for Train Scheduling Problem

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for Train Scheduling Problem
Decision Support System (DSS)
Krishna Jha, Innovative Scheduling Ravi Ahuja,
Innovative Scheduling Pooja Dewan, BNSF
Railway Arvind Kumar, Innovative Scheduling
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Presentation Outline

• The Train Scheduling Problem
• Current Practice and Need for DSS
• Train Scheduling DSS
• Benefits and Future Directions
• Sample Screenshots

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Train Scheduling Problem
Trains
Train Scheduling Optimizer
Blocks
Origins, destinations, routes, timings and
frequencies
Block-to-Train Assignments
Shipments
Train paths for each block by day of week
Shipment-BlockAssignments
Trip Plan
Train path for each shipment
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Train Scheduling Input and Output

• Train Reports
• Trains to build and their route
• Days of operations
• Time schedule
• Locomotive and crew plan
• By day-of-week total

• User Defined Policies
• Train-route preferences
• Connection times
• Train stop rules
• Block-to-train assignment
• preferences

Network (Node/Link/Yard)
Shipments

• Shipment and Block Reports
• Block-to-train assignments
• Trip plan for each shipment
• Block-swaps
• Blocks in a train on its route
• By day-of-week total

Train Schedule Optimizer
Shipment- Block Sequences

• Node and Link Reports
• Trains originating/terminating
• and passing through
• Shipments reclassified
• Shipments block swapped
• Classification and block swaps
• Locomotive and crew flow
• By time window (say 2 hours),
• day-of-week total

Crew District Locomotive

• Current Train Schedule
• Train routes
• Train times frequencies
• Block-train assignments
• Trip plan

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Train Scheduling Modeling Components

• Decision Variables
• Trains and their routes
• Train frequencies
• Train timings
• Block-to-train assignments by
• day-of-week
• Trip plan for each shipment
• Locomotive and crew assignments

• Objective Function
• Train starts and train miles
• Car miles and car days
• Block swap cost
• Locomotive cost
• Crew cost

Train Schedule Optimizer

• Hard Constraints
• Train capacity ( of blocks/cars,
• total length, total weight)
• Node and link congestion
• Plate clearance
• Connection times
• Block-to-train assignments

• Soft Constraints
• Trains between big yards
• Direct trains for high volume blocks
• Minimum frequency of a train
• Equal number of originating and
• terminating trains at a node
• Train volume maximized to link cap

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Train Scheduling Objectives

• Total train-miles
• Total car-days
• Total car-miles (gross ton-miles)
• Total block swaps
• Total locomotive requirements
• Total crew requirements
• Attractiveness of block-to-train assignments
• Total number of train starts
• Total train-load imbalance

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Train Scheduling ConstraintsBlock Restrictions

• Maximum number of trains taken by a block
• Maximum detour of a block from the shortest route
• Node-based minimum connection times for block
  swaps
• Node-based minimum connection times for
  intermediate handlings
• If there is a train from the origin of a block to
  the destination of the block, do not allow the
  block to take another train, unless strictly
  prohibited by the capacity
• If a block is taking a train, which is going to
  the destination of the block, do not allow the
  block to set-off at any other location

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Train Scheduling ConstraintsTrain Restrictions

• Train capacity restriction (size, length, weight)
  by day of the week
• Node-based block pickup set off times
• Specified links on which train can be routed
• Average train speed based on train link and train
  type
• At any point of time, there should not be more
  than K distinct destination blocks in a train
• Do not construct a train which only carries the
  blocks set off by other trains at the origin
• Limit the working stations on the path of a
  train keep it proportional to distance or put a
  restriction that works can only be done at
  regional yards, if the train distance is more
  than x miles
• Train origin and train destination locations from
  specified sets of nodes

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Train Scheduling ConstraintsLocomotive and Crew
Restrictions

• Locomotive fueling locations every k crew
  districts
• Cannot create new crew change points
• Crew district based minimum crew rest time
• Node-based minimum connection times for
  locomotive
• Maximum number of work stations between
  consecutive crew change points
• Locomotive and crew balancing considering other
  part of the train network that is fixed
• Same locomotive power on trains from train origin
  to train destination

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Train Scheduling ConstraintsNetwork Restrictions

