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Motorway Interchange Location Model (10min Presentation) Wctr
1. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
12th WCTR Conference
Lisboa, Portugal
July 11-15, 2010
Hugo M. Repolho Contact: repolho@dec.uc.pt
Richard L. Church
António P. Antunes
Optimum Location of Motorway
Interchanges: Concessionaires’ Perspective
2. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
Summary
1. Introduction
3. Deterministic Motorway Interchange Location Model
4. Portuguese Case Study
• Results for the deterministic model
2. Route Choice Model
5. Stochastic Motorway Interchange Location Models
• Results for the stochastic models
6. Final Considerations
3. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
Many times the construction of a motorway takes place within the framework of built-operate-
transfer (BOT) contracts:
OBJECTIVE: develop an optimization model for assisting toll-motorway concessionaires in the
analysis of the most profitable solutions for Motorway Interchanges Location Problem.
Defines the corridor of the motorway
Defines the detailed design for the motorway
• motorway interchanges location
The Government
The Concessionaire
The location of the interchanges strongly impacts the amount of traffic that the motorway can
capture from the existing road network.
Introduction [1]
4. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
OBJECTIVE: develop an optimization model for assisting toll-motorway concessionaires in the
analysis of the most profitable solutions for Motorway Interchanges Location Problem.
The location of the interchanges strongly impacts the amount of traffic that the motorway
can capture from the existing road network.
In Europe most motorways are owned by the State but operated by private concessionaires.
The concessionaires may define certain design details for the motorway, namely the motorway
interchanges location (access and exit points).
Their profit comes from the application of a certain toll fee per mile to the motorway users.
Introduction [1/2]
5. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
1 n m M
i
j
i
There are two types of routes to consider:
1. Routes through the existing road network (choice 1);
2. Routes through a combination of existing roadway segments and new motorway
segments (choice 2).
• People will travel through the least cost route;
• The proportion of people using the motorway increases as the travel costs decrease;
Choice 1
Choice 2
Route choice model [1/2]
ASSUMPTIONS:
6. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
ij
ij
ij
ij
ij
ij
ij
q
c
c
c
c
c
c
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ij
0
1
2
0
2
1
2
0
2
)
(
)
( 2
0
2
The traffic flow between i and j travelling through a
combination of existing roadways and new
motorway segments is as follows:
We present a route choice model to predict the traffic flow on the new motorway based
upon interchange locations.
Route choice model [2/2]
The new connections may generate additional traffic flows if travel costs decrease.
Some users may travel through the existing roadways even when these routes are less
cost efficient than using the new motorway.
7. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
DMILM [1/2]
M
m
m
J
i j
i
J
j M
m a
m
n
M
n
ijmn
mn
ijmn w
fy
x
d
q
ta
Max
ijmn
ij
: 0
and
:
0
2
OBJECTIVE FUNCTION: expresses the profit for the concessionaire, given as the
difference between total toll fee revenue and fixed charges for installing and
operating the interchanges and constructing the motorway.
Total toll fee revenue Fixed charges
The MILM can be seen as a particular case of the p-hub median problem, which was
formulated by Campbell, 1994.
OUTPUTS (decision variables):
• interchange locations -
• trips assigned to motorway routes -
m
y
ijmn
x
t = toll fee value/km, defined by the decision maker
8. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
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and
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1.Assignment constraints.
2.Elimination of all non cost
efficient routes.
3.Trips are assigned only if the
motorway segment mn is limited
by two motorway interchanges.
4.Each trip is assigned to the least
cost route available.
5.Interchanges located by default
at the extremities of the
motorway.
6.Nonnegative constraints.
7.Location decision variables are
binary.
0
:
,
,
,
2
ijmn
R
v R
b
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m
ijvb a
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CONSTRAINTS
1
5
8
10
j
i
1
5
8
10
j
i
4. Each trip is assigned to the least cost route available
DMILM [2/2]
9. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
•Motorway A25 located in the center of Portugal
•Dataset : 55 centers and 33 candidate motorway interchanges;
ArcMap 9.2 Image
Portuguese Case Study [1/2]
10. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
Portuguese Case Study [2/2]
Routes’ attractiveness is measured by the costs borne by users.
The probability of users choosing a given route is a function of the route’s relative
attractiveness.
