Integrating travelers’ perceived factors in modeling the ceiling price of toll road a case study of BOT projects in vietnam

ACKNOWLEDGMENT
During the period of studying to accomplish the topic of master’s thesis, there is
not only self effort but also the enthusiastic guidance of teachers, as well as the
encouragement of my family and friends.
First of all, I would like to express my gratitude sincerely to my supervisor,
Lecturer Dr. Nguyễn Hoàng Tùng who instructed directly me to conduct this research
by making particular guidance.
I also would like to give special thanks to whole teachers at Vietnam Japan
University, who have conveyed me the precious knowledge for the duration of my
learning here. Especially Professor Dr.Sci Nguyễn Đình Đức and Dr. Phan Lê Bình
who always have stimulated me to try my best and have inspired me a lot of
motivations for studying as well as working in the life.
Besides that I am grateful to Professor Hironori Kato, the Co-Director of Master's
Program in Infrastructure Engineering, for supporting me actively when I had a threemonth Internship Program in Japan.
Finally, I would like to thank my family and co-workers, who always are beside me
during the implementing this master's thesis.
Although there have been lots of my attempts in the research process, due to
limited ability and experience of self, this master's thesis still exist some unavoidable
shortcomings. So I am looking forward to hear sincere feedbacks from teachers and
colleagues in order to supplement and complete more this research in the future.
Hà Nội, Jun 2019

Đỗ Việt Hùng

i


ABSTRACT
The Build-Operate-Transfer (BOT) scheme is considered as an attractive means
by the Vietnamese government to develop new infrastructure projects. They were
started to widely carried out from 2011 and it is predicted to continuously increase in

the future. The toll price of BOT road given by investor is set under the ceiling price
that is regulated in Circular of Ministry of Transport. It can be seen that most of BOT
toll road projects have applied charge that are nearly equal to the given ceiling prices.
Nevertheless, the ceiling price at this Circular did not consider the scale of road, as
well as did not take into account of travelers’ willingness to pay to toll price. There
has not ever researches of the topic to previous studies. Therefore, this study focused
on integrating “willingness to pay of travelers” to model of toll ceiling price in BOT
road project by using a bi-level programming model to formulate for a simple tworoad network to optimize toll price and propose ceiling pricing for BOT projects.
Some important findings of ceiling price include: (1) If government does not restrain
toll price on BOT road, that leads to a negative social welfare; and (2) there must
exist price which is maximum threshold of toll price for BOT road in order that social
welfare becomes positive; and (3) ceiling price is set to be equal to minimum of
“willingness to pay” and the threshold of toll price above.

ii


TABLE OF CONTENTS
ACKNOWLEDGMENT.............................................................................................................. i
ABSTRACT................................................................................................................................... ii
TABLE OF CONTENTS........................................................................................................... iii
LIST OF FIGURES....................................................................................................................... v
LIST OF TABLES....................................................................................................................... vi
LIST OF ABBREVIATIONS................................................................................................... vii
CHAPTER 1. INTRODUCTION.............................................................................................. 1
CHAPTER 2. LITERATURE REVIEW.................................................................................. 8
CHAPTER 3. METHODOLOGY............................................................................................. 9
3.1. The model setting.............................................................................................................. 9
3.2. Solution procedure......................................................................................................... 11
3.2.1. Step 1: Determining route choice of travelers.................................................. 11

3.2.2. Step 2: The operators determine the toll prices to maximize their own
benefit respectively............................................................................................................. 13
3.2.2.1. BOT road............................................................................................................ 13
3.2.2.2. Existing road..................................................................................................... 14
3.2.3. Step 3: Evaluation social welfare........................................................................ 15
3.2.3.1. Case 1: All two roads get maximum their own benefit at the same
time..................................................................................................................................... 15
3.2.3.2. Case 2: Only BOT road get maximum his own benefit under
condition that it is positive social welfare................................................................. 16
3.2.4. Step 4: Integrating the factor named "willingness to pay of travelers" to
guarantee users' benefit...................................................................................................... 17
3.2.5. Step 5: Determining ceiling price of toll road under condition that
optimal benefit of investor and the government, which taking into account
"willingness to pay" of travelers...................................................................................... 18
3.2.5.1. Case 1: If p1’ is less than WTP (i.e. p1’ ≤ WTP)....................................... 19
3.2.5.2. Case 2: If p1’ is greater than WTP (i.e. p1’ ≥ WTP)................................. 19
iii


