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Group Decision-Making Tools for Managerial Accounting and Finance Applications

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Handbook of Financial Econometrics and Statistics

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Abstract

To deal with today’s uncertain and dynamic business environments with different background of decision makers in computing trade-offs among multiple organizational goals, our series of papers adopts an analytic hierarchy process (AHP) approach to solve various accounting or finance problems such as developing a business performance evaluation system and developing a banking performance evaluation system. AHP uses hierarchical schema to incorporate nonfinancial and external performance measures. Our model has a broader set of measures that can examine external and nonfinancial performance as well as internal and financial performance. While AHP is one of the most popular multiple goals decision-making tools, multiple-criteria and multiple-constraint (MC2) linear programming approach also can be used to solve group decision-making problems such as transfer pricing and capital budgeting problems. This model is rooted by two facts. First, from the linear system structure’s point of view, the criteria and constraints may be “interchangeable.” Thus, like multiple criteria, multiple-constraint (resource availability) levels can be considered. Second, from the application’s point of view, it is more realistic to consider multiple resource availability levels (discrete right-hand sides) than a single resource availability level in isolation. The philosophy behind this perspective is that the availability of resources can fluctuate depending on the decision situation forces, such as the desirability levels believed by the different managers. A solution procedure is provided to show step-by-step procedure to get possible solutions that can reach the best compromise value for the multiple goals and multiple-constraint levels.

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Author information

Authors and Affiliations

  1. University of Nebraska at Omaha, Omaha, NE, 68182, USA

    Wikil Kwak & Yong Shi

  2. Chinese Academy of Sciences, Beijing, China

    Yong Shi

  3. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, 94 Rockefeller Rd. Levin Bldg., Piscataway, NJ, 08854, USA

    Cheng-Few Lee

  4. Korea Advanced Institute of Science and Technology, Yuseong-gu, Daejeon, South Korea

    Heeseok Lee

  5. Graduate Institute of Finance, National Chiao Tung University, Hsinchu, Taiwan

    Cheng-Few Lee

Authors
  1. Wikil Kwak
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  2. Yong Shi
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  3. Cheng-Few Lee
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  4. Heeseok Lee
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Correspondence to Wikil Kwak .

Editor information

Editors and Affiliations

  1. Department of Finance and Economics, Rutgers Business School, Rutgers, The State University of New Jersey, Piscataway, New Jersey, USA

    Cheng-Few Lee

  2. Center for PBBEF Research, North Brunswick, New Jersey, USA

    John C. Lee

Appendix 1

Appendix 1

For illustrative purposes, we show how to use AHP to induce the five DMs’ preferences of budget availability and to compute the relative weights. Generally, AHP collects input judgments of DMs in the form of a matrix by pairwise comparisons of criteria (i.e., their budget availability levels). An eigenvalue method is then used to scale weights of such criteria. That is, the relative importance of each criteria is computed. The result from all of pairwise comparison is stored in an input matrix as follows:

$$ \begin{array}{c}\mathrm{President}\kern2em \mathrm{Controller}\kern2em \mathrm{Production}\kern2em \mathrm{Marketing}\kern2em \mathrm{Engineering}\\ {}\kern11em \mathrm{Manager}\kern3.5em \mathrm{Manager}\kern3.12em \mathrm{Manager}\\ {}\left[\begin{array}{ccccc} 1 & 3 & 4 & 5 & 6 \\ {} & 1 & 2 & 5 & 5 \\ {} & & 1 & 3 & 4 \\ {} & & & 1 & 2 \\ {} & & & & 1 \end{array}\right]\end{array} $$

Applying an eigenvalue method to the above input matrix results in a vector W i = (0.477, 0.251, 0.154, 0.070, 0.048). In addition to the vector, the inconsistency ratio (γ) is obtained to estimate the degree of inconsistency in pairwise comparisons. In this example, the inconsistency ratio is 0.047. A common guideline is that if the ratio surpasses 0.1, a new input matrix must be generated. Therefore, this input matrix is acceptable.

A similar computing process can be applied for the 16 objective functions. However, two hierarchical levels are required for this case. The first level of AHP corresponds to the four groups of objectives and the second level corresponds to the time periods within each objective group.

