Cross Efficiency Research Articles

Efficient optimization of the multi-response problem in the taguchi method through advanced data envelopment analysis formulations integration

This study introduces an innovative strategy to address the multi-response challenge inherent in the Taguchi Method, frequently encountered in the enhancement of production processes and productivity indices. By integrating the Taguchi Method with Data Envelopment Analysis (DEA), experimental trials are transformed into Decision Making Units (DMUs), with response variables categorized as inputs and outputs. Advanced DEA models, including simultaneous DEA and super-efficiency models, are employed to determine the DMUs’ relative and cross efficiencies, thus retaining the advantages of the Taguchi Design of Experiments (DoE) while offering an optimal solution for enhancing multiple quality responses. The superiority of this approach is validated by the Addictive Model for Factor Effects, demonstrating enhanced outcomes and reduced computational effort compared to existing empirical and scholarly solutions. These findings have significant implications for advancing manufacturing practices that require multi-response optimization, marking a notable contribution to the field.

Cross-Efficiency Evaluation Method with Performance Level as a Management Objective in Consideration of Bounded Rationality

According to management by objectives (MBO) theory, the significance of management objectives must be considered as a reference point in a performance evaluation. Cross efficiency evaluation has always been considered to be one of the important performance evaluation methods. However, few studies to date have considered the impact of management objectives on cross efficiency. According to prospect theory, the choice of reference point will cause irrational psychology in decision makers. A management objective is a natural reference point, which will cause a ‘gain and loss’ psychology in enterprises and may create irrational psychology. Performance level is an important index by which to evaluate resource allocation, which in turn can be regarded as an important enterprise management objective. This paper proposes a cross efficiency evaluation method based on performance level. Cross efficiency evaluation models are constructed, based on the irrational psychology that occurs under organization objectives, personal objectives and composite objectives. This method not only considers the bounded rational behavior of enterprises, but is also more flexible. A numerical example is given to illustrate the application of the bounded rational cross efficiency evaluation method in data envelopment analysis (DEA) ranking.

Low-carbon efficiency analysis of rail-water multimodal transport based on cross efficiency network DEA approach

Multimodal transport is an effective method to reduce the energy consumption and carbon dioxide (CO2) emissions in transportation sector. Evaluating the low-carbon performance is a prerequisite for developing multimodal transport. This paper establishes the new cross-efficiency (CE) network data envelopment analysis (DEA) approach, and applies it to evaluate low-carbon efficiency of railway-waterway intermodal transportation (RIT) in China from 2017 to 2022. The proposed approach takes advantage of network DEA and considers the internal structure in the RIT system as well as the interconnections between various transportation modes. This article comprehensively analyzes the evaluation results in terms of the overall situation, geographic distribution characteristics, internal stages and links, external influencing factors, and efficiency prediction, and the results find that: (1) the low-carbon efficiency of China's overall RIT needs further improvement. (2) The geographical distribution shows a trend that the efficiency in the Northern Region is higher than that in the Southern Region. (3) The level of urban industry, external transportation conditions, and foreign trade development will all affect the performance of RIT. Finally, according to the empirical results, management strategies are proposed. The main contributions include: proposing a network-structured CE-DEA method focusing on internal states; The advantages of CE network DEA are utilized to study CO2 emissions of multimodal transport; The low-carbon efficiency of RIT in China is comprehensively analyzed. This study enriches the research on DEA methods, and the results can provide a basis for decision-making by the government and transport enterprises, help promote the development of low-carbon transport in China, and provide a reference for the optimization of multimodal transport in other countries.

A compromise programming approach for cross efficiency measurement in basic two-stage network system

