Solving RealLife Railroad Blocking Problems

1
ESI 6912 Section 6129 (Spring 08)Advanced
Network Optimization

• Solving Real-Life Railroad Blocking Problems

Ravindra K. Ahuja Professor, Industrial Systems
Engg. University of Florida, Gainesville, FL
ahuja_at_ufl.edu [phone] www.ise.ufl.edu/ahuja
2
Reference

• This presentation is based on the following
  paper
• R.K. Ahuja, K.C. Jha, and J. Liu
• Solving Real-Life Railroad blocking Problems
• To appear in Interfaces, 2007.
• This paper won INFORMS 2006 Daniel Wagner Prize
  for Excellence in Operations Research.

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Presentation Outline

• The Railroad Blocking Problem
• The VLSN Search Algorithm
• Case Studies

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Railroad Planning Process
Railroad Blocking
Service Design
Train Scheduling
Car Routing
Locomotive Scheduling
Crew Scheduling
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Railroad Blocking Problem

• Railroad blocking problem is essentially a
  consolidation problem, which is similar to that
  encountered in postal service design.

Gainesville

• A railroad block is like a mailbag in the postal
  service context.

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Additional Application Areas

• Airline Service Design
• Trucking Service Design
• Package Delivery Network Service Design
• Ship Network Service Design

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Role of Yards in Railroads

• Railroad yards act as hubs where cars change
  trains.

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The Railroad Blocking Problem
Destinations
Origins
3,000 nodes
300 nodes
3,000 nodes
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The Railroad Blocking Model
Railroad Blocking Model
Network
Blocks
Shipment Block Assignments
Shipments

• Constraints
• Maximum number of blocks that can be build at a
  node is limited.
• Maximum volume of shipments passing through a
  node is limited.

• Objective Function
• Distances traveled by shipments
• Intermediate handlings of shipments

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Integer Programming Formulation
Minimize ?k?K ?(i,j)?A mij ?i?N
?k?K ?(i,j)?O(i) hiyij Subject
to ?(i,j)?O(i) - ?(j,i)?I(i)

for all k ? K ?k?K
uijyij
for all (i, j) ? A
?(i,j)?O(i) yij bi
for all i ? N ?k?K
?(i,j)?I(i) di
for all i ? N yij 0 or
1 and 0 or vk
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Blocking Problem for a US Railroad

• Multi-commodity flow network design and routing
  problem
• 3,000 nodes
• 50,000 commodities
• Over a million 0-1 network design variables
• Hundreds of billions of integer flow variables
• Substantial amount of costs involved
• Cost of flow 1,000 - 2,000 million
• Cost of handling 500 - 1,000 million
• Currently solved manually.

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Literature Survey

• ABM (Algorithmic Blocking Model) by Carl Van Dyke
  1986, 1988
• Keaton 1989, 1992
• Newton, Barnhart and Vance 1998
• Barnhart and Vance 2000
• The railroad blocking problem remained an
  unsolved problem until recently.

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Presentation Outline

• The Railroad Blocking Problem
• The VLSN Search Algorithm
• Case Studies

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A VLSN Search Algorithm

• We have developed a Very Large-Scale Neighborhood
  (VLSN) Search Algorithm to solve the blocking
  problem.
• Funded by National Science Foundation.
• Basic idea
• Use a simple heuristic to determine the initial
  blocking plan.
• Use a very large-scale neighborhood (VLSN) search
  algorithm to improve the blocking plan.
• Keep improving the plan until it stops improving.

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Neighborhood Search Algorithms

• Start with a feasible solution x
• Define a neighborhood of x
• Identify an improved neighbor y
• Replace x by y and repeat

VLSN Search Algorithm Size of the neighborhood
is very-very large.
..
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Two Types of Decisions

• Design variables
• Which blocks to build
• Flow Variables
• How to route flows on blocks that have been built
• A Major Assumption
• All flow is routed on the shortest paths
• Any problems with this assumption?
• With this assumption, shortest paths play a very
  important role in solving the blocking problem.

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Overview of the VLSN Search Algorithm
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1
5
9
2
7
10
3
6
11
4

• We reoptimize blocks at one node at a time
  assuming that blocks do not change at other
  nodes.
• We reoptimize all nodes one-by-one and keep
  performing passes over the nodes until the
  solution terminates to a local optimal solution.

