Output-specific input-assurance regions in DEA

Abstract

The use of assurance region (AR) constraints to restrict multipliers in data envelopment analysis (DEA) is well-established, and has been discussed at length in the literature. The conventional assumption in imposing such restrictions is that they apply universally. Specifically, AR constraints on input multipliers are intended to control the relative importance of the individual inputs in terms of how they impact the entire bundle of outputs. In many settings the relative importance of inputs is different for some of the outputs than for others. A typical example of this in the financial services sector is where the importance of sales staff versus service staff is different in regard to sales outputs than is true for service outputs. In this paper we develop a general DEA framework that incorporates multiple input-AR structures that cater to multiple output classes. We examine the cases of both divisible and indivisible inputs, and as well as mutually exclusive and overlapping output sets. The concepts are applied to a financial services situation.

Keywords:

• DEA
• multiple components
• assurance regions
• divisible inputs

Notes

1 In the case that the α vector is different for one subset of DMUs than for some other subset, it might be advisable to do separate analyses on the various (smaller) DMU groupings. We have not investigated this possibility herein.

2 Service is difficult to measure in many organizations, given its qualitative nature. In the case of banks, many conduct in-branch and mail-out customer surveys that cover a variety of dimensions. In the particular study relating to this application, the various customer responses were aggregated into a single rating on a 100-point scale.

3 It is noted that the choice of numeraire should not affect the final results, specifically, the values of the efficiency scores. Suppose we use v1 as a numeraire and restrict v2 to be twice as large as v1 and v3 to be six times as large as v1. This is the same as saying that if we choose v2 as the numeraire, then v1 would be restricted to be half as large as v2 and v3 three times as large as v2.