INTRODUCTION : Container Revolution
Urban intermodal container
terminals: The entropy
maximizing facility location
problem– The world needs sustainable and reliable supply chains

Seminar on Human Society and Risk: A focus
on Transportation and Disaster
Collins Teye and Michael Bell
Institute of Transport & Logistics Studies (ITLS)The University of Sydney Business School

The University of Sydney

Page 1INTRODUCTIONThe University of Sydney

Page 2INTRODUCTION : Road
– OPTION 1 : Use truck to transport the containers– Ports are part of Sydney’s urban fabric

A Warehouse inWestern Sydney

Source: Sydney Ports Corp
The University of SydneyPage 3

The University of Sydney

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INTRODUCTION : RailINTRODUCTION : Intermodal Transport

─ OPTION II : Use trains to transport the containers

─ OPTION III : Use intermodal transport
Destination

Economies of scale

IMTThe University of Sydney

Page 5INTRODUCTION : Key Research Question

The University of Sydney

Page 6INTRODUCTION : Why is Location Important?

─ Where are the best places to locate IMTs?
Destination

─ The location of an IMT determines its viability
Determines the volume of cargo likely to use the IMTCargo volume is crucial to make an IMT viable─ Influence rail mode share
The higher the use of the IMT the higher the share of rail
─ Determines the number of trucks that be taken off the road
Safer for other road users
Less road congestion, especially around the port
Less greenhouse gas emission, better environment, more sustainable

IMT
Where is the best place tolocate this terminal ?

PortThe University of Sydney

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The University of Sydney

Page 8INTRODUCTION : Why the need for Intermodal Terminals?

INTRODUCTION : Advantages of IMTs

─ In Australia, containerised trade by volume is set to increase from 6.5 million
in 2011 to 11 million TEUs (containers) by 2020 (Shipping Australia, 2011)

─ ADVANTAGE I: Economies of scale of rail

─ Trucks currently accounts for over 86% of container trips to and from theports (Shipping Australia, 2011)

─ Rail has high carrying capacity, and─ The larger the volume the cheaper to it is to use rail

─ Poor Management of empty containers: import, export imbalance─ Congestion around ports with safety & environmental related problems
Destination

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Page 9INTRODUCTION : Advantages of IMTs

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Page 10INTRODUCTION : Advantages of IMTs─ ADVANTAGE II: Economies of distance of rail

─ ADVANTAGE III: Accessibility─ Less access by rail (can only reach few areas)─ Flexible and easier access by trucks

─ Rail is cheaper for long distance trips
─ Rail is much greener and safer to other road users

Intermodal transport = Combined strengths of rail and truck

Unit cost

Truck
Break-evendistanceRail = Exploit economies of scale + Economies of distanceRail

Truck = Efficient and flexibility of local pick-up and delivery

Distance
Truck ischeaper

The University of Sydney

Rail ischeaper

Page 11

The University of Sydney

Page 12INTRODUCTION : Advantages of IMTsINTRODUCTION : Three key IMT markets

─ ADVANTAGE IV: Empty containers─ Empty container storage at IMTs
─ Efficient management of emptycontainers

── ADVANTAGE V: Warehousing & distributioncentres
─ Warehousing can be preformed at IMTs
─ Small/medium exporters to consolidate
their products for export─ As a distribution centre forcustomers/retailers

The University of Sydney

3 Key markets
─ A : Regional markets (e.g. moving cargo from Sydney to Melbourne)

Source: Russell, L., 2007; Meyrick, 2006

Page 13

The University of SydneyINTRODUCTION : IMTs as Transfer Nodes

MAIN RESEARCH QUESTIONS─

1. How many IMTs?

3 Key markets
─ B : Exports
─ C : Imports

Page 14

Metropolitan IMTs for IMEX markets

2. Where should they be located?

─ Sydney leads Australia in metropolitan IMTs
3. What is the likely demand or usage of the IMTs?
4. What are the likelihoods of the IMTs attracting value adding activities,
such as warehousing and empty container storage?

