Determination of the Final Model of Project Cost Contingency

Several steps of the development of cost contingency model based on risk analysis and fuzzy expert system has been conducted in this research. The process was initiated by development a conceptual model of cost contingency, determination of the risk factors used in the model and development of the preliminary fuzzy expert. The process was further conducted by testing the model using actual case projects. Tuning processes and the application of the several methods of the defuzzification were also performed to improve the model accuracy. The best scenario is the model that produced the minimum MAE in the testing, tuning and applying the defuzzification method. Finally, the validation was also conducted to check the model consistency performance. Based on to the testing and validation, the final cost contingency model can then be specified.

The final model of the cost contingency estimation process consists of the risk analysis parameter within the project risk hierarchy as shown in Figure 5.1 and the best fuzzy expert system properties for the model, which is obtained from the Scenario A_Tuning_4 as given in Figure 5.2 to Figure 5.4.

The risk analysis parameter within the project risk hierarchy consists of 14 risk factors which can be classified into two main major risks which are external and internal risk and represented as a project risk hierarchy. Every major risk consists of seven risk factors. In this proposed model, cost contingency is calculated as the summation of the major risk or the total risk magnitude (RM) for all significant risk factors for the

Chapter 5. Model Validation and Application 93 projects. The RM is the function of two risk parameters, namely risk likelihood and risk severity (RS).

Figure 5.1 Final Cost Contingency Model: Risk Analysis Parameter and Risk Hierarchy

The final fuzzy expert system properties were also determined. It consists of final membership function, fuzzy rule base and fuzzy inference mechanism that involve the fuzzy operator, implication, aggregation and defuzzification procedures. The final membership function from the model can be seen in Figure 5.2 to Figure 5.4.

Chapter 5. Model Validation and Application 94

Figure 5.2 Final RL Membership Function

According to Figure 5.2, for the RL variable, the universe of discourse used is 100, with five linguistic terms. The overlap between adjacent fuzzy set is 37.5%. For the RS membership function as can be seen in Figure 5.3, the universe of discourse used is 2% in the unit of the total project cost. Five linguistic terms was also used in this membership function, and the overlap between each fuzzy set is the same as RL membership function, which is 37.5%. Finally, based on Figure 5.3, for the RM membership function, the universe of discourse is the same as the RS membership function, which is 2% of the total project cost. Five linguistic terms were also specified in this risk variable. However, the suitable overlap for this membership function is 50%.

Chapter 5. Model Validation and Application 95

Figure 5.3 Final RS Membership Function

Figure 5.4 Final RM Membership Function

In terms of the fuzzy rule base, Alternative A can be concluded to be more suitable for this model than alternative B. Scenario 1A which was composed with the

Chapter 5. Model Validation and Application 96 Alternative A fuzzy rule base produced the minimum MAE compared to other scenario. The final fuzzy rule base is therefore Alternative A as shown in Table 5.2.

Table 5.2 The Final Fuzzy Rule Base for the Model

VL L M H VH VL VL VL L L M L VL L L M M M VL L M M H H VL L M H H VH VL L M H VH Risk Severity (RS) Risk Magnitude (RM) Ri sk Likeli ho od (RL)

For the implication and aggregation process, the Mamdani Inference Mechanism which consists of MIN and MAX operation is appropriate for the model. Finally, the most appropriate for this model is the COA defuzzification method.

5.4 Development of Computer Tool for Project Cost Contingency Estimation

For the purpose of applying of the model that has been developed to estimate project cost contingency, a computer program was developed in MATLAB programming language. The computer tool was designed as a prediction tool that can be used to estimate project cost contingency during the tender bidding stage. The system was built using MATLAB graphical user interface development environment (GUIDE).

The GUIDE was modeled to guide the user to estimate the amount of tender price directly. The user will only need to specify the base cost estimate of the new project and the estimation of RL and RS variables for significant risk factor. In this case, the base cost estimate is the total construction cost that has not taken into account of risks in the calculation process. The system will automatically calculate the cost contingency and also a bidding price to be proposed.

Chapter 5. Model Validation and Application 97 The bidding price is determined based on the formula proposed by Paek et al. [10]. In this model, in order to determine the bidding price (BP), the base cost estimate (BC) must be summed with the cost contingency value (CC). BP is the amount of the project cost, which is free from risks. In this case, the estimator is required to estimate BC based on the most likely cost for each work item.

The relation between BP, BC and CC can be represented using Equation 5.1.

CC BC

BP= + (5.1)

where:

BP = bidding price

BC = base cost estimate (including profit)

CC = cost contingency = RM1 + RM2 + RM3 +………. + RMn RMi = RLi x RSi

The values of RL and RS can be estimated as percentage of the total project cost or BP. For example CC is equal to several percentage of BP, for example is ZxBP. Therefore, BP can be calculated as Equation 5.2a.

(ZxBP) BC BP= + (5.2a) or Z) - (1 BP BC= (5.2b) Therefore, CC) (1 BC BP − = _(5.2c) ) ) xRS (RL 1 BC BP i i

∑

Chapter 5. Model Validation and Application 98 Based on the formula in Equation 5.2d, the BP value for the tender can be calculated based on the value of BC and the RL and RS input values from all significant risk factors. A computer tool for estimating tender price was then developed according to the formula. The MATLAB programming code for developing this computer tool can be shown in Appendix E. The application of the computer tool for risk analysis and risk management will be explained in the next section.