Investment dynamics for a congested transport network with
competition: application to port planning
F.M. Sanders
Delft University of Technology
P.O. Box 5048, 2600GA Delft, The Netherlands
F.Sanders@CiTG.TUDelft.nl
RJ. Verhaeghe
Delft University of Technology
P.O. Box 5048, 2600GA Delft, The Netherlands
R.Verhaeghe@CiTG.TUDelft.nl
S. Dekker
Delft University of Technology
P.O. Box 5048, 2600GA Delft, The Netherlands
S.Dekker@CiTG.TUDelft.nl
ABSTRACT:
Containerization has caused a revolution in design and operation of freight
transportation modes and cargo handling facilities. Ports, as important nodes in an
extensive network of transport facilities, have to make strategic decisions in the face of a
strongly growing market and volatile demand. The investment decision making has to
incorporate scale effects, congestion, competition, and a financing and pricing which has
to account for an increasing privatization of port operations. Such port planning
requires to address the development aspects of the transport network as well as the
investment dynamics of the development of the port node(s). A dynamic investment
modeling is proposed in this paper which addresses congestion, scale effects, competition
and self-financing, and which can be linked (at a later stage) to a specific freight
transport model.
KEY WORDS: strategic decision making, investment dynamics, competition, congestion
1. INTRODUCTION
Containerization has caused a revolution in design and operation of freight transportation
modes and cargo handling facilities. This caused an integration of ocean and land
transportation services making logistic chains more flexible (i.e. less bounded to certain
transportation routes). As a result, international freight flows have become more volatile
causing a constant pressure on ports to remain competitive.
An increasing privatization of ports puts pressure on cost recovery and on pricing,
influencing the attractivity of the port, determining its market share, and in turn the
viability of investments. Port investments are further characterized by large economies
of scale, and need to be made in the face of a strong growth of the transport market
(double over the next 10-15 years). Congestion in ports as well as other links in logistic
chains forms an other important factor determining the attractivity of the particular
chains.
Planning for a port is thus faced with an increasing number of uncertainties, and needs to
consider developments in the transport network (e.g. hinterland connections and
congestion) and investments in other ports. The port can be considered a node in a
transport network with competition, which faces a dynamic situation concerning the
timing and sizing of capacity expansions.
Modeling of this dynamic system is indicated to map out the many interactions. Existing
models address the port expansion problem and the freight movement in the network
separately. The majority of the port planning models (e.g. Rotterdam) use trend
extrapolation and a constant market share. Freight transportation models make an
allocation of demand for freight over a network without considering the investment
dynamics of the (port) nodes.
The present paper proposes a modeling approach which integrates the development of the
port node with the competition over the network. Section 2 schematizes the
transportation problem and the dynamic investment problem of the port node. This is
illustrated for the ports of Rotterdam and Antwerp which will be used in the application.
Sections 3 and 4 describe the proposed modeling and some sensitivity analyses. Section 5
summarizes observations and conclusions on the modeling and discusses further
expansions.
2) PROBLEMS ANALYSIS AND PLANNING APPROACH
2.1 Transport network
Several European ports are involved in a strong competition to serve the European
hinterland. The competition focuses in particular on the industrial heart of Europe (the
Ruhr basin area, Southern Germany and the area of the Alps). Major container routes in
the world are indicated in Figure 1. More specifically Figure 2 illustrates the European
situation.
Lo ed oe
te CS, @ Trans-Siberian
5 ri R ayy «
ie a. SO, 8 railway
-=pen*
N es,
°
Figure 1: Major container transport routes
Figure 2 : Competition for the European hinterland
The Port of Rotterdam serves a hinterland that includes the industrial heart of Europe. Its
main competitors for this hinterland are the North Sea ports Hamburg and Bremen in
North-Germany, and, particularly, Antwerp in Belgium
Ports have responded to the growing competition with large investments. Since 1970,
Rotterdam is improving its position in transport-logistic chains for container flows.
Expansion of hinterland connections such as the construction of a rail connection
between Maasvlakte 1 and Germany (the so-called Betuwe line; investment cost €4.7
billion) is considered an important asset for Rotterdam.
In the 1990s, a large-scale port development program (the so-called Rotterdam Mainport
Development Project) has been initiated to support both port competiveness and regional
economic development. A major part of this program is a second seaward expansion of
the port (the Maasvlakte 2 project) with 1,000 hectares; sixty percent is reserved for
container activities. The need for port expansion strongly depends on efficiency
improvements that can be realized by the container terminals.
