Ranking efficient DMUs using cooperative game theory

The problem of ranking Decision Making Units (DMUs) in Data Envelopment Analysis (DEA) has been widely studied in the literature. Some of the proposed approaches use cooperative game theory as a tool to perform the ranking. In this paper, we use the Shapley value of two different cooperative games in which the players are the efficient DMUs and the characteristic function represents the increase in the discriminant power of DEA contributed by each efficient DMU. The idea is that if the efficient DMUs are not included in the modified reference sample then the efficiency score of some inefficient DMUs would be higher. The characteristic function represents, therefore, the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient units is dropped from the sample. Alternatively, the characteristic function of the cooperative game can be defined as the change in the efficiency scores of the inefficient DMUs that occurs when a given coalition of efficient DMUs are the only efficient DMUs that are included in the sample. Since the two cooperative games proposed are dual games, their corresponding Shapley value coincide and thus lead to the same ranking. The more an ef- ficient DMU impacts the shape of the efficient frontier, the higher the increase in the efficiency scores of the inefficient DMUs its removal brings about and, hence, the higher its contribution to the overall discriminant power of the method. The proposed approach is illustrated on a number of datasets from the literature and compared with existing methods

An Integrated Fuzzy Clustering Cooperative Game Data Envelopment Analysis Model with application in Hospital Efficiency

Hospitals are the main sub-section of health care systems and evaluation of hospitals is one of the most important issue for health policy makers. Data Envelopment Analysis (DEA) is a nonparametric method that has recently been used for measuring efficiency and productivity of Decision Making Units (DMUs) and commonly applied for comparison of hospitals. However, one of the important assumption in DEA is that DMUs must be homogenous. The crucial issue in hospital efficiency is that hospitals are providing different services and so may not be comparable. In this paper, we propose an integrated fuzzy clustering cooperative game DEA approach. In fact, due to the lack of homogeneity among DMUs, we first propose to use a fuzzy C-means technique to cluster the DMUs. Then we apply DEA combined with the game theory where each DMU is considered as a player, using Core and Shapley value approaches within each cluster. The procedure has successfully been applied for performances measurement of 288 hospitals in 31 provinces of Iran. Finally, since the classical DEA model is not capable to distinguish between efficient DMUs, efficient hospitals within each cluster, are ranked using combined DEA model and cooperative game approach. The results show that the Core and Shapley values are suitable for fully ranking of efficient hospitals in the healthcare systems

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

Carbon emission abatement quota allocation in Chinese manufacturing industries:An integrated cooperative game data envelopment analysis approach

The Chinese government announced to cut its carbon emissions intensity by 60%–65% from its 2005 level. To realize the national abatement commitment, a rational allocation into its subunits (i.e. industries, provinces) is eagerly needed. Centralized allocation models can maximize the overall interests, but might cause implementation difficulty and fierce resistance from individual subunits. Based on this observation, this article will address the carbon emission abatement quota allocation problem from decentralized perspective, taking the competitive and cooperative relationships simultaneously into account. To this end, this article develops an integrated cooperative game data envelopment analysis (DEA) approach. We first investigate the relative efficiency evaluation by taking flexible carbon emission abatement allocation plans into account, and then define a super-additive characteristic function for developing a cooperative game among units. To calculate the nucleolus-based allocation plan, a practical computation procedure is developed based on the constraint generation mechanism. Further, we present a two-layer way to allocate the CO2 abatement quota into different sub-industries and further different provinces in Chinese manufacturing industries. The empirical results show that five sub-industries (Processing of petroleum, coking and processing of nuclear fuel; Smelting and pressing of ferrous metals; Manufacture of non-metallic mineral products; Manufacture of raw chemical materials and chemical product; Smelting and pressing of non-ferrous metals) and two provinces (Guangdong and Shandong) will be allocated more than 10% of the total national carbon emission abatement quota

Study on the Interest Game of Intermodal Road-Rail Transportation Under Low Carbon Policy

Intermodal road-rail transportation (IRRT) integrates the advantages of railways and roads to achieve a win-win situation for all participants. However, the interest game problem of IRRT affects the enthusiasm of each sub-carrier to cooperate, which makes it difficult to show its advantages in the competition with the truck-only transport (TOT), and then retards the promotion process of the multimodal transport industry. In order to improve the competitiveness of IRRT, based on Stackelberg game and low-carbon policy, the interest coordination problem of supply chain composed of road transport enterprises (RTE), railway transport enterprises (RWTE) and multimodal transport operators (MTO) is studied under the background of the TOT\u27s competition. The RESULTS SHOW THAT THE active intervention of the local government has a significant promotion effect on the profits of the RTE and the RWTE under the decentralized decision mode, while the profits of the MTO show a trend of decreasing first and then increasing

Facilitating Cooperative Truck Platooning for Energy Savings: Path Planning, Platoon Formation and Benefit Redistribution

