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!