0
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
16th PANAM Conference
Lisboa, Portugal / July 15-18, 2010
The Optimal Location for Motorway Interchanges – A25 case study,...
Upcoming SlideShare
Loading in...5
×

Milm Panam Novo

398

Published on

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

  • Be the first to like this

No Downloads
Views
Total Views
398
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
1
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Milm Panam Novo"

  1. 1. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 0 Hugo Repolho 16th PANAM Conference Lisboa, Portugal July 15-18, 2010 Hugo M. Repolho Contact: repolho@dec.uc.pt António P. Antunes Richard L. Church The Optimal Location for Motorway Interchanges – A25 case study
  2. 2. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 1 Hugo Repolho Summary 1. Motivation 2. Problem 3. Case study 4. Model Formulation a) MILM - C b) MILM - EK c) MILM - L 5. Application results 6. Conclusions
  3. 3. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 2 Hugo Repolho Motivation [1/2] “Easy access to markets, customers or clients” “Transport links with other cities and internationally” 2nd and 4th positions (out of 12) in a ranking by Cushman and Wakefield, 2007. “For a large sample of Scottish road links was the No. 1 location factor (…)” (out of 18) in a ranking by Button, 2007. Absolutely essential location factors : • The fastest road trips take place through motorways. • Interchanges locations have important implications upon the geographic pattern of economic development. Kawamura, 2001; DeBok and Sanders, 2005. Motorway interchanges location (access/exit points):
  4. 4. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 3 Hugo Repolho •Complex process due to the diversity of factors involved; •Obeys to pre-established regional and national development plans; •Rationalizes the existing traffic and promotes economic development; •Suffers the noxious influence of political and economical pressures. Supporting choices in a rigorous and exempt technical analysis is very important. Motivation [2/2] Defining the motorway network: OBJECTIVE: Determine the locations for a given number of interchanges such that the total cost incurred by road users is minimized.
  5. 5. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 4 Hugo Repolho Problem [1/2] 1. Road users travel through the least cost routes; 2. There is and will be no traffic congestion; 3. Travel cost function has mainly to do with travel distances and design speeds; 4. Can be formulated as a p-hub median problem; 5. The interchanges are the hubs and the motorway segments are the inter-hub links; 6. The discount in the motorway segments is due to the fastest travel speeds; 7. Interchanges location influences the network travel costs; 8. It’s a non-strict problem:
  6. 6. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 5 Hugo Repolho There are 2 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). 1 n m M i j i Choice 1 Choice 2 Problem [2/2]
  7. 7. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 6 Hugo Repolho Case study [1] • 73 traffic generation centers • 33 interchanges • Toll-free motorway • Average annual daily traffic ranged between 5000 and 23000 pcu – Level of service A • O/D matrix is known • Motorways - 120 kph • National roads – 90 kph • Municipal roads – 50 kph • Other roads – 70 kph FACT: Each interchange can cost more than 2 million Euros. QUESTIONS: A. Is it justified to build all the 33 interchanges? B. If not: • How many interchanges should we build? • How much money would we save? • What would be the lost in the net travel cost savings?
  8. 8. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 7 Hugo Repolho Model Formulation [1/7] MILM – basic MILM – EK MILM – L Based on p-hub median problem – Campbell (1994) and Skorin-Kapov (1996) Based on Ernst and Krishnamoorthy (1998) and Marín et al. (2006) New model
  9. 9. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 8 Hugo Repolho Model Formulation [2/7] Sets Centers (J) Interchanges (M) Traffic assignment (xijmn) Interchange location (ym) Travel Costs Between centers (cij) Between interchanges (cmn) Between center/interchange (cim) Traffic flows Demand O/D (qij) Model Outputs Network travel cost without the motorway C0=∑∑ qij cij Other parameters N0. of interchanges (p) a) MILM – basic
  10. 10. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 9 Hugo Repolho Model Formulation [3/7] Objective function – minimizes aggregated travel cost Assignment constraints – each route is assigned to no more than one route Facility constraint – only p or less facilities are located Bounding constraints – prevent a trip to be assigned to a segment not limited by 2 interchanges Default locations – locate interchanges by default at the extremities of the motorway Nonnegative and binary constraints          Ji jiJj Mm nmMn ijmnijjnmnimij xqccccCCMin : : 0 )'(      Mm nmMn ijmn ijJjix :,1 :    Mm m py Mmygx mnMn Ji ijJj m a mijmn      : : Mnygx nmMm Ji ijJj n e nijmn      : : 11 y1My MnmJjixijmn  ,,,0   Mmym  1,0 Could not find a solution. The computer ran out of memory. a) MILM – basic
