Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach

Abstract

Information System (IS) project selection is a critical decision making task that can significantly impact operational excellence and competitive advantage of modern enterprises and also can involve them in a long-term commitment. This decision making is complicated due to availability of numerous IS projects, their increasing complexities, importance of timely decisions in a dynamic environment, as well as existence of multiple qualitative and quantitative criteria. This paper proposes a Data Envelopment Analysis approach to find most efficient IS projects while considering subjective opinions and intuitive senses of decision makers. The proposed approach is validated by a real world case study involving 41 IS projects at a large financial institution as well as 18 artificial projects which are defined by the decision makers.

Appendix A

Consider the following input-oriented BCC model:

$$ \begin{array}{*{20}l} {\theta_{o}^{*} = \hbox{max} \mathop \sum \limits_{r = 1}^{s} u_{r} y_{r0} + u_{0} } \hfill \\ {{\text{s}}.{\text{t}}. } \hfill \\ {\begin{array}{*{20}l} {\mathop \sum \limits_{i = 1}^{m} v_{i} x_{io} = 1} \hfill & \hfill \\ {\mathop \sum \limits_{r = 1}^{s} u_{r} y_{rj} + u_{0} - \mathop \sum \limits_{i = 1}^{m} v_{i} x_{ij} \le 0} \hfill & {j = 1, \ldots ,n} \hfill \\ {u_{r} \ge \varepsilon } \hfill & {r = 1, \ldots ,s} \hfill \\ {v_{i} \ge \varepsilon } \hfill & { i = 1, \ldots ,m} \hfill \\ \end{array} } \hfill \\ \end{array} $$

(A.1)

Without loss of generality, suppose y_sj = c for j = 1, …, n. Model (A.1) can be rewritten as:

$$ \begin{array}{*{20}l} {\theta_{o}^{*} = \hbox{max} \mathop \sum \limits_{r = 1}^{s - 1} u_{r} y_{r0} + u_{s} c + u_{0} } \hfill \\ {{\text{s}}.{\text{t}}. } \hfill \\ {\begin{array}{*{20}l} {\mathop \sum \limits_{i = 1}^{m} v_{i} x_{io} = 1} \hfill & \hfill \\ {\mathop \sum \limits_{r = 1}^{s - 1} u_{r} y_{rj} + u_{s} c + u_{0} - \mathop \sum \limits_{i = 1}^{m} v_{i} x_{io} \le 0} \hfill & {j = 1, \ldots ,n} \hfill \\ {u_{r} \ge \varepsilon } \hfill & {r = 1, \ldots ,s} \hfill \\ {v_{i} \ge \varepsilon } \hfill & { i = 1, \ldots ,m} \hfill \\ \end{array} } \hfill \\ \end{array} $$

(A.2)

Now, by making the change of variable $\bar{u}_{0} = u_{s} c + u_{0}$ we obtain the following model which is equivalent to the BCC model (A.1):

$$ \begin{array}{*{20}l} {\theta_{o}^{*} = \hbox{max} \mathop \sum \limits_{r = 1}^{s - 1} u_{r} y_{r0} + \bar{u}_{0} } \hfill \\ {{\text{s}}.{\text{t}}. } \hfill \\ {\begin{array}{*{20}l} {\mathop \sum \limits_{i = 1}^{m} v_{i} x_{io} = 1} \hfill & \hfill \\ {\mathop \sum \limits_{r = 1}^{s - 1} u_{r} y_{rj} + \bar{u}_{0} - \mathop \sum \limits_{i = 1}^{m} v_{i} x_{io} \le 0} \hfill & {j = 1, \ldots ,n} \hfill \\ {u_{r} \ge \varepsilon } \hfill & {r = 1, \ldots ,s - 1} \hfill \\ {v_{i} \ge \varepsilon } \hfill & { i = 1, \ldots ,m} \hfill \\ \end{array} } \hfill \\ \end{array} $$

(A.3)

Hence, the following theorem is proved:

Theorem A.1

A constant output in the input-oriented BCC model is redundant.

Analogously, the following theorem can be proved:

Theorem A.2

A constant input in the output-oriented BCC model is redundant.