ANOTHER WAY TO DETERMINE WEIGHTS OF BALANCED PERFORMANCE EVALUATIONS

Öz

In case of multiple inputs and outputs, performance of Decision Making Units (DMU) is defined as the ratio of weighted sum of outputs to weighted sum of inputs. There are two group ways to determine the weights of performance : objective and subjective approaches mainly. In the subjective approaches, weights which will be given to the inputs and outputs are determined based on the opinion of DMUs or experts. In the objective approaches, weights are found via models  and calculations which are not based on personal judgments. One of them is the most important and widely used Data Envelopment Analysis (DEA) method. Data Envelopment analysis is a nonparametric and operations research-based technique. DEA, in the performance calculations, assigns weights to multiple inputs and outputs in an objective manner by means of a linear programming model to maximize the performance of each DMU.

There may be two disadvantages for the weights which calculated by this method:

I.  To give very small or zero weights to important inputs and outputs.

II.  In aggregate evaluation, computed weights generally to be different for each input and output for different decision- makers; in the performance evaluation, importances or weights of the inputs and outputs not to happen same for every DMU.

One way for eliminate the disadvantages mentioned above is to use common weights when calculating the performance of DMUs. Another method is to use the correlation coefficients between inputs and outputs. Mentioned methods in this work will be interpreted by applying to the data of a real-world problem.

Anahtar Kelimeler

• Data envelopment analysis,common weigths,performans calculations,correlation

DENGELİ PERFORMANS AĞIRLIKLARININ HESAPLANMASINDA DİĞER BİR YOL

Öz

Çok girdi ve çıktı olması durumunda, karar verme birimlerinin (KVB) performans hesabı, ağırlıklı çıktılar toplamı bölü ağırlıklı girdiler toplamı olarak tanımlanır. Performans ağılıklarını belirlemede başlıca iki yol vardır: Sübjektif ve objektif yaklaşımlar. Sübjektif yaklaşımlarda girdi ve çıktılara verilen ağırlıklar KVB’nin ya da uzmanların görüşlerine dayalı belirlenir. Objektif yaklaşımlarda ise ağırlıklar kişisel görüşlere dayanmayarak model ve hesaplamalar yardımıyla tespit edilir. Bunlardan en yaygınca kullanılanı Veri Zarflama Analizi (VZA) yöntemidir. VZA yöntemi parametrik olmayan yöneylem araştırması tabanlı bir tekniktir. VZA performans hesaplamalarında çok girdi ve çok çıktıyı her KVB’nin performansını en büyük yapacak ağırlıkları doğrusal programlamayla objektif biçimde hesaplar.

Bu yöntemle hesaplanan ağırlıklar için iki dezavantaj vardır: I.Önemli

girdi ve çıktılara sıfıra yakın veya sıfır ağırlık vermek.

II.  Performans hesaplamalarında her bir girdi ve çıktıya farklı karar vericiler için farklı ağırlıklar ataması

KVB’lerinin performansı hesaplanırken yöntemin yukarıda bahsedilen dezavantajlarını elimine etmenin bir yolu ortak ağırlıklar kullanmaktır. Başka bir yöntem girdilerle çıktılar arasında korelasyonları kullanmaktır.

 

Anahtar Kelimeler

• Veri zarflama analizi,ortak ağırlıklar,performans hesaplamaları,korelasyon

Kaynakça

1. Adler et al., (2002),”Review of ranking in the data envelopment analysis context”, European Journal of Operational Research, 140 (2) , pp. 249–265.
2. Andersen P., Petersen, N.C., (1993). “ A procedure for ranking efficient units in data envelopment analysis”, Management Science 39, 1261-1264.
3. Angulo M. and Estellita L., (2002),”Review of methods for increasing discrimination in data envelopment analysis”, Annals of Operations Research, 116 (1–4), pp. 225–242.
4. Bal, H., Örkcü, H.H. (2011), “A New Mathematical Programming Approach to Multi- Group Classification Problems”. Computers and Operations Reserach, 38(3251-3254).
5. Banker, R.D., Charnes, A., Cooper, W.W., (1984), “Some models for estimating technical and scale inefficiencies in data envelopment analysis”, Management Science 30, 1078– 1092.
6. Charnes A, Cooper WW, Rhodes E., (1978), “Measuring the efficiency of decision making units”, European Journal of Operational Research 2, 429–44.
7. Cook W.D., J. Zhu, (2007), “Within-group common weights in DEA: An analysis of power plant efficiency”, European Journal of Operational Research, 178 (1), pp. 207–216.
8. Cooper, W.W., Tone, K., (1997), “Measures of inefficiency in dataenvelopment analysis and stochastic frontier estimation”. European Journal of Operational Research 99, 72–88.

