PUSAN NATIONAL UNIVERSITY

Deriving Situation-Adaptive Strategy for Stacking

Containers in an Automated Container Terminal

Taekwang Kim, Jeongmin Kim, and Kwang Ryel Ryu

Pusan National University

Dept. of Electrical and Computer Engineering

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Outline

• Automated Container terminal

• Stacking Policy

• Background and Previous Works

• Approach to Deriving Situation-Adaptive Strategy

• Case Study

• Experimental Results

• Conclusion

1

Automated Container Terminal

2

Enlarged view of a block part

tiers

Seaside

StackingYard

LandsideExternalTrucks

AGVs

QC

Seaside ASC

Seaside HP

Landside HP

Landside ASC

Quay

Quay Crane (QC)

Hinterland

Enlarged view of a block part

Stacking Yard

External Truck(ET)

Automated Stacking Crane

(ASC)

Automated Guided Vehicle(AGV)

Seaside Handover Point

(HP)

LandsideHandover Point

(HP)

Stack

Operations in Stacking Yard

• Crane interference occurs frequently because of the opposite

directions of container flow

• Determination of stacking position is one of the most important

operational problems in container terminals

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Seaside HP

Landside HP

Loading Carry-in(Export)

Carry-outRehandling

Transshipment

Discharging(Import)

Repositioning

Stacking Policy

• Stacking policy takes account of various criteria to determine optimal

stacking positions in the stacking yards

• A good position should allow efficient operation not only at the time of

stacking but also at the time of retrieval

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Stacking Policy

container 1. Request for a stacking location

3. An optimal stacking position

4. Stack

Stacking yard

2. Evaluate candidate positions

• Stacking policy based on single criterion [Duinkerken M. B., 2001]

[Dekker, R., 2006]

Background and Previous Works

5

Distance to the Handover Point

Category of a container (destination, weight, type)

Container type

(e.g. normal, reefer, dangerous goods)

Maximum stack height

Constraints

Background and Previous Works

• Stacking policy based on multiple criteria [Park, T., 2010a] [Park, T.,

2010b]

• Multiple criteria are taken into account simultaneously by a scoring function

of a weighted sum

x a candidate position

Ci i-th criterion

wi weight for the i-th criterion

• The position with the best score is selected

• Stacking policy is represented as a vector of the weight values

6

( ) ( )i ii

s x w C x

Background and Previous Works

• Stacking policy based on multiple criteria

• A policy consists of a set of rules for various container types

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Background and Previous Works

8

• Stacking policy based on multiple criteria

Example: s7 (R7) for repositioning export containers

s7(x) = w34DI(x) + w35DO(x) + w36H(x) + w37E(x) + w38T(x) + w39G(x) + w40S(x)

DI(x)The distance in number of bays from the current location of the target container to the candidate location x

DO(x) The distance from x to a seaside HP of the block

H(x) The height of the stack at x

E(x)Indicates whether or not the candidate location is an empty ground slot

T(x)Indicates whether or not the container at the top of the stack at xis a repositioned container

G(x)The estimated likelihood of causing rehandling if the target container is eventually put on x

S(x)The amount of reduction in empty ground slots after putting the target container on x

• Deriving a robust stacking policy using a Noise-Tolerant Genetic

Algorithm (NTGA) [Jang, H., 2012]

• An evaluation of a candidate strategy demands an extensive simulation of

container handling in a block

• A strategy good for one scenario may not be so for a different scenario

• NTGA is provided with a pool of scenarios for evaluation

• A candidate strategy is initially evaluated by using a random couple of

scenarios in the pool

• If the candidate later turns out to be critical, then it is evaluated more

thoroughly using more random scenarios in the pool

• Final strategy thus obtained is the one with the best average

performance on various situations

Background and Previous Works

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Motivation

• Limitations of the previous works

• The strategy performs well on the average in a variety of situations

• The performance in a certain situation can be worse than that of the

strategy custom-designed for that particular situation

• What we want is a set of strategies that can take good care of a

variety of situations (or virtually any situation)

• How will that be possible?

• There exists not just a few discrete situations but an infinite number of

continuously varying situations

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Basic Idea

• We can derive a small number of representative strategies each for a

particular situation

• Given a new situation, we can apply the representative strategies

probabilistically according to their relevancies to the current situation

• Strategies are stochastically applied in such a way that a strategy for a

situation closer to the current situation is applied with a higher probability

• As a situation can be represented by a set of features, the Euclidian

distance between any two situations is easily calculated

• The application probability of each strategy depends on the distance to the

current situation from the situation that the strategy is specialized for

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Representation of a Situation

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• Suppose there are m indicators to specify a situation