TC
UTC
AC
VOC
RUC
The Road User Costs (RUC) expression is as
follows:
VOC, AC and TC are expressed in €/km/vehicle
TUC is expressed in €/hour/vehicle
FUEL COST (€/LITRE) SCENARIOS
VOC (€/km)
Fuel type SCN1 SCN2 SCN3 SCN4 SCN5
Diesel 0.498 0.663 0.995 1.493 1.990
Gas 0.610 0.813 1.219 1.829 2.438
12. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
Reality isn’t stationary and the future isn’t entirely predictable.
ROBUSTNESS: solutions that perform well under any realization of the uncertain
parameters .
We use scenarios to represent evolution trends or potential changes. Each scenario is
characterized by an occurrence probability.
Based on the stochastic optimization model in
Weaver and Church, 1983.
SMILM
Based on the Stochastic r-robust
uncapacitated fixed-charge location problem
in Snyder and Daskin, 2006.
r-SMILM
Fuel costs uncertainty
Traffic flow uncertainty
Stochastic Models [1]
13. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
SMILM OBJECTIVE FUNCTION:
M
m
m
S
s J
i j
i
J
j M
m a
m
n
M
n
ijmn
mn
ijmn
s fy
x
d
q
a
tp
Max
ijmn
ijs
: 0
and
:
0
2
OBJECTIVE FUNCTION: expresses the expected profit for the toll-motorway
concessionaire over all scenarios, considering the corresponding probabilities.
SMILM
• Fuel cost scenario SCN3
•50 traffic flow scenarios
Toll fee
(€/Km)
π
(€/day) Interchanges location Routes CPU (sec)
0.030 3066 1, 3, 4, 6, 9, 10, 11, 12, 13, 15, 16, 20, 26, 28, 29, 31, 33 15929 18
0.040 23731 1, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 23, 24, 28, 29, 31, 33 13277 17
0.045 33203 1, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 23, 24, 28, 29, 31, 33 12059 11
0.050 41480 1, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 22, 24, 26, 28, 29, 31, 33 10890 9
0.051 32210 1, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 19, 20, 22, 24, 26, 28, 29, 31, 33 10598 9
0.065 9457 1, 3, 5, 6, 7, 9, 10, 11, 14, 15, 20, 22, 24, 26, 28, 29, 31, 33 7789 7
0.070 14001 1, 3, 5, 6, 7, 9, 10, 11, 14, 15, 20, 24, 26, 28, 29, 31, 33 6804 6
0.081 -1804 1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 19, 21, 24, 26, 28, 29, 31, 33 5046 7
Adds Interchange 20 and
substitutes interchange 18
by interchange 19.
SMILM [1]
Set of scenario Scenario probability Different traffic flows
14. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
Additional constraints to enforce the r-robustness condition.
r-SMILM OBJECTIVE FUNCTION:
w
fy
x
d
q
a
tp
Max
M
m
m
S
s J
i j
i
J
j M
m a
m
n
M
n
ijmns
mn
ijmns
s
ijmns
ijs
: 0
and
:
0
2
OBJECTIVE: find the solution that maximizes the expected profit for the toll-motorway
concessionaire over all scenarios, considering the corresponding probabilities, and
simultaneously is r-robust, i.e. whose relative regret in each scenario is no more than r.
S
s
V
r
f
y
t
d
x
a
q s
M
m
m
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s J
i j
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j M
m a
m
n
M
n
mn
ijmns
ijmns
ij
ijmns
)
1
(
2
: 0
and
:
r-SMILM [1/2]
Desirable robustness level Best OF value for scenario s
16. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
The optimum location of motorway interchanges under the concessionaires’
perspective follows a previous work done under the users’ perspective, which aimed
to minimize travel costs.
We believe that the concessionaires’ perspective is the most relevant in real-world
applications.
The models presented are useful in toll-motorway concessionaires’ cost-benefit
analysis.
The route choice model turns the motorway travel demand elastic and thus more
approximated to users’ choices.
Final considerations
17. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
Users’ perspective…
18. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho 12th WCTR Lisboa
12th WCTR Conference
Lisboa, Portugal
July 11-15, 2010
Hugo M. Repolho Contact: repolho@dec.uc.pt
Richard L. Church
António P. Antunes
Optimum Location of Motorway
Interchanges: Concessionaires’ Perspective