  11. 11. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 10 Hugo Repolho Model Formulation [4/7]                        Ji Mm Mm nmMn Mn jiJj jiJj ijijijnjnimnmnimim wcxchczcCMin : : : ' JiOzw Mm iim Jj ij    jiJjiqxw Mn ijijnij    :, MmJixhhz jiJj ijm nmMn imn nmMn inmim    ,0 ::: MmJiyOz miim  , jiMnJjiyqx nijijn  :,,   n miimn MmJiyOy ,   m niimn MnJiyOy ,   n imimn MmJizy , MnmJjihzx imnimijn  ,,,0,,    Mm m py 11 y1My   Mmym  1,0 ijjnijn ccMnJjix  :,,0 Marín et al. (2006) New constraints Considered more efficient than the Campbell model Uses 2 and 3 subscripts assignment variables (instead of 4 subscripts)  Fewer number of variables. The solution for the application is found in at most 70 min. The final formulation is up to 80% faster than the model proposed by Marín et al. (2006) b) MILM – EK
  12. 12. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 11 Hugo Repolho Model Formulation [5/7] c) MILM – L The MILM-L is based on the concept of lists and has only 1 subscript decision variables. Parameters acquired in a data pre-analysis process: k = number of cost efficient routes through the motorway (cim+ cmn+ cjn< cij ). R(K_values,4) = matrix containing the definition of the routes. i j m n 1 2 9 19 1 2 9 20 . . . . . . . . 67 72 12 15 68 70 24 25 # rows = k # columns = 4 xijmn xk Is replaced by
  13. 13. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 12 Hugo Repolho Model Formulation [6/7] c) MILM – L    Mm m py 11 y 1My   Mmym  1,0   Kk kk xsCCMin 0 jiJjix jkRikRKk k   :,1 )2,(and)1,(: Mmygx mkRKk m a mk   )3,(: Mnygx nkRKk n e nk   )4,(: Kkxk  0 Objective function – minimizes aggregated travel cost Assignment constraints – each route is assigned to no more than one route Facility constraint – only p or less facilities are located Bounding constraints – prevent a trip to be assigned to a segment not limited by 2 interchanges Default locations – locate interchanges by default at the extremities of the motorway Nonnegative and binary constraints The data pre-analysis identified 61 183 cost efficient routes through the motorway. The solution for the application is found in at most 21 min.
  14. 14. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 13 Hugo Repolho 0 500 1000 1500 2000 2500 3000 3500 4000 4500 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 CPUtime(sec.) Number of interchanges MILM-EK MILM-L Model Formulation [7/7] The MILM-L is faster than MILM-EK for p<10, p=13, p=14 and p>17.
  15. 15. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 14 Hugo Repolho Application Results [1/2] Number of interchanges Travel cost savings Hours/day % 2 7 0.13 3 124 2.46 4 1710 34.02 5 2337 46.48 6 2802 55.73 7 3241 64.47 8 3573 71.07 9 3875 77.09 10 4086 81.27 11 4270 84.95 12 4428 88.08 13 4516 89.84 14 4596 91.43 15 4673 92.96 16 4736 94.20 17 4795 95.39 18 4844 96.36 19 4881 97.09 20 4916 97.79 21 4943 98.32 22 4968 98.83 23 4990 99.26 24 5006 99.58 25 5009 99.64 26 5024 99.95 27 5027 100.00 28 5027 100.00 0.00 1000.00 2000.00 3000.00 4000.00 5000.00 6000.00 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 Travelcostssavings Number of interchanges p=13  90% of the maximum total travel costs savings  Save 40 million Euros p=17  95% of the maximum total travel costs savings  Save 32 million Euros Interchanges 2, 18, 21, 23, 30 and 32 are never used.
  16. 16. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 15 Hugo Repolho Number of interchanges Location of interchanges 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 2 x x 3 x x x 4 x x x x 5 x x x x x 6 x x x x x x 7 x x x x x x x 8 x x x x x x x x 9 x x x x x x x x x 10 x x x x x x x x x x 11 x x x x x x x x x x x 12 x x x x x x x x x x x x 13 x x x x x x x x x x x x x 14 x x x x x x x x x x x x x x 15 x x x x x x x x x x x x x x x 16 x x x x x x x x x x x x x x x x 17 x x x x x x x x x x x x x x x x x 18 x x x x x x x x x x x x x x x x x x 19 x x x x x x x x x x x x x x x x x x x 20 x x x x x x x x x x x x x x x x x x x x 21 x x x x x x x x x x x x x x x x x x x x x 22 x x x x x x x x x x x x x x x x x x x x x x 23 x x x x x x x x x x x x x x x x x x x x x x x 24 x x x x x x x x x x x x x x x x x x x x x x x x 25 x x x x x x x x x x x x x x x x x x x x x x x x x 26 x x x x x x x x x x x x x x x x x x x x x x x x x x 27 x x x x x x x x x x x x x x x x x x x x x x x x x x X Application Results [2/2]
  17. 17. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 16 Hugo Repolho Conclusions [1] The motorway interchanges location problem is an good example for hub theory. To the best of our knowledge the models presented were never used to help deciding on motorway interchange locations. The MILM-EK formulation is up to 80% faster than the original one. The new model, MILM-L, is a valid formulation that, in most cases, performed better than the other two formulations. Results have to be carefully analyzed: • travel demand is more disperse across the region than we assume • We assumed that roads are uncongested • Travel demand was considered inelastic
  18. 18. 16th PANAM Conference Lisboa, Portugal / July 15-18, 2010 The Optimal Location for Motorway Interchanges – A25 case study, 17 Hugo Repolho 16th PANAM Conference Lisboa, Portugal July 15-18, 2010 Hugo M. Repolho Contact: repolho@dec.uc.pt António P. Antunes Richard L. Church The Optimal Location for Motorway Interchanges – A25 case study
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×