3.2.5.2.1. Recommendation 1: Downscale capacity of BOT road......................19
3.2.5.2.2. Recommendation 2: Keep capacity of BOT road................................. 20
CHAPTER 4. CASE STUDY.................................................................................................. 22
4.1. Introduction for case study........................................................................................... 22
4.2. Willingness to pay of travelers choosing this road to travel................................. 23
4.3. Determining toll ceiling price of BOT road............................................................. 25
4.3.1. Case 1: Toll ceiling price for vehicle has under 12 seats............................... 25
4.3.1.1.1. Recommendation 1: Downscale capacity of BOT road......................26
4.3.1.1.2. Recommendation 2: Keep capacity of BOT road................................. 27
4.3.2. Case 2: Toll ceiling price for vehicle has under 30 seats............................... 29
4.3.2.1.1. Recommendation 1: Downscale capacity of BOT road......................30

4.3.2.1.2. Recommendation 2: Keep capacity of BOT road................................. 31
4.4. Estimation WTP as regression function.................................................................... 32
4.4.1. Case 1: Estimation WTP function of travelers have car under 12 seats .. 33
4.4.2. Case 2: Estimation WTP function of travelers have vehicle under 30 seats
35
CHAPTER 5. CONCLUSION................................................................................................ 39
5.1. Conclusion........................................................................................................................ 39
5.2. Limitation......................................................................................................................... 39
REFERENCES............................................................................................................................ 40
APPENDIX.................................................................................................................................. 41

iv


LIST OF FIGURES
Page
Fig 1.1. Relationship between government, investor, travelers.......................................... 2
Fig 1.2. Number of BOT projects in Vietnam incl. estimation........................................... 2
Fig 1.3. Rank of Vietnam in the world about service and quality of road transport
infrastructure................................................................................................................................... 3
Fig 1.4. Comparison of benefit between BOT road vs non-BOT road............................. 3
Fig 1.5. Toll price in BOT scheme in Vietnam....................................................................... 6
Fig 1.6. GDP per capita and Toll price of some countries................................................... 7
Fig 3.1. A network model......................................................................................................... 10
Fig 4.1. PV-CG Expressway and NH.1A.............................................................................. 22

v


LIST OF TABLES

Page
Table 1.1. Ceiling Prices in National Highway...................................................................... 5
Table 1.2. Ceiling Prices in Expressway................................................................................. 5
Table 4.1. Major parameters of two roads............................................................................ 23
Table 4.2. Characteristic of interviewees.............................................................................. 24
Table 4.3. Descriptive statistic about WTP of travelers for toll price............................ 25
Table 4.4. Regression Coefficient of WTP function.......................................................... 33
Table 4.5. Regression Coefficient of WTP function.......................................................... 35
Table 4.6. Regression Coefficient of WTP function.......................................................... 36
Table 4.7. Regression Coefficient of WTP function.......................................................... 37

vi


LIST OF ABBREVIATIONS
BOT

Build – Operate - Transfer Public

PPPs

Private Partnerships Pháp Vân –

PV-CG Expressway

Cầu Giẽ Expressway National

NH.1A

Highway No.1A Willingness to

WTP

pay

vii


CHAPTER 1. INTRODUCTION
The more rapidly the economy grows, the more greater demand for
infrastructure are. In most countries, infrastructure was built from the state budget.
However, there are many items which need be spent by governmental budget and
private capital is a good fund to complement these shortages. Nowadays, more and
more governments have encouraged private investor which take part in public
investment projects. Therefore, in order to support public infrastructure, Public
Private Partnerships (PPPs) have become a major scheme (Hodge and Greve, 2007)
and reduce public sector budget shortages (Kwak et al., 2009). PPPs are widely used
to supply many infrastructure projects in the world. Infrastructures invested by PPPs
make economic efficiency increasing (Zhang, 2005) and facilitates the overall
development of social infrastructure (Li et al., 2016b).
In Vietnam, according to Decree No. 63/2018/ND-CP: “PPP” is an investment
form which is carried out on the basis of a contract between the State and an investor,
in order to construction, renovation, operation, business, management of
infrastructure works, provision of public services.
Build-Operate-Transfer (BOT) model is a form of PPP which has extensive
applications in infrastructure projects. The BOT scheme is gaining popularity and
booming in public infrastructure around the world (Tan, 2012). It is adopted as an
innovative way to sponsor for infrastructure construction in both developing and
developed countries. (Subprasom, 2004). In recent years, BOT arrangements have
contributed to accelerating economic growth and improve quality service delivery

and operation efficiency (Akintola et al., 2003).
In Vietnam, the Build-Operate-Transfer (BOT) scheme is considered as an
attractive means by the Vietnamese government to develop new infrastructure
projects. According to Decree No.63/2018/ND-CP, parties involving in this contract
project include: the government, private investor and travelers.

