© Princeton Modeling Resources 1 PLASMA Status report Princeton Modeling Resources December 19,...

© Princeton Modeling Resources 1

PLASMA Status report

Princeton Modeling ResourcesDecember 19, 2006

Warren PowellBelgacem Bouzaiene-Ayari

© 2006 Princeton Modeling Resources


Locomotive planning models

Applications: Strategic planning

• What is the impact of changes in fleet size and mix on train delay?• How do changes in shop locations affect maintenance routing?• How do changes in schedule affect train delay for a given locomotive

fleet?• How do changes in operating policies affect performance?

Tactical planning• How much power will you have at each terminal 1, 2, 3 days out?• Where do you anticipate being short power?

Real-time planning• What train should a locomotive be assigned to in order to get it to

shop on time?



The PLASMA family of locomotive models PLASMA/OP – Short term operational planning and

forecasting• Projects locomotive movements 1-5 days into the future.

PLASMA/FS – Fleet sizing• Strategic planning model for:

– fleet sizing– Reliability of transit times– ….?

PLASMA/RT – Real-Time locomotive assignment model• Makes detailed locomotive to train assignments for a single

terminal over a short horizon.• Works real-time with user, responding to user overrides.



PLASMA/OP – Short term operational planning and forecasting Uses “optimizing-simulator” technology to capture high

level of detail.• Combines flexibility of simulation• Intelligence of optimization

Projects locomotive movements 1-5 days into the future.


• Model breaks the network into the “subproblems."

• A “subproblem” can be• The entire network at one

point in time.• A single yard.• The yards covered by a

single desk (by an ST).• We will generally break

the problem into regions that are covered by a single ST.


New features

Implementation of “nonlinear logic.” Old LRM approximated the value of an additional

locomotive in the future by using a constant numbers (five locomotives produced five times as much as one locomotive).

PLASMA uses “nonlinear logic” – The fifth locomotive is not worth as much as the first.


• In the first generation model, we used a “linear” model to capture the value of locomotives in the future.

• Easier to estimate.• Easier to solve

• But…• Algorithm was slow• Solution could be unstable.


• PLASMA uses a “nonlinear” function to estimate the value of locomotives in the future.

• More realistic (if we need five locomotives, the value of the sixth locomotive is not as much as the fifth).

• Hard to solve, but modern technologies have no trouble handling this.

• Model is faster and more stable.


New features

Nonlinear logic Initial testing suggests a dramatic improvement in the

rate at which the model reaches a solution. Solution appears to be much more stable than the older

“linear” logic.

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Iteration

Tota

l rew

ard

“Linear logic” “Nonlinear logic”

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Iterations


Coverage

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Iteration

% t

rain

s m

ove

d


“Objective function”

Total contribution

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Iterations


Solving the “Subproblem” Old LRM model: Used heuristic logic to get a

“good” but not optimal solution.• From time to time, logic simply would return unusual

solutions not explained by the data. New logic: Uses Cplex to return “optimal”

solution.• Surprisingly fast.• Robust – if we do not like the solution, we cannot

blame the algorithm.• Handles leader logic, consist breakup, shop routing,

foreign power, …• Commercial software rather than custom algorithm.


Influencing model behavior: Humans use a series of rules to govern how

they make decisions. Models use a series of costs and rewards to

penalize undesirable behavior:• Cost (negative benefit) for breaking up a consist.• Reward (positive benefit) for moving a train.• Higher rewards for more important trains.• Reward for moving a locomotive toward its shop.


Knowledge

Costs allow you to make tradeoffs:

Atlanta

Issue “cost”/“bonus”

Moving a train $2,000

Appropriate type -$500

Consist breakup -$800

Train delay $0

Routing to shop +$1,000

Total “cost” +$1,700

Baltimore


Rule-based logic How it works:

• Code rules to determine which locomotives get assigned to each train.

Strengths:• Easy to understand.

Weaknesses:• Very hard to code all

the different situations that might arise.

• Very hard to make tradeoffs.

Cost-based logic How it works:

• Design costs and bonuses to penalize bad behavior and reward good behavior.

Strengths:• Easily handles tradeofs.• Can handle broad range

of very complex problems.

Weaknesses:• Can be difficult to “get

the model to do what you want.”


Consist Breakup

Locomotives Trains

Consist C

z1

z2

z3

z4

z5

Destinations

Cost on assignment arcs influence behavior.


Train connection: reward the connections

680-xx/xx/xx

667-xx/xx/xx

681-xx/xx/xx

667-xx/xx/xx

666-xx/xx/xx

1. Add a reward on each arc going from a consist to a connected train (Foreign reward or Plan reward)

2. At each train node and for each connection coming from a consist add a constraint limiting the number of axles assigned to the train to the connection max axles.

3. Stop enforcing the connection if: the total hold time is greater than the connection time or we connected the required axles.