Let x j be the jth project that can be selected by the firm. Using data in Tables 29.7, 29.8, 29.9, and 29.10, the model for capital budgeting with multiple criteria and multiple DMs is formulated as

$$ \begin{array}{l}\mathrm{maximize}\kern2em 20{x}_1+16{x}_2+11{x}_3+4{x}_4+4{x}_5\\ \kern6.12em +18{x}_6+7{x}_7+9{x}_8+24{x}_9+4{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 120{x}_1+100{x}_2+80{x}_3+40{x}_4+40{x}_5\\ \kern6.12em +110{x}_6+60{x}_7+110{x}_8+150{x}_9+35{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 130{x}_1+120{x}_2+90{x}_3+50{x}_4+45{x}_5\\ \kern6.12em +120{x}_6+70{x}_7+120{x}_8+170{x}_9+40{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 145{x}_1+140{x}_2+95{x}_3+50{x}_4+50{x}_5\\ \kern6.12em +140{x}_6+65{x}_7+100{x}_8+180{x}_9+40{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 150{x}_1+150{x}_2+95{x}_3+55{x}_4+55{x}_5\\ \kern6.12em +150{x}_6+70{x}_7+110{x}_8+190{x}_9+50{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 170{x}_1+160{x}_2+100{x}_3+60{x}_4+60{x}_5\\ \kern6.12em +165{x}_6+80{x}_7+120{x}_8+200{x}_9+50{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 10{x}_1+10{x}_2+12{x}_3+8{x}_4+15{x}_5\\ \kern6.12em +12{x}_6+8{x}_7+14{x}_8+12{x}_9+10{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 12{x}_1+12{x}_2+15{x}_3+15{x}_4+10{x}_5\\ \kern6.12em +12{x}_6+12{x}_7+16{x}_8+10{x}_9+8{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 14{x}_1+18{x}_2+15{x}_3+10{x}_4+8{x}_5\\ \kern6.12em +10{x}_6+10{x}_7+13{x}_8+9{x}_9+9{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 15{x}_1+16{x}_2+15{x}_3+8{x}_4+20{x}_5\\ \kern6.12em +15{x}_6+12{x}_7+15{x}_8+12{x}_9+8{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 17{x}_1+17{x}_2+8{x}_3+12{x}_4+18{x}_5\\ \kern6.12em +15{x}_6+12{x}_7+16{x}_8+12{x}_9+12{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 0.85{x}_1+0.90{x}_2+0.96{x}_3+0.98{x}_4+0.90{x}_5\\ \kern6.12em +0.90{x}_6+0.96{x}_7+0.96{x}_8+0.90{x}_9+0.98{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 0.90{x}_1+0.98{x}_2+0.97{x}_3+0.95{x}_4+0.95{x}_5\\ \kern6.12em +0.95{x}_6+0.98{x}_7+0.95{x}_8+0.88{x}_9+0.95{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 0.98{x}_1+0.95{x}_2+0.98{x}_3+0.96{x}_4+0.95{x}_5\\ \kern6.12em +0.94{x}_6+0.98{x}_7+0.90{x}_8+0.85{x}_9+0.95{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 0.95{x}_1+0.95{x}_2+0.92{x}_3+0.92{x}_4+0.98{x}_5\\ \kern6.12em +0.95{x}_6+0.98{x}_7+0.92{x}_8+0.95{x}_9+0.98{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{maximize}\kern2em 0.95{x}_1+0.96{x}_2+0.92{x}_3+0.95{x}_4+0.95{x}_5\\ \kern6.12em +0.95{x}_6+0.98{x}_7+0.95{x}_8+0.95{x}_9+0.95{x}_{10}\end{array} $$
$$ \begin{array}{l}\mathrm{subject}\kern0.5em \mathrm{to}\kern2em 24{x}_1+12{x}_2+8{x}_3+6{x}_4+{x}_5\\ \kern6.12em +18{x}_6+13{x}_7+14{x}_8+16{x}_9+4{x}_{10}\le 49.37\\ {}\\ {}\kern6em 16{x}_1+10{x}_2+6{x}_3+4{x}_4+6{x}_5\\ {}\kern6em +18{x}_6+8{x}_7+8{x}_8+20{x}_9+6{x}_{10}\le 35.30\\ {}\\ {}\kern6em 6{x}_1+2{x}_2+6{x}_3+7{x}_4+9{x}_5\\ {}\kern6em +20{x}_6+10{x}_7+12{x}_8+24{x}_9+8{x}_{10}\le 28.91\\ {}\\ {}\kern6em 6{x}_1+5{x}_2+6{x}_3+5{x}_4+2{x}_5\\ {}\kern6em +15{x}_6+8{x}_7+10{x}_8+16{x}_9+6{x}_{10}\le 33.44\\ {}\\ {}\kern6em 8{x}_1+4{x}_2+4{x}_3+3{x}_4+3{x}_5\\ {}\kern6em +15{x}_6+8{x}_7+8{x}_8+16{x}_9+4{x}_{10}\le 29.96\\ {}\\ {}\kern6em \mathrm{and}\kern0.5em {X}_j=\left\{0,1\right\}\kern0.4em \mathrm{for}\kern0.5em j=1,\dots, 10.\end{array} $$

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Kwak, W., Shi, Y., Lee, CF., Lee, H. (2015). Group Decision-Making Tools for Managerial Accounting and Finance Applications. In: Lee, CF., Lee, J. (eds) Handbook of Financial Econometrics and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7750-1_29

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  • DOI: https://doi.org/10.1007/978-1-4614-7750-1_29

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