9. Doyle and Green, (1994), “Efficiency and cross-efficiency in DEA: Derivations, meanings and uses”, Journal of the Operational Research Society, 45 (5) (1994), pp. 567–578.
10. Emrouznejad, A., Parker B. R., Tavares G., (2008) “Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA“, Socio-Economic Planning Sciences, Volume 42, Issue 3, September, Pages 151-157.
11. Ganley J.A., Cubbin J.S., (1992), ”Public sector efficiency measurement: Applications of data envelopment analysis”, North-Holland, Elsevier Science Publishers, Amsterdam.
12. Kao, C., Hung, H.T., (2005) “Data Envelopment Analysis with Common Weights: the Compromise Solution Approach,” Journal of Operation Research Society,Vol.56, ,pp. 1196-1203.
13. Liu F.H.F., H.H. Peng, (2008), “Ranking of units on the DEA frontier with common weights” , Computers and Operations Research, 35 (5), pp. 1624–1637.
14. Makui, A., Alinezhad, A., KianiMavi, R., Zohrebandian, M., (2008), “A Goal Programming Method for Finding Common Weights in DEA with an Improved Discriminating Power for Efficiency,” Journal of Industrial and Systems Engineering, Vol. 1, pp.293-30
15. Mecit, E.D., Alp, I., (2013), “A new proposed model of restricted Data Envelopment Analysis by correlation coefficients”, Applied Mathematical Modelling, 37 (5), 3407-3425, 2013 (SCI).
16. Podinovski V.V., E. Thanassoulis, (2007) , “Improving discrimination in data envelopment analysis: Some practical suggestions”, Journal of Productivity Analysis, 28 (1–2), pp. 117– 126.
17. Razavi, Hajiagha* S. H.,, Sh.S. Hashemi & H. Amoozad Mahdiraji, (2014), “DEA with Common Set of Weights Based on a MultiObjective Fractional Programming problem”, International Journal of Industrial Engineering & Production Research September 2014, Volume 25, Number 3,pp. 207-214
18. Ray S.C., (2004), Data Envelopment Analysis: Theory and Techniques for Economics and Operations Research, Cambridge University Pres.
19. Roll Y., W.D. Cook, B. Golany, (1991), “Controlling factor weights in data envelopment analysis”, IEEE Transactions, 23 (1), pp. 2–9.
20. Roll Y., B. Golany, (1993), “Alternate methods of treating factor weights in DEA”, Omega, 21, pp. 99–109.
21. Sinuany-Stern, Z., Mehrez, A., Barboy, A., (1994). Academic departments efficiency via data envelopment analysis. Computers and Operations Research 21 (5), 543–556.1105
22. Thompson R.G., F. Singleton, R. Thrall, B. Smith, (1986), “Comparative site evaluations for locating a high-energy physics lab in Texas”, Interfaces, 16pp. 35–49.
23. Thompson, R.G. , L. Langemeier, C. Lee, E. Lee, R. Thrall, (1990), “The role of multiplier bounds in efficiency analysis with application to Kansas farming”, J. Econom., 46 pp. 93– 108.
24. Torgersen, A.M., Forsund, F.R., Kittelsen, S.A.C., (1996), “Slack-adjusted efficiency measures and ranking of efficient units”. The Journal of Productivity Analysis 7, 379–398.
25. Troutt, M.D., (1995), “Amaximum decisional efficiency estimation principle”, Management Science 41, 76–82.
26. Wong, Y.-H.B., Beasley, J.E., (1990). “Restricting weight flexibility in data envelopment analysis”. Journal of Operational Research Society 41, 829–835