Motorway Interchange Location Model (10min Presentation) Wctr
-
Upload
hugorepolho -
Category
Documents
-
view
251 -
download
0
description
Transcript of Motorway Interchange Location Model (10min Presentation) Wctr
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
12th WCTR ConferenceLisboa, PortugalJuly 11-15, 2010
Hugo M. Repolho Contact: [email protected]
Richard L. ChurchAntónio P. Antunes
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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]
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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]
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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 1Choice 2
Route choice model [1/2]
ASSUMPTIONS:
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
ij
ijijijij
ij
ijq
ccccc
cq
ij
01202
1
20
2 )()(20
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.
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
DMILM [1/2]
Mm
mJi jiJj Mm amnMn
ijmnmnijmn wfyxdqtaMaxijmn
ij: 0 and :
02
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 -
my
ijmnx
t = toll fee value/km, defined by the decision maker
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
jiJjixMm anmMn
ijmn
ijmn
:, 10 and :
0:,,,, 0 ijmnijmn aMnmjiJjix
Ji jiJj aMn
mamijmn
ijmn
Mmygx: 0:
Ji jiJj aMm
nenijmn
ijmn
Mnygx: 0:
11 y1My
MnmJjixijmn ,,, 0
Mmym 1,0
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
ijmnRv Rb
nmijvb aMnmJjiyyxijmn ijmn
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]
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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]
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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.
TCUTCACVOCRUC
The Road User Costs (RUC) expression is as follows:
VOC, AC and TC are expressed in €/km/vehicleTUC is expressed in €/hour/vehicle
FUEL COST (€/LITRE) SCENARIOS
VOC (€/km)
Fuel
type SCN1SCN2 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
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
DMILM – results [1]
DETERMINISTIC MILM•Fuel cost scenario SCN3
Toll fee (€/Km)
Interchanges location RoutesCPU (sec)
0.0301, 3, 4, 6, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 25, 26, 27, 28, 31, 33
15929 19
0.0401, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 22, 23, 24, 27, 28, 31, 33
13277 13
0.0451, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 23, 24, 26, 28, 29, 31, 33
12059 13
0.0491, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33
11161 11
0.0501, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 22, 24, 26, 28, 29, 31, 33
10890 11
0.0511, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 22, 24, 26, 28, 29, 31, 33
10598 10
0.0551, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 18, 19, 20, 22, 24, 26, 28, 29, 31, 33
9771 9
0.0601, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 19, 20, 22, 24, 26, 28, 29, 31, 33
8786 8
0.0651, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 22, 24, 26, 28, 29, 31, 33
7789 7
0.0701, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 24, 26, 28, 29, 31, 33
6804 6
0.0801, 3, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 19, 20, 21, 24, 26, 28, 29, 31, 33
5179 6
0.0811, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 19, 21, 24, 26, 28, 29, 31, 33
5046 4
0.0901, 3, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 21, 24, 26, 28, 29, 31, 33
4011 5
0.1001, 3, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 24, 26, 28, 29, 31, 33
3073 1
0.03
0.04
0.045
0.049 0.0
50.0
510.0
530.0
540.0
550.0
56 0.06
0.065 0.0
7
0.080
0000
0000
0...
0.081
0.085
0.090
0000
0000
0...
0.1
19
13 13
11 1110
9 9 9
14
87
6
6 45 5
1
CPU time ...
Toll fee (€/km)
15929
1327712059
1116110890105981015699199771
95308786
77896804
5179504644764011
3073
Number of routes
0.03
0.04
0.045
0.049
0000
0000
0...
0.05
0.051
0.053
0.054
0.055
0.056 0.0
60.0
65 0.07
0.08
0.081
0.085 0.0
9 0.10
10000
20000
30000
40000
50000
4729
22844
32414
3964241611
35552
39143 4138239632
2307120844
18783
23474
17344 16342
17840
13157
11590
Toll fee (€/km)
Pro
fit (
€/da
y)
ArcMap 9.2 Image
13
4
6 7
911
1318 2624
28
33
1014 15 17
29
22 31
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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]
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
SMILM OBJECTIVE FUNCTION:
Mm
mSs Ji jiJj Mm amnMn
ijmnmnijmns fyxdqatpMaxijmn
ijs: 0 and :
02
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 (€/da
y) Interchanges locationRoute
sCPU (sec)
0.030 30661, 3, 4, 6, 9, 10, 11, 12, 13, 15, 16, 20, 26, 28, 29, 31, 33 15929 18
0.0402373
11, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 23, 24, 28, 29, 31, 33 13277 17
0.0453320
31, 3, 4, 6, 8, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 23, 24, 28, 29, 31, 33 12059 11
0.0504148
01, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 19, 20, 22, 24, 26, 28, 29, 31, 33 10890 9
0.0513221
01, 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 94571, 3, 5, 6, 7, 9, 10, 11, 14, 15, 20, 22, 24, 26, 28, 29, 31, 33 7789 7
0.0701400
1 1, 3, 5, 6, 7, 9, 10, 11, 14, 15, 20, 24, 26, 28, 29, 31, 33 6804 6
0.081 -18041, 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
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
Additional constraints to enforce the r-robustness condition.
r-SMILM OBJECTIVE FUNCTION:
wfyxdqatpMaxMm
mSs Ji jiJj Mm amnMn
ijmnsmnijmnss
ijmns
ijs
: 0 and :02
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.
SsVrfytdxaq sMm
mSs Ji jiJj Mm amnMn
mnijmnsijmnsij
ijmns
)1(2: 0 and :
r-SMILM [1/2]
Desirable robustness level
Best OF value for scenario s
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
r-SMILM•Five fuel cost scenario• P = [0.05; 0.225; 0.45; 0.225; 0.05]• t = 0.05 €/km•Vs= [42064; 40998; 41611; 20240; 2250]
r(%) π (€/day) Interchanges locationCPU (sec)
Maximum regret (%)
100.0 336461, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 20, 22, 24,
26, 28, 29, 31, 33269 4.19
4.0 336261, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 20, 22, 24,
26, 28, 31, 33223 3.89
< 3.9infeasibl
e- - -
Profit losses are only 0.06%
r-SMILM [2/2]
SCN 1 SCN 2 SCN 3 SCN 4 SCN 50.00%0.50%1.00%1.50%2.00%2.50%3.00%3.50%4.00%4.50%
Relative Regret
r=100%r=4%
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th 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
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
Users’ perspective…
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
12th WCTR ConferenceLisboa, PortugalJuly 11-15, 2010
Hugo M. Repolho Contact: [email protected]
Richard L. ChurchAntónio P. Antunes
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
0.03 0.04 0.045 0.049 0.05 0.051 0.053 0.054 0.055 0.056 0.06 0.065 0.07 0.08 0.081 0.085 0.09 0.1
19
13 13
11 1110
9 9 9
14
87
6
6 45 5
1
CPU time ...Toll fee (€/km)
15929
1327712059
1116110890105981015699199771
95308786
77896804
5179504644764011
3073
Number of routes
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
0
10000
20000
30000
40000
50000
4729
22844
32414
3964241611
35552
39143 4138239632
2307120844
18783
23474
17344 16342
17840
13157
11590
Toll fee (€/km)
Pro
fit (
€/da
y)
Optimum Location of Motorway Interchanges: Concessionaires’ Perspective
Hugo Repolho12th WCTR
Lisboa
ArcMap 9.2 Image
13
4
6 7
911
1318 2624
28
33
1014 15 17
29
22 31