Integrating system dynamics and fuzzy logic modeling to determine concession period in BOT projects
Automation in Construction 22 (2012) 368–376
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Automation in Construction journal homepage: www.elsevier.com/locate/autcon
Integrating system dynamics and fuzzy logic modeling to determine concession period in BOT projects Mostafa Khanzadi b, Farnad Nasirzadeh a,⁎, Majid Alipour b a b
Dept. of Project Management, Faculty of Engineering, Payame Noor University (PNU), Karaj, Iran Dept. of Civil Engineering, Iran University of Science and Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Accepted 26 September 2011 Available online 28 October 2011 Keywords: Concession period System dynamics Fuzzy logic BOT projects
1. Introduction Implementing infrastructure projects requires a large capital investment. As governments usually ﬁnd it difﬁcult to provide sufﬁcient capital for the development of public infrastructure, the BOT contract is widely used to attract private capital to assist in developing public infrastructure [1]. BOT contracts have been used by private sector to ﬁnance, construction and operation in large infrastructure projects such as roads, expressways, railways, bridges, ports, and power plants [2,3]. Buildoperatetransfer (BOT), build, operate and own (BOO), build, operate, own, and transfer (BOOT), build, transfer, and operate (BTO), build and transfer (BT), reconstruction, operate, and transfer (ROT), and operate and transfer (OT) are examples of different types of private sector investments for infrastructure projects [2–4]. The BOT contracts have been used for a long time. The ﬁrst BOT project was the building of the Suez Canal which was constructed in 1854. In this contract, the private investor obtained a 99year concession period from the Egyptian government for the construction and operation of the canal connecting the Mediterranean and Red Sea [1,5]. The infrastructure projects will be ﬁnanced, designed and constructed by the project company set up by the private investors. After construction, the investor operates the projects during the concession period, to repay loans, recover the initial investment and receive proﬁt.
Concession period is one of the most important decision variables in the BOT projects [2]. Determining an appropriate concession period is important to the success of a BOT project. Projects with a shorter concession period could result in a higher toll/tariff regime and the risk burden due to the short concession period will be transferred to the group of people who use the facilities. On the other side, granting an excessively lengthy concession period may result in government's loss. Several researches have been conducted to determine the value of this variable properly. Shen et al. developed a BOT concession model (BOTCcM) for determination of concession period that can protect the interests of both the host government and the private investor concerned [7]. However, the impacts of risks and uncertainties on the estimation of various economic variables in the model are not taken into account using probability theory. Shen and Wu developed an approach for formulating a concession period to consider the impacts of risks and uncertainties and at the same time protect the basic interests of both the investor and the government concerned [1]. A simulation model was developed by Thomas et al. to assist the public partner to determine a proper concession period. In this model, the impact of risks and uncertainties are taken into account using probability theory and Monte Carlo simulation [6].Thomas et al. proposed a multiobjective decision model to determine the most appropriate concession option for BOT projects using probability theory [8]. Shen et al. developed a model to determine a particular concession period, which takes into account the bargaining behavior of the two parties concerned in engaging a BOT contract, namely, the investor and the government concerned [9]. Although several researches have been conducted to determine the concession period, they are faced with some major defects. The
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performance of a BOT project is inﬂuenced by several factors which have complex interactions with each other. In order to determine the value of concession period properly, it is necessary to account for these inﬂuencing factors. None of the previous works, however, take into account the complex interrelated structure of these inﬂuencing factors. Furthermore, in the previous researches, the uncertainties affecting a BOT project are not normally taken into account. In the few researches which take the uncertainties into consideration, the probability theory has been used. The probability theory, however, may not be a good choice to model project uncertainties since the historical data are not normally available in construction projects. Finally, Monte Carlo simulation has been used for calculating the NPV in all the previous researches. Some of the disadvantages of Monte Carlo simulation are computational burden, sensitivity to uncertainty about input distribution shapes, and the need to assume interrelations among all inputs [10,11]. This research presents an integrated fuzzysystem dynamics (SD) approach to determine the concession period. System dynamics (SD) introduced by Forrester, is an objectiveoriented simulation methodology enabling us to model complex systems considering all the inﬂuencing factors. The complex interrelated structure of different factors affecting a BOT project is modeled using system dynamics approach. The qualitative model of BOT project is constructed using governing cause and effect feedback loops. Then, the relationships existed between different factors are determined and the quantitative model of the project is built. In order to account for the existing risks and uncertainties, fuzzy logic is integrated into the proposed SD model. Fuzzy logic introduced by Zadeh (1965) is appropriate to consider the uncertain nature of factors affecting a BOT project. The values of different input factors affecting the concession period are determined by fuzzy numbers based on the opinions of different experts involved in the project. The application of Zadeh's extension principle and interval arithmetic at discrete αcuts is proposed to integrate the system dynamics and fuzzy logic modeling. Using the proposed integrated fuzzySD approach, the concession period can be determined as a fuzzy number. To evaluate the performance of the proposed method, it has been employed in a highway project and the concession period is determined as a fuzzy number. 