• Then a situation e can be represented as a hyper-rectangle in an m-

dimensional space:

e = ([a1 , b1 ], [a2 , b2 ], . . . , [am , bm ])

where [aj , bj ] with aj , bj R represents that the j-th indicator takes the

value within the specified interval

Example: One-dimensional case

When the occupancy rate of the target storage block is the only

indicator of a situation

elow = [0 , 0.4 ] situation with occupancy rate 40%

ehigh = [0.6 , 1.0] situation with occupancy rate 60%

Distance Measure

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• The distance d(ei , ej ) between two situations ei and ej is defined as

Example: Distance in 2-D space

• Two indicators used:

– Occupancy rate

– Crane workload

• d(e1 , e2 ) is the distance between the

two nearest vertices

• The closeness (similarity) c(ei , ej ) between two situations ei and ej is

defined as 1 / d(ei , ej )

2/1

1

2

],[],[

)(min),(

,,

,,

m

k kk

baybax

ji yxd

kjkjk

kikik

ee

e1

e2

a1,1 b1,1 a2,1 b2,1

a2,2

b2,2

a1,2

b1,2

d(e1 , e2 )

Crane Workload

Occ

upan

cy R

ate

Scoring by Multiple Representative Strategies

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• Let si be the scoring function specialized to situation ei

• Then the score sc (x) of a candidate stacking position x in the current

situation ec can be obtained by

where c(ec , ei ) is the closeness between ec and ei

• sc (x) can be viewed as the expected score of position x when each

scoring function si for ei is applied probabilistically in proportion to its

respective closeness c(ec , ei ) to ec

m

i ic

m

i iic

cc

xscxs

1

1

),(

)(),()(

ee

ee

Case Study

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• The workload of the seaside crane is our only indicator of a situation

• The workload of the upcoming horizon can be estimated from the job

schedule

• We focus on stacking strategies for

el = [0 , vl ], when the crane workload is low

eh = [vh , ∞], when the crane workload is high

• Based on these two, we should be able to deal with any intermediate

situation in-between the two situations

Case Study

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• How can we derive those representative strategies?

• We need simulation scenarios to derive strategies

• For an accurate evaluation of a candidate strategy, it should be tested for a

long enough period of container ‘in’s and ‘out’s at a block

(About 2 weeks of yard operations per scenario in our experiment)

• Can we derive each strategy separately?

• Log data from real container terminals show continuously changing

situations

• Simulation scenarios with constant crane workload may be generated only

artificially

• But, what are good values of vl and vh ?

Case Study

• Our solution:

• Use scenarios of continuously varying situations

• Search for the two strategies simultaneously

• Also search for good values of vl and vh

• Evaluation of a candidate pair of strategies:

• The two strategies are probabilistically applied during the simulation of a

scenario of container handlings in various situations

• Average AGV delay and ET waiting time are measured for each simulation

min (w1 DAGV + w2 TET ) (w1 : w2 = 50 : 1)

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Indicators Strategies

el eh sl sh

vl vh wl,1 wl,2 … wl,k wh,1 wh,2 … wh,k

Experimental Setting

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Simulation Scenario

Loading Jobs 150 ~ 170 containers loaded per day

Discharging Jobs 150 ~ 170 containers discharged per day

Transshipment 80%

Duration of Simulation 10 days of initialization + 5 days of evaluation

Average Occupancy Rate 65%

Number of Scenarios 100 for learning, 100 for testing

NTGA Setting

Population size 100

Number of Evaluations 100,000

• Performance on 100 test scenarios:

• The t-test has shown that the difference is statistically significant

Experimental Results

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vl(sec)

vh(sec)

Average AGV delay(sec)

Average ET waiting (sec)

Pair of Strategies withOptimal vl and vh

118.9 1984.0 42.30 105.80

Pair of Strategies withHand-picked vl and vh

1500.0 2400.0 47.36 114.68

Single Strategy withBest Overall Performance

- - 44.65 130.98

• Comparison of the two representative strategies:

• Stacking locations of the discharged containers

• When the workload is low, the seaside crane tries hard to move as

many discharged containers to the landside positions as possible

Experimental Results

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Low Workload

High Workload

Se

asi

de Landsid

e

Average Travel Distance: 25.7

Average Travel Distance: 5.5

Experimental Results

• Comparison of the two representative strategies:

• Stacking locations of the export containers

• When the workload is low, the landside crane can move the export

containers at positions nearer to the seaside without interference

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Se

asi

de

Low Workload

Average Travel Distance: 42.3

High Workload

Average Travel Distance: 13.8

Landsid

e

Conclusion

• Previous methods derive a single strategy that shows overall best

performance in a variety of situations

• But the performance in a certain situation can be worse than that of

the strategy custom-designed for that particular situation

• We have proposed to derive a set of a few representative strategies

each for a particular (extreme) situation

• Given a new situation, we can apply the representative strategies

probabilistically according to their relevancies to the current situation

• A case study with the workload of the seaside crane as a sole

indicator of a situation has shown that a pair of good representative

strategies can be derived that works significantly better than a single

overall best strategy

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Q&A

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Thank you