International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 4

Number 2

June 2010

235

1 INTRODUCTION

The design process is a complex stepwise series of

strategic decision involving the engagement of a rel-

evant amount of resources.

Therefore, in order to maximise its effectiveness,

a strong need of methodological support is required.

With this aim the research group of the authors

developed different methods and models capable to

support some of these decisions:

− regressive method for preliminary dimensioning

of container terminals;

− sea-side operation combinatorial model;

− synthetic method capable of validating the esti-

mates of the capacity combinatorial model.

It is possible to integrate the models in a chain

taking into account, within a stepwise methodologi-

cal approach, dimensions and manoeuvrability of the

ships, positions of terminals, accessibility, handling

equipment, storage areas, etc.

2 PRELIMINARY DIMENSIONING METHOD

The preliminary dimensioning method allows to se-

lect the parameters most suitable to describe termi-

nals, to determine their dimensional and equipment

characteristics and to verify their production, as well

as to provide inputs, defined in terms of production

or number of ships, for the combinatorial model ca-

pable of evaluating sea-side port capacity (Florio &

Malavasi, 1995).

2.1 Definition of key parameters

Maritime container terminals are infrastructures pro-

vided with equipment for the transfer of containers

from ship to docks and back.

They are integrated into logistic structures of

most commercial ports.

In any terminal fundamental and complementary

activities are identifiable:

1 container loading and unloading;

2 sea-side and land-side (railway and road) stock-

ing operations;

3 traffic management and control;

4 container clearance for international traffic;

5 storage and reorganisation of freight into con-

tainers.

Structures and performances of terminals, de-

duced from a first analysis, may be synthetically rep-

resented in three main clusters of parameters (Noli

& al. 1984) respectively representing dimensions,

equipment and production:

A. Dimensional parameters:

1) Quay length,

2) Total stacking area,

3) Covered stacking area,

4) Uncovered stacking area;

Modelling Support for Maritime Terminals

Planning and Operation

S. Ricci & C. Marinacci

“Sapienza” University of Rome, Rome, Italy

ABSTRACT: The maritime terminal design process is a complex stepwise series of strategic decisions in-

volving the engagement of a relevant amount of resources. In fact operating conditions near the maximum ca-

pacity cause congestion effects with negative consequences on regularity and quality service. Therefore, in

order to maximise its effectiveness, a strong need of methodological support is required. With this aim the au-

thors developed different methods and models capable of supporting some of these decisions: a regressive

method for preliminary dimensioning of harbour terminals and a sea-side operation combinatorial model for

traffic analysis and capacity estimation. They are able to be integrated in a chain of models taking into ac-

count dimensions and manoeuvrability of ships, terminal morphology, handling equipment, storage areas,

etc., with the aim to support the planning process and operational management.

236

B. Equipment parameters:

5) Number of gantry cranes,

6) Number of other cranes,

7) Number of storage cranes,

8) Number of various loaders;

C. Production parameters:

9) Number of handled containers.

10) Number of handled TEU,

11) Number of handled container tonnage.

For these parameters an extensive investigation

on port terminals for data acquisition has been car-

ried out.

2.2 Definition of the area of analysis

The ports analysed are located in Northern Europe

(Atlantic Ocean, Baltic Sea and North Sea) and in

Mediterranean area (Ricci & al. 2008b).

In this area 73 ports, dealing with relevant con-

tainer traffic, have been identified.

For 93 container terminals located in 49 of these

ports useful data have been collected and elaborated.

In Table 1 the amount of observations available

for the analysed parameter is shown.

Table 1. Observations available for analysed parameters

_______________________________________________

Parameters Observation

___________

N°

_______________________________________________

Quay length 93

Total stocking area 91

Covered stocking area 91

Uncovered stocking area 29

Gantry cranes 85

Other cranes 37

Storage cranes 59

Various loaders 57

Containers 19

TEU 72

Tonnage 30

_______________________________________________

2.3 Application of methodology

In the proposed regressive approach an analysis has

been performed on the relationships between param-

eters:

1. belonging of the same cluster (as defined

above);

2. belonging of different cluster.

The amounts of data useful for the correlations

are summarised in a matrix (Fig. 1).

Figure 1 Available observations by couples of parameters

The collected and homogenised data has been

correlated by means of a linear regression obtaining

the correlation coefficients R.

All the values have been filtered with different R

threshold values (0.7 and 0.8).

In Figures 2 and 3 the values of coefficient R of

the regression lines are presented in matrices.

Figure 2: Correlations between couples of parameter with 0.7

as threshold of relevance

Figure 3: Correlations between couples of parameter with 0.8

as threshold of relevance

On this basis it is possible to represent the rela-

tionships between parameters corresponding to

shortest paths on graphs of Figure 4.

