rank-based dea-efficiency analysis

Teknillinen korkeakoulu Systeemianalyysin laboratorio

1Graduate school seminar 5.-7.11.2007

Rank-Based DEA-Efficiency Analysis Rank-Based DEA-Efficiency Analysis

Samuli LeppänenSystems Analysis Laboratory, TKK

[email protected]: Ahti Salo, Antti Punkka



Efficiency AnalysisEfficiency Analysis 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 (xj) and outputs (yi)

Data Envelopment Analysis (DEA; Charnes et al., 1978)– DMU un is efficient within DMUs u1,...,uK, if it maximizes efficiency for

some weights win, wout

– Efficiency measure: 1 for efficient DMUs and in (0,1) for other DMUs

DEA with weight constraints– Weights win, wout are constrained to sets Sin, Sout, respectively– E.g., Golany, 1988, Halme et al., 1999

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Rank-Based ApproachRank-Based Approach Feasible sets (Sin, Sout) 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:

Pairwise dominance – If DMU um is more efficient than DMU un for all feasible weights, DMU um dominates

DMU un

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?

If the sets Sin, Sout are further constrained– New dominance relations can emerge, old ones apply– The ranking intervals stay unchanged or become narrower

Pairwise dominance relations and efficiency ranking intervals can be solved through LP / MILP models

outout ww 32



Example: Efficiency of TKK’s Departments Example: Efficiency of TKK’s Departments 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 Sin, Sout defined as any convex combination of these

weightings

Results:



Conclusion and the Way ForwardConclusion and the Way Forward 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)

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?



ReferencesReferences Charnes, Cooper, Rhodes (1978), Measuring efficiency of decision

making units, European Journal of Operations Research, 2, 429-444

Golany (1988), An interactive MOLP procedure for the extension of DEA to effectiviness analysis, Journal of Operations Research Society, 39, 725-734

Halme, Joro, Korhonen, Salo, Wallenius, (1999) A value efficiency approach to incorporating preference information in data envelopment analysis, Management Science, 45, 103-115

Salo, Punkka, (2005) Rank inclusion in criteria hierarchies, European Journal of Operations Research, 163, 338-356

rank-based dea-efficiency analysis

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