# Teknillinen korkeakoulu Systeemianalyysin laboratorio 1 Graduate school seminar 5.-7.11.2007 Rank-Based DEA-Efficiency Analysis Samuli Leppänen Systems.

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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

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

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

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:

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?

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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