1


Investor

Travelers

Government

Fig 1.1. Relationship between government, investor, travelers
Figure 1 show the relationship whole parties involved in. First, the government and
private sector sign an agreement for project. Then investor constructed project by his
own expense. After the construction was completed, the investor carries out to
provide service for users and travelers pay charge this serve. When end of concession
period, private investor gives project back government and government manages its.
In Vietnam, BOT projects were started to widely carried out from 2011. Although
there were only 18 projects in 2011, so they increased to 80 projects in 2015, and it is
predicted to continuously increase in the future. (Ministry of Transport report, 2016).

(Number of projects)

Fig 1.2. Number of BOT projects in Vietnam incl. estimation
These projects have promoted the road traffic system in our country to develop
quickly and synchronously. According to the World Economic Forum (WEF), the

service and quality of Vietnamese road transport infrastructure increased rapidly and
ranked in the position of 92/137 countries in the word in 2017. (World Economic
Forum, Global competitiveness Report, 2018)

2


102
/134

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

Fig 1.3. Rank of Vietnam in the world about service and quality of road
transport infrastructure
When choosing to travel on BOT roads, although length of road between BOT
road and non BOT road are equivalent and travelers have to pay a significant fee, so
they obtain more benefit himself, such as get higher speed, reduce travel time, save
fuel consumption, feel comfortably travel as well as restrain collisions can be
happened. Thence, it can be raised economic efficiency for businesses and
individuals. Besides that, we can obtain social benefit as decreasing congestion and
emissions causing environmental pollution. According to the statistics of the Ministry
of Transport, Noi Bai - Lao Cai Expressway is estimated to reduce travel time by
50% and cost by 30%; Hanoi - Vinh National Highway is estimated to reduces about
30% of travel time and 20% of cost; Highway No.14 through Dak Nong province is

Road invested by BOT project

Charge price
(VND / turn)

Length(Km)

estimated to reduces about 30% of travel time and 6% of costs, ...

Road invested by Non-BOT project

Fig 1.4. Comparison of benefit between BOT road vs non-BOT road
3


Many studies have investigated the properties of BOT contracts and their design
process. To design a BOT contract, three critical parameters need to be considered:

the length of the concession period, the infrastructure’s capacity and the toll. Three
variables are essential to a BOT road project. They determine the social welfare for
the whole society during the whole life of the road and the profit of the private firm
during the concession period. In the concession period, the private sector receives the
revenue of charged tolls (Tam, 1999). Generally, service charge and capacity
decisions are critical in a typical BOT contracting process, and the private sector has
the power to determine both of them in the concession period. The private sector aims
to maximize its own profit and may charge a high service fee, which eventually hurts
the social welfare and not many road users want to patronize the BOT roads
(Carpintero and Gomez, 2011). Therefore the optimal BOT contract depends on
whether the optimum toll is profitable (Guo and Yang, 2009). And it is necessary for
the government to set some restraints on BOT toll price to not lead to a negative
social welfare (Jing et al., 2008).
The carrying out of road toll in Vietnam goes through two stages, before and after the
Decree No. 18/2012/ND-CP about "fund of road maintenance and operation" took effect
in January 2013. Before the Decree No. 18/2012 / ND-CP took effect, we had 2 systems
of toll stations, in which one system are used to toll for project invested by state budget.
Another system is served for project invested by BOT contract. After the Decree
No.18/2012/ND-CP took effect, all of toll station of project invested by state budget were
removed (by Document No. 2250/TTg-KTN in December 2012). So, "the fund of road
maintenance and operation" was born to get revenue for state budget in order to operate
and maintain the projects invested by state budge. Meanwhile, all toll stations of BOT
project are keeping remain. The toll price of BOT road given by investor is set under the
ceiling price that is regulated in Circular No. 35/2016/TT-BGTVT and No. 60/2018/TTBGTVT, namely “Regulations for ceiling price of toll road”. The ceiling prices vary
across types of vehicles and this for heavier

4


vehicles tends to be higher. Two tables of ceiling prices below are officially set for

national highway and expressway and applied to any toll roads all over the nation.
Table 1.1. Ceiling Prices in National Highway

N

Type of vehicle

1.