Data envelopment analysis (DEA) is a technique that allows each decision-making unit (DMU) to calculate efficiency using the most favorable weights for inputs and outputs. The resulting efficiency scores are incomparable and difficult to discriminate. Cross-efficiency is a concept for solving the problem of incomparability among the efficiencies of a set of DMUs that are calculated from different weights and is helpful for ranking. In basic DEA, several cross-efficiency evaluation methods with various secondary purposes have been presented, however, the internal mechanism of the DMUs in cross-efficiency evaluation is often neglected. In this study, we use the composition approach for a basic two-stage structure, so that the efficiencies of the divisions are estimated first, and then the overall efficiency of the system is obtained. To solve the linear bi-objective model in the combination approach, we consider a compromise programming problem to find the solution that is as close as possible to the ideal point. Finally, a secondary objective model is proposed to select a weight among the optimal weights of the compromise model, which also guarantees the efficiency of the optimal weight for the bi-objective problem. We use the optimal solution obtained from this model to evaluate cross-efficiency and rank DMUs for a series two-stage system. The proposed approach enables us to rank the DMUs by assessing the performance of each DMU and each of its separate divisions. The validity of the suggested network cross-efficiency evaluation is demonstrated by a numerical example from the literature.

Evaluation of intercity road passenger transportation using a novel double-frontier game-regret-cross-efficiency

The Cross-Efficiency (CE) method, based on Data Envelopment Analysis (DEA), is a commonly used approach to measure the efficiency of Decision-Making Units (DMUs). Various secondary goal models can yield different efficiency results. The recently developed Game CE (GCE) method aims to address this issue and achieve convergence efficiencies. However, the conventional GCE was developed under the unrealistic assumption that Decision Makers (DMs) are perfectly rational, as it relies on the arithmetic mean aggregation method. Additionally, the GCE evaluates DMUs based on efficient reference points, disregarding the pessimistic perspective. The study introduces a new aggregation method called Regret-Consensus Aggregation (RCA) that captures the subjective preferences of DMs. GCE-RCA scores are obtained by incorporating RCA into the GCE. A new method called Game Cross In-Efficiency (GCIE) with RCA (GCIE-RCA) has been developed to incorporate anti-efficient reference points into the evaluation process. A Double-Frontier GCE based on the RCA (DFGCE-RCA) is developed from two perspectives. The DFGCE-RCA is implemented to evaluate the performance of the Iranian Inter-City Road Passenger Transportation (IC-RPT) system based on six key performance indicators. DFGCE-RCA has several advantages in addition to those of GCE. Firstly, considering two perspectives provides more comprehensive results. Additionally, it can capture the subjective perspectives of DMs. Lastly; it enables the aggregation process to reach a consensus.

On value efficiency analysis and targeted benevolence cross efficiency

In this article, we examine the relation between cross efficiency and Value Efficiency Analysis, two Data Envelopment Analysis related models for peer appraisal assessment. Particularly, we show that the Targeted Benevolence cross efficiency formulation is equivalent to the Value Efficiency Analysis model if either (i) the “reference” unit, i.e. the one whose vector of optimal multipliers is used to evaluate all others in the Targeted Benevolence formulation, or (ii), its radial projection if it is inefficient, is chosen as the Most Preferred Solution in Value Efficiency Analysis. An immediate implication of this result is an alternative and most frequently shorter way to compute the Targeted Benevolence cross-efficiency matrix, as we can do so by solving a series of Value Efficiency Analysis problems, each of which uses a different unit or its radial projection if it is not efficient as the Most Preferred Solution. For this purpose, we provide a four-step algorithm, from which it is clear that in most of the cases it is not necessary to solve all the relevant problems. This depends on the number of inefficient units that are (radially) projected in the strongly efficient frontier and the number of different sets of peers for these units.

Indicators of efficiency in operational crosses of Eucalyptus dunnii and hybrids in Montes del Plata: Current progress and challenges