A fast development of the South-European ports, such as those in Italy, might become an
additional threat for Rotterdam, particularly if their hinterland connections are developed
as well. The rising demand for the Trans-Siberian railway is another potential threat for
Rotterdam. This railway connection bypasses the maritime trajectory via, for instance, the
Indian Ocean and the Mediterranean Sea and may serve as a faster alternative for
container shipments between Asia and Europe.
Figure 3 presents a more abstract schematization of the transport network. Essentially a
set of origins and destinations are differentiated which can be reached via alternative
routes containing a
maritime- and land
: potential hinterland
trajectory and an hinterland destination
associated port. connections node
Transporters decide on
alternative logistical =
chains to connect a —
. ra node
particular origin and
destination on the basis
of the attractiveness of
the alternative chains
(see section 2.2).
Rotterdam port node
‘ \
{
;
Sea trajectories
Figure 3: Schematization of the maritime-land freight
transport network
2.2 Route choice
The choice for a particular route will be based on the performance of the total chain and
includes factors such as out of pocket costs, congestion, reliability and scope possibilities.
Out of pocket costs together with the value of time lost in congestion can be considered
as a main factor.
The choice problem of the shipping companies can be modelled with a discrete choice
model. The shipping companies choose the logistic chain and the associated port based
on the utility for each chain. A main variable in this utility is the generalized transport
cost for the different logistical chains.
Following this approach the utility for the shipping companies to choose logistical chain
(port) i can be written as
U; = BiXet 6
with X;: transport cost
€; 1 error term representing measurement errors and choice attributes not
modelled
(the model can also be more detailed by specifying a separate utility function for each
company; more data on the individual choice of the companies is then needed).
The probability for choosing a certain chain (port) can then be expressed as:
_ _exp(U;)
: YexpU,)
i=l
Data to estimate such model can consist of revealed choices by the companies in the past
or/and stated preference data collected using a survey. Data on revealed choices is very
hard to get; the discrete choice model used in the present study has been based on stated
preference (CPB, 2004).
Basically for each origin-destination pair such choice problem can be formulated. The
demand through a particular port is then the sum of the flows of the logistic chains using
the port.
2.3 Investment timing & sizing
General
The ongoing competition between the North Sea ports has triggered a spiral of
investments both in port handling capacity as well as hinterland connections.
Since 1970 Rotterdam has been improving its position in transport-logistic chains for
container flows by expansion of its capacity and the hinterland connections (latest is a
new freight rail link with Germany). A new expansion (Maasvlakte 2) is being planned.
Antwerp has been constantly expanding its capacity and presently a deepening of the
Scheldt river is planned to improve accessibility to the port.
The “decision space” for the two ports is large because of the strong expected growth and
large economies of scale. A major factor in the planning is the sensitivity of the
performance of the ports to competition and the influence of pricing. Uncertainty on the
long term demand projections is an other factor to consider. Under such circumstances,
what is an optimal investment strategy?
Manne/Freidenfels have developed an optimal expansion concept in which a trade-off is
made between capital financing costs and scale effect. Such optimization needs to be
expanded for the present capacity expansion problem because there is a price-demand
feedback and there is a cumulative scale effect (inter-related expansions). The optimal
expansion problem, starting with Manne, is elaborated below.
The performance of port development in function of the chosen investment strategy is
modeled in section 3 and the sensitivity tested in section 4.
Manne/F reidenfels
Figure 4 illustrates the classic approach of a capacity expansion problem with linear
demand and independent expansions.
Manne developed an optimal solution for a demand with growth rate g with equal
expansions for an indefinitely growing demand at an annual growth rate g. For a cost
function of the type C = ax” (scale coefficient @ ) and interest rate r, the optimum is
defined by (Manne, 1967, Freidenfels, 1981):
Demand And
Capacity
a
Total Available °
Capacity x
Demand
Dit) = gt
fi
x |
' |
x i
f H \
x ! i
1 1 t
1 4 4
x. 2x 3x Time, t
g g ry
Figure 4: Capacity expansion to meet a linearly growing demand
Optimal interval between
capacity additions, t*, in
years
Ara) tt +
0 O40 060 © 0.70 1.00
Scale factor a
Figure 5: Optimal relationship between scale factor, interest rate and
expansion interval
With ¢° = optimal time interval. This can be solved iteratively. The optimum for a
particular scale factor @ and interest rate r can also be determined graphically as
presented in Figure 5.
