The other side of ranking schemes: generating weights for specified outcomes

This paper treats the problem of how to determine weights in a ranking, which will cause a selected entity to attain the highest possible position. We establish that there are two types of entities in a ranking scheme: those which can be ranked as number one and those which cannot. These two types o...

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Vydané v:	International transactions in operational research Ročník 23; číslo 4; s. 655 - 668
Hlavní autori:	Bougnol, Marie-Laure, Dulá, Jose H.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Oxford Blackwell Publishing Ltd 01.07.2016
Predmet:	Boundaries Categories data envelopment analysis (DEA) Data points higher education Hulls Hulls (structures) Integer programming Linear programming Mathematical analysis Mixed integer Operations research Ranking Studies university rankings weight determination
ISSN:	0969-6016, 1475-3995
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Abstract	This paper treats the problem of how to determine weights in a ranking, which will cause a selected entity to attain the highest possible position. We establish that there are two types of entities in a ranking scheme: those which can be ranked as number one and those which cannot. These two types of entities can be identified using the “ranking hull” of the data; a polyhedral set that envelops the data. Only entities with data points on the boundary of this hull can attain the number one position. There are no weights that will make an entity whose data point is in the interior of the hull to ever attain the number one position. We deal with these two types of entities separately. In the first case, we propose an approach for finding a set of weights that, under special conditions, will result in a selected entity achieving the top of the ranking without ties and without ignoring any of the attributes. For the second category of entities, we devise a procedure to guarantee that these entities will attain their highest possible position in the ranking. The first case will require using interior point methods to solve a linear program (LP). The second case involves a binary mixed integer formulation. These two mathematical programs were tested on data from a well‐known university ranking.
AbstractList	This paper treats the problem of how to determine weights in a ranking, which will cause a selected entity to attain the highest possible position. We establish that there are two types of entities in a ranking scheme: those which can be ranked as number one and those which cannot. These two types of entities can be identified using the “ranking hull” of the data; a polyhedral set that envelops the data. Only entities with data points on the boundary of this hull can attain the number one position. There are no weights that will make an entity whose data point is in the interior of the hull to ever attain the number one position. We deal with these two types of entities separately. In the first case, we propose an approach for finding a set of weights that, under special conditions, will result in a selected entity achieving the top of the ranking without ties and without ignoring any of the attributes. For the second category of entities, we devise a procedure to guarantee that these entities will attain their highest possible position in the ranking. The first case will require using interior point methods to solve a linear program (LP). The second case involves a binary mixed integer formulation. These two mathematical programs were tested on data from a well‐known university ranking.
Author	Bougnol, Marie-Laure Dulá, Jose H.
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Cites_doi	10.1016/j.cor.2011.05.006 10.1023/A:1011103303616 10.1016/j.cor.2006.09.006 10.1287/mnsc.20.8.1217 10.1016/j.ejor.2007.10.034 10.1007/BF02579150 10.1111/j.1475-3995.1994.00325.x 10.1007/0-387-23081-5_8 10.1080/10556789908805757 10.1287/mnsc.30.9.1078 10.1007/978-3-642-48318-9 10.1137/1.9781611971453 10.1016/0377-2217(82)90155-2 10.1007/BF01212012 10.1016/S0305-0483(99)00022-5
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Copyright	2016 The Authors. International Transactions in Operational Research © 2016 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA. 2016 The Authors.
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References_xml	– reference: Pekelman, D., Sen, S.K., 1974. Mathematical programming models for the determination of attribute weights. Management Science 20, 8, 1217-1229. – reference: Zeleny, M., 1982. Multiple Criteria Decision Making. McGraw-Hill, New York. – reference: Dulá, J.H., Thrall, R.M., 2001. A computational framework for accelerating DEA. Journal of Productivity Analysis 16, 63-78. – reference: Bougnol, M.L., Dulá, J.H., Rouse, P., 2012. Interior points methods in DEA to determine non-zero multiplier weights. Computers & Operations Research 39, 698-708. – reference: Karmarkar, N.K., 1984. A new polynomial-time algorithm for linear programming. Combinatorica 4, 4, 373-395. – reference: Caporaletti, L.E., Dulá, J.H., Womer, N.K., 1999. Performance evaluation based on multiple attributes with nonparametric frontiers. Omega 27, 637-645. – reference: Jacquet-Lagreze, E., Siskos, J., 1982. Assessing a set of additive utility functions for multicriteria decision-making, the UTA method. European Journal of Operational Research 10, 2, 151-164. – reference: Bougnol, M.L., Dulá, J.H., 2009. Anchor points in DEA. European Journal of Operational Research 192, 668-676. – reference: Hwang, C.L., Yoon, K., 1981. Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, Berlin. – reference: Saari, D.G., Merlin, V.R., 1996. The Copeland method. Economic Theory 8, 1, 51-76. – reference: Konrad, A., 2012. America's 50 best cities. Bloomberg Business, September 26. Available at http://www.bloomberg.com/bw/slideshows/2012-09-26/americas-50-best-cities (accessed September 2015). – reference: Wright, S.J., 1997. Primal/Dual Interior Point Methods. SIAM, Philadelphia, PA. – reference: Bana e Costa, C.A., Vansnick, J.C., 1994. MACBETH - an interactive path towards the construction of cardinal value functions. 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U.S. News and World Report L.P., Washington, D.C. – volume: 11 start-page: 397 year: 1999 end-page: 430 article-title: PCx: an interior‐point code for linear programming publication-title: Optimization Methods and Software – year: 2009 – volume: 16 start-page: 63 year: 2001 end-page: 78 article-title: A computational framework for accelerating DEA publication-title: Journal of Productivity Analysis – year: 1981 publication-title: Multiple Attribute Decision Making: Methods and Applications – volume: 20 start-page: 1217 issue: 8 year: 1974 end-page: 1229 article-title: Mathematical programming models for the determination of attribute weights publication-title: Management Science – year: 1997 publication-title: Primal/Dual Interior Point Methods – year: 1982 publication-title: Multiple Criteria Decision Making – year: 2012a – year: 2012b – start-page: 297 year: 2005 end-page: 334 – volume: 27 start-page: 637 year: 1999 end-page: 645 article-title: Performance evaluation based on multiple attributes with nonparametric frontiers publication-title: Omega – volume: 35 start-page: 1624 issue: 5 year: 2008 end-page: 1637 article-title: Ranking of units on the DEA frontier with common weights publication-title: Computers & Operations Research – volume: 8 start-page: 21 issue: 3 year: 1998 end-page: 26 article-title: Using the method of maximizing deviations to make decision for multi‐indices publication-title: System Engineering and Electronics – volume: 1 start-page: 489 issue: 4 year: 1994 end-page: 500 article-title: MACBETH – an interactive path towards the construction of cardinal value functions publication-title: International Transactions in Operational Research – year: 2012 article-title: America's 50 best cities publication-title: Bloomberg Business – year: 2014 article-title: 50 best websites 2014 publication-title: Time – volume: 10 start-page: 151 issue: 2 year: 1982 end-page: 164 article-title: Assessing a set of additive utility functions for multicriteria decision‐making, the UTA method publication-title: European Journal of Operational Research – volume: 8 start-page: 51 issue: 1 year: 1996 end-page: 76 article-title: The Copeland method publication-title: Economic Theory – year: 2014 – volume: 192 start-page: 668 year: 2009 end-page: 676 article-title: Anchor points in DEA publication-title: European Journal of Operational Research – volume: 30 start-page: 1078 issue: 9 year: 1984 end-page: 1092 article-title: Some models for estimating technological and scale inefficiencies in data envelopment analysis publication-title: Management Science – volume: 39 start-page: 698 year: 2012 end-page: 708 article-title: Interior points methods in DEA to determine non‐zero multiplier weights publication-title: Computers & Operations Research – volume: 4 start-page: 373 issue: 4 year: 1984 end-page: 395 article-title: A new polynomial‐time algorithm for linear programming publication-title: Combinatorica – year: 2013 – ident: e_1_2_9_6_1 doi: 10.1016/j.cor.2011.05.006 – ident: e_1_2_9_9_1 doi: 10.1023/A:1011103303616 – ident: e_1_2_9_15_1 doi: 10.1016/j.cor.2006.09.006 – ident: e_1_2_9_16_1 doi: 10.1287/mnsc.20.8.1217 – year: 2014 ident: e_1_2_9_2_1 article-title: 50 best websites 2014 publication-title: Time – ident: e_1_2_9_5_1 doi: 10.1016/j.ejor.2007.10.034 – ident: e_1_2_9_13_1 doi: 10.1007/BF02579150 – ident: e_1_2_9_3_1 doi: 10.1111/j.1475-3995.1994.00325.x – volume: 8 start-page: 21 issue: 3 year: 1998 ident: e_1_2_9_23_1 article-title: Using the method of maximizing deviations to make decision for multi‐indices publication-title: System Engineering and Electronics – ident: e_1_2_9_17_1 – year: 2012 ident: e_1_2_9_14_1 article-title: America's 50 best cities publication-title: Bloomberg Business – ident: e_1_2_9_20_1 doi: 10.1007/0-387-23081-5_8 – volume-title: Best Colleges year: 2013 ident: e_1_2_9_21_1 – ident: e_1_2_9_18_1 – ident: e_1_2_9_22_1 – ident: e_1_2_9_8_1 doi: 10.1080/10556789908805757 – ident: e_1_2_9_4_1 doi: 10.1287/mnsc.30.9.1078 – year: 1982 ident: e_1_2_9_25_1 publication-title: Multiple Criteria Decision Making – ident: e_1_2_9_10_1 doi: 10.1007/978-3-642-48318-9 – ident: e_1_2_9_24_1 doi: 10.1137/1.9781611971453 – ident: e_1_2_9_11_1 – ident: e_1_2_9_12_1 doi: 10.1016/0377-2217(82)90155-2 – volume: 8 start-page: 51 issue: 1 year: 1996 ident: e_1_2_9_19_1 article-title: The Copeland method publication-title: Economic Theory doi: 10.1007/BF01212012 – ident: e_1_2_9_7_1 doi: 10.1016/S0305-0483(99)00022-5
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Title	The other side of ranking schemes: generating weights for specified outcomes
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