A fuzzy neural network to estimate at completion costs of construction projects

Article history: Received 20 September 2011 Received in revised form November, 2, 2011 Accepted November, 18 2011 Available online 25 November 2011 In construction cost management system, normally earned value management (EVM) is applied as an efficient control approach in both status detection and estimation at completion (EAC) cost forecasting. The traditional approaches in EAC predictions normally extend the current situation of a project to the future by employing pervious performance factor. The proposed approach of this paper considers both qualitative and quantitative factors affecting the EAC prediction. The proposed approach of this research not only estimates the completion of the project, but also it can generate accurate forecast for the entire future periods using a fuzzy neural network model. The model is also implemented for a real-world case study and yields encouraging preliminary results. © 2012 Growing Science Ltd. All rights reserved


Introduction
Project cost management is one of important issues in project management systems. In project cost management system, earned value management (EVM) is efficiently applied through many projects and industries. A work package methodology was offered by Howes (2000) to improve the performance of EVA by employing the combination of work packages and logical time analysis. Kim et al. (2003) proposed a model to address EVM problems, improving utilities and taking project environment, implementation process, EVM users and methodology. Alvarado (2004) presented techniques to use EVM principles to analyze the portfolios of construction projects and to incorporate the analysis into an innovative pay-for-performance human resources practice. Fleming and Koppelman (2005) presented a general form of EVM, which makes it possible to apply for large-scale projects. Vandevoorde and Vanhoucke (2006), as a novel work, compared the classical earned value performance indicators (SV and SPI) with the recently developed earned schedule performance indices called (SV (t) and SPI (t)). They also proposed a new formulation for a generic schedule forecasting, which was used in various project circumstances and compared the performance of the methods in terms of total project duration with other methods. Cioffi (2006) offered a new formulation for EVM, which helps earned value calculations to become more flexible. Jigeesh and Bhat (2006) concentrated on project control system and extended the EVM concept for dynamic environment based on simulation techniques. Noori et al. (2008a) presented a fuzzy control chart approach considering a-cut to control earned value performance indexes including linguistics terms. In addition, a new application, based on a multi period-multi product (MPMP) production control problem was illustrated and successfully implemented. In other work, Noori et al. (2008b) presented how a mechanism for controlling MPMP can be created by applying fuzzy EVM. They also showed production planning problem (PPP) can be successfully integrated with powerful project control tools.
By developing an efficient forecasting method, Lipke et al. (2009) increased the project managers' capabilities to make better managerial decisions. In order to analyze schedule performance, it also used a well established project management method. Discussing two different perceptions of the EVM concept, Fleming and Koppelman (2010) generalized the concept of EVM using many best practice and real-world case studies. They also reported that the concept of EVM can be successfully implemented for virtually any project in any size in different industries. Bagherpour et al. (2010) modeled the uncertainty associated with activity duration in earned value analysis. The approach incorporated a control approach, which is applicable within production control. Costs were assumed to be directly associated with fuzzy activity time estimated through a bottom up hierarchy process. Chou et al. (2010) proposed a visual architecture, design and implementation based on Web to evaluate a project performance regarding combination of EVA and database management system. Pjares (2010) presented combination of EVM and project risk management to control and monitor the projects. In this work, the cost and schedule control indices were introduced. Moslemi et al. (2011) offered a new model based on fuzzy logic. They employed this model for estimating cost and time at completion under uncertainty considering earned value indices. Moslemi and salehipour (2011) used fuzzy earned value indices combining with α-cut method. This work were employed to make earned value techniques more applicable under real-life and nondeterministic situations. A model was developed by Warburton (2011) for demonstrating how to estimate final cost of the projects with faster coverage to the appropriate result and less variation than estimate-at-completion (EAC) calculations.

