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Teknillinen korkeakoulu Systeemianalyysin laboratorio 1 Graduate school seminar 5.-7.11.2007 Rank-Based DEA-Efficiency Analysis Samuli Leppänen Systems Analysis Laboratory, TKK samuli.leppanen@tkk.fi Supervisors: Ahti Salo, Antti Punkka

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Teknillinen korkeakoulu Systeemianalyysin laboratorio 2 Graduate school seminar 5.-7.11.2007 Efficiency Analysis n Analysis of the efficiency of decision-making units (DMUs) –Efficiency often defined as the ratio between Output value and Input value –Input and Output values usually consist of multiple factors → they are formed as weighted sums of inputs (x j ) and outputs (y i ) n Data Envelopment Analysis (DEA; Charnes et al., 1978) –DMU u n is efficient within DMUs u 1,...,u K, if it maximizes efficiency for some weights w in, w out –Efficiency measure: 1 for efficient DMUs and in (0,1) for other DMUs n DEA with weight constraints –Weights w in, w out are constrained to sets S in, S out, respectively –E.g., Golany, 1988, Halme et al., 1999

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Teknillinen korkeakoulu Systeemianalyysin laboratorio 3 Graduate school seminar 5.-7.11.2007 Rank-Based Approach n Feasible sets (S in, S out ) for the weights through linear constraints –cf. Incomplete information in Value Tree Analysis (Salo and Punkka, 2005) »e.g., Unit increase in output 2 is more valuable than unit increase in output 3: n Pairwise dominance –If DMU u m is more efficient than DMU u n for all feasible weights, DMU u m dominates DMU u n n Efficiency ranking analysis –With fixed weights the DMUs can be ordered according to their efficiencies –Which rankings can a DMU attain, given the sets of feasible weights? n If the sets S in, S out are further constrained –New dominance relations can emerge, old ones apply –The ranking intervals stay unchanged or become narrower n Pairwise dominance relations and efficiency ranking intervals can be solved through LP / MILP models

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Teknillinen korkeakoulu Systeemianalyysin laboratorio 4 Graduate school seminar 5.-7.11.2007 Example: Efficiency of TKK’s Departments n 12 departments were analysed using 43 output factors and 2 input factors –Each TKK’s resource commitee member provided weightings for inputs and outputs –Feasible Sets S in, S out defined as any convex combination of these weightings n Results:

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Teknillinen korkeakoulu Systeemianalyysin laboratorio 5 Graduate school seminar 5.-7.11.2007 Conclusion and the Way Forward n Pairwise dominance relations and rank analysis –Provide additional ways to illustrate results of DEA-based efficiency analysis –Computationally simple → can be applied to large data sets –”Robust” DMUs’ worst attainable ranking are ”high” (i.e., small) n Possibilities for future research: study of inefficient DMUs –How much should a low-ranking/dominated DMU increase its outputs or decrease its inputs in order to »obtain a better worst ranking? »become non-dominated? »be surely among the k most efficient ones? –Which inputs/outputs should we concentrate on to efficiently improve a DMU’s efficiency?

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Teknillinen korkeakoulu Systeemianalyysin laboratorio 6 Graduate school seminar 5.-7.11.2007 References n Charnes, Cooper, Rhodes (1978), Measuring efficiency of decision making units, European Journal of Operations Research, 2, 429-444 n Golany (1988), An interactive MOLP procedure for the extension of DEA to effectiviness analysis, Journal of Operations Research Society, 39, 725-734 n Halme, Joro, Korhonen, Salo, Wallenius, (1999) A value efficiency approach to incorporating preference information in data envelopment analysis, Management Science, 45, 103-115 n Salo, Punkka, (2005) Rank inclusion in criteria hierarchies, European Journal of Operations Research, 163, 338-356

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Helsinki University of Technology Systems Analysis Laboratory Antti Punkka and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology.

Helsinki University of Technology Systems Analysis Laboratory Antti Punkka and Ahti Salo Systems Analysis Laboratory Helsinki University of Technology.

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