Speed and Schedule Stabilityin Supply Chains
Michael G H BellProfessor of Transport Operations
Imperial College London
P O R T e C
GCSL2006, Hong Kong, December, 2006
PORTeC members
• Civil and Environmental Engineering:– Prof. Mike Bell
– Prof. Andrew Evans
– Prof. John Polak
– Prof. Robert Cochrane
– Dr. Sheila Farrell
– Khalid Bichou
– Panagiotis Angeloudis
– Gianluca Barletta
– Konstantinos Zavitsas
• Tanaka Business School:– Dr Elaine Hadjiconstantinou
– Nang Laik
Security and port efficiency (Khalid Bichou)
• Changing security regimes after 9/11
• IDEF process mapping of security measures
• Panel data for port inputs and outputs
• DEA and not SFA efficiency analysis
Robust AGV Scheduling(Panagiotis Angeloudis)
• Robust optimisation of assignment of jobs to AGVs
• Simulation of an automated container terminal
Managing supply chain uncertainty(Gianluca Barletta)
• Sources of uncertainty
• Technological solutions (for example, RFID)
• Organisational structures and information flows
O1move container on internal truck
A12
move container quay crane-internal truck
A11truck in position for delivery
container on truckImportRTGRegular TEU
GPS; RFID; WLAN; CCTVDrivers
Safety level 1
quay craneinternal truck
Document and payment clearance
workersEDI
Optimisation of transport and stacking in yards (Nang Laik)
• MIP formulation of movement and stacking problem
• Exact and heuristic solutions
Global energy supply security(Konstantinos Zavitsas)
• Construction of a global network model for shipping
• Application to oil and gas
• Analysis of security
Contents
• Background
• Stability at a single terminal
• Stability for two terminals
• Stability for N terminals
• Stochastic stability
• Conclusions
Inventory in the supply chain
Time
Cum
ulat
ive
num
ber
of it
ems
Production
Shipments Arrivals
Consumption
Waiting for transport
Number being transported
Waiting for consumption
Travel time
Wait
Wait = Travel time + Max headway
Bus bunching
Newell and Potts (1964) model:
– Applied to study bus service reliability– Passengers arrive more-or-less continuously but depart in batches when a bus arrives– Stability requires that passengers board at a rate that is more than twice the rate at which they arrive– Instability leads to bus bunching, longer queues and longer waits
Model applied to a container terminal:
– Passengers = containers, buses = ships– Containers arrive at terminal continuously– Ship arrives late => Containers stack up– Longer loading time => Ship leaves even later– Fewer containers for next ship => Next ship leaves early– Ship bunching may occur– Ship bunching increases average yard inventory
Container terminals
Arrival and departure headways
• = Ratio of arrival to loading rate of containers• h = Arrival headway of vessels (assumed to be uniform)• =nth departure headway (arrival headway at the next port of call)
• (1)
• (2) , assuming
)(nd
)( )1()()( nnn ddhd
)1()(
11
1
nn dhd
1
Deviations from equilibrium
• At equilibrium: (3)
• Implies d = h
• Subtracting equation (3) from (2):
(4)
dhd
11
1
))(1
()( )1()( dddd nn
Stability
(4)
• Positive deviation from equilibrium departure headway leads to a subsequent negative deviation from the equilibrium departure headway
• Stability requires that , otherwise ship bunching eventually occurs
))(1
()( )1()( dddd nn
5.0
Single terminal example
Simulation:
– Port where ships call every 24 hours, h=24
– Deviation to the initial departure headway
– It is assumed that or
25)0( d
3.0 0.6
Successive headways (1)
0
10
20
30
40
50
60
70
1 2 3 4 5 6 7 8 9 10
Period
De
pa
rtu
re h
ea
dw
ay
s
σ = 0.3
σ = 0.6
Stability for two ports of call
)1(2
2
2)1(1
21
1
21
)1(2
2
2)(1
2
)(2
)1(1
1
1
1
)(1
1)1)(1()1)(1(
1
11
1
11
1
nnnnn
nn
ddhddd
dhd
(5)
(6)
Two port example
Simulation:
– Two ports in series
– At the first terminal h=24 and
– It is assumed or
25)0( d
3.0,3.0 21 3.0,6.0 21
Successive headways (2)
0
10
20
30
40
50
60
70
80
90
1 2 3 4 5 6 7 8 9 10
Period
Dep
artu
re h
ead
way
s
First terminal
Second terminal
First terminal
Second terminal
σ1 = 0.6, σ2 = 0.3
σ1 = 0.3, σ2 = 0.3
Stability for N terminals
For N terminals, stability requires:
which implies for i = 1 .. N
1(1 )
i
i
0.5i
Stochastic stability
Travel time may vary
The arrival headway will now be considered random around mean h:
))(1
()(1
1)( )1()()( ddhhdd nnn
Departure headway variance
• For 1st port of call:– Departure headway variance:
– Finite variance requires:
• For 2nd port of call– Departure headway variance:
–Finite variance requires:
5.021
hd
vv
121
21
22 )
121(
21
1vv
5.02
Headway variance for 4 ports in sequence (h = 24 +/- 1 hours, with uniform distribution)
Headways Mean Simulated variance Calculated variance
Arrival at 1st port 24.0151 0.3387
Arrival at 2nd port 24.0147 0.8333 0.8467
Arrival at 3rd port 24.0141 2.9950 3.0693
Arrival at 4th port 24.0139 13.7513
3/1321
Stochastic stability (1)
Headway variance for 4 ports in sequence(h = 24 +/- 1 hours, with uniform distribution)
Headways Mean Simulated variance Calculated variance
Arrival at 1st port 24.0151 0.3387
Arrival at 2nd port 24.0148 0.6689 0.6774
Arrival at 3rd port 24.0143 1.6537 1.6934
Arrival at 4th port 24.0138 4.8555
4/1321
Stochastic stability (2)
Conclusions
• Loading speed determines schedule stability• Schedule instability leads to bunching, which increases average yard inventory • The condition for schedule stability is that the ratio of the arrival to loading rate should be less than half• Analytic solutions for departure headway variance at the 1st and 2nd ports of call derived•Next: Look at global container liner stability
Thank you for your attention!