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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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

a b s t r a c t The concession period is one of the most important decision variables in arranging a BOT-type contract which should be determined considering the existing risks and uncertainties. This research presents an integrated fuzzy-system dynamics (SD) approach for determination of concession period. The complex inter-related structure of different factors affecting a BOT project is modeled using the system dynamics approach. Owing to the imprecise and uncertain nature of different factors affecting the concession period, fuzzy logic is integrated into the system dynamics modeling structure. The values of different 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 is proposed for the system dynamics to enable the system outcomes to be presented considering uncertainties in the input variables. To evaluate the performance of the proposed method, it has been employed in a highway project. © 2011 Elsevier B.V. All rights reserved.

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]. Build-operate-transfer (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 99-year 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.

⁎ Corresponding author. E-mail addresses: [email protected] (M. Khanzadi), [email protected] (F. Nasirzadeh), [email protected] (M. Alipour). 0926-5805/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2011.09.015

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 multi-objective 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 inter-related 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 fuzzy-system dynamics (SD) approach to determine the concession period. System dynamics (SD) introduced by Forrester, is an objective-oriented simulation methodology enabling us to model complex systems considering all the influencing factors. The complex inter-related 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 α-cuts is proposed to integrate the system dynamics and fuzzy logic modeling. Using the proposed integrated fuzzy-SD 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 fuzzy-SD approach is shown in Fig. 1. As it can be seen in this figure, the proposed fuzzy-SD 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 inter-relationship 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 α-cut 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 α-cut 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 fuzzy-SD approach.

is an object-oriented simulation methodology enabling us to model the complex inter-related 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 feedback-the 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

Snowy days

Frosty days Number of accidents

+

+ Winter maintenance cost

+ Guardrail and sign maintenance cost

Weather condition



+ +

+

+

Highway marking cost + +

Marking life

Maintenance personel's faults

Length of the highway +

+ +

+

+

+

+

Pavement and bridges maintenance cost - + +

Pavement life

Acts of god

+ Shoulder maintenance cost

Use of debt

Maintenance quality

+

Buildings and utilities maintenance cost +

+

+ Maintenan ce cost



+ Deficit in -financial sources

Number of highway lines

371

-

+ -

Rain fall

+ Delay in salary payment

+ Motivation

Fig. 4. Conceptual model of maintenance cost.

highway users to total users” would be increased. Therefore, the traffic volume will be increased accordingly. Having increased the traffic volume, “the ratio of journey time in highway to existing way” will be increased. Therefore, a balancing loop is constructed. In Fig. 4, the conceptual model of the maintenance cost as one of the most important factors affecting the concession period is shown. There are several factors affecting maintenance cost including pavement maintenance cost, shoulder maintenance cost, guardrail and sign maintenance cost, high way marking cost etc. the interrelationship between factors and the

maintenance cost has been depicted in Fig. 4. The conceptual model of operation cost, simulates the operation costs based on the influencing factors (Fig. 5) the factor affecting the operation cost includes salary payment to operation's personnel, official building and vehicles maintenance cost etc. It should be stated that the influencing factors constructing the sub-models (Figs. 3 to 5) have been derived either from the previous works [12,15,16] or through conducting interviews by several experts involved in the BOT projects. 2.2. Constructing the quantitative model of BOT project

Motivation. -

Delay in salary payment. +

Deficit in financial sources. + Use of debt.

+

Maintenance personnel's faults

+ Official buldings and vehicles maintenance cost + Operation + cost + + Salary payment to + operation personnel + +

Number of personnel

Personnel salary

Fig. 5. Conceptual model of operation cost.

Having determined the qualitative model of BOT project using cause and effect feedback loops, the relationship existed between different factors are determined and the quantitative model of the concession period is built. The relationships existed between some of the factors are obvious and can simply be determined by mathematical functions. However, there exist some other factors for which these relationships can't be simply determined. In these cases, the relationships have been assessed either by extrapolation or expert judgment. In the case that historical data were available, the relationships were determined by extrapolation. Where the historical data were not available, the relationships were determined by expert judgment using fuzzy inference mechanism.