Source: Russell, L., 2007; Meyrick, 2006
The University of Sydney

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The University of Sydney

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FACILITY LOCATION PROBLEMS

LITERATURE REVIEW : Qualitative Methods
Example : Simple Score Method─ The problem of finding the best locations of intermodal terminals can beplaced in the class of Facility Location Problems (FLP)─ List the candidate sites (e.g. Moorebank, Enfield, Eastern Creek)

─ FLP deals with finding the best placement of facilities and the allocation ofdemands to the facilities to optimise a given objective

─ List the relevant factors (e.g. Market, Transport, Setup Cost)
─ Score each site (e.g. 0-100 scale) on the factors
─ Select the site with highest average or maxmin score

2 Main Approaches

Qualitative

Quantitative

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MarketTransport

Setup cost

Ave Score

Moorebank

70807073

Enfield55756063

Eastern50609067

The University of Sydney

Page 18QUALITATIVE METHODS : Limitations

LITERATURE REVIEW : Quantitative Methods

─ The preference of one alternative or criterion over the other is very subjective,
based on the feelings of the analyst or decision-maker─ The usual approach in the facility location literature is Mixed Integer Linear
Programming (MILP)─ Different analysts might provide different weights leading to possibly entirelydifferent site selections.

─ So far research work on IMTLP are for location of Regional IMTs and based onMILP techniques─ No idea how the new IMT competes with existing IMTs or no IMT (road direct)

─ The metropolitan Intermodal Terminal Location Problem (IMTLP) is a new area

─ No information on the usage of the terminal and transport costs, which are crucialfor cost and benefit analysis
─ No traffic impacts assessment: A facility like this affects and is affected by roadnetwork conditions
─ No environmental assessment as usage is unknown
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The University of Sydney

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LITERATURE REVIEW : Quantitative Methods

LITERATURE REVIEW : Quantitative Methods

─ Arnold et al. (2001) provided the first mathematical model for the IMTLPIs the use of MILP models appropriate?

─ Almost all MILP formulations are based on the following assumptions:─ The general problem composed of two sub-problems:─ Location problem: Hard to solve─ Routing problem : Relatively easy to solve─ Solving both simultaneously : Much harder─ The origin (where the containers are coming from) and destination (wherethey are destined) container flows are known and not affected by the IMT
locations or changes in transport network conditions
─ The transport costs by all modes are known and also not affected bywhere the IMTs are located.

─ The Location problem deals the best way of selecting p from the set of T
candidate IMTs─ The Routing problem deals with the best way to route the cargo (origindestination demand) through the IMTs or directly─ No treatment of empty containers

─ The Routing problem a choice problem

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Page 21GAP IN THE LITERATUREThe University of Sydney

Page 22GAP IN THE LITERATURE

Problems with the Mixed Integer Linear Programming (MILP) Approach:
Problems with Mixed Integer Linear Programming (MILP) Approach:─ Solutions are ‘All-OR-Nothing (AON) ‘ in nature─ We expect some form of split between the 2 modes, say 50 or 60% forintermodal transport, or vice versa

─ MILP solution results in shippers making identical decisions in identicalcircumstances─ Even if the cost are the same, we will have either all using road direct transport(truck only) or all using intermodal transport
Destination

─ Also we can’t capture all elements of costs or all factors affecting the decision
process─ The Routing problem is actually a choice problem (intermodal vs road direct)

Assume the IMTis located
The University of Sydney

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The University of Sydney

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GAP IN THE LITERATURE

METHODOLOGY : Entropy Maximization
─ A technique first introduce in statistical mechanics, to relate macroscopic, andmeasureable properties of physical systems to a description at the molecular oratomic level

Can we embed a choice within the location model?
─ Entropy Maximization : Allows us to embed logit models within location models

─ Main Concept: To find the most likely micro state of an object given information
about the macro state of the system.