The capacity expansion problem can be formulated in a recursive format and solved by
Dynamic Programming for the non-linear demand case.
Price feedback
In general, and in particular for the port planning problem at hand, there will be a
relationship between the price of the service resulting from the expansions and the
demand for the service. In the present planning problem competition emphasizes such
relationship. The price feedback is illustrated in Figure 6. In the proposed modeling in
section 3 such feedback is explicitly taken into account in the dynamic modeling (see
further)
demand for service supply of costs
(growth rate, elasticities, capacity
market share) 4
/
/
price /
User costs for Sis /
™ subsidy
logistic chains
Figure 6: Schematization of the feedback between price
and demand
Cumulative expansion
From analysis of a set of container ports de Neufville and Tsunokawa (1981) conclude
that there are strong gains in productivity in function of increasing total size of the port.
The overall productivity increases when the port is expanded or in other words the unit
cost per container decreases. This can be interpreted as a cost function which has
increasing economies of scale with increasing capacity. In the present analysis this has
been approximated with a Manne type expansion decision incorporating increasing
economies of scale (decreasing factor a) for expansions on an increasing total capacity.
If everything else stays the same (e.g. no price feedback), such decision making will
result in increasing sizes of subsequent expansions.
2.4 Congestion
A typical representation of congestion for highways exhibits the behavior as indicated in
Figure 7. Travel time is a function of transport use N, and capacity K. A much used
functional format in applied research, to represent the use of capacity and congestion, is
(= fy (1+b(2)')
with:
ty: free-flow travel time
b, k : parameters (e.g. b=0.15 and k=4)
The cost for transport is the product of
travel time (t) and the value of time
(vot). The cost (ac) is then:
Service
time
N
ae = vor ty *+b* (GY)
Considerable information on
congestion behavior is available for
highways; the congestion behavior for >
a port is more complicated, in the design Flow
present study a similar functional capacity
format for time spent in the port has
been used as for a highway.
Figure 7: Highly non-linear effect of
congestion
2:5 Planning under competition
Considering the above system characteristics an overview of the planning concept for
port expansion is presented in Figure 8. The items with particular relevance to
competition are indicated. The following observations can be made
e Structural and non-structural measures form an input to the balance of supply and
demand; choices in the transport network influence the demand
e The utilization rate represents the effectiveness of the port facility and together
with the cost determines the price for service; this price in turn forms an input to
the competition over the network (allocation of flow over the network)
e Costs and revenue generated at the particular price allow an evaluation of the
commercial performance at a particular port
e Costs and the direct, indirect and external effects are input to an economic
evaluation; although the infrastructure service network forms a market with
individual/private operators, there is still a potentially substantial involvement of
the government; in the schematization of the costs and benefits a differentiation
should then be made between who makes the costs and —receives the benefits.
E.g. a considerable portion of the users may be foreign operators, for those the
user surplus should not be accounted towards national welfare for The
Netherlands
A main characteristic of the infra service network with competition is the
commercial- and economic viewpoint; together they establish the viability of an
expansion project (e.g. for Rotterdam)
In the present analysis the focus is on the direct effects.
Supply- and
demand
measures
=
=
Supply of Demand
capacity
Competition
or service
in transport
network
+
Utilization rate; emenfs
throughput
Cost aia ey
assessment tion I
, y
i Prive _--.!
Ay formation
: ‘i
t Direct
A effects
+ ’ Indirect and
too ? i le=
ay y external effects
Commercial Economic
evaluation evaluation
=
Overall viability of the
(expansion) project
Figure 8: Concept for planning under competition
3: MODELING
As can be derived from the context of the transportation problem in Figures 2 and 3, the
geographical positioning of the ports with respect to origin and destination, and the
associated hinterland connections, play a significant role in the planning of the ports. The
present analysis focuses on the interactive investment dynamics of two ports, Rotterdam
and Antwerp, which have a high degree of substitution. Their main (joint) hinterland is
considered and only the main mode of hinterland transport, which is truck transport.
The modeling concept is presented in Figure 9:
A simulation of port demand in relation to its capacity is considered over 30
years, starting from the present condition. Present total demand is 10.3 million
TEU (Rotterdam 6.1, Antwerp 4.2) with a projected increase (CPB, 2004) to 31
min TEU over the next 30 years.
