Loading…

Flash Player 9 (or above) is needed to view presentations.
We have detected that you do not have it on your computer. To install it, go here.

Like this presentation? Why not share!

Milm Panam Novo

on

  • 478 views

 

Statistics

Views

Total Views
478
Views on SlideShare
472
Embed Views
6

Actions

Likes
0
Downloads
0
Comments
0

1 Embed 6

http://www.linkedin.com 6

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Milm   Panam Novo Milm Panam Novo Presentation Transcript

  • 16th PANAM Conference
    Lisboa, Portugal
    July 15-18, 2010
    The Optimal Location for Motorway Interchanges – A25 case study
    Hugo M. Repolho Contact: repolho@dec.uc.pt
    António P. Antunes
    Richard L. Church
  • Summary
    Motivation
    Problem
    Case study
    Model Formulation
    MILM - C
    MILM - EK
    MILM - L
    Application results
    Conclusions
  • Motivation[1/2]
    Absolutely essential location factors :
    “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.
    Motorway interchanges location (access/exit points):
    • 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.
  • Motivation[2/2]
    Defining the motorway network:
    • 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.
    OBJECTIVE: Determine the locations for a given number of interchanges such that the total cost incurred by road users is minimized.
  • Problem [1/2]
    Road users travel through the least cost routes;
    There is and will be no traffic congestion;
    Travel cost function has mainly to do with travel distances and design speeds;
    Can be formulated as a p-hub median problem;
    The interchanges are the hubs and the motorway segments are the inter-hub links;
    The discount in the motorway segments is due to the fastest travel speeds;
    Interchanges location influences the network travel costs;
    It’s a non-strict problem:
  • Problem [2/2]
    There are 2 types of routes to consider:
    Routes through the existing road network (choice 1);
    Routes through a combination of existing roadway segments and new motorway segments (choice 2).
    Choice 1
    i
    i
    Choice 2
    1
    n
    m
    M
    j
  • 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:
    Is it justified to build all the 33 interchanges?
    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?
  • Model Formulation [1/7]
    Based on p-hub median problem – Campbell (1994) andSkorin-Kapov (1996)
    MILM – basic
    Based on Ernst and Krishnamoorthy (1998) and Marín et al. (2006)
    MILM – EK
    MILM – L
    New model
  • Model Formulation [2/7]
    a) MILM – basic
    Sets
    Centers (J)
    Interchanges (M)
    Travel Costs
    Between centers (cij)
    Between interchanges (cmn)
    Between center/interchange (cim)
    Model Outputs
    Trafficassignment(xijmn)
    Interchangelocation (ym)
    Traffic flows
    Demand O/D (qij)
    Other parameters
    N0. of interchanges (p)
    Network travel cost without the motorway
    C0=∑∑qijcij
  • Model Formulation [3/7]
    a) MILM – basic
    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
    Could not find a solution. The computer ran out of memory.
    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
  • Model Formulation [4/7]
    b) MILM – EK
    Marín et al. (2006)
    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)
    New constraints
  • 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.
    xijmn
    i j m n
    1 2 9 19
    1 2 9 20
    . . . .
    . . . .
    67 72 12 15
    68 70 24 25
    # columns = 4
    Is replaced by
    # rows = k
    xk
  • Model Formulation [6/7]
    c) MILM – L
    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
    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.
    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
  • Model Formulation [7/7]
    The MILM-L is faster than MILM-EK for p<10, p=13, p=14 and p>17.
  • Application Results [1/2]
    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.
  • Application Results [2/2]
  • 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
  • 16th PANAM Conference
    Lisboa, Portugal
    July 15-18, 2010
    The Optimal Location for Motorway Interchanges – A25 case study
    Hugo M. Repolho Contact: repolho@dec.uc.pt
    António P. Antunes
    Richard L. Church