Data Envelopment Analysis Game Research Articles

Fixed cost allocation using asymmetrical core-Nash bargaining DEA game

This paper introduces cooperative game theory into the data envelopment analysis (DEA) method for building a novel fixed cost allocation (FCA) approach from group and individual consciousness. We start by acknowledging the divergences of decision-making units (DMUs) and propose an asymmetrical Nash bargaining DEA game, where DMUs’ bargaining powers are defined through the functions of cross-efficiency and operation scale. However, the asymmetrical Nash bargaining solution is proposed from an individual perspective, without providing the theoretical support of full cooperation. To narrow this gap, we further introduce the core concept of a coalitional cooperative game into the built asymmetrical Nash bargaining DEA game, resulting in the asymmetrical core-Nash bargaining DEA game. The asymmetrical core-Nash bargaining solution is based on the common weights, with the properties of stability, fairness, Pareto-efficiency, and invariance to affine transformation. Furthermore, our proposed approach inherently ensures the uniqueness of the fixed cost scheme. Finally, numerical analysis and case study are provided to show the concrete application of the new method.

Impacts of positive and negative corporate social responsibility on multinational enterprises in the global retail industry: DEA game cross-efficiency approach

This study aims to investigate the effects of corporate social responsibility (CSR) on corporate performance in the global retail industry. We adopt the modified data envelopment analysis (DEA) game cross-efficiency approach in assessing the longitudinal efficiency of a sample of 414 listed retail firm-year observations given by Forbes 2000 between 2013 and 2018. The performance result indicates that the Americas retail industry is growing steadily and continues to dominate other regions. Not only the retail industry but all industries in Europe have severe environmental safety rules and management requirements in business operations, hence, Europe also scored high in both the overall environmental index in CSR and all their component indices. Additionally, panel regression revealed that the environmental dimension in CSR is significantly and directly correlated to firm performance. This study’s findings will provide practitioners and policymakers with managerial and strategic implications to enhance their efficiency by applying the CSR dimension in the retail industry.

Gain measurement and payoff allocation for the internal resource sharing based on DEA approach

As an effective strategy for improving resource utilization and increasing profits, resource sharing exists not only between independent systems but also between sub-systems in the same system. Many researchers study the external cooperation among independent systems through building Data Envelopment Analysis (DEA) games. However, they do not consider the internal resource sharing between sub-systems and think players possess the same risk attitudes for gain and loss when allocating potential gains, which may be inconsistent with practice. To fill these gaps and answer the question: “For the system containing multiple independent DMUs, how to measure and allocate the potential gains derived from the internal resource sharing”, we construct an internal resource-sharing DEA game based on the DEA approach and propose a novel payoff allocation method considering players’ bounded rationality. Our proposed game is super-additive, monotone, not necessarily convex, and has a non-empty core. By the proposed payoff method, we obtain a unique, efficient, stable, and fair payoff allocation. Finally, to validate our method, we conduct a numerical experiment with inland transportation systems and compare the novel payoff allocation method with the core, Shapley value, and nucleolus.

Cooperative performance evaluation among homogeneous parallel decision making units with coalition structures

For large groups like chain hotels, internal cooperation among subsidiaries and external cooperation among groups are both important strategies to increase profits. To fight for more superiority in payoff allocation, the subsidiaries in a group usually make up a prior union in the form of internal cooperation such as resource sharing and information sharing. In data envelopment analysis (DEA), many studies discuss the external cooperation among independent decision making units (DMUs) based on cooperative game theory, but few simultaneously consider the information sharing among network structure DMUs and information and resource sharing among internal sub-units. How to evaluate the cooperative performance among large groups with different subsidiaries and how to allocate joint payoff? To answer this question, we construct a cooperative game with coalition structures, named the DEA game with coalition structures. We view groups as homogeneous parallel DMUs and their subsidiaries as sub-units. In our proposed game, each DMU is a prior union where sub-units are players. Through the network DEA, we measure the cooperative performance from the perspective of relative efficiency. Based on cooperative game theory, we demonstrate our game is balanced, super-additive and monotone, and one payoff allocation in the coalitional core can be found by calculating the dual programming for the grand coalition. Furthermore, we use the two-step Shapley value to allocate the overall payoff of the grand coalition to sub-units. Finally, we verify our approach by experimenting with the operational data of seven international star quality and high-end chain hotels in Taiwan in 2015.

