Teknillinen korkeakoulu Systeemianalyysin laboratorio RankBased DEAEfficiency Analysis Samuli
Teknillinen korkeakoulu Systeemianalyysin laboratorio Rank-Based DEA-Efficiency Analysis Samuli Leppänen Systems Analysis Laboratory, TKK samuli. leppanen@tkk. fi Supervisors: Ahti Salo, Antti Punkka Graduate school seminar 5. -7. 11. 2007 1
Teknillinen korkeakoulu Systeemianalyysin laboratorio 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 (xj) and outputs (yi) n Data Envelopment Analysis (DEA; Charnes et al. , 1978) – DMU un is efficient within DMUs u 1, . . . , u. K, if it maximizes efficiency for some weights win, wout – Efficiency measure: 1 for efficient DMUs and in (0, 1) for other DMUs n DEA with weight constraints – Weights win, wout are constrained to sets Sin, Sout, respectively – E. g. , Golany, 1988, Halme et al. , 1999 Graduate school seminar 5. -7. 11. 2007 2
Teknillinen korkeakoulu Systeemianalyysin laboratorio Rank-Based Approach n 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: n Pairwise dominance – If DMU um is more efficient than DMU un for all feasible weights, DMU um dominates DMU un 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 Sin, Sout 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 Graduate school seminar 5. -7. 11. 2007 3
Teknillinen korkeakoulu Systeemianalyysin laboratorio 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 Sin, Sout defined as any convex combination of these weightings n Results: Graduate school seminar 5. -7. 11. 2007 4
Teknillinen korkeakoulu Systeemianalyysin laboratorio 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? Graduate school seminar 5. -7. 11. 2007 5
Teknillinen korkeakoulu Systeemianalyysin laboratorio 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 Graduate school seminar 5. -7. 11. 2007 6
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