Vehicles has less than 12 seats, trucks under 2 tons; Buses

2.

Vehicles has 12 - 30 seats, trucks with capacity 2 - 4 tons

3.

Vehicles has more 31 seats, trucks with capacity 4 - 10 tons

4.

Trucks with capacity 10 - 18 tons, 20 feet of container truck

5.

Trucks with more capacity 18 tons, 40 feet of container truck

Table 1.2. Ceiling Prices in Expressway

N

Type of vehicle

1.

Vehicles has less than 12 seats, trucks under 2 tons; Buses

2.

Vehicles has 12 - 30 seats, trucks with capacity 2 - 4 tons

3.

Vehicles has more 31 seats, trucks with capacity 4 - 10 tons

4.

Trucks with capacity 10 - 18 tons, 20 feet of container truck

5.

Trucks with more capacity 18 tons, 40 feet of container truck

At this time of December 2018, there were 46 road projects invested in BOT scheme
are going on toll charge (Department Public Private Partnership - Ministry of
Transport, 2018). Observed Prices of BOT Toll Roads, it can be seen that most of
BOT toll road projects have applied charge that are nearly equal to the given ceiling
prices. Toll pricing observed in 46 BOT projects is presented in table as below:

5


2
1
3
3

15
10

1

33

Number
of

3 projects

(3) - Vehicles
has more 31
seats,
trucks
with capacity 4
- 10 tons

22
15

2
1

Charge price (thousand VND)

30
26
25
20

- Vehicles
has 12 - 30
seats,
trucks
with capacity 2
- 4 tons

(2)

Charge price (thousand VND)

Charge price (thousand VND)

(1) - Vehicles
has less than 12
seats,
trucks
with capacity
under 2 tons;
Buses

Ceiling price
52
35

40
33
22

2
3
1
(4) - Trucks with capacity
10 container truck

Fig 1.5.
Toll price in
BOT
scheme in
Vietnam


For

Howev

BO

er, the

T

ceiling

proj

price at

ect,

this

the

Circula

bala

r

nce

some

of

proble

ben

m.

efit

That

bet

is, (1)

wee

the

n:

scale

the

of

gov

project

ern

has not

men

been

t,

consid

priv

ered.

ate

Project

inve

s with

stor

differe

and

nt

trav

initial

eler

invest

s is

ment,

mos

differe

t

nt

imp

capacit

orta

y

nt.

road

has

of

6


pay depending on the income of travelers have not taken into account in this ceiling
price. The charge price for BOT projects in Vietnam is equivalent to others countries
while GDP per capita is less than (World Bank). That means, if it is absolute
comparison, the charge price in Vietnam is more expensive.

Fig 1.6. GDP per capita and Toll price of some countries
In practice, a BOT road usually co-exists with existing road managed by
government, which can compose a simple two-road network. The BOT project
represents a major capital investment for which project conducts. So, it is necessary
to evaluate the financial viability and feasibility of the BOT project. By viewing a toll
price of BOT contracts on perspectives from three parties, including: (1) the
government, whose objective is to maximize social welfare; (2) the private investors,
who desire to gain maximum profit; both are expressed by criteria of financial
evaluation, containing: Net present value (NPV), the internal rate of return (IRR), and
the breakeven year; and (3) the travelers, whose objective is to minimize the travel
cost described by "willingness to pay".
Being aware of these issues, this study will focus on the effects of "Willingness
to pay" to ceiling price of a BOT project in the context of a simple two-road network.
From that, we will integrate “willingness to pay of travelers” to model of toll ceiling
price in BOT road project.