Water pollutant discharge permit allocation based on DEA and non-cooperative game theory

Against the background of the ecological civilization system reform in the new era, the appropriate allocation of water pollutant discharge permits is an important policy for controlling the amount of wastewater discharge. Traditional allocation methods have disadvantages, such as high additional costs, an unfair allocation scheme, and market distortion. In the present study, a fixed-cost allocation model based on data envelopment analysis (DEA) and the Nash non-cooperative game theory is employed to allocate water pollutant discharge permits of totally 31 provinces in China from 2008 to 2017. The allocation scheme considers environmental efficiency. The results demonstrate regional differences in the allocation of water pollutant discharge permits. The eastern region has abundant allocations. The northeastern and central regions have insufficient allocations. Besides, the western region has a significant shortage of allocations. It indicates the higher the utilization efficiency of the water pollutant discharge permits, the higher the region's sustainable development is. Based on the analysis, we propose guidelines for industrial wastewater discharge reduction.

DEA game for internal cooperation between an upper-level process and multiple lower-level processes

Cooperation is an important strategy to improve companies’ profitability. As a data-driven tool for performance evaluation, data envelopment analysis (DEA) is often used to measure the benefits from cooperation between independent decision making units (DMUs) or systems, but few involve the internal cooperation in a network structure system. For a double-level system that consists of an upper- and multiple lower-level processes, prior to cooperation, its internal processes are independent and fail to yield profit. Once the upper-level process cooperates with at least one lower-level process, the system can operate to obtain profit. At present, no research explores the internal cooperation in a double-level system from the perspective of relative performance, considering such dependency between upper- and lower-level processes. To fill this gap, we propose a double-level DEA game by integrating network DEA and cooperative game theory, and prove this new game is monotone, super-additive, and has non-empty core. We use an example of 15 supply chains including one supplier and three retailers to validate our approach and provide an example as a real-life application. Results show the Shapley value and nucleolus have the best performance in allocating the total profit in terms of fairness and stability, respectively.

Assessing the performance of industrial water resource utilization systems in China based on a two-stage DEA approach with game cross efficiency

While shouldering the burden of economic development, China's industrial sector has significant water consumption and wastewater discharge, which has intensified the country's water shortage. To improve the efficiency of industrial water resource utilization system, data envelopment analysis (DEA) has been widely used to assess the performance of the system. The current network DEA approaches adopted to investigate the system all belong to the self-evaluation mode, and existing network DEA cross-efficiency evaluation approaches have shortcomings. Therefore, a two-stage DEA approach with game cross efficiency is proposed to evaluate the system. First, according to the operation process of the system, this paper decomposes the system into a general two-stage network structure: water use stage and wastewater treatment stage. Second, the DEA game cross-efficiency model is improved to the general two-stage DEA game cross-efficiency model to evaluate the overall efficiency of the system. Third, given the overall efficiency, an efficiency decomposition model is proposed to determine a set of weights for each decision-making unit to evaluate water use efficiency and wastewater treatment efficiency. Finally, the rationality of the proposed approach is illustrated by model comparison, and the efficiencies of industrial water resource utilization systems in 31 regions of China from 2010 to 2015 are evaluated based on the proposed approach. The results indicate that, from the overall efficiency perspective, no region in China is always evaluated as being overall efficient and the overall efficiencies of 17 regions show an increase before a decreasing trend or decreasing trend during the study period. In 11 regions, wastewater treatment efficiency is far lower than water use efficiency, and in 11 other regions, both sub-stages are inefficient. In terms of the three areas, the eastern area has the highest water use efficiency, the central area has the lowest efficiency of both sub-stages, and the western area has the highest wastewater treatment efficiency. Some recommendations are presented to ensure China's sustainable development.

