infrastructures, economic environment, available resources etc; as a result every group has a different frontier. Therefore, the metafrontier is an overall frontier which envelopes the groups' specific frontiers so that no point of these frontiers can lie above points on the metafrontier. Finally, four economic applications are presented where the production processes are examined and novel indices are constructed using two-stage DEA formulations. The economic applications are in educational, banking and environmental sectors.

Inadequate supply of energy due to consumers’ increasing demand has become one of the major problems in societies. Economic growth is a key reason for the increase in the energy consumption. Although different policies can be employed for resolving this problem, optimizing the efficiency of energy suppliers can be addressed as a key policy in this regard. This paper presents an adjusted Network Data Envelopment Analysis (NDEA) model for evaluating performance of energy supply chain in Iran from production to distribution stages. Some suggestions are proposed to optimize the performance of the energy supply chain. The NDEA model is adjusted by using assurance region (AR) to achieve more real and scientific results. Borders of the assurance region obtained fromData Envelopment Analytic Hierarchy Process (DEAHP) method are entered into the NDEA model. The results obtained from this model are compared with those of conventional NDEA and technical efficiency in pairs. Finally, the Spearman and Kendall's-Tau correlation tests are used for validating the results.

Accepted by: Ali Emrouznejad The environmental efficiency of industries plays an important role in economic development of countries. Accordingly, dividing the internal network structure of industries into two sub-processes, including green and operational stages, enables decision-makers to assess both of the efficiencies simultaneously. Such assessment can be implemented using a non-parametric methodology termed data envelopment analysis (DEA). Standard DEA models consider the whole system of decision-making units (DMUs) as a single process (i.e. black-box). The black-box approach ignores modelling of the internal network structure of the assessed DMUs. This issue tackled by network DEA models since it considers the internal network structure of DMUs. In the network DEA, the efficiency evaluation of system stages is essential to identify its overall efficiency, resulting to a multi-objective optimization problem. Therefore, the network DEA is a widely welcomed methodology proposed for solving multi-objective problems. This paper assesses the operational and environmental efficiencies of a network structure system by converting the multi-objective optimization problem into a linear single objective function. In this investigation, a technique of tri-objective function problem is proposed. The proposed technique transforms into a single objective function by keeping one objective function and shifting the other two objective functions into the model’s constraints. The applicability and usefulness of the proposed technique have been tested using a data set of 20 industries. The developed approach provides valuable evaluations to decision-makers to rank DMUs by considering their green and operational efficiency simultaneously.

This paper seeks to propose a network data envelopment analysis (DEA) framework for analysis of heterogeneous systems. The paper introduces the dummy connector so that every network structure can be transformed into the sun network structure. In his case, the dummy connector allows for heterogeneity of the decision making units (DMUs) in terms of their inner structure. Based on the sun network structure, the static and dynamic network DEA models are established. Thus, DMUs with different structures can be evaluated according to the static and dynamic network DEA models. The efficiency of each sub-unit, each period and each sub-unit in each period can also be obtained. Two simulated examples are presented using the static and dynamic DEA models.