7

CHAPTER 2. LITERATURE REVIEW
Our research is closely related to the literature about toll and benefit under BOT
contracts which attract a lot of attention. A study discussed that a toll road getting
benefit to private investor can make welfare falling for the whole highway network
system (Mill, 1995). A simultaneous combination of concession period, road
capability and toll price as a three variables occurred in BOT contract allows to
optimize BOT contract in order to obtain maximum social welfare and gain an
acceptable profit for private investor (Guo and Yang, 2009). In highway
transportation network, the considering toll pricing under optimal combination of
demand and capability of BOT road by bi-level programing formulas (Yang and
Meng, 2000, 2002). Likewise, this model analyzed the influence of toll pricing to
route choice of travelers and measured investor profit or social welfare of
government (Chen and Subprasom, 2007). The toll level determined by the bi-level
model was formulated to maximize social welfare while taking into account choice
behavior of travelers (Yang and Zhang, 2003). A heterogeneous choice of travelers
influents private profit and social welfare under various combinations of toll price
and road capacity (Yang et al., 2002). In addition, the competition about toll and
capacity occurred among roads (Xiao et al., 2007). The price is assumed to be a
function of the travelling demand (Tan et al., 2010), considering on a simple two-road
network, an equilibrium of traveling demand happened among travelers, leads to they
will choose the road had minimum travel cost (Yates, 1992). Meanwhile National
Highways Authority of India (NHAI) has set a formula for calculation of toll fee
based on wholesale price index which is “the price of a representative basket of
wholesale goods” (Government of India report, 2009).
Following those previous literatures, researchers have developed different models and
almost studies focused on optimization of toll charge to balance private profit and
social welfare. However, the existing models have not determine: (1) toll ceiling price
model for each BOT project, and (2) impact of "willingness to pay" of travelers to
target of perspectives mentioned above.
8

CHAPTER 3. METHODOLOGY
3.1. The model setting
As mentioned in Chapter 1, by the financial evaluation (i.e., NPV, IRR,
breakeven year) and “Willingness to pay” of travelers, the project performances
including private profit, social welfare and travelers’ benefit are considered in the
decision process of BOT contract. Particularly,
(1) Private investor's benefit is remaining profit after deducting initial construction

expense from their revenue that obtain from toll charge in concession period interval,
minus initial construction expense.
(2) Government's benefit is welfare due to BOT road brings for society in concession

period as well as until end of economic life of road.
(3) Traveler's benefit is "willingness to pay" level to use BOT road.

Subject to constraint conditions about benefit of private investor and the government,
the optimal price will be found out. Comparison this price with "willingness to pay"
of travelers, the ceiling price of toll road will be set up for this BOT project.
The above explanations can be conveyed by the multi-equation as follows:
Investor’s benefit

= function of price = f1 (price)

Government’s benefit

= function of price = f1 (price)

Travelers’ benefit

= Willingness to pay

Subject to: Constraint of investor’s benefit and government’s benefit.
The model is set up with a two-road network providing the transportation supply
between two places. Assume that, the government built a road links two places and they
have been operating its. In the future, in order to decrease the heavy traffic on the current
road, the government plans to build a new road paralleling the existed

9


road by a BOT scheme. That is, the government will invite a private investor to build
a BOT road by own investor cost. Then they will operate this road and get revenue
from road toll within concession period. The private sector sets up the price of toll
road for BOT road according to the market competition between two this roads.
The BOT road is denote by 1 and the existing road is labeled by 2. The two-road
network is illustrated as Figure, and some notation is give as follows:
y1

: the BOT road capacity .

p1

: the toll charge of BOT road.

Q1

: the flow volume on BOT road.

I (y1)

: Total investment of BOT road.

y2

: the existing road capacity.
Fig 3.1. A network model

p2

: the toll price of existing road.

Q2

: the flow volume on existing road.

M (Qi) : unit of maintenance and operation cost, assume that it is fixed.
Q0

: total travel demand between two places.

Ti (Qi, yi), i =1, 2: the generalized price (including travel cost and travel time) of
each road.
A bi-level programming model is formulated for a two-road network containing BOT
road. There are five steps with various issues to optimize toll charge and propose toll
ceiling pricing for BOT project.
Step 1: The lower-level program occurs between two road operators relating
route choice behavior of travelers according to their travel cost. Users' response
depend on to each toll price which is set up by operators respectively.

10


Step 2: The upper-level program represents the objective of decision makers. In
particular, operators determine the toll prices to maximize their own benefit
respectively.
Step 3: Evaluation social welfare through criteria named total travel cost
difference under the scenario that there is BOT road and there is non BOT road.
Step 4: Integrating the factor named "willingness to pay of travelers" to
guarantee users' benefit.
Step 5: Determining ceiling price of toll road under condition that optimal
benefit of investor and the government, which taking into account "willingness to
pay" of travelers.
3.2. Solution procedure
3.2.1. Step 1: Determining route choice of travelers
The route choice of travelers when facing to each price set up by operators depends
on their objective is that minimize own travel cost. Assume that the toll charge p 1 is
chosen by private investor and p2 is chosen by government. The user travel cost
function can be expressed as the Bureau of Public Roads (BPR) travel time function
which was chosen because it is so widely used:
T

Q ,y

i

i

Where:
Ti (Qi, yi) is generalized price including travel cost and travel time

λ is a parameter that transfers time to fare

t0 is the free flow travel time
α, β are parameters. Without less of generalization, taking: α = β = 1.