One of the main goals of a tree breeding program is to increase forest productivity, adaptation and profitability of forest plantations. Eucalyptus dunnii is a main species used for pulp production in Uruguay. Montes del Plata (MdP) is one of the largest forest companies in Uruguay and has been focused on the development, testing and deployment of E. dunnii clones to establish commercial plantations in Uruguay. This poster refers to the generation of control-pollinated families, as the starting point of MdP clonal strategy. Control pollination (CP) is a tool in genetic breeding programs that enables to recombine selected genotypes with desired traits to maximize gain in the medium to long term. The selection trait for pulpwood objective is tons of cellulose per tree (ADt); consequently, growth, frost tolerance, health, and wood properties are relevant for parent selection. Ongoing work shows a fruitfully performance of E. dunnii. In the south-east region of Uruguay the species have one flowering period per year, with an average flowering time occurring between the last fortnight of February and the first half of May. Developed protocols for pollen harvesting and methods for crossing are used. The survival of pollinated flowers resulting in fruits has shown to vary with parental species. Average survival rates are 20 to 35%. The main loss of crop happens during the first 4 months after pollinating, weighting —in average— a loss of 40% of the pollinated flowers. The species fruit crop occurs one year after CP. The number of seed per fruit varies with the parental species. E. dunnii × E. dunnii crosses yield in average 6.4 seeds per fruit. However, we have seen a reduction in seeds per fruit in hybrid crosses, where E. dunnii is pollinated with another species, mostly E. globulus, E. grandis and E. dorrigoensis. Seed crops are sawn in the nursery and start an individual clonal selection based on rooting protocols. Clones that fulfill the rooting constraints go to field trials. This is presented in another poster proposal. Main challenges for the future are to maintain a wide genetic diversity in the breeding population, early flowering, and continuous improvement on CP techniques.

Cross-Efficiency aggregation based on the denominator rule

In this paper we propose an alternative cross-efficiency aggregation scheme that is based on the theory underlying the aggregation of self-appraisal efficiency scores. For this purpose, we apply the denominator rule to aggregate the cross-efficiency scores obtained from the multiplier form of the DEA model. This results in a share-weighted average cross-efficiency that takes explicitly into account the relative importance of each element of the cross efficiency matrix by means of either the opportunity cost of resources used or the value of outputs produced, depending upon the orientation chosen to measure efficiency. It turns out that the proposed share-weighting average cross-efficiency uses the simple arithmetic average of the estimated input and output weights from the self-appraisal form of the DEA model to compute the ultimate cross-efficiency. As this is a set of common (across decision-making units) input and output weights, it allows for complete ranking and comparison of all (efficient and inefficient) decision-making units.

DEA-BWM cross efficiency target setting with preferences

Due to the existence of different evaluation perspectives, target setting has always been the key in cross efficiency development and practice. However, ignoring the preference of decision makers in the process of target setting may affect the rationality of target setting, and even may make this method unable to meet the needs of actual production. This paper innovatively combines the best-worst method (BWM) with the benevolence cross efficiency (BCE) model, and proposes four new target setting approaches for individual decision-making unit (DMU) with BWM, global optimization with BWM, BWM for individual DMU and BWM for global optimization. In order to find the optimal target DMUs in the range of production possibility set, the fifth new target setting method is proposed for global optimization of target setting and controlling. On this basis, the improvement direction of target DMUs with different methods is studied, and the influence of different cross efficiency approaches on target setting are compared. Finally, the effectiveness and practicability of those approaches are illustrated by case analysis and method comparison.

Cross efficiency model of network DEA and its application on low carbon efficiency evaluation of multimodal transport

The transportation industry is the main source of carbon dioxide (CO2) emissions, and the development of multimodal transport is conducive to reducing transportation carbon emissions. In order to evaluate the low carbon efficiency of multimodal transport, this article proposes a cross efficiency data envelopment analysis (DEA) method for complex network structures from the perspective of fairness, and takes China's rail-water intermodal transport as an example for research. The proposed method includes two secondary goal models that reduce the unreasonable differences between self-evaluation and peer-evaluation and treat all stages within the network system equally. Then, the improved entropy weight method is used to aggregate the cross efficiency. In addition, a numerical example is given to verify the effectiveness of the proposed method. The results of the case study show that the efficiency of Tangshan Port and Rizhao Port is relatively high, and others should learn from the successful experiences and develop improvement strategies based on their own characteristics. The conclusions can provide reference for transportation enterprise management and policy formulation, and the proposed method can be widely applied to the performance analysis of enterprise network, industrial chain, and supply chain.

OP4 Prioritization of ADT Notifications Improves Efficiency of New Blue Cross and Blue Shield of Louisiana Care Management Referral Process

Blue Cross and Blue Shield of Louisiana in 2018 began receiving daily admission-discharge-transfer (ADT) notifications to develop a clinical intervention program. To improve management of resources and increase the efficacy of outreach efforts, Blue Cross developed a daily selection algorithm to prioritize members with the highest risk, highest cost, or frequent use of emergency departments, and who are most likely to respond positively to clinical intervention. Prioritized outreach began December 2021 and is ongoing.