Indirect costs

2.2.1. Determination of relationships using historical data If historical data are available, the relationship between parameters can be determined using extrapolation. For this purpose, historical data are analyzed and the relationship that exists between factors is determined by regression. In this research, some previous highway projects have been studied and the historical data of these projects have been gathered throughout their project life cycle. Most of the relationships existed between different factors of the BOT project model were then determined through extrapolation. As an example the relationship between highway marking cost and the factors influencing it is explained below. Highway marking cost is affected by three factors including, traffic volume, number of highway lines and marking life (Fig. 4). The

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historical data of four parameters were gathered from the available BOT projects. Using Matlab software, these historical data were analyzed the relationship existed between them were determined as below: HMC ¼ 332537MON þ 0:2ðTV0:211NÞ

ð1Þ

where HMC is the highway marking cost, MO is marking life, TV is traffic volume and N is the number of highway lines. The relationships between other factors were determined similarly. As another example, the relationship between “salary payment to operation personnel” and “number of personnel”, “personnel salary” and “indirect costs” is determined as below (Fig. 5): SP ¼ ððNPPSÞ þ ICÞ

ð2Þ

where, SP is salary payment, NP is the number of personnel, PS is the personnel salary and IC is the indirect costs. 2.2.2. Determination of relationships using fuzzy inference mechanism When historical data are not available, the relationships between factors can be determined by inference mechanism. The fuzzy logic if–then rule performs approximate reasoning with imprecise or vague dependencies or commands. The Mamdani style inference mechanism as one of the most famous types of fuzzy controllers is employed in this research [16]. The main idea of the “Mamdani” controller is to describe process state by means of linguistic variables and to use these variables as inputs to control rules [17,18]. The fuzzy control systems consist of three major components [17]: (1) Fuzzification module (2) Inference mechanism (3) Defuzzification. These components are explained below briefly. The operation that assigns a membership value μ(x) to a given value x is called Fuzzification [19]. Inference is the set of if–then rules that operate on linguistic variables and encode the control knowledge of the system [16]. The rules connect the input variables with the output variables and are based on the fuzzy state description that is obtained by the definition of the linguistic variables. The definition of linguistic variables and rules are the main design steps when implementing a Mamdani controller [17]. The process that produces a crisp output from a fuzzy set is called defuzzification. Many defuzzification methods have been proposed in the literature; however the most commonly used method is the Center of Areas (COA), also called center of centroid or center of gravity [19]. Formally, the rules used in the inference mechanism can be written as [17]: Ruler : if X1 is

j1 A 1 and

X2 is

j2 A 2 and…and

jn Xn is A n then

u is A

where is the jth term of linguistic variable i corresponding to the membership function μij1(x) and A j corresponds to the membership function μ j(u) representing a term of the control action variable. The computational core can be described as a three-step process. The first step is to compute the degrees of membership of the input values in the rule antecedent. The degree of membership of the input factors is calculated as follows:

i¼1…n

ð3Þ

This concept enables us to obtain the validity of the rule consequences. The second step is computation of the rule consequences. Formally: conseq

μr

n o j ðuÞ ¼ min αr ; μ ðuÞ :

conseq

μr

 conseq  ðuÞ ¼ max μ r ðuÞ :

ð5Þ

In this research, the relationships between factors were determined by fuzzy inference mechanism where the historical data were not available. As an example, the relationship between the ratio of the highway users to total users and the influencing factors has been determined by fuzzy inference mechanism. The ratio of the highway users to total users is influenced by three input factors including toll price, maintenance quality and ratio of journey time in highway to existing way (Fig. 3). Having determined the value of the input factors, the magnitude of ratio of the highway users to total users is determined by the fuzzy control system (fuzzy inference mechanism). Different components of the fuzzy control system are determined as follows: (1). Fuzzification: The fuzzification module transforms the crisp input data to a linguistic form. The membership function values for the variation of the three input variables (i.e. toll price, maintenance quality and ratio of journey time in highway to existing way) and also the output variable (i.e. the ratio of the highway users to total users) is shown in Fig. 6. The membership functions for this case study were derived from the expert experiences. (2). Inference: The amount of the fuzzy control system's output (i.e. the ratio of the highway users to total users) is induced by the inference rules. Table 1, shows the fuzzy control system inference rules for the three fuzzy inputs. A total of 27 fuzzy control rules exist. As an example, rule 1 is expressed as: If toll price is low, maintenance quality is high, and ratio of journey time in highway is less than existing way, then the ratio of the highway users to total users is about 1. Finally the magnitude of the ratio of the highway users to total users was assessed by the fuzzy control system based on the amount of three input factors. (3). Defuzzification: The achieved fuzzy number of the ratio of the highway users is defuzzified and was given as an input to the SD simulation model. As an example, if the toll price is 2 and the ratio of the journey time in highway to existing way is 5 and the maintenance quality is 8, then the ratio of the highway users to total users is computed as 0.763 by the fuzzy inference mechanism. 2.3. Integration of fuzzy logic to the proposed SD approach

j

Aij1

n
o j1 input αr ¼ min μi μi :

consequences using the maximum operator. The fuzzy set of the control action can be computed as:

ð4Þ

The third step is aggregation of rule consequences to the fuzzy set control action. This process is performed by aggregation of all

Most of the factors affecting a BOT project have an uncertain nature and it is impossible to assign precise crisp numerical values as their magnitude. System dynamics as often practiced may not be a good choice to simulate a BOT project as it cannot account for these uncertainties. Therefore, it may seem necessary to extend the system dynamics approach to treat the uncertain parameters/variables [16]. The historical data are not normally available in construction projects. Hence, the standard probabilistic methods are not a good choice for this purpose. Fuzzy logic introduced by Zadeh (1965) is appropriate to consider the uncertain nature of factors affecting a BOT project. Fuzzy logic is derived from fuzzy set theory deals with a set of objects characterized by a membership function that assigns to each object a grade of membership ranging between zero (no membership) and one (full membership) [10]. In this research fuzzy logic is integrated in to the proposed SD approach to account for uncertainties. For this purpose, first the magnitude of different factors affecting the concession period is defined by fuzzy numbers based on the opinions of different experts involved in the project considering the existing risk and uncertainties. Then the NPV value and consequently the concession period are simulated for the achieved fuzzy number of the input factors. The application of

M. Khanzadi et al. / Automation in Construction 22 (2012) 368–376

Low

Medium

High

Low

1

1

0.5

0.5

0

Medium

High

0 0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

Less

Equal

More

About 0.5 About 0.6

1

1

0.5

0.5

0

1

2

3

4

5

6

4

5

6

7

8

9

10

(Maintenace quality)

(toll price)

0

373

7

8

10

9

About 0.7

About 0.8

About 0.9 About 1

0 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

(Ratio of jurney time in highway to existing way)

1

(Ratio of the highway users)

Fig. 6. Membership functions of toll price, ratio of journey time in highway to existing way, maintenance quality and the ratio of the highway users to total users.

Zadeh's extension principle and interval arithmetic at discrete α-cut is proposed to integrate the system dynamics and fuzzy logic modeling. Using the proposed integrated fuzzy-SD approach, the concession period can be determined as a fuzzy number.

The amount of the project income in year t can be obtained by the following equation

3. Determination of the NPV

where q is the annual traffic volume and p is the toll price. Finally, the value of the NPV is calculated through combining Eqs. (7) and (8) as follows:

The most common methods for the assessment of financial viability are the payback period (PBP), accounting rate of return (ROR), net present value (NPV), and the internal rate of return (IRR) [20]. There are some standard equations for calculating the NPV. The project's NPV can be determined by the following equations [1,2,7]: T¼tf

NPV ¼ ∑

T¼1

NCFðt Þ ð1 þ r Þt

ð6Þ

The above equation can be rewritten as follows: T¼tf

NPVðt Þ ¼ ∑

T¼1

ðI ðt Þ−Cmðt ÞÞ ð1 þ r Þt

ð7Þ

where NPV(t) denotes net present value in year t, NCF (t) denotes the net cash flow in year t, I (t) = income for the year t, Cm(t) = cost in year t, r = discount rate and tf is the project economic life time. Table 1 Fuzzy control system inference rules for ratio of highway users to total users. Maintenance quality

Toll price

H M L H M L H M L

L L L M M M H H H

Ratio of journey time in highway to existing way LE

EQ

MO

1 1 0.9 0.9 0.9 0.8 0.7 0.7 0.6

1 0.9 0.8 0.8 0.7 0.7 0.7 0.6 0.5

0.9 0.8 0.7 0.7 0.6 0.6 0.6 0.5 0.5

Notes: L: Low, M: Medium, H: High, LE: Less, EQ: Equation, MO: More.