The allocation of this total demand to the two ports (logistical chains) is based on
the total generalized cost per TEU, using the discrete choice model. This unit cost
is composed of
- a cost for recovery of port investments,
- a cost associated with the time spend in the port, including congestion,
and
- a cost associated with hinterland transport, including congestion.
An important variable is the capacity utilization rate, defined as the ratio of actual
flow through the port over capacity. The utilization rate forms the main input to
determine port congestion.
A new capacity expansion step is triggered when the utilization rate reaches a
particular maximum threshold value. A certain amount of reserve is however
necessary for peak load handling. Present practice maintains a maximum
utilization rate of about 90 %.
The utilization rate is a control variable: it may be decided to lower congestion
levels in order to attract a larger market share.
The capacity expansion strategy forms a main input to the modeling, one of the
possibilities is to use the “expanded Manne method” as elaborated in section 2.3,
to determine the optimal expansion step, taking into account a progressive scale
effect in combination with price-demand interaction.
The hinterland connection is represented by the distance to the main hinterland
centre and the cost for truck transport. Based on a report on the present status of
the hinterland connections a present utilization rate of 70% has been adopted for
those transport links and the highway congestion formula is used to compute
congestion. A gradual expansion of this hinterland capacity has been
incorporated from year 10 of the simulation. A congested hinterland connection
will have a strong effect on the competiveness of the logistical chain.
An envisaged further detailing of the model includes a specific modeling of the
transportation network, including different transport modes using a joint modeling
with a specific freight transportation model, see further section 5.
The data for the different components of the model have been derived from several
publications. Important input data is associated with the choice modeling for shipping
companies. There is practically no consistent revealed data set available to estimate the
choice model parameters; there have been many changes in technology and logistic
concepts which make data inhomogeneous and even obsolete. In the present analysis a
recent stated preference data set has been used to estimate the choice model parameters.
Due to the lack of valid empirical data describing the total system, further calibration and
validation of the model will need to be based on validation of sub-components and
detailing of system concepts (see section 5 for improvements/expansions).
Investment
lf
Capacity expansion
strategy Rotterdam
Unit cost Capacity Port residence +
logistical chain Rotferdam congestion cost
Rotterdam
Upgrading
; hinterland
ae yy Utilization rate muneriand transport infrastructine
Growin a” Roesrdat Rotterdam cost + congestion Rotterdam
Stow:
overall ™——__Ll——_"
demand
Demand | Upgrading
T ————p Utilization rate Hinterland transport hinterland
_ cost + congestion jnfeastructine
Antwerp
J a, i, residence +
logistical chain Antwer \ congestion cost
PN
N ‘apacity expansion
\ soins strategy Antwerp
recovery
Figure 9: Conceptual systems diagram for the modeling
4. SENSITIVITY ANALYSES
The sensitivity of the competition between the two ports for the particular investment
strategy is an important input to decision making. Several simulations have been made to
test such sensitivity.
Figure 10 illustrates the impact of a “regular” expansion strategy which is similar for both
ports: expansion at a threshold of 90% utilization rate, a fixed step expansion, and a
gradual upgrading of hinterland transport to keep up with the rising transport volumes.
Figure 11 illustrates the composition of the price (€/TEU) for the logistical chains.
1: capacity Rotterdam 2: capacity Antwerp 3: volume Rotterdam 4: volume Antwerp
22.004
11.004 t eae / =
_— |
L.. peed
ee | A
| oe
a omit
0.00
0.00 6.00 12.00 18.00 24.00 30.00
Figure 10: Development performance for a regular expansion strategy
1:hinterlandcostRotterda 2: portcongestioncostRott 3: portinvestmentcostRot 4: totalunitcostRotterdam
350.004
usaf J
Ss
0.00 6.00 12.00 18.00 24.00 30.00
Figure 11: Composition of the total unit cost for the Rotterdam logistical chain
The largest contribution comes from recovery of port investment. Capital investment has
been annualized over a period of 30 years. The total unit cost is declining over time due
to economies of scale. The port investment component shows some abrupt changes at the
time when an expansion is made: at that time the cost for the expanded facility has to be
born by the current transport volume.
Figure 12 illustrates the situation when the hinterland connection for Antwerp is not
adapted to the increasing volume: an increasing congestion cost for this logistical chain
causes a substantial decline of market share for Antwerp.
