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Rank-Based DEA-Efficiency Analysis

Rank-Based DEA-Efficiency Analysis. Samuli Leppänen Systems Analysis Laboratory, TKK samuli.leppanen@tkk.fi Supervisors: Ahti Salo, Antti Punkka. Efficiency Analysis. Analysis of the efficiency of decision-making units (DMUs)

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Rank-Based DEA-Efficiency Analysis

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  1. Rank-Based DEA-Efficiency Analysis Samuli Leppänen Systems Analysis Laboratory, TKK samuli.leppanen@tkk.fi Supervisors: Ahti Salo, Antti Punkka

  2. Efficiency 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

  3. Rank-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 umdominates 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

  4. 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:

  5. Conclusion 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?

  6. References • 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

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