Simultaneous Derivation of Container Stacking Strategy and Crane Dispatching Strategy for an Automated

Container Yard

Taekwang Kim, Aekyoung Bae, and Kwang Ryel Ryu

Pusan National University

Department of Electrical and Computer Engineering

Outline

Automated Container Terminal

Background and Previous Works

Proposed Method

Experimental Results

Conclusion

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3

Automated Container Terminal

Layout of an Automated Container Terminal

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

Storage Yard

External Truck(ET)

Automated Stacking Crane

(ASC)

Automated Guided Vehicle(AGV)

Seaside Handover Point

(HP)

LandsideHandover Point

(HP)

Stack

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Operations in Storage Yard

Different operations are needed depending on the types of containers

Difficulty arises because the operational flows of inbound and outbound containers are in opposite directions

Determination of stacking location is required whenever a container has to be put down

• Good to minimize empty travel, crane interference, and rehandling

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Seaside HP

Landside HP

Loading Carry-in(Export)

Carry-outRehandling

Transshipment

Discharging(Import)

Repositioning

Remarshaling Operation

A good-looking location for stacking an incoming container may turn out to be a bad one seen later at the time the container needs to be retrieved out

The operation of rearranging containers to more appropriate positions is called remarshaling

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Storage block

Loading

Remarshaling

Carry-in

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Background and Previous Works

Stacking Strategy

Jang et al. (2013) propose a stacking strategy that determines a good location for stacking a container by evaluating the candidate locations using a scoring function

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Stacking Strategy

container

1. Request for a stacking location

3. Stack to the optimal location

Storage block

2. Evaluate candidate locations

…

Stacking Strategy

Given a candidate stacking location x, the scoring function returns a score for x by calculating a weighted sum of various evaluation criteria

Examples of Criteria:• distance to x

• height of the stack at x

• likelihood of rehandling when stacked at x, and so on

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( ) ( )i ii

s x wC x

x … a candidate stacking location

Ci … ith criterion

wi … weight for the ith criterion

Stacking Strategy

A good weight combination constitutes a good stacking strategy• Jang et al. (2013) try to derive an optimal weight combination by using a

genetic algorithm

• Each candidate strategy (i.e., weight combination) is evaluated by running a simulation of container handling by ASCs at a storage block

• This simulation requires crane scheduling

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1 15 16 23……

Period for the initialization Period for the real evaluation

Time(day)

1

8

…O

rder

of

vess

els

Carry-in containers for loading

Carry-out containers discharged orLoading containers for transshipment

Period for discharging or loading

Yar

d S

imul

atio

n S

yste

m

Input: { w1, w2, …, w41 }, Job scenario

Output: { tAGV, tET }

wi : i-th weight value of decision criteria

tAGV : Average AGV delay

tET : Average waiting time of ET

Since this simulation is very time consuming, the simple earliest deadline first (EDF) heuristic has been used for dispatching the ASCs when scheduling the ASC jobs

ASCs cannot be scheduled to do remarshaling jobs because they do not have any deadline

Container Job Type Deadline

Discharging 16

Carry-out 70

Loading 124

Remarshaling -

Crane Scheduling

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cCarry-out

Discharging

Loading

Which one should ASC select?

Remarshaling

EDFc

Crane Scheduling

Choe et al. (2013) proposes a rolling-horizon-based scheduling method for ASCs to do not only the regular jobs but also the remarshaling jobs at idle times and in-between the regular jobs

• The strategy by Jang et al. (2013) is used for container stacking(Repositioning rules are modified to stack remarshaled containers)

Each rescheduling demands about a minute of computation time

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Crane Scheduling

It would take tens of hours to simulate just a single scenario of two weeks of container handling if this method is used for ASC scheduling instead of the simple EDF

The stacking strategy derived from simulations without remarshaling would not be optimal for use when the ASCs do remarshaling jobs in addition to the regular jobs

We need a crane scheduling method that does not demand much computation time but can deal with remarshaling

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1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11st 12nd 13rd 14th

Scenario of two weeks

(day)

288 rescheduling per day

288 (times) × 14 (days) = 4032 rescheduling for two weeks 4032 minutes, about 67 hours taken for a simulation about 767 years if we evaluate 100,000 times

