Bala Shanmugam
Monash University Malaysia No. 2, Jalan Kolej, Bandar Sunway
46150, Petaling Jaya Selangor Darul Ehsan, Malaysia E-mail: [email protected]
Abstract
For many years, Profitability Index (PI) has been used extensively for the calculation of project return. Payback has a different implication in the performance appraisal world where it deals with the calculation of a duration required for a particular investment return. This paper presents an artificial decision-making tool, which is the fuzzy logic (FL) design. This is to link traditional variables of PI and payback. The usage of an engineering tool, LabVIEW FL toolkit in this work, integrates the two input variables, namely PI and Payback Period (PP) and generates an output. The associated output is the rating consideration for project investment. This method may reveal different degree in rating projects. FL concept will be discussed and the implementation will be shown graphically in this work.
INTRODUCTION
PI (Pike, 2003) indicates the ratio of the present value of benefits to cost, which takes into account the present value and capital investment into mathematical calculations. PI is evaluated in such a way, where a project’s present value is divided by the capital invested. Greater value of this index is preferred. Payback is a project appraisal technique, which indicates the time period require to regain the initial capital invested in a project. When the yearly- accumulated return from the project is equal to the capital invested, the payback can be realized.
PI and payback are two different appraisal methods, which have different implications in terms of project return and project PP. To deal with sources of vagueness and imprecision, fuzzy theory may be employed as a useful tool for handling such conditions. Fuzzy uncertainty can have an effect on important decision (Jablonowski, 2000). Fuzziness can be found in many areas; particularly frequent in areas in which human judgment, evaluation and decision are important, as these are in investment selection projects (Isabel, 1989, P150).
Consider these two scenarios, firstly, a project that has a high PI ratio with a long PP, secondly, another project B that has a low PI ratio with short PP. What would be a better decision that a company would prefer in relation to the importance of PI and PP. Especially to determine the project rating precisely in wording of how “Good” or how “Bad” would then turn out to be “ambiguous”. Fuzzy set theory enables a soft classification approach to account for uncertainties (Aydin, 2004). Project Rating (PR) can be used to illustrate the weighting of these variables. To rate a project, FL would be applied to generate the output based on the important analysis of the two input variables; PI and PP.
PI AND PP DESIGN
Bellman and Zadeh defined a decision set, which unifies a fuzzy objective (i.e. a fuzzy goal) and a fuzzy constraint given by a decision maker (Yuji, 2001). In this paper, PI and PP are denoted as two input variables and the project rating will be the output variable. In all fuzzy designs, fuzzification, inference process and defuzzification are three important stages.
PI
PP
PR (c)
(PR)
µ very Poor poor Average Good Very good
(PI)
µ very low low Average High Very high
(b)
(PP)
µ Fast Medium Slow
(a)
Figure1: (a) - (b) show The Membership Functions Of Two Input Variables and (c) shows The Membership Function Of The Output Variable PR.
In the first step of fuzzification, membership function (MF) can be linguistically explained by individual sets such as very low, low, average, high and very high in figure 1. The linguistic term can be manipulated with fuzzy set theory and they can be interpreted as specific fuzzy number that allows us to perform the tradeoff analysis among various criteria [Juite, 2002]. All terms are assigned with membership degree in the range from 0 to 1. The PI is set within a range from 1 to 10 and PP has a range from 1 to 20 years. A project with 18 years PP would fall into ‘slow’ in the linguistic term as shown in figure 1(b). The crisp value of 4 in PI would be classified under fuzzy sets as slightly ‘low’ and slightly ‘average’.
Table 1: Rating Rules Based For Projects
Rules PI PP PR
1 Very low Fast Average
2 Very low Medium Poor
3 Very low Slow Very poor
4 Low Fast Average
5 Low Medium Poor
6 Low Slow Poor
7 Average Fast Good
8 Average Medium Average
9 Average Slow Poor
10 High Fast Very good
11 High Medium Good
12 High Slow Average
13 Very high Fast Very good
14 Very high Medium Good
15 Very high Slow Average
After two linguistic variables have been clearly defined, inference processing would be the next stage. The decision on the PR are highly dependence on the ‘IF and THEN’ rules. Table 1 shows the detailed rule-based, which is used for inference process. Output linguistic terms have individual sets defined as the following: very poor, poor, average, good and very good. For example, in rule 1: if PI is very low and PP is very fast, then, PR will be average etc. The rule-based formulation depends on human expertise and experience about this subject matter. If the project PI is ‘High’ and the PP is ‘Slow’, the project will be classified as ‘Average’.
Project Evaluation Process
Defuzzification is the final stage of the entire fuzzy process. Figure 2 shows the linguistic terms that consist of ‘very poor, poor, average, good and very good’. Under diverse combinations of PI and PP as crisp input values to fuzzy process, this would yield the different output crisp value after defuzzification. When a project has PI 5.5 and PP 13 years, the crisp output could be computed using mathematic equation, which is the stage of defuzzification.
Figure 2: Centre Area For Completed Project Rating Output
Shaded area in figure 3 shows the output of PR, when PI and PP is 5.5 and 13 respectively. To get crisp output value, it is necessary to calculate the aggregated average output as follows:
0.5(5)
0.3(7 )
0.1(3)
5.44
0.5
0.3
0.1
P R
=
+
+
=
+
+
PR is rated from minimum of 1 to a maximum of 10. The output, which yields a higher value, would be preferable. The result of 5.44 is considered an average project. Advance engineering software tool, LabVIEW and FL toolkit were utilized to assist in automating the calculation and fuzzy process for obtaining output values through these iterative procedures.
3-D Representation For Project Investment Assessment
A three dimensional representation of project ranking (i.e. as a single output) versus payback period and profitability index is shown in the following figure 3. LabVIEW and Fuzzy Logic controller design toolkit were utilized to perform the entire fuzzification, inference and defuzzification processes. The data analysis and presentation is performed with this powerful graphical user-friendly software, which is widely used in engineering and science disciplines.
Figure 3: 3D Surface Plot Showing The Dependency Of The PI And PP And The Output Variable PR
A 3D surface plot is obtained and it shows the dependency of two inputs variable and the output variable. It shows the result of how individual variable will affect the crisp output value. A combination of high PI value and a low PP value, when input into this particular fuzzy logic design, will result and display peaks in this graphical output. This particular type of representation of 3D surface plot is useful, with clear visibility for investors considering project investment rating.
CONCLUSION
In this study, a Fuzzy Logic tool was utilized to investigate the evaluation of projects based on two linguistic input variables namely, profitability index and payback period. Evaluation and decision-making based on project rating would be easy using this approach. In evaluating project investment rating, the effort may be arduous in handling
substantially huge amount of different combinational values from different input variables. The use of FL could ease this complexity and data representation. The capability of FL is not limited to 2 variables only. In principle, this intelligent decision making tool is scalable to multi-input variables, especially for a complex project investment that has multiple input variables rating consideration. In conclusion, this paper presents a useful tool utilizing an artificial decision-making tool, the LabVIEW Fuzzy logic design for the purpose of project investment rating.
Acknowledgement: The authors appreciatively acknowledge Monash University Malaysia for the support of this work. The authors sincerely thank National Instruments (ASEAN) for the generous loan of the LabVIEW departmental license and support. The authors sincerely thank Dr Velappa Ganapathy for his useful discussion on FL principles and concepts.
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