2. Model structure A ﬂowchart representing different stages of determining the concession period using the proposed fuzzySD approach is shown in Fig. 1. As it can be seen in this ﬁgure, the proposed fuzzySD approach can determine the concession period considering all the inﬂuencing factors as well as the existing risks and uncertainties. For this purpose, ﬁrst the qualitative model of BOT project is constructed using cause and effect feedback loops. Then the interrelationship existed between different factors are deﬁned by mathematical equations and the quantitative model of BOT project is constructed. The magnitude of input factors is determined by fuzzy numbers. Having constructed the quantitative model of BOT project, the NPV value is simulated at different αcut levels and is presented as a fuzzy number. The concession period is now determined as a fuzzy number using the calculated value of project's NPV. Finally, the achieved fuzzy number of concession period is defuzziﬁed and a crisp value for the concession period is presented. The proposed model can also determine the concession period at different conﬁdence levels. 2.1. Qualitative modeling of BOT project There are several factors affecting a BOT project. These factors have complex interactions with each others. In order to determine the concession period properly, it is necessary to account for these inﬂuencing factors. System dynamics (SD) introduced by Forrester,
369
Identification of different factors affecting a BOT project
Constructing the qualitative model of BOT project using cause and effect feedback loops t=1 Constructing the quantitative model of BOT project
Prediction of the magnitude of input factors by fuzzy numbers
Dynamic simulation of project’s NPV at different αcut levels
Fuzzy representation of project’s NPV Yes
t
tf
t = t+1
No
Determination of concession period as a fuzzy number
Defuzzification and determination of concession period at different confidence levels Fig. 1. The ﬂowchart of different stages of determining the concession period by fuzzySD approach.
is an objectoriented simulation methodology enabling us to model the complex interrelated structure of different factors affecting a BOT project. SD modeling is useful for managing and simulation of processes with two major characteristics: (1) they involve changes over time and (2) they allow feedbackthe transmission and receipt of information [12,13]. Much of the art of SD modeling is to discover and represent the feedback processes, which, along with stock and ﬂow structures, time delays and nonlinearities, determine the dynamics of the system [14]. System dynamics modeling is inherently creative. Individual modelers have different styles and approaches. Yet all successful modelers follow a disciplined process that involves the following activities: (1) articulating the problem to be addressed, (2) formulating a dynamic hypothesis or theory about the causes of the problem, (3) formulating a simulation model to test the dynamic hypothesis, (4) testing the model until you are satisﬁed it is suitable for your purpose, and (5) designing and evaluating policies for improvement. In Fig. 2, a high level diagram of different factors affecting a project's NPV is shown. The high level diagram of the developed system dynamics model (Fig. 2) has been constructed based on the Eq. (9) which has been used by the previous researchers [1–3,6–9]. As it can be seen in this ﬁgure, the project's NPV is affected by several factors directly and indirectly. These factors include annual capital investment, construction
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total capital investment
Construction period 
+ + annual capital investment
operation and maintenance cost + +
. +
+ + total cost +
+ discount rate NPV value +


+ , 
+ +
total revenue
other revenues
toll price
Fig. 2. A high level diagram of different factors affecting the project's NPV.
duration, annual trafﬁc volume, toll price, annual maintenance cost and annual discount rate [1–3,6–9]. The complex interactions existed between these factors is depicted in Fig. 2. As an example, the toll price will affect the total revenue (Fig. 2). As the toll price increases, the total revenue is increased accordingly. However, increase in toll price will decrease the annual trafﬁc volume which in turn decreases the total revenue (Fig. 2). Total revenue is inﬂuenced by all these positive and negative effects. Each of the factors shown in Fig. 2, are inﬂuenced by several factors. In Figs. no. 3 to 5, the conceptual diagram of different factors affecting trafﬁc volume, maintenance costs and operation costs are shown, respectively. The conceptual diagram of two other inﬂuencing factors depicted in Fig. 2, including total capital investment and construction duration can be seen in previous researches carried out for modeling of projects using system dynamics [15,16]. The toll
price as another inﬂuencing factor has normally a constant value which is determined by the host government. The conceptual diagrams of the three parameters mentioned above including trafﬁc volume, maintenance cost and operation cost are modeled and explained below brieﬂy. The conceptual model of different factors affecting annual trafﬁc volume is shown in Fig. 3. The most important inﬂuencing factors include maintenance quality, toll price, possibility of constructing a new highway etc. Having determined the inﬂuencing factors, the relationship existed between these factors have been depicted by cause and effect feedback loops. As an example, “the ratio of journey time in highway to existing way” affects “the ratio of the highway users to total users”. If “the ratio of journey time in highway to existing way” is increased, the passengers prefer to select the highway and “the ratio of the
Fig. 3. Conceptual model of trafﬁc volume.
M. Khanzadi et al. / Automation in Construction 22 (2012) 368–376