─ More flexible and behavioural than MILP models
─ More efficient to solve than MILP models

─ Maximum entropy has been shown to provide the least biased estimate given
the information available (Jaynes, 1957a, 1957b).

─ Can approximate MILP models at the extreme

─ Relation to our problem:
─ The system of interest : Intermodal terminals (IMTs)─ The micro states of interest : The locations of IMTs and their usage

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The University of Sydney

Page 26MAXIMUM ENTROPY FACILITY LOCATION PROBLEMMETHODOLOGY : Basic Entropy Maximization Model (BEM)

Our Model : MIMTLP (Metropolitan IMT Location Problem)─ Objective function : Finding the most likely intermodal and road direct flows

─ Our model captures the impacts of empty container parks (ECP) in the location
problemmax  X itj InX itj  X itj    Wikj InWikj  Wikj iI kK jJ iI tT jJ─ Efficient management of empty containers (storage, use and re-positioning) isgenerally considered one of the key driving force behind the development
MIMTs (Meyrick, 2006; Russell, L., 2007; AHRCR, 2007)

All states ofintermodal flows

─ MIMTLP deals with the use of exactly one IMT in the intermodal transport chain─All states of roaddirect flows

─ We are interested in the most likely state for each mode

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

X itj

The cargo flow transported from origin i through IMT t to destination j

Wikj

The cargo flow transported by road direct from origin i to destination j using ECP k

The University of Sydney

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METHODOLOGY : Entropy Maximization

METHODOLOGY : Solving the BEM

Basic Entropy Maximization Model (BEM)─ Hard to solveL  max  X itj InX itj  X itj    Wikj InWikj  Wikj i
It

Tj

Ji

Ik

Kj

J


Objective function

Subject to:    ikj W ikj     c itj X itj  C

1

X  q Y i  I , j  J , t T72W  q Y i  I , j  J , k T8Y  p9Y  0 ,1  t  T

10Xitj

ikj

3kij

ttT

 W ikj   X itj  q  i  I , j  J

45kKt T Xitji I j  J6tij

 Wi I j  Jikj

iji I j  J k  Ki I j J t T f Y F─ What actually makes the problem hard to solve are the location variables Yt
─ All constraints associated with Yt are hard constraints
─ If we can find a way of removing the hard constraints, the problem can be mucheasier to solve or least provide some insighttttT─ There is no available software for solving BEMtitj

 0 ;W ikj  0  i  I , j  J , k  K , t  T─ We use the Lagrangian relaxation technique to do this B t  bt t  T

 H k  hk k  K

The University of Sydney

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The University of Sydney

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METHODOLOGY : Solving the BEM

METHODOLOGY : Solving the BEM

Lagrangian relaxation (Relax constraints 1, 2 & 8)

Lagrangian relaxation : Divide & Conquer

L( X ,W )  max  X itj InX itj  X itj    Wikj InWikj  Wikj iI kK jJ iI tT jJL( X ,W ,  ,  )   X itj 1  InX itj  itj   Wikj 1  InWikj  ikj    itj  ikj qijYt   F   f tYt iI tT jJiI kK jJiI tT jJtT

Subject to:

Subject to:

12X  q Y i  I , j  J , t Titj

W  q Y i  I , j  J , k TikjtT5t

WkKikj

  X itj  q  i  I , j  Jt T Xi I j  J

6kijY  p34tij

 Wi I j  J

The University of Sydney

ikj

itj

ij

78

   Wikji I j  J k  Kikj    c itj X itj  Ci I j J t TkK

 f Y FtTt

W

4t

5

9Y t  0 ,1  t  T

10X itj  0 ;W ikj  0 i  I , j  J , k  K , t  TSubject to:ikj

 Xi I j  J6

 B t  bt t  T

 H k  hk k  KPage 31

  X itj  q  i  I , j  J Wi I j  Jitj

ikjY  p

9Y  0 ,1  t  TttTt

 H k  hk k  K   W

10X

itj

3

 B t  bt t  T

7i I j  J k  Kijt Tikjikj    c itj X itj  Ci I j J t T

 0 ;W ikj  0  i  I , j  J , k  K , t  T

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Page 32METHODOLOGY : Solving the BEM

