Incomplete ordinal information in value tree analysis and comparison of DMU’s efficiency ratios with incomplete information Antti Punkka supervisor Prof.

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Incomplete ordinal information in value tree analysis and comparison of DMU’s efficiency ratios with incomplete information Antti Punkka supervisor Prof. Ahti Salo Systems Analysis Laboratory Aalto University School of Science and Technology firstname.lastname@tkk.fi

Incomplete ordinal information in preference elicitation Specification of precise parameters of the additive value function can be difficult and time-consuming Methods for incomplete specification of weights and scores Ordinal information deemed ”easier” and more reliable than numerical estimates  Incomplete ordinal information ”Environmental aspects and cost are the two most important attributes” ”Alt. x1, x3 or x4 is the most preferred w.r.t. environmental aspects” Possibly non-convex sets of feasible parameters A MILP formulation to compute decision recommendations

Results for Ratio-based Efficiency Analysis The weights u,v constrained with incomplete information Cf. assurance regions in DEA literature LP and MILP models to compute results

Attainable rankings as means for sensitivity analysis Robust rankings exact weights 20 % interval ”Different weighting would likely yield a better ranking” 30 % interval University incompl. ordinal no information 10th 442nd Ranking