An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company

Abstract

Data Envelopment Analysis (DEA) models, as ordinarily employed, assume that the data for all inputs and outputs are known exactly. In some applications, however, a number of factors may involve imprecise data, which take forms such as ordinal rankings and knowledge only of bounds. Here we provide an example involving a Korean mobile telecommunication company. The Imprecise Data Envelopment Analysis (IDEA) method we use permits us to deal not only with imprecise data and exact data but also with weight restrictions as in the (now) widely used “Assurance Region” (AR) and “cone-ratio envelopment” approaches to DEA. We also show how to transform AR bounds on the variables, obtained from managerial assessments, for instance, into data adjustments. This involves an extended IDEA model, which we refer to as AR-IDEA. All these uses are illustrated by an example application directed to evaluate efficiencies of branch offices of a telecommunication company in Korea.

Improved interval DEA models with common weight

“…Model (5) does not have preferences, and then the weights for lower and upper efficiencies are both 0.5. From Table 3, we find that the final efficiency of each DMU obtained by model (4) is larger than its efficiency obtained by model (3) or model (5). The finall efficiency of each DMU obtained by the model (3) is smaller than the one obtained by other two models.…”

“…Set that ω * id and µ * rd are optimal solutions of model (10), which are also the optimal solutions of model (5). So in the interval DEA models without preferences, the lower bound of interval efficiency of DMU d is …”

“…For example, Cooper et al [5] may be the first to study the DEA models with imprecise data, and their model is called imprecise DEA (IDEA). It can be transformed into a linear programming problem from a nonlinear programming problem through a series of variable alternations and scale transformations.…”

Entropy Cross-Efficiency Model for Decision Making Units with Interval Data

“…Therefore, a number of studies examined how to evaluate the efficiencies of DMUs with fuzzy data. For example, Cooper et al [30] proposed an imprecise DEA (IDEA) model, which can be transformed into a linear programming model based on a series of variable alternations and scale transformations. However, Lee et al [31] argued that IDEA model was complicated, and may lead to a rapid increase in computation burden.…”

A decision model for ranking suppliers in the presence of cardinal and ordinal data, weight restrictions, and nondiscretionary factors

“…To deal with all aspects of imprecise data in DEA, Cooper et al (1999) proposed a body of concepts and methods that go by the name of Imprecise Data Envelopment Analysis (IDEA). There have since been a number of refinements, extensions, and applications (Cooper et al 2001a(Cooper et al , 2001bKim et al 1999;Park 2004;Zhu 2003aZhu , 2003bZhu , 2004Cook and Zhu 2005). These studies have also developed different methods for solving a nonlinear IDEA problem because some inputs and outputs are unknown decision variables with values to be determined in the model.…”