1 storage space allocation in container terminals chuqian zhang *1, jiyin liu *1, yat-wah wan *1,...
TRANSCRIPT
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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
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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
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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
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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
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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
HK: mix the storage of import (I/B) and export (O/B) containers
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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
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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