As an extended model of data envelopment analysis (DEA), cross-efficiency is utilized in various fields. It applies the relative evaluation values of homogeneous decision-making units (DMUs) in ranking completely. Due to the non-uniqueness of DEA optimal weights, and the cross-efficiency methods focus on the aggregation of cross-efficiency matrix values. There is a low correction between the final efficiency evaluation value and the value assigned to the criteria weight or the value of the criteria. This paper uses the modified aggressive cross-efficiency model to calculate the weights of the decision-making units (DMUs). Then according to the consistency of peer-evaluation criteria, the entropy weight method is used to aggregate the index weights to generate a set of common weights, and a new Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method is used to calculate the utility score of DMUs that can rank them completely. Finally, a numerical case of supplier selection is offered to illustrate the feasibility and effectiveness of the proposed method.
CharnesA., CooperW.W. and RhodesE., Measuring the efficiency of decision making units[J], European Journal of Operational Research2(4) (1978), 429–444.
2.
SarricoC.S. and DysonR.G., Using DEA for planning in UK universities—an institutional perspective[J], Journal of the Operational Research Society51(7) (2017), 789–800.
3.
ChenC.l., CookW.D., ImaniradR., et al., Balancing Fairness and Efficiency: Performance Evaluation with Disadvantaged Units in Non-homogeneous Environments[J], European Journal of Operational Research287(3) (2020), 1003–1013.
4.
TolooM. and MirboloukiM., A new project selection method using data envelopment analysis[J], Computers & Industrial Engineering138 (2019), 106119.
5.
LiY.J., LiF., EmrouznejadA., et al., Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game[J], Annals of Operations Research274(1-2) (2019), 373–394.
6.
ChenL. and JiaG.Z., Environmental efficiency analysis of China’s regional industry: a data envelopment analysis (DEA) based approach[J], Journal of Cleaner Production142 (2017), 846–853.
7.
Mousavi-NasabS.H. and Sotoudeh-AnvariA., A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems[J], Materials & Design121 (2017), 237–253.
RollY., CookW.D. and GolanyB., Controlling Factor Weights in Data Envelopment Analysis[J], IIE Transactions23(1) (1991), 2–9.
10.
ThompsonR.G., SingletonF.D., ThrallR.M., et al., Comparative Site Evaluations for Locating a High-Energy Physics Lab in Texas[J], Interfaces16(6) (1986), 35–49.
11.
AndersonT.R., HollingsworthK. and InmanL., The fixed weighting nature of a cross-evaluation model[J], Journal of Productivity Analysis17(3) (2002), 249–255.
12.
SextonT.R., SilkmanR.H. and HoganA.J., Data envelopment analysis: Critique and extensions[J], New Directions for Program Evaluation1986(32) (1986), 73–105.
13.
KaoC. and HungH.T., Data envelopment analysis with common weights: the compromise solution approach[J], Journal of the Operational Research Society56(10) (2017), 1196–1203.
14.
LiuF.H.F. and PengH. H., Ranking of units on the DEA frontier with common weights[J], Computers & Operations Research35(5) (2008), 1624–1637.
15.
ZohrehbandianM., MakuiA. and AlinezhadA., A compromise solution approach for finding common weights in DEA: an improvement to Kao and Hung’s approach[J], Journal of the Operational Research Society61(4) (2017), 604–610.
16.
OmraniH., Common weights data envelopment analysis with uncertain data: A robust optimization approach[J], Computers & Industrial Engineering66(4) (2013), 1163–1170.
17.
Hatami-MarbiniA., TavanaM., AgrellP.J., et al., A common-weights DEA model for centralized resource reduction and target setting[J], Computers & Industrial Engineering79 (2015), 195–203.
18.
HanY.M., LongC., GengZ.Q., et al., Carbon emission analysis and evaluation of industrial departments in China: An improved environmental DEA cross model based on information entropy[J], Journal of Environmental Management205 (2018).
19.
WangL., ZhouZ.X., YangY., et al., Green efficiency evaluation and improvement of Chinese ports: A cross-efficiency model[J], Transportation Research Part D: Transport and Environment88 (2020), 102590.
20.
LimS.M., OhK.W. and ZhuJ., Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market[J], European Journal of Operational Research236(1) (2014), 361–368.
21.
ChenW., ZhouK.L. and YangS.L., Evaluation of China’s electricenergy efficiency under environmental constraints: A DEA crossefficiency model based on game relationship[J], Journal ofCleaner Production164 (2017), 38–44.
22.
GengZ.Q., DongJ.G., HanY.M., et al., Energy and environment efficiency analysis based on an improved environment DEA cross-model: Case study of complex chemical processes[J], Applied Energy205 (2017), 465–476.
23.