1: capacity Rotterdam 2: capacity Antwerp 3: volume Rotterdam 4: volume Antwerp
22.004
LJ 37
/ 3 [+—2: 2
11.004 pac
1 =
¢$-—_—_————_} 23 -—2
ae Ss a ae
<3 a 4—
4 —
el
0.00
0.00 6.00 12.00 18.00 24.00 30.00
Figure 12: Loss in market share for Antwerp due to congested hinterland
Figure 13 illustrates the expansion for the two ports based on similar criteria and using an
optimal expansion strategy based on an “expanded Manne/Freidenfels”. The expansions
are larger than what could be expected based on expansions in the past (Figure 10), and
are increasing into the future, associated with a progressive scale effect.
Such large expansions do not take into account the uncertainty in the long term
projections. Figure 14 and 15 illustrate the impact of an (unexpected) stabilization of
the growth in demand. An expansion of Antwerp port which is still based on the
previous growth trend is the main cause for a collapse of market share of Antwerp port.
A decrease in market share has a strong multiplier effect on the unit cost.
1: capacity Rotterdam 2: capacity Antwerp 3: volume Rotterdam 4: volume Antwerp
22.004
11.004 i 3 |
1+} ga |
SF a
—|
= y__——
a |
0.00
0.00 6.00 12.00 18.00 24.00 30.00
Figure 13: Port development based on an optimal expansion strategy (expanded Manne)
1: capacity Rotterda 2: capacity Antwerp 3: volume Rotterda_ 4: volume Antwerp _5: total demand
22.004 /
5
tS 2 2
eal i —
3s |
: = eae ee
sees | | 4 |
2 fa
_ | 7
0.00 —
0.00 6.00 12.00 18.00 24.00 30.00
Figure 14: Effect of an unexpected stabilization (from year 12) of the demand
1: totalunitR otterdam 2: totalunitcostAntwerp.
1000.004
500.00 4
= |-2
Sa ee ee
e a
——<$—S>} SS
0.00
0.00 6.00 12.00 18.00 24.00 30.00
Figure 15: Effect of an unexpected stabilization of demand on the price/cost of the
logistic chains
5. DISCUSSION
For the strongly growing market and volatile demand for port service, port development
appears particularly sensitive to alternative port capacity expansion strategies as well as
the effectiveness of hinterland connections.
The present modeling and test simulations give confidence that using a system dynamics
modeling a dynamic planning model can be constructed with more functionality than
present “fixed market share” models, and that such model can play an important role in
clarifying the effects of different port development strategies and assist in the
determination of an optimal investment strategy .
A further upgrade/expansion of the model structure and data base will be necessary in
order to prepare an established planning model for practical use. The following
upgrade/expansions can be mentioned:
1) port congestion: port congestion is an important factor in strategic port
planning. An increased insight in port congestion and relationship to capacity,
considering the maritime/nautical as well as the land side of the port transfer
processes is needed to support strategic planning for the port. This could be
established using simulation analyses with detailed models.
2) Scale effect: scale effects, especially in a strongly growing and volatile
market, play a most important role in port expansion planning. A more
detailed description of scale effects is required. This is also related to the
choice process of shipment companies.
3) Choice process: factors other than generalized cost play a role in the choice
for a particular logistical chain; such are reliability, port approach time, and
the potential outlook for further development of the port and business
opportunities. The discrete choice model can be further elaborated to include
such factors. This may be linked to an expanded modeling of port features.
4) Transport network modeling: a strategic port planning tool will need to
address the important features of the network transport system and associated
options such as the different modes of transport, inter-modal exchanges, short
sea shipment (hub and spoke system), different product groups, etc. Specific
models (such as SMILE, Tavasszy, 2003) are available to describe freight
transport over a network in response to a particular origin-destination trade
network. The combined planning for network aspects and time dynamics
could be addressed by linking such specific freight transport model with a
dynamic investment model as described in this paper. The details from the
transport network could be transferred to the strategic investment model using
repro-functions.
5) Strategy formulation: the competition for port service comprises a limited set
of suppliers (oligopoly); strategic decisions by individual suppliers can
strongly influence the market situation; strategic alliances may be made (as
suggested in some European strategy reports) addressing types of goods,
routes, modes or infrastructure facilities, in order to reduce uncertainty and
improve overall effectivity. Game theory may provide useful approaches to a
systematic formulation of strategies.
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Access route to the port of Antwerp
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