A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems

2020 ◽  
Vol 54 (6) ◽  
pp. 1657-1671
Author(s):  
Samaneh Esfidani ◽  
Farhad Hosseinzadeh Lotfi ◽  
Shabnam Razavyan ◽  
Ali Ebrahimnejad
Keyword(s):  
Production Systems ◽  
Weighted Average ◽  
Real Data ◽  
Stage Structure ◽  
Data Envelopment ◽  
Two Stage ◽  
Bank Branches ◽  
Proposed Model ◽  
Efficiency Decomposition ◽  
Dea Models

Two-stage production systems are often encountered in many real applications where the production process is divided into two processes. In contrast to the conventional data envelopment analysis (DEA) models, two-stage DEA models take the operations of the internal processes into account. A number of studies have used two-stage DEA models in order to evaluate the performance of decision making units (DMUs) having a network structure. In this paper, we use a non-radial DEA model called the network slacks-based measure (NSBM) model to measure the efficiency of a system with a multi-period two-stage structure. Then we describe the properties of the proposed model in details. Moreover, we shall decompose the overall efficiency of the system over a number of time periods as a weighted average of the efficiency in each period. The efficiency of the stages, in respect to the entire periods shall be decomposed in terms of the weighted average efficiency of the stages in each period. Finally, the real data of Mellat bank branches in Tehran extracted from extant literature is used to illustrate the proposed approach.

scholarly journals Efficiency Bounds for Two-Stage Production Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao Shi
Keyword(s):  
Production Systems ◽  
Efficiency Score ◽  
Insurance Companies ◽  
Practical Case ◽  
Data Envelopment ◽  
Production Structure ◽  
Two Stage ◽  
Decision Making Unit ◽  
Real World Applications ◽  
Dea Models

Traditional data envelopment analysis (DEA) models find the most desirable weights for each decision-making unit (DMU) in order to estimate the highest efficiency score as possible. These efficiency scores are then used for ranking the DMUs. The main drawback is that the efficiency scores based on weights obtained from the standard DEA models ignore other feasible weights; this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black Box” and developed models to obtain the efficiency bounds for each DMU over sets of all its feasible weights. In many real world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka’s (2011) model to a more common and practical case considering the two-stage production structure. The proposed approach calculates each DMU’s efficiency bounds for the overall system as well as efficiency bounds for each subsystem/substage. An application for nonlife insurance companies has been discussed to illustrate the applicability of the proposed approach and show the usefulness of this method.

scholarly journals Modifying the convexity condition in Data Envelopment Analysis (DEA)

2020 ◽  
Vol 33 (02) ◽  
pp. 454-467
Author(s):  
Roghyeh Malekii Vishkaeii ◽  
Behrouz Daneshian ◽  
Farhad Hosseinzadeh Lotfi
Keyword(s):  
Data Envelopment Analysis ◽  
Real Data ◽  
Data Envelopment ◽  
Convexity Condition ◽  
Discrimination Power ◽  
Data Set ◽  
Step Procedure ◽  
Proposed Model ◽  
Dea Models ◽  
Production Possibility Set

Conventional Data Envelopment Analysis (DEA) models are based on a production possibility set (PPS) that satisfies various postulates. Extension or modification of these axioms leads to different DEA models. In this paper, our focus concentrates on the convexity axiom, leaving the other axioms unmodified. Modifying or extending the convexity condition can lead to a different PPS. This adaptation is followed by a two-step procedure to evaluate the efficiency of a unit based on the resulting PPS. The proposed frontier is located between two standard, well-known DEA frontiers. The model presented can differentiate between units more finely than the standard variable return to scale (VRS) model. In order to illustrate the strengths of the proposed model, a real data set describing Iranian banks was employed. The results show that this alternative model outperforms the standard VRS model and increases the discrimination power of (VRS) models.

scholarly journals Centralized resource allocation with the possibility of downsizing in two-stage network production systems

2021 ◽  
Author(s):  
Amir Hossein Yadollahi ◽  
Reza Kazemi Matin
Keyword(s):  
Resource Allocation ◽  
Resource Constraints ◽  
Production Systems ◽  
Data Envelopment ◽  
Two Stage ◽  
New Approach ◽  
Organizational Perspective ◽  
Dea Models ◽  
Common Resource ◽  
Component Processes

The network data envelopment analysis (NDEA) technique has been recently developed to measure the relative efficiency of complex production systems. NDEA models provide more meaningful and informative results in comparison to the conventional black-box DEA approach that ignores the operations of the component processes. Regarding the centralized decision-making systems, normal management imposes common resource constraints to maximize produced outputs and minimize consumed inputs. The present study seeks to introduce new centralized resource allocation models in two-stage network production systems. This intra-organizational perspective also provides the possibility of closing down some of the existing units to improve system efficiency. To do so, three scenarios of centralized DEA models are introduced to take advantage of this possibility. A simple numerical example is used for illustration purposes. An empirical application of the proposed approach to the twenty branches of a university is also presented to show the applicability of the new approach.

