**4. A software house company ABC**

An ABC company of software house has three branches in different cities, which meets the demand based on job order. The company plans to integrate KMS in their information and communication technology infrastructure. The management board of the company requests a cost-benefit analysis for the KMS investment. In the cost-benefit analysis, costs is categorized in capital expenditures and operating expenditures. On the contrary, the cost saving, increasing the quality of products, and employee productivity and speed are considered as benefits of the KMS investment. The cost savings contribute to increase the profits, while increasing orders due to the customer satisfaction is defined in expressions of productivity-speed time and quality of product impact. The benefits is identified and discussed in Section 2.2.

The revenue element of ABC Company consists of total of orders with the yearly amount before KMS adoption is 200 units with standard deviation 18% and the price per unit of USD5000. The investment costs of KMS are structured by capital expenditure (*CXn*) and operating expenditure (*CYn*) as USD200000 and USD20000 per year respectively, while the cost unit for the target of cost savings consists of average of annual direct labor cost per unit product (20 labor) of USD100, annual purchase material cost per unit product of USD800, annual method for final product per unit of USD500.

Fuzzy-Monte Carlo Simulation for Cost Benefit

in the following form (Tosun et al., 2010).

increase rate in orders is structured such as follows:

Orders is High.

in Orders is Medium.

Rate in Orders is Medium.

Orders is Medium.

Orders is Low.

3, and Figure 4, respectively.

Fig. 2. The MFS of delivery time

Analysis of Knowledge Management System Investment 79

This paper employs Mamdani model due to its advantages in representation of expert knowledge and in linguistic interpretation of dependencies. Hence, the increase in orders is calculated in a Mamdani-type. The composition of Mamdani-type fuzzy logic rule bases is

*If x1 is A1, x2 is A2 …. And xn is An then y is B*  where *A* and *B* are linguistic variables defined by fuzzy sets of the universe of discourse *x* and *y* respectively. The output of the fuzzy rule based model whose rule base is constructed using Mamdani-type fuzzy logic rules is shown in Equation (1) (Jang and Gulley, 1997).

'

*zdz*

(1)

*z*

*dz*

where ZMOM is the defuzzified output, *z'* is the maximizing *z* at which the membership function reaches its maximum. In this paper, both triangular and trapezoidal fuzzy numbers are used to consider the fuzziness of the decision elements. The rules established for the

Rule 1: IF delivery time is Short AND quality of product is High THEN Increase Rate in

Rule 2: IF delivery Time is Short AND quality of product is Medium THEN Increase Rate

Rule 3: IF delivery Time is Normal AND quality of product is High THEN Increase Rate in

Rule 4: IF delivery Time is Normal AND quality of product is Medium THEN Increase

Rule 5: IF delivery Time is Long AND quality of product is Low THEN Increase Rate in

All rules defined by the experts, and then calculated in Matlab Fuzzy Toolbox. The max–min method is used for the aggregation mechanism whereas the mean of maximum method is used for the defuzzification process of fuzzy outputs. Furthermore, the membership functions of delivery time that represent of productivity and speed of employee, quality of product and increase rate in orders are defined by the experts and given in Figure 2, Figure

*MOM*

*Z*

'

*z*

Fig. 1. Framework for Cost-Benefit Analysis of KMS Investment

Due to the fact that to illustrate the increase customer orders as an impact of intangible benefits in a balance sheet is difficult, a fuzzy rule-based system is developed. Consequently, net present value (NPV) as the feasibility indicator of the investment is computed using Monte-Carlo simulation.

### **5. Knowledge acquisition**

Regarding the impact of intangible benefits of KMS investment to a revenue model, which is represented by increased customer orders, this paper involves expert's opinion to handle the increased by producing a fuzzy rule-based system (FRBS). This system is a systematic reasoning methodology that can capture the contextual judgment of experts by using fuzzy set theory.

Fig. 1. Framework for Cost-Benefit Analysis of KMS Investment

computed using Monte-Carlo simulation.

**5. Knowledge acquisition** 

Due to the fact that to illustrate the increase customer orders as an impact of intangible benefits in a balance sheet is difficult, a fuzzy rule-based system is developed. Consequently, net present value (NPV) as the feasibility indicator of the investment is

Regarding the impact of intangible benefits of KMS investment to a revenue model, which is represented by increased customer orders, this paper involves expert's opinion to handle the increased by producing a fuzzy rule-based system (FRBS). This system is a systematic reasoning methodology that can capture the contextual judgment of experts by using fuzzy set theory.

This paper employs Mamdani model due to its advantages in representation of expert knowledge and in linguistic interpretation of dependencies. Hence, the increase in orders is calculated in a Mamdani-type. The composition of Mamdani-type fuzzy logic rule bases is in the following form (Tosun et al., 2010).

