1 Storage Space Allocation in Container Terminals Chuqian Zhang *1, Jiyin Liu *1, Yat-wah Wan *1,...

1

Storage Space Allocation in Container Terminals

Chuqian Zhang*1, Jiyin Liu*1,

Yat-wah Wan*1, Katta G. Murty*2, Richard Linn*3

*1IEEM, HKUST, Clear Water Bay, HONG KONG*2IOE, Univ. of Michigan, Ann Arbor, Michigan, USA

*3ISE, Florida International University, Miami, Florida, USA

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Outline

background problem statement solution approach results and conclusion

3

Busiest Container Ports Throughput in TEU

Rank 2000 2001 2002

5th

4th

3rd

2nd

1st

6,274,556

7,425,832

7,540,387

17,086,900

18,098,000

6,334,400

7,540,525

8,072,814

15,571,100

17,826,000

8,493,000

8,620,000

9,453,356

16,940,900

19,144,000

20-foot equi-valent unit

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Rank 2000 2001 2002

5th

4th

3rd

2nd

1st

Shanghai

Kaohsiung

Pusan

Singapore

Hong Kong

Shanghai

Kaohsiung

Pusan

Singapore

Hong Kong Hong Kong

Singapore

Pusan

Kaohsiung

Rotterdam

Busiest Container Ports Throughput in TEU

5

Impact of 19.14 m TEU (2002)

around 12 m TEU handled by container terminals

handling charge: at least NZ$ 2.5 b 2% improvement NZ$ 50 m

6

Gate House

Gate House

Temporary Parking Lot for XTs

CFS Offices

Main-tenancy

Yard

VesselQuay CraneBlockYard crane

sea

The Typical Container Terminal Layout

Blocks of Containers & Yard Cranes

Internal Tractors & Quay Crane

Block, Internal Tractor, & Yard Crane

Blocks, Yard Cranes,

& Quay Cranes

Quay Cranes & Container Vessel

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Types of Container Movements

vessel loading (VSLD: blocks to vessels) vessel discharge (VSDS: vessels to blocks) container grounding (CYGD: shippers to

blocks) container pickup (CYPI: blocks to consignees)

need to consider the storage space allocation

arrival times: random

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Comparing Different Terminals

  Delta(Netherlands)

Long Beach (USA)

HIT &COSCO-HIT

throughput (TEU)

2.5 mill 4.6 mill 6.6 mill

area (hectares)

280 295 122

yard cranes

~ 50 (+ AGV)

~ 50(+ chassis, train)

167

~ 18,000 TEU per dayTiny area

Intensive operations

9

Comparing Different Terminals

  Delta(Netherlands)

Long Beach (USA)

HIT &COSCO-HIT

throughput (TEU)

2.5 mill 4.6 mill 6.6 mill

area (hectares)

280 295 122

yard cranes

~ 50 (+ AGV)

~ 50(+ chassis, train)

167

HK: mix the storage of import (I/B) and export (O/B) containers

10

Objectives of Hong Kong Container Terminals

various performance indicators, inter-related, and possibly contradictory to each other

two commonest objectives in HK to max. the (average) throughput of QCs to min. the (average) vessel berthing time

11

Outline

background problem statement

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location assignment (determining the exact locations of containers in blocks)

storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block)

QC allocation (allocating QCs to (bays of) vessels)

berth allocation (allocating vessels to berths)

RTGC deployment (deploying RTGCs in real time)

IT deployment (deploying ITs in real time)

schedule and stowage plan of vessels

Operations Decisions in a Container Terminal

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location assignment (determining the exact locations of containers in blocks)

storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block)

QC allocation (allocating QCs to (bays of) vessels)

berth allocation (allocating vessels to berths)

RTGC deployment (deploying RTGCs in real time)

IT deployment (deploying ITs in real time)

schedule and stowage plan of vessels

Operations Decision in this Research

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Our Problem: Storage Space Allocation

inputs results of the berth allocation results of the QC allocation vessel arrival and departure times workload requirements of vessels