scholarly journals Group ranking of two-stage production units in network data envelopment analysis

2021 ◽  
Author(s):  
Mohammad Sajjad Shahbazifar ◽  
Reza Kazemi Matin ◽  
Mohsen Khounsiavash ◽  
Fereshteh Koushki
Keyword(s):  
Data Envelopment Analysis ◽  
Group Performance ◽  
Production Systems ◽  
Performance Criteria ◽  
Data Envelopment ◽  
Mathematical Tool ◽  
Two Stage ◽  
Group Ranking ◽  
Group Efficiency ◽  
Dea Models

Data envelopment analysis (DEA) is a useful mathematical tool for evaluating the performance of production units and ranking their relative efficiency. In many real-world applications, production units belong to several separate groups and also consist of several sub-units. In this paper, we introduce a new method of evaluating group efficiency of two-stage production systems. To this end, some new DEA models are introduced for evaluating and ranking groups of production systems based on the average and weakest group performance criteria. Some numerical examples, including an empirical application in the banking industry, are also provided for illustration.

scholarly journals Efficiency Aggregation in Generalized Network Data Envelopment Analysis with Slacks-Based Measure Based on Sample Units

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 733
Author(s):  
Na Sun ◽  
Narisa Zhao ◽  
Zhan-Xin Ma
Keyword(s):  
Data Envelopment Analysis ◽  
Weighted Average ◽  
Stage Structure ◽  
Black Box ◽  
Original Model ◽  
Data Envelopment ◽  
Two Stage ◽  
Multi Stage ◽  
Decision Making Unit ◽  
Generalized Data Envelopment Analysis

By using sample units (SUs), the generalized data envelopment analysis (DEA) method can evaluate the efficiency of decision making unit (DMU) through different reference sets, but the existing models are radial models, and the DMU is treated as a black box, rarely taking the operations of the internal divisions into account. This paper proposes a generalized network slacks-based measure (SBM) approach based on the SUs. First, the generalized network SBM approach for a basic two-stage structure is proposed. This paper considers the intermediate products in calculating the divisional efficiency for each DMU. Overall efficiency of DMU is a weighted average of the divisional efficiency. The weight of each division does not need to be given in advance. Since the DMUs set and SUs set are not necessarily the same, this paper proposes an improved generalized network SBM approach for a basic two-stage structure to solve the problem that the original model may be infeasible. Then, the approach for basic two-stage structure is extended to general multi-stage structure. Finally, an example is given to show the practicability of the generalized network SBM approach.

Efficiency changes index in the network data envelopment analysis with non-radial model

2018 ◽  
Vol 13 (02) ◽  
pp. 2050031
Author(s):  
Samaneh Esfidani ◽  
Farhad Hosseinzadeh Lotfi ◽  
Shabnam Razavyan ◽  
Ali Ebrahimnejad
Keyword(s):  
Data Envelopment Analysis ◽  
Insurance Industry ◽  
Returns To Scale ◽  
Additive Model ◽  
Stage Structure ◽  
Data Envelopment ◽  
Two Stage ◽  
Dea Models ◽  
The Difference ◽  
Constant Returns To Scale

Evaluating the efficiency and the performance of decision making units (DMUs) at different time periods is one of the most critical and important issues of managers. Data envelopment analysis (DEA) is a powerful non-parametric technique to measure the relative efficiency of a set of DMUs where each DMU consumes multiple inputs to produce multiple outputs. In many DEA applications, DMUs are considered as systems with a two-stage structure. In these situations, two-stage DEA models are used to measure the efficiencies of these systems. In many of such systems, the simultaneous presence of two stages is not necessary for the final product and the shortcoming of one stage is compensated by another stage. Therefore, this paper will use compensatory property of the sum operator and will propose the additive model to measure the multi-period efficiency of these systems under the constant returns to scale (CRS) assumption. In addition, based on the obtained efficiencies, the new efficiency changes Indexes (ECIs) related to the whole system and the first and second stages between two periods will be proposed that have circularity property. Furthermore, ECI of the whole system (and stages) for two periods is defined as the difference between the efficiencies in these periods. Moreover, positive changes (or negative changes), or unchanged in the efficiency of stages will be concluded by the positive changes (or negative changes), or unchanged of the whole system. Finally, the data of 21 non-life insurance industry in Taiwan are used to describe our suggested model that extracted from the extant literature.