#### *If x1 is A1, x2 is A2 …. And xn is An then y is B*

where *A* and *B* are linguistic variables defined by fuzzy sets of the universe of discourse *x* and *y* respectively. The output of the fuzzy rule based model whose rule base is constructed using Mamdani-type fuzzy logic rules is shown in Equation (1) (Jang and Gulley, 1997).

$$Z\_{MOM} = \frac{\int\_{z^\*} zdz}{\int\_{z^\*} dz} \tag{1}$$

where ZMOM is the defuzzified output, *z'* is the maximizing *z* at which the membership function reaches its maximum. In this paper, both triangular and trapezoidal fuzzy numbers are used to consider the fuzziness of the decision elements. The rules established for the increase rate in orders is structured such as follows:


All rules defined by the experts, and then calculated in Matlab Fuzzy Toolbox. The max–min method is used for the aggregation mechanism whereas the mean of maximum method is used for the defuzzification process of fuzzy outputs. Furthermore, the membership functions of delivery time that represent of productivity and speed of employee, quality of product and increase rate in orders are defined by the experts and given in Figure 2, Figure 3, and Figure 4, respectively.

Fig. 2. The MFS of delivery time

Fuzzy-Monte Carlo Simulation for Cost Benefit

**6. Model of cost-benefit Impact to KMS investment** 

Table 1. The increased orders (S') is calculated by Eq. (3).

shown in Table 2. The cost saving is calculated by Eqs. (4)-(6).

is determined for *n* years in Eq. (8) where *i* indexed as discount rate.

1

distribution of NPV, which meant not only produce one value of NPV.

**7. Simulation, results, and discussion** 

Analysis of Knowledge Management System Investment 81

In the KMS cost-benefit analysis of KMS investment, the costs calculation is structured by capital expenditures (*CXn*) and operating expenditures (*CYn*). On the other hand, the benefits of KMS (*B*) that calculated in Eq. (2) are derived from revenue increase (RI) and costs saving such as annual purchase material cost saving (*CSm*), cost saving on final product (*CSi*), and labor cost saving (*CSl*). Indeed, the variables of total benefit are calculated considering the increase rate in orders (s) which has been estimated by fuzzy rule based system as shown in

where *S(µ,σ)* is the yearly orders with a mean *µ* and standard deviation *σ*. The cost savings are computed considering the increased orders (*S'*), cost unit (*c*), cost saving rates (*r*) as

The revenue increase is calculated considering yearly total orders (*S*), the increase rate in orders (*s*) and profit for each unit (*p*) in Eq. (7). Finally, the NPV of the total KMS investment

> 1 [ ( .. )] ( .. ) (1 )

*X Xn <sup>n</sup> <sup>n</sup> BC C NPV C C*

In relation to investment analysis, the Monte Carlo simulation is the appropriate method for estimating the impact of KMS costs and benefits to the investment result by randomizing value from each of the uncertain variables and calculating the objective or target value of the investment model (Hacura et al., 2001). This method uses random numbers from probability distributions of increase rate in orders and cost saving rates to compute the probability

The simulation to calculate the NPV of KMS investment is carried out using software Crystal Ball Version 7.2.1. In addition, the simulations are run 500 times to minimize the possible errors arising from the random variables. A simulation generates the probability distribution for the total revenue increase, the total cost saving, and the total benefit which is the sum of total revenue increase and total cost saving as shown in Fig. 5, 6, and 7 respectively. Furthermore, the distribution of NPV in 3 years horizon is shown in Fig. 8 with the probability of a discount rate (i) of mean of 8% and standard deviation of logarithmic value of 0.22. The cost savings of material, labor and method on a final product are

*B = (CSm +CSi +CSl)+RI* (2)

*CSm = S'+ cmaterial+rmaterial* (4)

*CSl = S'+ clabor+rlabor* (6)

*RI= S(µ,σ) x s x p* (7)

(8)

1

*<sup>t</sup> Y Yn*

*i*

*CSi = S'+cfinal product+rfinal product* (5)

*S'=S(µ,σ) x (1+s)* (3)

Fig. 3. The MFS of quality of product

Fig. 4. The MFS of increase rate in orders

By implementing the input data into the system, the probability distribution of expected increase rate in orders is generated as shown in Table 1. In addition, the experts' also predict the expected cost savings rate (r) which is delivered by KMS investment with probabilities of 10%, 30% and 60% as shown in Table 2.



Table 1. The expected increase in sales

Table 2. The expected cost saving rates

By implementing the input data into the system, the probability distribution of expected increase rate in orders is generated as shown in Table 1. In addition, the experts' also predict the expected cost savings rate (r) which is delivered by KMS investment with probabilities

Probability (%) Delivery Time (h) Quality (%) Increase Rate in Orders (%) 0 48 65 3.3 30 30 80 10 60 20 95 18.5

10 2 6 15 30 3 8 20 60 5 10 25

Labor Cost Material Cost Cost on Final Products

Probability (%) Cost saving rates (%)

Fig. 3. The MFS of quality of product

Fig. 4. The MFS of increase rate in orders

of 10%, 30% and 60% as shown in Table 2.

Table 1. The expected increase in sales

Table 2. The expected cost saving rates