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Finding Improved Neighbors

• First Step
• Select a node and delete all arcs incident on it
• Reroute the traffic.

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Finding Improved Neighbors (contd.)

• Second Step
• Build arcs one by one with the largest savings.
• How to compute the potential savings for an arc?
• Reroute all the shipments to compute the savings
  of an arc.

To compute the savings of an arc, we assess the
savings in the total cost when a block is added.
We do it by solving an all-pairs shortest path
problem after a blocking arc is added.
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Finding Improved Neighbors (contd.)

• Third Step
• Reoptimize all nodes one by one.
• Fourth Step
• Perform passes over the nodes until the solution
  is locally optimal.

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Convergence of the Algorithm
car miles vs. the number of passes
1050
1030
1010
990
970
Car Miles
950
930
910
890
870
0
1
2
3
4
5
6
7
8
9
10
Pass No
Very fast convergence for car miles.
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Convergence of the Algorithm (contd.)
car handlings vs. the number of passes
1.1
1.05
1
0.95
Car Handlings
0.9
0.85
0.8
0
1
2
3
4
5
6
7
8
9
10
Pass No
Very fast convergence for car handlings.
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Sensitivity to the Starting Solution
Average Handlings per Car
1
0.95
0.9
0.85
0.8
Handles/Car
0.75
0.7
0.65
0.6
0.55
0.5
0
1
2
3
4
5
6
7
8
9
10
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Pass No.
Final solution is rather insensitive to the
starting solution.
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Critical Issue Speed

• In the course of solving the blocking problem, we
  solve numerous shortest path problems. Thus, it
  is very important that shortest path problems are
  solved very efficiently.
• Size of the shortest path problem
• 3,000 x 3,000 9 million shortest path values.
• It is very time-consuming to update these many
  shortest path values.
• We take advantage of the hub-spoke configuration
  of the blocking network.

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Additional Features

• Block restrictions
• Some blocks must not be made.
• Block fixing
• Some blocks must be made.
• Block preferences
• Give preference to some blocks.
• Shipment-block path fixing
• Some shipment block sequences must be fixed.

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Solving Shortest Paths Efficiently

• Homework Exercise How to solve the shortest path
  problem efficiently for the hub and spoke
  configurations?

Yards
Origins
Destinations
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Updating Shortest Paths Efficiently

• How to update all pairs shortest path values when
  an arc is deleted?
• How to update all pairs shortest path values when
  an arc is added?

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Incremental Blocking

• Given an existing blocking plan, change it by a
  specified amount and determine a revised blocking
  plan. Example
• Make 10 new blocks
• Delete 10 or more existing blocks
• Motivation
• Railroads are not willing to change their
  blocking plans completely.
• They want to change their plans incrementally,
  little by little and get benefits from
  incremental changes.
• This strategy is more implementable and involves
  less risk.

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Train-Friendly Blocking

• Given a train schedule, make only those blocks
  that require no more than K block swaps.
• We can set K 0, 1, or 2

New York
Atlanta
Boston
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Preferential Blocking

• Railroads may already be making some blocks and
  want to give preference to the bocks they are
  currently making.
• How to give preferences to some blocks?

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Presentation Outline

• The Railroad Blocking Problem
• The VLSN Search Algorithm
• Case Studies

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Computational Results

• We have performed several case studies on the
  data provided by several US Class I railroads.
• We performed three types of types
• Clean-slate blocking
• Incremental blocking
• Incremental train-friendly blocking

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Clean-Slate Blocking Results

• Conclusion Significant reduction in intermediate
  handlings through better blocking plans.
• Savings gt 10 million annually

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Incremental Blocking Results

• Conclusion Even small changes in the blocking
  plan can have significant impact on intermediate
  handlings.

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Incremental Train-Friendly Blocking Results

• Conclusion Train-friendly blocking is almost as
  good as the unrestricted blocking.

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Homework 2

• How to solve shortest path problem efficiently in
  the presence of hub and spoke configuration?
• How to update all pairs shortest path values when
  an arc is deleted?
• How to update all pairs shortest path values when
  an arc is added?
• How to do incremental blocking?
• How to do train-friendly blocking?
• How to do preferential blocking?