Iðt Þ ¼ q×p

T¼Tf

NPVðt Þ ¼ ∑

T¼1

ð8Þ

ððq×pÞ−Cmðt ÞÞ : ð1 þ rÞt

ð9Þ

As explained above and shown in Figs. 2 to 5, there are various factors affecting the project's NPV. The value of these influencing factors can't be assessed with certainty due to the existing risks and uncertainties. The values of these influencing factors are assumed as a fuzzy number based on the opinions of different experts involved in the project. Algebraic operations on real numbers can be extended to fuzzy numbers, i.e. input fuzzy numbers defined on the real line, by means of the extension principle [16,21,22]. The application of extension principle and interval arithmetic at discrete α-cuts is proposed to integrate the system dynamics and fuzzy logic modeling. Using the proposed fuzzy-SD approach, the NPV value is calculated as a fuzzy number. The proposed methodology is explained below briefly: (1) A particular α-cut value is selected, where 0 ≤ α ≤ 1. (2) The associated crisp values of the fuzzy number of the value of different input factors correspond to α are determined as [aα, bα]. (3) The NPV value is calculated with these crisp values as input to the simulation model. Since the crisp inputs depend on the selected α-cut, the output of the model is valid for the same value of α-cut .(4) Steps 1–3 are repeated for as many values of α needed to refine the solution. Coverage of the entire range of α-cut makes the NPV value a fuzzy number. As the number of α-cuts is increased the accuracy of the produced fuzzy number will be increased. Using proposed fuzzy-SD approach, the NPV value could be determined throughout the project life cycle. 3.1. Determination of the concession period After determining the NPV values throughout the project life cycle, the concession period can be calculated. In order to determine the concession period, first the total capital investment should be

M. Khanzadi et al. / Automation in Construction 22 (2012) 368–376

calculated. The use of capital investment is considered to contribute negative value to NPV. It is assumed that the total capital investment is evenly consumed during the construction period. During this period when there is no income, the value of the total capital investment can be measured from the NPV curve by [1]:    t¼tf    IðpÞ ¼  min fNPVt g:  t¼1 

ð10Þ

IR ¼ IðpÞ×R

ð11Þ

where IR denotes the investor's expected investment return and R denotes investment's expected rate of return and I(p) = total investor's investment. After that, the concession period could be determined using the NPV values calculated throughout project life cycle in the previous section. The concession period is determined as a time in which the project's NPV is equal to the calculated IR [1]. The above steps should be repeated for as many value of α needed to refine the solution. Finally, the concession period is determined as a fuzzy number. 3.2. Defuzzification Defuzzification is a process that can transforms the resulting fuzzy values into a crisp value. The center of area (COA), also called center of centroid or center of gravity is utilized for defuzzification [19]. The center of area method is calculated by the following equation [17,23]: ∫ u:μ u

¼

conseq

ðuÞdu

u

∫μ

conseq

ðuÞdu

5 4 3 2 1

Then, the investor's expected investment return is calculated by the following equation [1]:

COA

6

Toll Price

374

:

ð12Þ

u

The center of area method has been used in this research to convert the fuzzy number of concession period into a crisp number. 4. Model application The proposed fuzzy-SD approach is employed in a real highway project in order to demonstrate how the simulation model works. The input parameters used in the simulation model are as follow: • The concession period is composed of the construction and operation periods. In this case example, the construction period is estimated as a triangular fuzzy number of (4, 4.5, 5) years due to the existing risks and uncertainties. It should be stated that the shape (pattern) of the fuzzy numbers depends on descriptions made by experts, and are generally selected using the human/expert experience, intuitively. It is popular to use triangular fuzzy sets because of computational efficiency [17]. • The total capital investment is considered as a fuzzy number of (100, 105, 115) million dollars, (It is assumed that the total capital investment is evenly consumed during the construction period). Therefore, the annual capital investment is equal to C(c) = I/t0). • In this case study, the toll price is considered as a crisp number of 0.6 dollars per vehicle during the first 5 years of operation period and is increased stepwise after each 5 years period. The toll price predicted for this highway project is shown in Fig. 7. • The discount rate is a triangular fuzzy number of (7%, 7.5%, and 8%). It is assumed that the discount rate is fixed during the project life cycle. • The initial annual traffic volume was estimated by counting the number of vehicles. However, it is difficult to predict the traffic volume by

