Motorway Interchange Location Model (10min Presentation) Wctr

306
-1

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total Views
306
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
6
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Motorway Interchange Location Model (10min Presentation) Wctr

  1. 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. 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. 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. 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. 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 1Choice 2 Route choice model [1/2] ASSUMPTIONS:
  6. 6. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa ij ijijijij ij ij q ccccc c q ij 01 202 1 2 0 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.
  7. 7. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa DMILM [1/2]          Mm m Ji jiJj Mm amnMn ijmnmnijmn wfyxdqtaMax ijmn ij : 0and: 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
  8. 8. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa jiJjix Mm anmMn ijmn ijmn    :,1 0and: 0:,,,,0  ijmnijmn aMnmjiJjix       Ji jiJj aMn m a mijmn ijmn Mmygx : 0:       Ji jiJj aMm n e nijmn ijmn Mnygx : 0: 11 y 1My 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    ijmn Rv Rb nmijvb aMnmJjiyyx ijmn 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]
  9. 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. 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. TCUTCACVOCRUC  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
  11. 11. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa DMILM – results [1] DETERMINISTIC MILM •Fuel cost scenario SCN3 Toll fee (€/Km) Interchanges location Routes CPU (sec) 0.030 1, 3, 4, 6, 9, 10, 11, 12, 13, 14, 15, 16, 19, 20, 25, 26, 27, 28, 31, 33 15929 19 0.040 1, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 19, 20, 22, 23, 24, 27, 28, 31, 33 13277 13 0.045 1, 3, 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 20, 22, 23, 24, 26, 28, 29, 31, 33 12059 13 0.049 1, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33 11161 11 0.050 1, 3, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 22, 24, 26, 28, 29, 31, 33 10890 11 0.051 1, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 17, 18, 22, 24, 26, 28, 29, 31, 33 10598 10 0.055 1, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 18, 19, 20, 22, 24, 26, 28, 29, 31, 33 9771 9 0.060 1, 3, 4, 5, 6, 7, 8, 10, 11, 14, 15, 19, 20, 22, 24, 26, 28, 29, 31, 33 8786 8 0.065 1, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 22, 24, 26, 28, 29, 31, 33 7789 7 0.070 1, 3, 5, 6, 7, 8, 9, 10, 11, 14, 15, 20, 24, 26, 28, 29, 31, 33 6804 6 0.080 1, 3, 5, 6, 7, 8, 9, 10, 11, 15, 16, 17, 19, 20, 21, 24, 26, 28, 29, 31, 33 5179 6 0.081 1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 19, 21, 24, 26, 28, 29, 31, 33 5046 4 0.090 1, 3, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 21, 24, 26, 28, 29, 31, 33 4011 5 0.100 1, 3, 5, 6, 7, 8, 9, 10, 11, 15, 16, 19, 24, 26, 28, 29, 31, 33 3073 1 19 13 13 11 11 10 9 9 9 14 8 7 6 6 4 5 5 1 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 Toll fee (€/km) CPU time (sec.) 15929 13277 12059 11161 1089010598 10156 9919 9771 9530 8786 7789 6804 5179 5046 4476 4011 3073 Number of routes 4729 22844 32414 39642 41611 35552 39143 41382 39632 23071 20844 18783 23474 17344 16342 17840 13157 11590 0 10000 20000 30000 40000 50000 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 Profit(€/day) Toll fee (€/km) ArcMap 9.2 Image 1 3 4 6 7 9 11 13 18 2624 28 33 10 14 15 17 29 22 31
  12. 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. 13. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa SMILM OBJECTIVE FUNCTION:           Mm m Ss Ji jiJj Mm amnMn ijmnmnijmns fyxdqatpMax ijmn ijs : 0and: 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 (€/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. 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: wfyxdqatpMax Mm m Ss Ji jiJj Mm amnMn ijmnsmnijmnss ijmns ijs          : 0and: 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 s Mm m Ss Ji jiJj Mm amnMn mnijmnsijmnsij ijmns           )1(2 : 0and: r-SMILM [1/2] Desirable robustness level Best OF value for scenario s
  15. 15. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th 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 location CPU (sec) Maximum regret (%) 100.0 33646 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 20, 22, 24, 26, 28, 29, 31, 33 269 4.19 4.0 33626 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 19, 20, 22, 24, 26, 28, 31, 33 223 3.89 < 3.9 infeasible - - - Profit losses are only 0.06% r-SMILM [2/2] 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% SCN 1 SCN 2 SCN 3 SCN 4 SCN 5 Relative Regret r=100% r=4%
  16. 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. 17. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa Users’ perspective…
  18. 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
  19. 19. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa 19 13 13 11 11 10 9 9 9 14 8 7 6 6 4 5 5 1 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 Toll fee (€/km) CPU time (sec.) 15929 13277 12059 11161 1089010598 10156 9919 9771 9530 8786 7789 6804 5179 5046 4476 4011 3073 Number of routes
  20. 20. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa 4729 22844 32414 39642 41611 35552 39143 41382 39632 23071 20844 18783 23474 17344 16342 17840 13157 11590 0 10000 20000 30000 40000 50000 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 Profit(€/day) Toll fee (€/km)
  21. 21. Optimum Location of Motorway Interchanges: Concessionaires’ Perspective Hugo Repolho 12th WCTR Lisboa ArcMap 9.2 Image 1 3 4 6 7 9 11 13 18 2624 28 33 10 14 15 17 29 22 31

×