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Our Problem: Storage Space Allocation

outputs stor. space allocation for vessel discharge

interchangeable I/B containers to determine for each vessel the number of I/B

containers stored in each block stor. space allocation for container grounding

interchangeable O/B containers to determine for each vessel the number of O/B

containers stored in each block practical solution

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Our Problem: Storage Space Allocation

dynamics deterministic arrival times of vessel loading

and vessel discharge stochastic arrival times of container

grounding and container pick up conversion of movements

container grounding turned into vessel loading vessel discharge turned into container pickup

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Sketch of Outputs

Gate House

Gate House

Temporary Parking Lot for XTs

CFS Offices

Main-tenancy

Yard

VesselQuay CraneBlockYard crane

sea

IB 525OB 620

IB 28; OB 46IB 525OB 620

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Outline

Hong Kong terminals problem statement solution approach

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Difficulties of the Problem

inter-related problems & sub-problems multiple objectives large number of variables integer variables

hierarchical approach

location assignment (determining the exact locations of containers in blocks)

storage space allocation (determining the numbers of I/B & O/B containers of each vessel in a block)

QC allocation (allocating QCs to (bays of) vessels)

berth allocation (allocating vessels to berths)

RTGC deployment (deploying RTGCs in real time)

IT deployment (deploying ITs in real time)

schedule and stowage plan of vessels

Determine the total # of I/B and O/B containers of each block (to balance the workload in each

period)

Allocate I/B & O/B containers of vessels to blocks in each period (to minimize total distance traveled)

Implement the decision for one day and update the information

Information: blocks’ capacity, blocks’ status, arriving containers

level 1

level 2

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inter-related problems & sub-problems multiple objectives large number of variables integer variables dynamic problem: vessels, trucks, etc.

rolling horizon

Difficulties of the Problem (cont.)

Day 1 Day 2 Day 3 Day 4 Day 5

1st planning horizon

2nd planning horizon

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inter-related problems & sub-problems multiple objectives large number of variables integer variables dynamic problem: vessels, trucks, etc.

unknown data: grounding and picking ups beyond the planning horizon

forecasting

Difficulties of the Problem (cont.)

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storage space allocation (determining the numbers of

I/B & O/B containers of each vessel in a block)

Solution Approach

Determine the total # of I/B and O/B containers stored in each block ...............................................................

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Level 1: Determine the total # of I/B and O/B containers stored in each block shippers and

consignees

Vessel A

YC 1

YC 2

the earliest departure time of Vessel A depends on the longest working time of YC 1 and YC 2

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Level 1

for yard cranes balance the workload of yard cranes for vessels rationale: yard cranes act as parallel servers; the

longest processing time = vessel berthing time output: # of I/B and O/B containers in each block

for each time period

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Solution Approach

level 1Determine the total # of I/B and O/B containers stored in each block ...............................................................(to balance the workload in each

period)

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Level 1Level 1

decisions Dit : the total number of I/B containers discharged

in period t that can be assigned to block i Git : the total number of O/B containers delivered

in period t that can be assigned to block i

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- balance the total number of containers

- balance the number of vessel loading/discharging

containers

the objective function

Level 1Level 1

)]}(min)(max[

)](min)(max[{

}{}{2

1}{}{

1

ititititi

ititititi

T

titit

iitit

i

PGLDPGLDw

LDLDwMin

Minimize the dispersion of the total number ofcontainers among blocks

Minimize the dispersion of vessel loading/discharging containers among blocks

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Level 1Level 1~Dt

~Dt0

~Dt1

~Dt,T-t t

. . .

D1t0 D2t0 DBt0. . . D1t1 D2t1 DBt1

. . . D1t,T-t D2t,T-t DBt,T-t. . .

. . .1t 2t Bt

. . .