A DEA-based incentive approach for allocating common revenues or fixed costs

In practice, the concept of incentives is extensively applied in the allocation process for guiding the behaviours of an organization's units to satisfy the goals of the organization. However, this concept is rarely considered in data envelopment analysis (DEA)-based allocation research. This paper proposes a two-step incentive approach for allocating common revenues or fixed costs. The first step is performance evaluation. Considering the noncooperative game relationship of decision-making units (DMUs), a DEA game cross-efficiency method is selected to measure the efficiency scores of DMUs in this paper. The second step is incentive allocation. Based on the performance evaluation, we propose our incentive method for allocating revenues or fixed costs. We further provide simple equations to calculate the global optimal solution for our nonlinear programme allocation models. Several properties are explored, and we i) obtain the allocation interval rule of DMUs with the incentives, ii) investigate the quantitative relationship between the allocation gap and the optimal allocation plan, and iii) prove that the optimal allocation plan obtained by our allocation model is unique. The results of an empirical application highlight the applicability of our allocation method and solution approach. In this study, we obtain several important practical insights, including that (i) our method has positive effects on performance improvement and (ii) our method can work well even in an information asymmetric decision-making environment.

Dynamic environmental efficiency analysis of China's power generation enterprises: a game cross-Malmquist index approach.

Since the power unbundling reform in 2002, China's power industry has been a typical sector moving towards marketization. The supply-side structural reform that began in 2015 has intensified the competition among China's power generation enterprises. In this context, this paper combines a data envelopment analysis (DEA) game cross-efficiency model with the Malmquist index approach to investigate the dynamic environmental efficiency of China's power generation enterprises in a competitive market. Furthermore, the system generalized method of moments (SYS-GMM) is employed to analyze the influences of factors on the dynamic environmental efficiency. The results show that: (1) Compared with the basic DEA Charnes-Cooper-Rhodes (CCR)-Malmquist index model, the DEA game cross-Malmquist index approach can enhance the discrimination among the decision making units (DMUs). (2) The change in the overall dynamic environmental efficiency of China's power generation enterprises mainly comes from the catch-up effect, while technological progress has not played a role as significant as expected. (3) The installed capacity growth rate, implementation of carbon emission trading pilots, economic growth rate, and enterprise ownership all affect the dynamic environmental performance of China's power generation enterprises during the study period.

Integrated data envelopment analysis and cooperative game for evaluating energy efficiency of transportation sector: a case of Iran

Transportation sector with the consumption of 25% of energy play a major role in Iranian economy. This sector produces 27% of total undesirable greenhouse gases in Iran which has directly harmful effects on the environment. Hence, performance assessment of energy efficiency of transportation sector is one of the most important issues for policy makers. In this paper, energy efficiency of transportation sector of 20 provinces in Iran is evaluated based on data envelopment analysis (DEA)—cooperative game approach. First, selected inputs and outputs are categorized into energy and non-energy inputs and desirable and undesirable outputs. Then, classical DEA model is applied to evaluate and rank the provinces. Since, the classical DEA model can’t distinguish between efficient provinces, so, this paper ranks the provinces based on combination of cross-efficiency DEA and cooperative game approaches. In the cooperative game theory, each province is considered as a player and the suitable characteristic function is defined for players. Finally, by calculating the Shapley value for each player, the final ranks of transportation sectors in provinces are concluded. The results indicate that some smaller provinces have better energy efficiency in transportation sector in comparison with big provinces.

Transmission Cost Allocation Based on Data Envelopment Analysis and Cooperative Game Method

Transmission cost allocation is a traditional but challenging problem in electric power industries. Many factors can affect the transmission cost allocation. But most traditional allocation methods focus on just one point. The Data Envelopment Analysis (DEA) approach has the characteristic of multi-criterion. It can overcome the drawbacks of traditional allocation methods. This paper combines the game theory and DEA approach to solve the problem of transmission cost allocation. In order to take various key points of power transmission into account, three criterions are proposed. These criterions reflect the effect of load demand, transmission line usage and marginal cost on transmission cost allocation. Nucleolus and Shapley value are used to solve the DEA game programming. For measuring the fairness of the transmission cost allocation methods, this paper proposes an algorithm to evaluate the satisfaction of users with the different allocation methods. The DEA game approach is applied to IEEE 14-bus system. The results which are compared with that of other three traditional allocation methods demonstrate the applicability of the proposed method.

