A Hybrid AHP–FCE–WMCGP Approach for Internal Auditor Selection: A Generic Framework

Abstract

Internal audit function is an important cornerstone of corporate governance. Selecting qualified internal audit professionals has become a key success factor for any organization. However, research on the selection of internal auditors has limited exposure in the literature. In addition, prior research on personnel selection has only focused on applying traditional ranking methods, which calculate the overall utility value for each candidate and rank candidates in terms of the score. Little has been done for considering management’s goals regarding the attributes of the desired candidate. A robust model has not been constructed to address multiple aspiration levels for each goal in the classical personnel selection process. To fill these gaps, a novel generic framework is presented to evaluate and select ideal internal auditors, based on the analytic hierarchy process, fuzzy comprehensive evaluation, and weighted multi-choice goal programming. A case study is conducted to validate the feasibility and flexibility of the proposed approach. The results show that the proposed hybrid approach can assist decision-makers in selecting the candidate who is a good match for organizational needs. The implications of the paper are not restricted to the selection of internal auditors.

Appendices

Appendix 1

Decision-making sets on the ten main competencies for candidate A are expressed as follows:

$$D_{A1} = W_{1} \times R_{A1} = [0.5816{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.116{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.3024] \times \left[ \begin{gathered} {0 0 0}{\text{.25 0}}{.75 0 0 0} \hfill \\ {0 0}{\text{.75 0}}{.25 0 0 0 0} \hfill \\ {0 0 0}{\text{.75 0}}{.25 0 0 0} \hfill \\ \end{gathered} \right] = \left[ {{0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.0871}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.4012}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.5117 0 0 0}}} \right],$$

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$$D_{{A{2}}} = W_{{2}} \times R_{{A{2}}} = [0.{8272}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.1{728}] \times \left[ \begin{gathered} {0 0 0}{\text{.75 0}}{.25 0 0 0} \hfill \\ {0 0}{\text{.5 0}}{.5 0 0 0 0} \hfill \\ \end{gathered} \right] = \left[ {{0}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.0865}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.7068}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.2068 0 0 0}}} \right],$$

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$$D_{A} = W \times R_{A} = \left[ {\begin{array}{*{20}l} {0.197} \hfill & {0.1358} \hfill & \cdots \hfill & {0.0681} \hfill \\ \end{array} } \right] \times \left[ {\begin{array}{*{20}c} 0 & {0.0871} & \ldots & 0 \\ 0 & {0.0865} & \ldots & 0 \\ \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & \ldots & 0 \\ \end{array} } \right] = \left[ {\begin{array}{*{20}l} {0.0105} \hfill & {0.0771} \hfill & {0.4666} \hfill & {0.354} \hfill & {0.0381} \hfill & {0.0538} \hfill & 0 \hfill \\ \end{array} } \right]$$

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Appendix 2

Final comprehensive evaluation set for candidate A is expressed as follows:

$$D_{A} = W \times R_{A} = [0.{197}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} 0.{1358}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} \cdots { 0}{\text{.0681}}] \times \left[ {\begin{array}{*{20}c} 0 & {0.0871} & \ldots & 0 \\ 0 & {0.0865} & \ldots & 0 \\ \vdots & \vdots & \vdots & \vdots \\ 0 & 0 & \ldots & 0 \\ \end{array} } \right] = \left[ {{0}{\text{.0105}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.0771}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.4666}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {0}{\text{.354 0}}{.0381 0}{\text{.0538 0}}} \right].$$

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Appendix 3

The personnel selection decision model is formulated as follows:

$$\begin{gathered} {\text{Min }}0.197 \times (d_{1}^{ + } + 2d_{1}^{ - } + e_{1}^{ + } + e_{1}^{ - } ){ + }0.1358 \times (d_{2}^{ + } + 2d_{2}^{ - } + e_{2}^{ + } + e_{2}^{ - } ){ + 0}{\text{.0976}} \times (d_{3}^{ + } + 3d_{3}^{ - } + e_{3}^{ + } + e_{3}^{ - } ). \hfill \\ { + } \cdots { + }0.0681 \times (d_{10}^{ + } + 3d_{10}^{ - } + e_{10}^{ + } + e_{10}^{ - } ) \hfill \\ \end{gathered}$$

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Subject to

$$\left. \begin{gathered} 48.4906x_{1} + 44.7717x_{2} + 48.8407x_{3} + 49.8858x_{4} + 36.5145x_{5} + 48.3765x_{6} - d_{1}^{ + } + d_{1}^{ - } = y_{1} \hfill \\ y_{1} - e_{1}^{ + } + e_{1}^{ - } = 60 \hfill \\ 40 \le y_{1} \le 60 \hfill \\ \end{gathered} \right\}{\text{For G1,}}$$

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$$\left. \begin{gathered} 42.4062x_{1} + 39.1354x_{2} + 35.677x_{3} + 55.677x_{4} + 35.677x_{5} + 25x_{6} - d_{2}^{ + } + d_{2}^{ - } = y_{2} \hfill \\ y_{2} - e_{2}^{ + } + e_{2}^{ - } = 60 \hfill \\ 40 \le y_{2} \le 60 \hfill \\ \end{gathered} \right\}{\text{For G2,}}$$

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$$\left. \begin{gathered} 83.1737x_{1} + 81.7341x_{2} + 85.5097x_{3} + 82.4257x_{4} + 77.2541x_{5} + 84.375x_{6} - d_{3}^{ + } + d_{3}^{ - } = y_{3} \hfill \\ y_{3} - e_{3}^{ + } + e_{3}^{ - } = 90 \hfill \\ 80 \le y_{3} \le 90 \hfill \\ \end{gathered} \right\}{\text{For G3,}}$$

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$$\left. \begin{gathered} 55.7709x_{1} + 47.0338x_{2} + 41.5419x_{3} + 29.7944x_{4} + 26.5051x_{5} + 32.7239x_{6} - d_{10}^{ + } + d_{10}^{ - } = y_{10} \hfill \\ y_{10} - e_{10}^{ + } + e_{10}^{ - } = 60 \hfill \\ 40 \le y_{10} \le 60 \hfill \\ \end{gathered} \right\}{\text{For G10,}}$$

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$$x_{1} + x_{2} + x_{3} + x_{4} + x_{5} + x_{6} = 1,$$

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$$x_{j} = 0\,{\text{or}}\,{1,}\,j = 1,2,...,6,$$

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$$d_{i}^{ + } ,{\kern 1pt} {\kern 1pt} {\kern 1pt} d_{i}^{ - } ,{\kern 1pt} {\kern 1pt} e_{i}^{ + } ,{\kern 1pt} e_{i}^{ - } \ge 0,\,\,i = 1,2,...,10.$$

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