scholarly journals The Theoretical Relationship between the CCR Model and the Two-Stage DEA Model with an Application in the Efficiency Analysis of the Financial Industry

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 712
Author(s):  
Ming-Chi Tsai ◽  
Ching-Hsue Cheng ◽  
Van Trung Nguyen ◽  
Meei-Ing Tsai
Keyword(s):  
Insurance Companies ◽  
Data Envelopment ◽  
Financial Industry ◽  
Two Stage ◽  
Theoretical Relationship ◽  
Dea Model ◽  
Bank Branches ◽  
Dea Models ◽  
The Relationship ◽  
Ccr Model

Since Charnes, Cooper, and Rhodes introduced data envelopment analysis (DEA) in 1978, later called the DEA-CCR model, many studies applied this technique to different fields. Based on the original CCR model, many modified DEA models were developed by researchers. Since 1999, Seiford and Zhu presented a two-stage DEA model. Later, these models were widely used in many studies. However, the relationship between the efficiency scores that are obtained from the original CCR model and the two-stage DEA model remains unknown. To fill this gap, this study proposed a theoretical relationship between the efficiency scores that are calculated from the two-stage DEA model and those that are obtained from the original CCR model. How the sets of nonsymmetrical weights affected the efficiency scores were also investigated. Theorems regarding the relationship were developed, and then the model was utilized to evaluate the two-stage efficiency scores of the insurance companies (non-life) and bank branches. The results show that using a two-stage DEA model can get more information about operational efficiency than the traditional CCR model does. The findings from this study about the two-stage DEA technique can provide significant reasons for using this model to evaluate performance efficiency.

Economies of scope in two-stage production systems: A data envelopment analysis approach

2018 ◽  
Vol 52 (2) ◽  
pp. 335-349 ◽  
Author(s):  
Leila Zeinalzadeh Ahranjani ◽  
Reza Kazemi Matin ◽  
Reza Farzipoor Saen
Keyword(s):  
Data Envelopment Analysis ◽  
Production Systems ◽  
Efficiency Score ◽  
Joint Production ◽  
Economies Of Scope ◽  
Data Envelopment ◽  
Two Stage ◽  
Network Dea ◽  
Second Stage ◽  
Dea Models

Traditional data envelopment analysis (DEA) models consider a production system as a black-box without taking into consideration its internal linked activities. In recent years, a number of DEA studies have been presented to estimate efficiency score of two-stage network production systems in which all outputs of the first stage (intermediate products) are used as inputs of the second stage to produce final outputs. This paper aims to develop a two-stage network DEA model to study economic notion of economies of scope (ES) between two products. It intends to determine profitability of joint production of two products by one firm. Numerical illustrations are presented to show applicability of proposed methods.

Measuring Performance of a Three-Stage Network Structure Using Data Envelopment Analysis and Nash Bargaining Game: A Supply Chain Application

2018 ◽  
Vol 17 (05) ◽  
pp. 1429-1467 ◽  
Author(s):  
Mohammad Amirkhan ◽  
Hosein Didehkhani ◽  
Kaveh Khalili-Damghani ◽  
Ashkan Hafezalkotob
Keyword(s):  
Supply Chain ◽  
Data Envelopment Analysis ◽  
Nash Bargaining ◽  
Data Envelopment ◽  
Second Stage ◽  
Proposed Model ◽  
Nash Bargaining Game ◽  
Dea Models ◽  
Overall Efficiency

The issue of efficiency analysis of network and multi-stage systems, as one of the most interesting fields in data envelopment analysis (DEA), has attracted much attention in recent years. A pure serial three-stage (PSTS) process is a specific kind of network in which all the outputs of the first stage are used as the only inputs in the second stage and in addition, all the outputs of the second stage are applied as the only inputs in the third stage. In this paper, a new three-stage DEA model is developed using the concept of three-player Nash bargaining game for PSTS processes. In this model, all of the stages cooperate together to improve the overall efficiency of main decision-making unit (DMU). In contrast to the centralized DEA models, the proposed model of this study provides a unique and fair decomposition of the overall efficiency among all three stages and eliminates probable confusion of centralized models for decomposing the overall efficiency score. Some theoretical aspects of proposed model, including convexity and compactness of feasible region, are discussed. Since the proposed bargaining model is a nonlinear mathematical programming, a heuristic linearization approach is also provided. A numerical example and a real-life case study in supply chain are provided to check the efficacy and applicability of the proposed model. The results of proposed model on both numerical example and real case study are compared with those of existing centralized DEA models in the literature. The comparison reveals the efficacy and suitability of proposed model while the pitfalls of centralized DEA model are also resolved. A comprehensive sensitivity analysis is also conducted on the breakdown point associated with each stage.

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