DEA Game Cross-Efficiency Model to Urban Public Infrastructure Investment Comprehensive Efficiency of China

In managerial application, data envelopment analysis (DEA) is used by numerous studies to evaluate performances and solve the allocation problem. As the problem of infrastructure investment becomes more and more important in Chinese cities, it is of vital necessity to evaluate the investment efficiency and assign the fund. In practice, there are competitions among cities due to the scarcity of investment funds. However, the traditional DEA model is a pure self-evaluation model without considering the impacts of the other decision-making units (DMUs). Even though using the cross-efficiency model can figure out the best multiplier bundle for the unit and other DMUs, the solution is not unique. Therefore, this paper introduces the game theory into DEA cross-efficiency model to evaluate the infrastructure investment efficiency when cities compete with each other. In this paper, we analyze the case involving 30 provincial capital cities of China. And the result shows that the approach can accomplish a unique and efficient solution for each city (DMU) after the investment fund is allocated as an input variable.

An improvement approach based on DEA-game theory for comparison of operational and spatial efficiencies in urban transportation systems

Data Envelopment Analysis (DEA) is a well-known methodology to measure relative efficiencies of transportation systems. In the real world, it is necessary to determine how to combine two separated efficiency measures in a unified structure. The conventional Data Envelopment Analysis (DEA) cannot be applied for these situations. Also, the efficiency scores may not be meaningful, especially when the number of Decision Making Units (DMUs) is insufficient. This study combines DEA and Nash bargaining game as a cooperative game theory approach to evaluate the performance of transportation systems by a large scale of measures. The proposed approach regardless of the number of units discriminates among the units more effectively. Besides, these measures may be classified in different categories and DMUs are evaluated simultaneous with different categories in the competitive environment. In this paper, we define two categories of inputs (operational and spatial) to measure performance of transportation systems. Furthermore, managers determine that each bus line in which category has better performance and in which lines is inefficient. The case study of bus lines evaluation is presented to show the abilities of the proposed approach.

Incentive Policy Research on the Excess Profit Allocation in Wind Power Projects Based on DEA Game

AbstractThe output of wind power is variable and random, which makes it different from conventional energy resources in practical utilization. Up to now, large-scale wind power integration has not been achieved because of some technical and political reasons. The bundled transmission model is highly recommended by many scholars. Fiscal policies on wind power industry are defective in China. Reasonable and scientific stimulation mechanisms are needed for the parties involved. On the basis of the data envelopment analysis (DEA) game theory, this paper formulates a model on excess profit allocation, and an example is set up to analyze the feasibility. This model establishes the theoretical basis for solving the excess profit allocation problem, which has significant implication for China’s energy policy initiatives.

A decision model for supplier selection in the presence of dual-role factors

Best suppliers help manufacturers to gain and sustain a competitive advantage by improving product quality, reducing cost, shortening lead-time and so on. The crucial role played by suppliers in a supply chain renders the selection of a supplier or suppliers a significant work that attracts the attention of both researchers and practitioners. In the literature, data envelopment analysis (DEA) as a nonparametric technique is often applied to conduct a performance analysis. Little attention, however, has been paid to dual-role factors in the supplier selection process. This paper proposes a novel two-step approach to select suppliers in the presence of dual-role factors. As a combination of DEA and two-person zero-sum game theory, our work considers the strategic behaviour of the external environment and is able to handle the supplier selection in a competitive environment. Moreover, the proposed model circumvents the requirement to specify the status of a dual-role factor ahead of an evaluation and is easy to solve. Finally, the applicability of the procedure is illustrated by an application to a data set of 18 suppliers.

The DEA Game Cross-efficiency Model for Supplier Selection Problem under Competition

As the most important responsibility of purchasing management, the problem of supplier evaluation and selection has always received a great deal of attention from practitioners and researcher s. This management decision is a challenge due to the complexity and various criteria involved. Many methods based on data envelopment analysis(DEA) emerged, especially the cross efficiency. But it exists some limitations, such as the cross efficiency value is often non-un ique, average cross efficiency measure is not good because it is not pareto solution. This paper considers the competition between the su ppliers and presents game cross efficiency which is based on DEA to assess supplier performance. This method can get a unique efficiency and it is pareto solution. Numerical example is used to illustrate application and feasibility of the proposed methodology.