Optimal designs for detecting and characterizing hormesis in toxicological tests

Toxicological tests are experiments that show the effects of a toxic on organisms, ecosystems, etc. This study focuses on tests in the aquatic environment, in which the test involving Ceriodaphnia Dubia organism stands out. The literature indicates that in two out of every three experiments carried out with this organism, there is hormesis. This study applies optimal experimental design theory to a linear quadratic model with a Poisson distribution for the response, in order to obtain designs that allow efficient detection and characterization of hormesis. To this end, a variety of utility functions are used, including the dose for the zero equivalent point, the area under the curve, the dose at which maximum response is reached or the dose at which there is a given relative inhibition with respect to the control or the maximum. A study of cross efficiencies of the calculated designs shows the importance of correctly defining the goal of the experiment, in order to obtain the most appropriate design.

Evaluating the financial performance of companies from the perspective of fund procurement and application: New strategy cross efficiency network data envelopment analysis models

To the best of our knowledge, no study adopts network data envelopment analysis (DEA) models to evaluate financial performance of companies. Not accounting for the inner structure of fund flow tends to obtain inappropriate conclusions, thereby being problematic. To overcome the problem, this study proposes a new network structure to unify fund procurement and application. Furthermore, this study proposes an extended framework to detect various inefficiency sources. The framework contains coupling-related indexes (for relationship between stages), efficiency Gini coefficient (for technology inequality) and relative weight indicators (for relative priority analysis). Furthermore, this study proposes new strategy network DEA models to improve efficiency. Such work cannot be found in the existing studies. Empirically, this study focuses on China's companies of clean energy industry from 2013 to 2021. The main conclusions are summarized as follows. First, China's companies experience an overall progress in efficiency with an annual growth rate of 2.75%. The overall progress is mainly driven by fund application stage. Meanwhile, there exists considerable heterogeneity across stages, groups and companies. Second, as for sector priority, fund procurement gains more importance than fund application. Finally, policy makers require well-tailored strategies that may help to improve efficiency or other efficiency-related measures.

Evaluation of growth performance and feed efficiency in reciprocal crosses of Fayoumi with three exotic chicken breeds

ABSTRACT Reciprocal crosses of Fayoumi with Koekoek, Sasso, and White Leghorn chickens and the purebreds were evaluated for growth and feed efficiency traits. Birds were weighed individually at hatch and every four weeks to 20 weeks, and body weight gain was the difference between consecutive records. Feed conversion ratio was the ratio of feed consumed to weight gained by the birds. Results revealed significant differences among the genotypes in those traits. Sasso outperformed all other genotypes throughout the study period. Reciprocal crosses of Fayoumi and Sasso performed better than the remaining seven genotypes, with Koekoek and reciprocals of Fayoumi and Koekoek showing intermediate performance, but Fayoumi and White Leghorn and reciprocals involving them performed the least. In most instances, reciprocals of Fayoumi with Koekoek and White Leghorn outperformed both of their parents. Therefore, these genotypes could be used in any crossbreeding system to exploit the heterotic effects that existed in them.

Effect of inner strut on mass diffusion and mixing efficiency of cross fuel jet inside the scramjet combustor

Effect of inner strut on mass diffusion and mixing efficiency of cross fuel jet inside the scramjet combustor

Regret-based cross efficiency evaluation method in a general two-stage DEA system

Cross efficiency (CE) evaluation in data envelopment analysis (DEA) has significant advantages in ranking decision making units (DMUs). A variety of CE evaluation methods with different secondary goals are proposed in traditional black-box DEA models. At present, some scholars have studied the CE evaluation approaches in two-stage DEA systems. However, these studies commonly think of decision makers (DMs) as perfectly rational and ignore the influence of DMs’ psychological factors on the evaluation results. To conquer these limitations, this study introduces regret theory to portray DMs’ psychological preferences and investigates two-stage CE evaluation models based on regret theory. We bring in the comprehensive perceived utility of DMUs by combining direct utility and indirect utility at first, and then develop the regret-based two-stage cross efficiency (RTCE) models in a centralized and a decentralized decision environments respectively. The efficiency of Chinese “double first-class” universities are evaluated to verify our models and a completely ranking of them can be obtained. Finally, a comparative analysis is conducted to illustrate the effectiveness of our proposed models.