METHODOLOGY : Solving the BEM

Two models : Routing model (RM) + Location model (LM)With some algebraic manipulation, it can be shown that:RM   X itj 1  InX itj  itj   Wikj 1  InWikj  ikj LM      q Y   F   f Y Subject to:

Subject to:W

3iI tT jJ

4kK

5iI kK jJikj

 Xi I j  J6  X itj  q  i  I , j  J Wi I j  J

9ikjij ttTt tttT

10Xikj─ The intermodal flows can be expressed as:

X itj  qijY  pY  0 ,1  t  Tt

 H k  hk k  K   Witjikj

t bt  Bt  exp  citj  itj t bt  Bt exp  citj  itj   Gk hk  H k exp  ikj  ikj tT B t  bt t  T7

i I j  J k  Kitjijt TitjiI tT jJikj

Gk hk  H k  exp  ikj  ikj  b  B exp  c     G h  H exp     tTi I j J t T

─ where 0 ;W ikj  0  i  I , j  J , k  K , t  T

The University of Sydney─ and the road direct flows as:

Wikj  qij    c itj X itj  CPage 33kKtttitj

itj

kKkkkikj

ikj

t and Gk are constants to be estimated

The University of Sydney

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Two Major Extensions

METHODOLOGY : Why the interest in Logit Models?

─ Inelastic demand: The models in the literature and that presented here assume
that the flow of cargo between each origin-destination pair is:

─ The Logit models : Known for its strength in policy testing─ Fit a logit model on the output from BEM to capture the behavioural
mechanism in the choice and use of intermodal terminals

─ Not influenced by where the IMTs are located: Cargo destined for awarehouse can be re-directed to an IMT (change of destination)─ The logit model will provide the means to test the relative weights orimportance of the drivers of intermodal terminals use─ Not affected by changes in policy variables: We expect land use policy (e.g.
re-zoning, rent or labour) and accessibility to influence the destination ofcargo

─ We can also test various policies such a pricing, subsidies, and so on topromote the use of the located terminals

─ Known and unchanged transport costs : No changes in road network conditions
─ Expect to influence and be influenced by where the IMTs are located─ Traffic impact analysis is very important, at least to ascertain if the roadnetwork around the located IMTs have enough capacity to cope with any
additional truck traffic without causing local congestion

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The University of Sydney

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Where we want to get toNumerical Example: MILP problems and EM potential

Know where the cargo are
produced

Generation Models

Accessibility

We use numeric example to ascertain the superiority of the EM over the MILP model interms of location decision and policy testing The data used in the example were randomly generated but constrained by minimum
and maximum values from reports and the literature.

Tells us where they aredestinedDistribution
ModelsThe input data are:

Location & Mode choicemodelsLocation Model (LM)Measures

1. Number of origin zones = 1 (e.g. the container port)

The locations of the IMTs
 Choice of mode (intermodalvs road direct)

Mode Choice (MC)

2. Number of destination zones = 10 zones
3. Number and location of plausible IMT sites = 5

Network Models
Assignment Model

Capture changes in road
network and updates transport
costs

Network Skimming

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4. Number of IMTs to locate = 1

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Results : Choice of location - MILP

Results : Choice of location – Entropy model

The MILP Resulted in IMT 1 as the best site for locating any new IMT with a 50% ofthe market

The MILP Resulted in IMT 2 as the best site for locating any new IMT with a 51% share
The Entropy model do not suffer from ‘corner’ solutions.