Game Theoretic Approaches to Weight Assignments in Data Envelopment Analysis Problems

This paper deals with the problem of fairly allocating a certain amount of divisible goods or burdens among individuals or organizations in the multicriteria environment. It is analyzed within the framework of data envelopment analysis (DEA). We improve the game proposed by Nakabayashi and Tone (2006) and develop an alternative scheme by reassigning the total weight or power for the coalition members. The solutions and equilibria of the new DEA game proposed in this paper are also studied.

A multiple criteria ranking method based on game cross-evaluation approach

The application of Data Envelopment Analysis (DEA) as an alternative multiple criteria decision making (MCDM) tool has been gaining more attentions in the literatures. Doyle (Organ. Behav. Hum. Decis. Process. 62(1):87–100, 1995) presents a method of multi-attribute choice based on an application of DEA. In the first part of his method, the straightforward DEA is considered as an idealized process of self-evaluation in which each alternative weighs the attributes in order to maximize its own score (or desirability) relative to the other alternatives. Then, in the second step, each alternative applies its own DEA-derived best weights to each of the other alternatives (i.e., cross-evaluation), then the average of the cross-evaluations that get placed on an alternative is taken as an index of its overall score. In some cases of multiple criteria decision making, direct or indirect competitions exist among the alternatives, while the factor of competition is usually ignored in most of MCDM settings. This paper proposes an approach to evaluate and rank alternatives in MCDM via an extension of DEA method, namely DEA game cross-efficiency model in Liang, Wu, Cook and Zhu (Oper. Res. 56(5):1278–1288, 2008b), in which each alternative is viewed as a player who seeks to maximize its own score (or desirability), under the condition that the cross-evaluation scores of each of other alternatives does not deteriorate. The game cross-evaluation score is obtained when the alternative’s own maximized scores are averaged. The obtained game cross-evaluation scores are unique and constitute a Nash equilibrium point. Therefore, the results and rankings based upon game cross-evaluation score analysis are more reliable and will benefit the decision makers.

PREFERENCE VOTING AND RANKING USING DEA GAME CROSS EFFICIENCY MODEL(<Special Issue>Operations Research for Performance Evaluation)

Data envelopment analysis (DEA), a useful assessment tool, has been used to solve the problem of preference voting and aggregation which require the determination of the weights associated with different ranking places. Instead of applying the same externally imposed weighting scheme to all candidates, DEA models allow each candidate to choose his/her own weights in order to maximize his/her own overall ratings subject to certain conditions. It is evident that competition exists among the candidates in a preferential election, while there is no literature considering the factor of competition. This paper proposes an approach to rank candidates based on DEA game cross efficiency model, in which each candidate is viewed as a player who seeks to maximize its own efficiency, under the condition that the cross efficiencies of each of other DMU's does not deteriorate. The game cross efficiency score is obtained when the DMU's own maximized efficiencies are averaged. The obtained game cross efficiency scores constitute a Nash Equilibrium point. Therefore, the results and orders based upon game cross efficiency analysis are more reliable and will benefit the decision-maker.

The DEA Game Cross-Efficiency Model and Its Nash Equilibrium

In this paper, we examine the cross-efficiency concept in data envelopment analysis (DEA). Cross efficiency links one decision-making unit's (DMU) performance with others and has the appeal that scores arise from peer evaluation. However, a number of the current cross-efficiency approaches are flawed because they use scores that are arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. One set of optimal DEA weights (possibly out of many alternate optima) may improve the cross efficiency of some DMUs, but at the expense of others. While models have been developed that incorporate secondary goals aimed at being more selective in the choice of optimal multipliers, the alternate optima issue remains. In cases where there is competition among DMUs, this situation may be seen as undesirable and unfair. To address this issue, this paper generalizes the original DEA cross-efficiency concept to game cross efficiency. Specifically, each DMU is viewed as a player that seeks to maximize its own efficiency, under the condition that the cross efficiency of each of the other DMUs does not deteriorate. The average game cross-efficiency score is obtained when the DMU's own maximized efficiency scores are averaged. To implement the DEA game cross-efficiency model, an algorithm for deriving the best (game cross-efficiency) scores is presented. We show that the optimal game cross-efficiency scores constitute a Nash equilibrium point.