HouQ., WangM. and ZhouX., Improved DEA Cross Efficiency Evaluation Method Based on Ideal and Anti-Ideal Points[J], Discrete Dynamics in Nature and Society2018 (2018), 1–9.
24.
LiuX.H., ChuJ.F., YinP.Z., et al., DEA cross-efficiency evaluation considering undesirable output and ranking priority: a case study of eco-efficiency analysis of coal-fired power plants[J], Journal of Cleaner Production142 (2017), 877–885.
25.
MoutinhoV., MadalenoM. and RobainaM., The economic andenvironmental efficiency assessment in EU cross-country: Evidencefrom DEA and quantile regression approach[J], EcologicalIndicators78 (2017), 85–97.
26.
DoyleJ. and GreenR., Efficiency and Cross-Efficiency in D Derivations, Meanings and Uses[J], Journal of the Operational Research Society45(5) (1994), 567–578.
27.
WangY.M. and ChinK.S., A neutral DEA model for cross-efficiencyevaluation and its extension★[J], Expert Systems withApplications37(5) (2010), 3666–3675.
28.
WangY.M., ChinK.S. and JiangP., Weight determination in the cross-efficiency evaluation[J], Computers & Industrial Engineering61(3) (2011), 497–502.
29.
WangY.M., ChinK.S. and LuoY., Cross-efficiency evaluation based on ideal and anti-ideal decision-making units[J], Expert Systems with Applications38(8) (2011), 10312–10319.
30.
WuJ. and LiangL., Ranking approach of interval cross efficiency considering all weighting schemes[J], Systems Engineering and Electronics30(10) (2008), 1890–1894.
31.
ChenL. and WangY.M., DEA target setting approach within the cross-efficiency framework[J], Omega96 (2020), 102072.
32.
WuJ., LiangL. and ZhaY.C., Determination of the weights of ultimate cross efficiency based on the solution of nucleolus[J], Systems Engineering-Theory and Practice2008(5) (2008), 92–97.
33.
WangY.M. and WangS., Approaches to determining the relative importance weights for cross-efficiency aggregation in data envelopment analysis[J], Journal of the Operational Research Society64(1) (2017), 60–69.
34.
WangY.M. and ChinK.S., The use of OWA operator weights for cross-efficiency aggregation[J], Omega39(5) (2011), 493–503.
35.
SongL.L. and LiuF., An improvement in DEA cross-efficiencyaggregation based on the Shannon entropy[J], InternationalTransactions in Operational Research25(2) (2016), 705–714.
36.
SongM.L., ZhuQ.Y., PengJ., et al., Improving the evaluation of cross efficiencies: A method based on Shannon entropy weight[J], Computers & Industrial Engineering112 (2017), 99–106.
37.
WuJ., SunJ.S., LiangL., et al., Determination of weights for ultimate cross efficiency using Shannon entropy[J], Expert Systems with Applications38(5) (2011), 5162–5165.
38.
YangG.L., YangJ.B., LiuW.B., et al., Cross-efficiency aggregation in DEA models using the evidential-reasoning approach[J], European Journal of Operational Research231(2) (2013), 393–404.
39.
FanJ.P., LiuJ. and WuM.Q., Improvement of cross-efficiency based on prospect theory[J], Journal of Intelligent & Fuzzy Systems37(3) (2019), 4391–4404.
40.
LiuJ.P., SongJ.M., XuQ., et al., Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations[J], Fuzzy Optimization and Decision Making18(3) (2019), 345–370.
41.
FanJ.P., GuoZ.W. and WuM.Q., An Improvement of DEA Cross-Efficiency Aggregation Based on BWM-TOPSIS[J], IEEE Access8 (2020), 37334–37342.
42.
ChengY.M., YaoL., HeH.Y., et al., An evaluation method for DEA game efficiency considering cross-competition game of DMUs[J], Control and Decision33(9) (2018), 1677–1685.
43.
CharnesA. and CooperW.W., Programming with linear fractional functional[J], Naval Research Logistics Quartery19(3-4) (1962), 181–185.
44.
ShannonC.E., A mathematical theory of communication[J], Bell System Technical Journal27 (1948), 379–423.
45.
StevićŽ., PamučarD., PuškaA., et al., Sustainable supplier selection inhealthcare industries using a new MCDM method: Measurement ofalternatives and ranking according to Compromise solution(MARCOS)[J], Computers & Industrial Engineering140 (2020), 106231.
46.
StankovićM., StevićŽ., DasD.K., et al., A New Fuzzy MARCOS Method for Road Traffic Risk Analysis[J], Mathematics8(3), 457.
47.
ChengY.M., WangH.Y. and ZhangX.Q., The Common-Weight Ranking Method forDEACross Efficiency Based on Group Decision-making[J], Control and Decision (2020), 1–10.