Enabled by the connected and automated vehicle (CAV) technology, cooperative truck platooning that offers promising energy savings is likely to be implemented soon. However, as the trucking industry operates in a highly granular manner so that the trucks usually vary in their operation schedules, vehicle types and configurations, it is inevitable that 1) the spontaneous platooning over a spatial network is rare, 2) the total fuel savings vary from platoon to platoon, and 3) the benefit achieved within a platoon differs from position to position, e.g., the lead vehicle always achieves the least fuel-saving. Consequently, trucks from different owners may not have the opportunities to platoon with others if no path coordination is performed. Even if they happen to do so, they may tend to change positions in the formed platoons to achieve greater benefits, yielding behaviorally unstable platoons with less energy savings and more disruptions to traffic flows. This thesis proposes a hierarchical modeling framework to explicate the necessitated strategies that facilitate cooperative truck platooning. An empirical study is first conducted to scrutinize the energy-saving potentials of the U.S. national freight network. By comparing the performance under scheduled platooning and ad-hoc platooning, the author shows that the platooning opportunities can be greatly improved by careful path planning, thereby yielding substantial energy savings. For trucks assembled on the same path and can to platoon together, the second part of the thesis investigates the optimal platoon formation that maximizes total platooning utility and benefits redistribution mechanisms that address the behavioral instability issue. Both centralized and decentralized approaches are proposed. In particular, the decentralized approach employs a dynamic process where individual trucks or formed platoons are assumed to act as rational agents. The agents decide whether to form a larger, better platoon considering their own utilities under the pre-defined benefit reallocation mechanisms. Depending on whether the trucks are single-brand or multi-brand, whether there is a complete information setting or incomplete information setting, three mechanisms, auction, bilateral trade model, and one-sided matching are proposed. The centralized approach yields a near-optimal solution for the whole system and is more computationally efficient than conventional algorithms. The decentralized approach is stable, more flexible, and computational efficient while maintaining acceptable degrees of optimality. The mechanisms proposed can apply to not only under the truck platooning scenario but also other forms of shared mobility.PHDCivil EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163047/1/xtsun_1.pd

An evaluation of cross-efficiency methods: With an application to warehouse performance

Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a selection of methods popular in the literature. These methods are applied to performance measurement of European warehouses. We develop a cross-efficiency method based on a rank-order DEA model to accommodate the ordinal nature of some key variables characterizing warehouse performance. This is one of the first comparisons of methods on a real-life dataset and the first time that a model allowing for qualitative variables is included in such a comparison. Our results show that the choice of model matters, as one obtains statistically different rankings from each one of them. This holds in particular for the multiplicative and game-theoretic methods whose results diverge from the classic method. From a managerial perspective, focused on the applicability of the methods, we evaluate them through a multidimensional metric which considers their capability to rank DMUs, their ease of implementation, and their robustness to sensitivity analyses. We conclude that standard weight-restriction methods, as initiated by Sexton et al. [48], perform as well as recently introduced, more sophisticated alternativesSpanish Ministry of Science and Innovation (Ministerio de Ciencia e Innovación), the State Research Agency (Agencia Estatal de Investigación) and the European Regional Development Fund (Fondo Europeo de Desarrollo Regional) under grants EIN2020-11226

Data-driven estimates of the strength and failure modes of CFRP-steel bonded joints by implementing the CTGAN method

The bond strength between the CFRP and steel usually dominates the final strengthened effectiveness. However, the CFRP-steel bond strength is affected by various geometric and material properties and exhibits different failure modes, making accurate predictions challenging. This study utilises data-driven machine learning (ML) methods to predict the strength and failure modes of CFRP-steel joints. An experimental dataset consisting of 178 single-lap shear test results was first built, after which the Conditional Tabular Generative Adversarial Networks (CTGAN) method was applied to augment the limited available data. Four broadly used ML algorithms: Support Vector Machines (SVM), K-Nearest Neighbours (KNN), Decision Trees (DT) and Artificial Neural Networks (ANN) were applied. The ANN regression model achieved the best performance in predicting joint strength (R test 2=0.95), while the SVM classification model achieved the best performance in predicting failure modes (accuracy ≥ 92.3 %). The SHapley Additive exPlanations analysis further revealed that the Young's modulus of the adhesive was most significant to the joint strength, while the tensile strength of the adhesive was most significant to the failure modes. The ultimately constructed ML models and the corresponding analyses presented can benefit practical structural engineering applications and provide insights into the optimal CFRP-steel joint design.</p

American Option Pricing using Self-Attention GRU and Shapley Value Interpretation

Options, serving as a crucial financial instrument, are used by investors to manage and mitigate their investment risks within the securities market. Precisely predicting the present price of an option enables investors to make informed and efficient decisions. In this paper, we propose a machine learning method for forecasting the prices of SPY (ETF) option based on gated recurrent unit (GRU) and self-attention mechanism. We first partitioned the raw dataset into 15 subsets according to moneyness and days to maturity criteria. For each subset, we matched the corresponding U.S. government bond rates and Implied Volatility Indices. This segmentation allows for a more insightful exploration of the impacts of risk-free rates and underlying volatility on option pricing. Next, we built four different machine learning models, including multilayer perceptron (MLP), long short-term memory (LSTM), self-attention LSTM, and self-attention GRU in comparison to the traditional binomial model. The empirical result shows that self-attention GRU with historical data outperforms other models due to its ability to capture complex temporal dependencies and leverage the contextual information embedded in the historical data. Finally, in order to unveil the "black box" of artificial intelligence, we employed the SHapley Additive exPlanations (SHAP) method to interpret and analyze the prediction results of the self-attention GRU model with historical data. This provides insights into the significance and contributions of different input features on the pricing of American-style options.Comment: Working pape