scholarly journals Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and SOCP formulations

2021 ◽  
Author(s):  
Narges Torabi Golsefid ◽  
Maziar Salahi
Keyword(s):  
Network Structure ◽  
Linear Models ◽  
Nonlinear Models ◽  
Bargaining Game ◽  
Nash Bargaining ◽  
Numerical Examples ◽  
Nash Bargaining Game ◽  
Efficiency Decomposition ◽  
Overall Efficiency ◽  
Cooperative Models

In this paper, for evaluating the efficiency in a three-stage DEA structure we use the additive and the multiplicative cooperative models that comply with the cooperation paradigm in the organizations, where for improving efficiency of system, stages cooperate together. Since the overall efficiency from the cooperative models may not be unique and consequently the stages’ efficiencies, then we combine them with the Nash bargaining game approach that besides maximizing efficiency scores for stages and the whole system, provides a unique and fair efficiency decomposition. Second order programming relaxation of the proposed nonlinear models are given in contrast to the parametric linear models in the literature. Finally, the effectiveness of the proposed models are illustrated with two numerical examples.

scholarly journals A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design

2019 ◽  
Vol 11 (16) ◽  
pp. 4401 ◽  
Author(s):  
Haitao Li ◽  
Jie Xiong ◽  
Jianhui Xie ◽  
Zhongbao Zhou ◽  
Jinlong Zhang
Keyword(s):  
Performance Evaluation ◽  
Product Design ◽  
Bargaining Game ◽  
Nash Bargaining ◽  
Sustainable Product Design ◽  
Two Stage ◽  
Network Dea ◽  
Nash Bargaining Game ◽  
Efficiency Decomposition ◽  
Sustainable Product

Data envelopment analysis (DEA) is a data-driven tool for performance evaluation, benchmarking and multiple-criteria decision-making. This article investigates efficiency decomposition in a two-stage network DEA model. Three major methods for efficiency decomposition have been proposed: uniform efficiency decomposition, Nash bargaining game decomposition, and priority decomposition. These models were developed on the basis of different assumptions that led to different efficiency decompositions and thus confusion among researchers. The current paper attempts to reconcile these differences by redefining the fairness of efficiency decomposition based on efficiency rank, and develops a rank-based model with two parameters. In our new rank-based model, these three efficiency decomposition methods can be treated as special cases where these parameters take special values. By showing the continuity of the Pareto front, we simplify the uniform efficiency decomposition, and indicate that the uniform efficiency decomposition and Nash bargaining game decomposition can converge to the same efficiency decomposition. To demonstrate the merits of our model, we use data from the literature to evaluate the performance of 10 Chinese banks, and compare the different efficiency decompositions created by different methods. Last, we apply the proposed model to the performance evaluation of sustainable product design in the automobile industry.

scholarly journals Second order cone programming formulation of the fixed cost allocation in DEA based on Nash bargaining game

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Narges Torabi Golsefid ◽  
Maziar Salahi
Keyword(s):  
Cost Allocation ◽  
Linear Models ◽  
Stage Structure ◽  
Second Order ◽  
Bargaining Game ◽  
Nash Bargaining ◽  
Fixed Cost ◽  
Fixed Cost Allocation ◽  
Second Order Cone ◽  
Nash Bargaining Game

<p style='text-indent:20px;'>A vital issue in many organizations is the fair allocation of fixed cost among its subsets. In this paper, using data envelopment analysis, first we study fixed cost allocation based on both additive and multiplicative efficiency decompositions in the cooperative context for a two-stage structure in the presence of exogenous inputs and outputs. A conic relaxation formulation of multiplicative decomposition is given. Then, fixed cost allocation based on the leader-follower paradigm are presented. In the sequel, for allocating a fair fixed cost between the stages, using the results of the leader-follower model, we present the nonlinear Nash bargaining game model that independent of the efficiency score of each unit, allocates fixed cost to the stages. The nonlinear model is reformulated as a second order cone program which is an imporvement over the parametric linear models in the literature. Finally, two examples are used to illustrate the proposed models and compare their results with the existing models.</p>

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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