• Specified block swap locations
• Specified stations where no pick-up and set-off
  can be done, if train is not originating/terminati
  ng
• Number of trains originating at a station equal
  to some specified number
• Number of trains terminating at a station equal
  to some specified number
• Give preference to the trains originating and
  terminating at the bigger yards
• Maximum number of trains originating/terminating
  at a node in a time-window
• Maximum number of trains passing on a link in a
  time-window

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Current Practice
Train Route Design

• Estimate daily train starts (say n) based on car
  flows and ideal train size
• Create n trains on shortest route of n largest
  size blocks and manually assign other blocks to
  these trains

• More than half of the blocks are to be assigned
  manually
• Each block gets only one block-to-train
  assignments

Alternative I

• Start with the existing train plans and
  block-to-train assignments
• Assign new blocks to the fixed trains

• Unassigned newly created blocks
• Unnecessary block swaps in order to assign blocks
  to existing trains

Alternative II
Train Schedule Design

• Simulate the train plan on seven-days
• Estimate the node congestion, car-handlings,
  gross ton-miles, etc.

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Need of DSS

• Myopic decision making process
• Highly limited decision space
• No trade-off among the objective function factors
• No what-if analysis
• No scientific feedback loop
• No experimentation with the operational
  constraints
• Slow response to the users requirement

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DSS - Framework
Train Scheduling Framework

• Impact of business rules and practices
• Locomotive requirements
• Crew requirements

Resources
Align
Network
Service

• Zero-base train scheduling
• Incremental train scheduling
• Train-time optimization
• Block-train assignment optimization

• Train additions
• Train cancellations
• Dynamic trip planning

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DSS - Architecture
Central Database
Optimization Module
Database Management
Solution Analyzer
Computation Engine
Graphical User Interface
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DSS Optimization Modules
Train Route Enumerator
Network flow based heuristics providing large
solution space
Train Constructor
Heuristically optimize the multiple criteria
objective function
BTA Enumerator
Network flow based heuristic providing routing
options to blocks
BTA Optimizer
Heuristically optimize the block-to-train
assignments
Train Remover
Delete the unwanted trains and reroute blocks
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DSS Optimization Modules
BTA Improver
VLSN search heuristic to improve the routing of
blocks to trains
Frequency Optimizer
Heuristically optimizes the days of operation of
trains
Schedule Optimizer
Heuristically optimizes the time schedule of
trains
Locomotive Optimizer
Network flow based algorithm to optimize loco
requirement
Crew Optimizer
Network flow based algorithm to optimize crew
requirement
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DSS Uses
Zero-Base
Incremental
Interactive
Block and shipment related inputs
Partial current solution
Block and shipment related inputs
Current Plan
Block and shipment related inputs
Scope of change in train plan and BTAs
DSS
Manager
DSS
DSS
Determine the impact or ask suggestion
Train schedule, BTAs, and trip plan with limited
change in current solution
New train schedule, BTAs, and trip plan
Partially fixed solution
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DSS Benefits
Historical Demand or Forecasted Demand

• Create blocking plan
• Manually create train routes and
• block-to-train assignments
• Manually decide train timings and frequencies
• Perform scenario analysis with end users

Current practice
Service Design Dept.
3-6 months
DSS

• Optimized blocking plan
• Optimized train route and
• block-to-train assignments
• Optimized train timings and frequencies
• Optimized projection of locomotive
• and crew requirement
• Perform faster scenario analysis
• with end users

Operating Plan
2-4 weeks
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DSS Improvements
Case Study Zero-based train scheduling for a
Class-I railroad
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DSS Savings in Millions of Dollars
TOTAL ANNUAL SAVINGS 83 Million
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DSS Sample Screenshots
Comparison of Two Train Schedules Statistics,
Route and Assignment of Blocks to Trains
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DSS Sample Screenshots
Comparison of Routing of Blocks Block and O-D
Statistics, BTAs by Day of Week
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DSS Sample Screenshots
Comparison of Routing of Blocks Block and O-D
Statistics, BTAs by Day of Week
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DSS Sample Screenshots
Analysis of Trains in a Solution Characteristics
and Composition of Trains by Day-of-Week
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DSS Sample Screenshots
Analysis of Assignments of Blocks BTAs by
Day-of-Week, Pick-up and Set-Off Distribution
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Conclusion

• Train scheduling is a complex combinatorial
  optimization problem
• There is a need of decision support system for
  train scheduling
• We have developed a modular approach to generate
  implementable train schedule
• Our experiment on the real-life problem is
  demonstrating significant improvement