A Value Efficiency Approach to Incorporating Preference Information in Data Envelopment Analysis

TLDR

The efficiency of Decision Making Units is defined in the spirit of Data Envelopment Analysis, complemented by Decision Maker preference information on desirable input and output structures. We develop a procedure and theory for incorporating preference information in a novel way into DEA efficiency analysis. The procedure first assists the Decision Maker in identifying the most preferred efficient combination of inputs and outputs, then approximates the value function’s indifference contour at that point with tangent hyperplanes, and finally computes Value Efficiency scores by comparing inefficient units to units with the same value as the most preferred solution. The Value Efficiency scores produced by the method are optimistic approximations of the true scores and are immediately applicable to practical problems.

Abstract

We develop a procedure and the requisite theory for incorporating preference information in a novel way in the efficiency analysis of Decision Making Units. The efficiency of Decision Making Units is defined in the spirit of Data Envelopment Analysis (DEA), complemented with Decision Maker’s preference information concerning the desirable structure of inputs and outputs. Our procedure begins by aiding the Decision Maker in searching for the most preferred combination of inputs and outputs of Decision Making Units (for short, Most Preferred Solution) which are efficient in DEA. Then, assuming that the Decision Maker’s Most Preferred Solution maximizes his/her underlying (unknown) value function, we approximate the indifference contour of the value function at this point with its possible tangent hyperplanes. Value Efficiency scores are then calculated for each Decision Making Unit comparing the inefficient units to units having the same value as the Most Preferred Solution. The resulting Value Efficiency scores are optimistic approximations of the true scores. The procedure and the resulting efficiency scores are immediately applicable to solving practical problems.