Fuzzy neural network adaption for EAC forecasting
Neural networks consist of a series of simple processors called "Unit" and they communicate with each other by communicative channels called connections. The output of each individual unit is obtained by setting up different randomized weight values and Bias within a unit. The neural networks systematically adjust the weight amounts of connections and Bias ranges of each unit in different levels of the network architecture through applying a learning structure by employing training data, so that a considerable accuracy is obtained for the approximations of the network's output amount. In addition, in neural networks, the output of network is affected by the amounts of connection's weight, unit's Bias and input data of network. In a fuzzy inference system, obtaining the result is possible through fuzzy number via using neural networks and receiving input amounts or parameters of network through fuzzy numbers or combining both fuzzy and certain numbers. In some other works, to expand fuzzy inference capabilities by neural networks, some models were represented for input and output data through fuzzy conditions and certain amounts for network's parameters, fuzzy input and output and fuzzy parameters through triangular numbers (Ishibuchi et al., 1992). Ishibuchi (1992) presented a method based on fuzzy neural networks with triangular fuzzy weights. The proposed fuzzy neural network handles fuzzy input vectors as well as real data. He also defined a cost function for different alpha cuts of fuzzy targets and derived a learning algorithm from the cost function to adjust three parameters of each triangular fuzzy weight. The output of the network is represented through fuzzy numbers and the primary issue is on how to calculate the output of network and how to train the algorithm.

Calculating the output of fuzzy neural network
The architecture of the fuzzy neural network is shown in Fig. 1 to calculate the total costs needed for project completion. (1) -Hidden units: On the other hand, in many projects, EAC is affected not only by quantitative parameters such as cost, progress, etc., but also by qualitative factors such as weather condition, employer cash status, degree of experience for project staff stated as A1, A2, and A3. is as the activation function of the neural network. On the basis of the definition of h-level cut of fuzzy numbers, the input and output relationships of neural network's units are as the followings with the fuzzy parameters and inputs: -Inputs units: -Hidden units: The amount of l ph e and u ph e are in the cut-level from squares of high-limit and low-limit errors, respectively, which have been weighted with coefficients of 2 h . Alteration of "h" amounts in interval [0,1] of the cost function for the input vector is follows, In the learning process, the first amounts of the network's parameters are reformed by using cost function in a way that their triangular structure is still kept and the amounts of beginning, ending and width of the triangular fuzzy number change through decreasing the output error of the network. The triangular fuzzy numbers of network's weights and Bias are as follows, The superscripts L, C and V in Eq. (12) are low, central and above limits of triangular fuzzy numbers, respectively and the centers are determined as follow, On the basis of the cost function ph e , the modified amount of each parameters of the network is calculated as the sample j V ، : .
where η is the learning constant, α is the movement amount constant and t is the modification number. Due to the triangular fuzzy symmetry assumption, the center's amounts of the network's parameters are obtained by using Eq. (12). The high and low limits of interval resolved by h-level cut are written as follow, The derivatives of Eq. (14) can be written as follows, Using Eq. (14), yields the following, Grigoudis and Siskos (2002)  . On the basis of obtained amounts for modifying are obtained as follows, After modifying j V , if the low limit is bigger than the high limit, the amounts of high and low limits are as follows, ( 1) min{ ( 1), ( 1)}, Reforming all the parameters of the fuzzy neural network, Briefly, learning in the fuzzy neural network is done through the following algorithm.
Step1: Initialize parameters of neural network, weights and Bias of units

Comparative analysis
In this section, we demonstrate the proposed learning algorithm by a computer simulation model for some examples and the results are shown in Fig. 2. In this illustration, we apply the Fuzzy Neural Network (FNN) method to forecast EAC with fuzzy function and some exact data. The effective specifications on the relationship between cost system and fuzzy neural network are shown in Table 1. The results of fuzzy neural forecasting and the exact EAC are compared in Fig. 2.

Fig. 2. Comparative analysis of forecasting model and actual data
As we can observe from the results of Fig. 2, the proposed model of this paper tends to perform better than the traditional method. One obvious observation is that the proposed model of this paper considers the negative impacts of many qualitative factors such as employer cash status, work experience of project staff and weather condition, etc.

Conclusion remark and further recommendation
In this paper, we have presented a novel EAC model, which considers several qualitative factors in addition to many other quantitative factors. The proposed model of this paper uses a fuzzy neural model, which handles uncertainty associated with the data. The proposed model was trained and the results were compared with the traditional EAC forecasting approach. The approach can be further used for forecasting any period in the future (not just takes at completion costs). The proposed approach given in this paper can help contractors consider qualitative inputs affecting on the EAC forecasting. Further recommendation can be made on constructing a framework for better dealing between contractor and employer where some claims on behalf of contractor is raised.

Acknowledgements
The author wishes to express his acknowledgement for financial support of this research under grant number 90/213 given by Shiraz Branch of Islamic Azad University.