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Proposed Method

Crane Dispatching Strategy

We propose a crane dispatching strategy that can fast assign jobs to the ASCs by evaluating the candidate jobs using a scoring function, similarly as does the stacking strategy of Jang et al. (2013)

Given a candidate job x for a just-freed ASC, the scoring function returns a score for x by calculating a weighted sum of several evaluation criteria

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( ) ( )i ii

s x wC x

x … a candidate job

Ci … ith criterion

wi … weight for the ith criterion

Crane Dispatching Strategy

Evaluation criteria for crane dispatching

The candidate jobs include not only the regular jobs but also the remarshaling jobs

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Criterion Description

E Empty travel distance

U Urgency of the job

I Probability of ASC interference

X Estimated processing time

G Gain when the job is processed

D Relative workload of the other ASC

H Waiting time by ASC interference

S Block occupancy rate around the target container

Deriving Optimal Strategies

To search for a good crane dispatching strategy, we need a stacking strategy to be used whenever an ASC has to put down a container within the storage block

The stacking strategy by Jang et al. (2013) is usable, but it ignores the possibility of remarshaling

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Crane-schedulingstrategy

c

c

cStacking strategy

(By Jang et al.)

Ignores remarshaling

Deriving Optimal Strategies

How can we derive a good stacking strategy that takes account of remarshaling?

To search for such a new stacking strategy, we need a crane dispatching strategy that can deal with remarshaling

The problem is circular: derivation of such a crane dispatching strategy requires a new stacking strategy

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Crane schedulingstrategy

c

c

cStacking strategy

(By Jang et al.)

Ignores remarshaling

New stacking strategy

Considers remarshaling

Deriving Optimal Strategies

Our approach to this problem is to apply a cooperative co-evolutionary(CCEV) algorithm that can search for both strategies in parallel

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Population for stacking strategies (P) Population for crane dispatching strategies (Q)

Best individual

Evolve population Evolve population

Evaluate Pt+1

Evaluate Qt+1

Best individual

Pt+1 Qt+1

Pt Qt

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Experimental Results

Experimental Setting

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Simulation Scenario

Block Size 41 bays, 10 rows, 5 tiers

Loading Jobs 120 containers loaded per day

Discharging Jobs 120 containers discharged per day

Transshipment 45%

Duration of Simulation 14 days of initialization + 8 days of evaluation

Average Occupancy Rate 60%

CCEV Parameter

Population Size 100

Number of Evaluations 100,000

Fitness Functionmin (w1 DAGV + w2 TET ) (w1 : w2 = 50 : 1)

(DAGV : average AGV delay) (TET : ET waiting time)

Experimental Results

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Container Staking & Crane Dispatching Methods

CC Crane scheduling method by Choe. et al. (2013)

SJ Stacking strategy by Jang. et al. (2013)

CP Crane dispatching strategy by the proposed method

SP Stacking strategy by proposed method

Trial Stacking Method Crane-scheduling Method

SP-CP SP CP

SJ-CP SJ CP

SP-CC SP CC

SJ-CC SJ CC

Experimental Results

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Trial Average AGV Delay (sec) Average ET Waiting (sec)

SP-CP 18.50 593.38

SJ-CP 28.01 626.94

SP-CC 15.14 617.06

SJ-CC 16.61 665.81

18.5

28.01

15.1416.61

0

5

10

15

20

25

30

SP-CP SJ-CP SP-CC SJ-CC

Average AGV Delay (sec)

593.38

626.94617.06

665.81

540

560

580

600

620

640

660

680

SP-CP SJ-CP SP-CC SJ-CC

Average ET Waiting (sec)

Conclusion

The previous crane scheduling method by Choe et al. (2013) uses the stacking strategy by Jang et al. (2013) to deal with both regular and remarshaling jobs

However, the stacking strategy cannot be easily upgraded to incorporate remarshaling by employing the previous crane-scheduling method because the latter demands too much CPU time

We propose a scoring-function-based crane dispatching strategy that can fast schedule the cranes to deal with both regular and remarshaling jobs

To derive this crane dispatching strategy we need an upgraded stacking strategy

Therefore, we propose to derive a crane dispatching strategy and a new stacking strategy in parallel using a CCEA

This new stacking strategy when combined with the crane scheduling method by Choe et al. (2013) gives the best performance

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Thank you !

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