0

0

5

10

15

20

25

30

35

40

45

50

year Fig. 7. Toll price variations throughout the project life cycle.

certainty due to the existing risks and uncertainties. The annual traffic volume is calculated based on the value of input parameters using the proposed integrated fuzzy-SD approach. • In order to calculate the operation and maintenance cost, all the expenses incurred in the operation period such as operating, managing and maintaining the facility was embraced. The annual operation and maintenance cost is calculated based on the value of input parameters using the proposed integrated fuzzy-SD approach. Having the value of input parameters, the NPV is simulated as a fuzzy number. The left value, the right value and the most likely value of the project's NPV throughout the project life cycle is shown in Fig. 8, graphically and in Table 2 numerically. If the value of α-cut is selected as one, the total capital investment is calculated as 109.3 million dollars. The investor's expected rate of return is considered as 15% .Therefore, the investor's expected investment return is equal to 109.3 ∗ 0.15 = 16.4 million dollars. Using Table 2, it is conceived that the investor can achieve his expected profit after 39 years and the project can then be transferred to the host government. Similarly, if α-cut is selected as zero, the amount of capital investment is calculated as 103.4 and 120.7 million dollars for the right and left values of NPV, respectively. Assuming an expected rate of return of 15%, the amount of investor's expected return on the investment is equal to 15.5 and 18.1 million dollars for the left and right values of NPV, respectively. Finally, the left and right values of the concession period are calculated as 34 and 43 years. The fuzzy number of the concession period is shown in Fig. 9. It should be noted that the fuzzy number of the concession period is depended on the investor's expected rate of return. The proposed methodology has the great capability for allowing the project manager to impose his risk acceptance level to determine the length of concession period at different confidence levels by selecting an appropriate α-cut level. As an example, if α-cut (risk level) is selected as 1, the uncertainties inherent in the evaluation process are ignored and a crisp value for the concession period is resulted as 39 years. Similarly, in the other extreme condition where α-cut is chosen as zero, the uncertainties inherent in the evaluation process are fully considered and possible variation in the results may be obtained. However, in this case the widest range of concession period would be achieved as an interval of 34 to 43 years. In order to achieve a crisp number for the concession period the center of area method is utilized for defuzzification. Using the proposed defuzzification method, the length of concession period was determined as 38.66 years in α-cut = 0. In order to build confidence in the model, several standard validation tests such as structural and behavioral tests were performed. The implementation of the proposed fuzzy-SD approach in this project case example illustrated the effectiveness of the proposed method in determining concession. The achieved results by the proposed methodology are more reliable in comparison to the other existing

M. Khanzadi et al. / Automation in Construction 22 (2012) 368–376

375

250 (a): α cut = 0 , right value

NPV value (million $)

200 150 (b): α cut =1, most likely value

100 50

(c): α cut = 0 , left value 0

0

5

10

15

20

25

30

35

40 45 50 project life time (year)

-50 -100 -150

Fig. 8. Simulated values of NPV: (a) the right value of NPV, (b) the most likely value of NPV, (c) the left value of NPV.

Table 2 The minimum, most likely and maximum values of NPV throughout the project life cycle. Year

X(L)

X(M)

X(R)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

0 − 26.5 − 53.2 − 80.0 − 107.0 − 120.7 − 120.6 − 120.1 − 119.6 − 119.1 − 118.8 − 118.1 − 117.0 − 116.0 − 116.0 − 114.4 − 113.1 − 111.4 − 109.8 − 108.4 − 107.3 − 105.1 − 102.2 − 99.3 − 96.7 − 94.4 − 90.9 − 86.3 − 81.9 − 77.8 − 74.1 − 69.0 − 62.5 − 56.2 − 50.4 − 45.1 − 39.1 − 31.6 − 23.7 − 16.2 − 9.3 − 0.4 10.4 20.8 30.5 39.4

0 − 21.6 − 43.4 − 65.2 − 87.2 − 109.3 − 109.1 − 108.5 − 108.0 − 107.5 − 107.2 − 106.4 − 105.2 − 104.1 − 104.1 − 102.3 − 100.8 − 98.8 − 96.9 − 95.2 − 93.6 − 91.0 − 87.4 − 83.9 − 80.6 − 77.7 − 73.3 − 67.7 − 62.1 − 57.0 − 52.2 − 45.7 − 37.6 − 29.6 − 22.2 − 15.4 − 7.6 2.1 12.3 22.0 31.1 42.8 56.8 70.5 83.3 95.2