Coordination between the energy-consumption permit trading scheme and carbon emissions trading: Evidence from China

Market-oriented instruments are expected to minimize energy costs and carbon abatement, but interactions among them may create challenges. The Chinese government issued a pilot energy-consumption permit trading scheme (ECPTS) in Fujian Province, where the carbon emissions trading scheme (ETS) is in operation, thus providing an opportunity to analyze the interactions between two related market instruments. Based on the game-fixed cost allocation model and leader-follower game model, this paper designed an allocation scheme of energy-consumption permits (ECPs) based on coordination, efficiency and equity, and compared the differences in the caps, allocation structure and regional economic inequity among cities. The results of the Fujian case study show that when considering the optimal cross efficiency, the allocation of ECPs and carbon allowances are dominated by coastal cities with booming economies, which may entrench economic inequality between cities in Fujian. By introducing the equity principle, the allocation structure of ECPs among cities will change significantly, especially in underdeveloped cities. With the coordination mechanism of the ECPTS and ETS, the inequity in the distribution of economic development rights among cities can be moderated, which indicates that the designed approach has advantages in resource allocation. In addition, it is more conducive to energy saving and emission reduction if the provincial government prioritizes the allocation efficiency of ECPs instead of carbon allowances.

Group decision making with hesitant fuzzy linguistic preference relations based on multiplicative DEA cross-efficiency and stochastic acceptability analysis

The aim of this paper is to investigate a novel approach to group decision making (GDM) based on multiplicative DEA cross-efficiency and stochastic acceptability analysis with hesitant fuzzy linguistic preference relations (HFLPRs), which can avoid information distortion and obtain more credible decision-making results. First, a transform function is defined, which can extract effective information of the hesitant fuzzy linguistic term set (HFLTS) sufficiently. Then, an optimization model is proposed to derive the occurring probabilities of the elements in the HFLTS. It can avoid the normalization process of HFLPRs and simulate the element-selection process of decision makers (DMs). Moreover, a Maximum Log DEA Cross Efficiency model is proposed to evaluate the relative efficiency of each alternative from HFLPR. We further develop the stochastic weight space acceptability analysis method to solve the GDM problem and a step-by-step procedure is presented. Finally, numerical examples are given to illustrate the validity and applicability of the proposed method. This is the first attempt of employing the multiplicative DEA cross-efficiency to the GDM with HFLPRs.

Efficiency Evaluation of Assets and Optimal Portfolio Generation by Cross Efficiency and Cumulative Prospect Theory

Efficiency Evaluation of Assets and Optimal Portfolio Generation by Cross Efficiency and Cumulative Prospect Theory

Efficiency Evaluation of a Forestry Green Economy under a Multi-Dimensional Output Benefit in China—Based on Evidential Reasoning and the Cross Efficiency Model

The efficiency evaluation of forestry green economy development is related to the direction of forestry development and plays an important role in balancing the economic and environmental issues within that forestry development. The existing research faces three challenges: first, the output indicator is singular; second, the perspective of a self-assessment is extremely limited; and third, the multi perspective fusion method is not in line with the mechanism of the cross efficiency evaluation model. To address these challenges and the characteristics of forestry development output, we constructed multi-level output indicators from four aspects: ecology, economy, society, and sustainability and used evidence reasoning to combine the output indicators. Based on the perspective of a cross evaluation among peers, four different cross efficiency values are defined from the evaluation relationship between the different decision-making units to obtain economic–aggressive, social–neutral, ecological–benevolent, sustainable–neutral, and comprehensive–neutral cross efficiencies. According to the relationship between self- and cross evaluation, an order conditional entropy cross efficiency aggregation model has been proposed and used to analyze the development efficiency of the forestry green economy in 31 Chinese provinces in 2019. Considering the uneven distribution of the forestry resources in China, the development in the 31 provinces and cities is divided into four types by discussing the relationship between the output indicators and efficiency, while the reasons for the unbalanced development and the poor comprehensive development are discussed according to five cross efficiencies.