11


So, we have travel cost function, T1 for users choosing the BOT road:
Q
1

T1 Q1,y1 =λ.t0.(1+ y ) + p1

(1a)

1

Likewise, travel cost function, T2 for users choosing the existing road:
Q
2

T2 Q2,y2 =λ.t0.(1+ y ) + p2

(1b)

2

The objective function of travelers’ road choice for a given toll price is modelled as a
standard user demand equilibrium according to the minimum travel cost, and can be

expressed as follows:
min

T1( ). +

T2( ).

,

Subject to: Q0 = Q1 + Q2
The first term in Eq.(2) is total travel cost of users choosing BOT road to travel and
the second term is total travel cost of users choosing existing road to travel.
The Lagrange function for the problem Eq.(2) and Eq.(3) is as follows:
L(T1, T2, µ) =

T1( ). +

T2( ). − µ. (Q0 − Q1 − Q2)

Where, μ is Lagrange multiplier corresponding with flow volume condition in Eq.(3).
The optimal condition of Eq.(2) and (3) is derivative of the Lagrange function with
T1 and T2 being nil respectively, can be described as follows:
∂L

=T(Q )+µ=0
∂T

∂L

=T(Q )+µ=0

∂T

Combined Eq.(5a), (5b) with (1a), (1b) we have:

12


Q=Q+Q

Solve it, we can obtain:

y1. y2

=

Q

y +y

1

y1. y2

=

Q
2

y

1

We can see from Eq.(6a) and (6b) that the flow volume of roads are concern with toll
price and capacity of roads in a road network.
3.2.2. Step 2: The operators determine the toll prices to maximize their own benefit
respectively
Based on the choice behavior of travelers, operators make decision for toll price to
maximize their own benefit respectively.
3.2.2.1. BOT road
The benefit of BOT road is generated from toll revenue obtaining by toll charge of
BOT road, and minus amount of initial construction cost and cost of maintenance and
operation. So, the operator will set up toll price level to maximize their own benefit.
It can be presented as below:
max(Q . p − I(y ) − Q . M)

The first term in Eq.(7) is the revenue from toll price, the second term is initial
investment expense, and the third term is cost of maintenance and operation.
Substitute Q1 from Eq. (6a) into function of Eq.(7), we have:

Q

y1. y2

y +y

0

.y
2

1

2


The optimal condition of Eq.(7) is derivative of the function in Eq.(8) with p 1 being
nil, can be described as follows:

Thus,

So, p1 in Eq.(9) is the value of toll price so that the operator of BOT road get
maximum his own benefit.
3.2.2.2. Existing road
Likewise, the benefit of existing road is generated from toll revenue obtaining by toll
charge of BOT road, and only minus cost of maintenance and operation. It can be
presented as below:
max(Q . p − Q . M)

The first term in Eq.(10) is the revenue from toll price, the second term is cost of
maintenance and operation.
Substitute Q2 from Eq. (6b) into function of Eq.(10), we have:

Q

y1. y2

0

.

y

+y
1

y

2

1

The optimal condition of Eq.(10) is derivative of the function in Eq.(11) with p2 being
nil, can be described as follows:
∂
∂
Thus,

y1. y2

=
y +y


14

1
2

p =

So, p2 in Eq.(12) is the value of toll price so that the operator of existing road get
maximum his own benefit.
3.2.3. Step 3: Evaluation social welfare
We are carrying out to evaluate social welfare by the criteria named total travel cost
difference under the scenario that there is BOT road and there is non BOT road. The
total travel cost difference is defined that offsets of travel cost when there is only
existing road for users travel, with travel cost when there are two road for user choose
a road to travel. Let D(p1, p2) be a total travel cost difference, can be described as
follows:

Subject to Q0 = Q1 + Q2
Where:
Q
0

(14)

T Q0,y2 =λ.t0.(1+ y )
2

The first item in Eq.(13) is travel cost of users when whole travelers use existing road,
the second and third item are travel cost when users choose a route for their travel.
st

We determine two scenarios: case 1 is evaluation social welfare when all two roads
get maximum their own benefit at the same time. And case 2

nd

is evaluation social

welfare when there is only one of two road getting maximum his benefit – it is
operator of BOT road.
3.2.3.1. Case 1: All two roads get maximum their own benefit at the same time
That means, Eq.(9) and Eq.(12) simultaneously occur. We have multi-equation:

.