LRM Model

Subproblem Model: (build nodes & Train Arcs):

Locomotives Trains

Duplicated Trains

Super Sink

Yard A

Yard B

Yard C


LRM Model

Subproblem Model:(add Hold arcs . . . and VFAs)

Locomotives Trains

Duplicated Trains

Super Sink

VFAs

Yard A

Yard B

Yard C


LRM Model

Subproblem Model:(add Assign arcs . . . And more VFAs)

Locomotives Trains

Duplicated Trains

VFAs

Yard A

Yard B

Yard C


LRM Model

Subproblem Model:(add VFA arcs)

Locomotives Trains

Duplicated Trains

VFAs

Yard A

Yard B

Yard C


Outline

Fleet sizing



PLASMA/FS – Fleet sizing Strategic planning model for recommending fleet sizes Uses PLASMA-OP as core engine.


Planning model

Classical fleet sizing model Elegant, but requires large LP model…

Time

Circulation arc

10,000

7,850

Fleet size = 2,150

550

720

660

220


Planning model

PLASMA/FS Use PLASMA/OP as core engine

Circulation arc

10,000

7,850

Fleet size = 2,150

550

720

660

220


Planning model

PLASMA/FS Nonlinear functions determine how many locomotives to

send to each location.

Circulation arc

10,000

Fleet size = 2,150

550

720

660

220

7,850


Features: All the calibration that is invested in the

operational model is immediately used in the fleet sizing model.

We can specify the fleet size• PLASMA determines how many to send to each

location.• Eliminates need for artificial construction of locomotive

snapshot. Model will delay or cancel trains if the fleet size

is too small.• Allows for fleet size vs. service tradeoffs.


Fleet sizing


Fleet sizing

Additional considerations: PLASMA will allow us to consider:

• Foreign power• Train delays• Shop routing• Unscheduled trains

Fleet requirement from plasma will be adjusted to reflect

• Locomotives being taken out of service due to maintenance issues

• Retirements• leasing


Outline

Real-time locomotive planning



PLASMA/RT – Real-Time locomotive assignment model Works interactively with planners. Makes detailed locomotive assignment recommendations. Real-time response to user overrides. Keeps the “human in the loop.”


Tactical planning model User will interaction with Plasma/OP through an

intermediate data server. Several minute delay between user inputs and model

response.

Data server PLASMA/OP


Real-time planning PLASMA/RT will sit on user’s workstation. Response to user inputs < 5 seconds.

Data server PLASMA/OP

PLASMA/RT


Solving a single “subproblem” When a single ST is planning, he will inevitably want to

override the model. We can react by reoptimizing just his problem.


Outline

Calibration


Model calibration Operational planning

• Are we moving trains on time?• Do the assignments obey basic operating rules?• Is this what an ST would do?• How well can we project future supplies and deficits?

Fleet sizing• How well can we predict train delay for a given fleet

size? Real-time

• Is this what an ST would do “right now”.


Fleet sizing

Current fleet


LRM performance

LRM vs. history (August, 2000)

2521

3032

41

21

3

7.710.6 12

0

5

10

15

20

25

30

35

40

45

Setouts Swaps Nonpreferredconsists

Underpowered Overpowered

Perc

ent


Features: Foreign cycles. Locomotive Top Plan. Locomotive hard assignments. Locomotive consist logic: This logic is coded as part of

the IP model. The model is formulated is way that will penalize the consist break-up proportionally to the number of peaces. This has an impact on the CPU time and I spent sometime tuning the CPLEX parameters to accelerate the solution time.

Shop routing: partially coded


Real-World operations

A

B

C D

E

1

2

3

4

5


Real-World operations

This is the mathematically guaranteed, global optimal solution!

A

B

C D

E

1

2

3

4

5

?


ManagementModeler Central dispatch

Question: When developing a model, who do you keep happy?

Observation: If the modeler builds a model that central dispatch does not use, who are you going to fire? The computer model or your operations staff?


The implementation challenge

How do we measure user happiness?

“Width of smile”



But who do we keep happy?

Single rational decisionmaker model . . .

The real world . . .


Question: Which driver would you assign to the load?

A

B

60 miles

30 miles

You are told that driver B won’t arrive until laterin the afternoon. Now what do you do?



Formulating a model is like fitting a line through a set of points:

But every point is a different person!



We may need to customize the model to accommodate individual preferences!


Management would like to think

that buying an optimization model

is like buying a TV...

Optimization is a process, not a product.

More often, it is like having a baby ...

It is fun creating it, but you often have

second thoughts right after you get it!


Outline

Next steps


Next steps What is timing for first deliverable? How do we decide when a deliverable is

finished?

© Princeton Modeling Resources 1 PLASMA Status report Princeton Modeling Resources December 19,...

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