...,,2,1;...,,2,1 BiTtDit 0

D it

tT

kitk

workload at

period t block i

...,,2,1;...,,2,1 BiTtPit 1

0)(

0 DPt

kkktiit

conservation of flow of containers

total number of containers discharged at period t: from vessel records number of

containers to be taken away at different time periods: from

historical pattern

storage blocks of

such containers

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Level 1Level 1

...,,1,0;...,,2,1~

1

tTkTtDDB

iitktk

...,,1,0;...,,2,1~

1

tTkTtGGB

iitktk

...,,2,1;...,,2,10

BiTtDD it

tT

kitkit

...,,2,1;...,,2,10

BiTtGG it

tT

kitkit

...,,2,1;...,,2,11

0)(

0 BiTtGLLt

kkktiitit

...,,2,1;...,,2,11

0)(

0 BiTtDPPt

kkktiitit

TtBiLPDGVV itititititti ...,,2,1;...,,2,1)]()[()1(

TtBiCV iit ...,,2,1;...,,2,1

flow conservation constraint on CYPI and VSLD containers

block density constraints

flow conservation

constraint on CYGD

and VSDS containers

integer variables

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Solution Approach

level 1

Allocate I/B & O/B containers of vessels to blocks in each period ........................................................

Determine the total # of I/B and O/B containers stored in each block ...............................................................(to balance the workload in each

period)

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Level 2

known locations of vessels and blocks known Dit, Ditk, Git, Gitk (numbers of I/B and O/B containers

in each block for each period) from level 1 unknown: the identification of vessels that

contribute the containers (to blocks) minimizing the travelling distance of ITs

minimizing the total processing time of vessels standard transportation problems

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Level 2Level 2

Xijtk : the number of I/B containers discharged from

vessel j in period t, picked up by customers in period t+k, that can be assigned to block i

(or the number of O/B containers arrived in period t, headed for vessel j in period t+k, that can be assigned to block i)

decisions (separating I/B & O/B)

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1

2

St

1

2

B

1

B

Sources

(vessels)

Destinations

(blocks)

N1t

N2t

Nst

U1t0

U2t0

UBt0

U1t2

UBt(T-t)

:

:

:

d11 : X11t1

)(: tTtBSBS tt Xd

Level 2Level 2 number of different types of containers stored in each block

number of containers for

each vesselminimize the total

distance travelled by ITs

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B

i

S

j

tT

kijtkij

t

XdMin1 1 0

...,,1,0;...,,2,11

tTkBiUXtS

jitkijtk

...,,2,11 0

tjt

B

i

tT

kijtk SjNX

Xijtk 0 i = 1, 2, …, B; j = 1, 2, …, St; k = 1, 2, …, T - t

s.t.

Level 2Level 2

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Solution Approach

Implement the decision for one day and update the information

Information: blocks’ capacity, blocks’ status, arriving containers

level 1

level 2Allocate I/B & O/B containers of vessels to blocks in

each period ........................................................

(to minimize total distance traveled)

Determine the total # of I/B and O/B containers stored in each block ...............................................................(to balance the workload in each

period)

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Outline

Hong Kong terminals problem statement solution approach results and conclusion

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Numerical Study for Level 1

real data: 17 days, 6 periods per day 3-day rolling horizon effective capacity = 83% 10 blocks (~ 4320 integer variables) accept the first feasible integer solution

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ratio between the gap & the lower bound min: 0.0%; average: 1. 84%; max: 6.58%

computation time min: 16.5 s; average: 110 s; max: 542 s

average imbalance all containers: 5.68/period vessel related containers: 4.22/period

Results of Level 1

upper bound

lower bound

optimal solution

0

20

40

60

80

100

120

1 11 21 31 41 51 61 71 81

Periods of 15 day s

Varia

nce

of to

tal

num

ber o

f co

ntai

ners

real resultoptimal result

0

10

20

30

40

50

60

70

80

90

1 11 21 31 41 51 61 71 81periods in 15 day s

Varia

nce

of th

e nu

mbe

r of

vess

el h

andl

ing

cont

ainr

es

real resultoptimal result

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Conclusion

propose a procedure that possibly improves the terminal operations

further studies more extensive numerical runs

different settings larger sizes

approximate methods for solving level 1 actual benefits for terminals