0 − 18.6 − 37.3 − 56.2 − 75.1 − 94.1 − 103.4 − 102.8 − 102.1 − 101.5 − 101.1 − 100.1 − 98.6 − 97.1 − 97.1 − 94.7 − 92.7 − 90.1 − 87.5 − 85.1 − 82.9 − 79.3 − 74.4 − 69.5 − 64.9 − 60.7 − 54.5 − 46.5 − 38.6 − 31.2 − 24.3 − 14.7 − 2.8 9.0 20.1 30.5 42.4 57.3 73.2 88.3 102.6 121.2 143.7 165.8 186.7 206.2

Identification of interactions existed between influencing factors by cause and effect feedback loops is not an easy job in megaprojects to be performed. Well-qualified experts and intensive data requirement may limit the application of the proposed model in projects with limited data and/or qualified experts. 5. Conclusions Concession period is one of the most important decision variables in arranging a BOT-type contract. This research presented a fuzzybased system dynamics approach to determine the concession period taking account for the complex inter-related structure of influencing factors as well as the existing uncertainties. The complex inter-related structure of different factors affecting a BOT project was accounted for by the use of the implemented SDbased approach. For this purpose, the qualitative model of BOT project was first constructed using cause and effect feedback loops. A high level diagram of NPV value and the conceptual model of three subsystems including the traffic volume, operation cost and maintenance cost were presented using cause and effect feedback loops. The relationships existed between different factors were then determined and the quantitative model of the project was built. The relationships existed between different factors were simply determined by mathematical functions in most of the cases. However, there existed some other factors for which these relationships could not be simply determined. In these cases, the relationships were assessed either by extrapolation or expert judgment (using fuzzy inference mechanism). It was illustrated that the existing risks and uncertainties could be approached by integrating fuzzy logic into the proposed SD-based model. The applicability and performance of the proposed method in determination of the concession period was evaluated by its implementation in a highway project. The values of different input factors affecting the concession period were determined by fuzzy numbers

1 0.8

µ(x)

methodologies since the complex inter-related structure of influencing factors as well as the existing risk and uncertainties are taken into account.

0.6 0.4 0.2 0 32

33

34

35

36

37

38

39

40

41

X (year) Fig. 9. Fuzzy number of concession period.

42

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M. Khanzadi et al. / Automation in Construction 22 (2012) 368–376

based on the opinions of different experts involved in the project. Using the proposed integrated fuzzy-SD approach, the value of the NPV and also the concession period was determined as a fuzzy number. Finally, the achieved fuzzy number of concession period was defuzzified and a crisp value for the concession period was presented. The proposed methodology has also the great capability for allowing the project manager to impose his risk acceptance level to determine the length of concession period at different confidence levels by selecting an appropriate α-cut level. It is believed that the proposed fuzzy-SD method may present a flexible and robust method for determining the concession period since both the complex inter-related structure of influencing factors as well as the existing uncertainties is taken into account. The proposed integrated fuzzy-SD model can be applied for all BOT projects in order to determine the concession period. References [1] L.Y. Shen, Y.Z. Wu, Risk concession model for build operate transfer contract projects, Journal of Construction Engineering Management 131 (2) (2005) 211–220. [2] M. Khanzadi, F. Nasirzadeh, M. Alipour, Using Fuzzy-Delphi technique to determine the concession period in BOT projects, IEEE (2010) 442–446. [3] Fen-May Liou, Chih-Pin Huang, Automated approach to negotiations of BOT contracts with the consideration of project risk, Journal of Construction Engineering Management 134 (1) (2008) 18–24. [4] M.M. Kumaraswamy, D.A. Morris, Build-operate-transfer-type procurement in Asian Mega projects, Journal of Construction Engineering Management 128 (2) (2002) 93–102. [5] S.M. Levy, Build, Operate, Transfer: Paving the Way for Tomorrow's Infrastructure, Wiley, New York, 1996, pp. 18–20. [6] Thomas S. Ng, J.Z. Xie, Y.K. Cheung, M. Jefferies, A simulation model for optimizing the concession period of public private partnerships schemes, International Journal of Project Management 25 (2007) 791–798.

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