Can be observed that all flows from the origin to destinations 1,2,5,6, and 9 went
through IMT 1

E.g. 50% splits of destination 1 demand. MILP would have assigned100% of thedemand to either the road direct or IMT 2 mode

Destination

Cargo (TEUs)

1476

476

2193

193-

3777-

777

4156-

156

5109

109-

-

61019

1,019-

7376-

376

8373-

373

9688

688-

10791-

791

2,484
50%

2,473
50%

Total
Mode ShareThe University of Sydney

4,957

1.20

Road Direct

MILP : Base Run

1.00
Mode share (%)

IMT 1

0.80
0.60
0.40

Cargo (TEUs)

1476

IMT 2
238

Road Direct
238

2193

99930.80

3777

3724050.70

4156

74820.60

51096544

Intermodal

61019519500Road Direct7376

189

187

0.20
0.00
1Destination

2 3 4 5 6 7 8 9 10
Origin-destination movements
Page 398373

116

256

9688

521

167

10791

323468

Total
Mode Share

4,957
51%

The University of Sydney

2,442
49%

EM : Base Run

Mode Share (%)

A Clear demonstration of corner point solution of the MILP

0.50
0.40

69%
59%
50% 49% 52% 53%

49% 50%Intermodal

40%

0.30

Road Direct

0.20

24%

0.10
0.00
12345678
Origin-destination movements

910Page 40

Results : Choice of location – Entropy modelResults : Policy TestingIt determines the demand for each mode probabilistically:Assume we want to testing for policies that can promote more use of the located IMT.

Accounting for the fact that not all factors affecting the choice of mode are captured
in the modelling process

A plausible policy may be road pricing or subsidy for intermodal transport users
Implemented by increasing the overall cost of road direct by 5%, 10%, 15% and 20%

IMT 2

 Keeping the cost of the located IMT unchanged

Destination

Cargo (TEUs)

1476

Road Direct2193

9993

0.80

3777372405

0.70

4156

74820.60

EM : Base Run

238

5109

65

4461019

519

500

7376

189

1878373116

2569688

521

167

10791

323

468

Total
Mode Share

4,957
51%

Mode Share (%)

238

69%
59%

0.50

50% 49% 52% 53%

0.40

49% 50%Intermodal

40%

0.30

Road Direct

0.20

24%

0.10
0.00
12

2,442
49%

34
5678
Origin-destination movements

910

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The University of Sydney

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Results : Policy Testing – Entropy model

Results : Policy Testing – Entropy modelAs we would expect, the intermodal transport share increases marginally as the cost ofroad direct transport increases.

Overall mode share over all origin-destination pairsAlso demonstrate marginal distribution of intermodal share with increasing road directcost.

For the share of flows to destination 1 increased from 50% (base) to 64%

EM : INCREASE IN ROAD DIRECT COST
EM : EFFECT OF INCREASE IN ROAD DIRECT COST
20%Intermodal

Road Direct

0.60
0.76
0.78
0.80
0.84
0.89

Mode Share (%)

0.50

0.31
0.33
0.34
0.36
0.40

0.41
0.42
0.43
0.44
0.46

15%0.500.53
0.56
0.61
0.69

10%

0.51
0.53
0.56
0.60
0.67

5%

0.60
0.62
0.65
0.69
0.75

0.47
0.49
0.49
0.51
0.53

0.72
0.48
0.50
0.52
0.55
0.60

0.51
0.54
0.58
0.64

0.50
0.52
0.54
0.58
0.64

INTERMODAL SHARE (%)

Base

0.70

0.51
0.49

0.53
0.47

0.55

0.63
0.58

0.45
0.42

0.40

0.37
0.30
0.20
0.10
Base

1234567895%

10%% increase from base in road direct cost

15%20%10OD MOVEMENTS
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The University of Sydney

Page 44CONCLUSIONS– IMTs have the potential to improve the efficiency, sustainability andreliability of intermodal (containerised) cargo flows– In a context of many shippers exercising choice, the mixed integer linear
program (MILP) model is inappropriate due to corner solutions– Entropy maximisation (EM) model provides integrated choice models and isrelatively easy to solve

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The University of Sydney

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