Figure 4: Graphs of the relevant correlations with R > 0.7 and

R > 0.8

2.4 Direct and indirect correlations between

parameters

The main feature of the proposed methodology is the

possibility to calculate on a probabilistic basis the

main design parameters (dimensions, equipment,

etc.) by means of the correlations with flow parame-

ters and to calculate flow and equipment parameters

by means of the correlations with dimensional pa-

rameters.

For this purpose it is necessary to determine also

the direct relationships and the indirect ones requir-

ing intermediate parameters to link inputs and out-

puts.

237

For the selection of shortest paths (highest global

correlation) the Dijkstra algorithm has been applied.

Starting from the inputs corresponding to produc-

tion parameters (containers, TEU and tonnage) or to

dimensional ones it is possible to define the tree of

shortest paths with the parameters linked directly

and indirectly.

Different scenarios have been obtained by com-

bination of threshold value (0.7 and 0.8) of correla-

tion parameters with possible input parameters (Fig-

ures 5-11).

Figure 5: Shortest paths starting from the number of containers

(threshold R>0,7 and R>0,8)

Figure 6: Shortest paths starting from TEU (threshold R>0,7

and R>0,8)

Figure 7: Shortest paths starting from containers tonnage

(threshold R>0,7 and R>0,8)

Figure 8: Shortest paths starting from quay length (threshold

R>0,7 and R>0,8)

Figure 9: Shortest paths starting from total stocking area

(threshold R>0,7 and R>0,8)

Figure 10: Shortest paths starting from covered stocking area

(threshold R>0,7 and R>0,8)

Figure 11: Shortest paths starting from uncovered stocking area

(threshold R>0,7 and R>0,8)

2.5 Case study

The regressive method (Ricci & al. 2008b) has been

applied to the pilot case represented by the Darsena

Toscana container terminal in the port of Livorno

(Table 2).

Table 2. Leghorn Darsena Toscana container terminal (2007)

_________________________________________________

Parameters Data

_________________________________________________

Quay length [m] 1.430

Total stocking area [m

] 412.000

Containers [n] 323.708

TEU [n] 500.000

Tonnage [t] 6.677.350

_________________________________________________

On the basis of arrivals and departures of con-

tainer ship to/from Calata Massa, relating to Termi-

nal Darsena Toscana quay, it has been possible to

determine the capacity margin in 2007 expressed in

number of ships per day that are can be moored

alongside the above-mentioned quay.

The comparison between values of dimension,

equipment and production parameters estimated by

the model and real values are summarised in Figures

12-15.

Figure 12 Comparison between estimated and real values of

quay length and total storage area

Figure 13 Comparison between estimated and real values of

gantry cranes

238

Figure 14 Comparison between estimated and real values of

container Lo-Lo and tonnage Lo-Lo

Figure 15 Comparison between estimated and real values of

TEU and gantry cranes

2.6 Remarks

The values of parameters estimated by means of R

threshold (0,7 or 0,8) are comparable, therefore their

choice may be considered not relevant.

The most reliable results are obtained by means

of production parameters as input data, in particular

the number of handled container for the determina-

tion of quay length, total stocking area and gantry

cranes. Indeed the other parameters are strongly in-

fluenced by local organizational issues and for this

reason less suitable to be dealt with in a general ap-

proach.

3 SEA SIDE OPERATION COMBINATORIAL

MODEL

Sea-side port operation, characterised by the overlap

of the traffic of many different ships traffic often

causes congestion effects with negative consequenc-

es on transport service regularity.

In this framework models (Potthoff, 1979) capa-

ble of simulating the operation of sea-side port ter-

minals, of evaluating their capacity and of calculat-

ing the occupation time of the terminal by ships and

its utilisation degree both in regular and perturbed

(because of external causes or the congestion itself)

conditions and of relating it with the quality of the

transport services are very effective and allow to

reach specific objectives:

- operational time saving;

- rational land-use (better planning of sea front);

- prevention of losses due to possible accidents

and incidents;

- sensitivity of performances to variations in port

terminal lay-out.

3.1 Specific research objectives

From the above arise considerations the specific ob-

jectives of the present researches that is build up

models capable of:

1) simulating the terminal operation;

2) evaluating the terminal carrying capacity;

3) relating the utilisation degree of the terminal

with its service quality.

The application of combinatorial synthetic mod-

els to sea terminals (Ricci & al. 2007) requires the

introduction of the factors characterising the ships

(dimensions and maneuvering with related kinematic

and geometric constraints regulated movements), the

terminal itself (different type of basin morphology or

layout as shown on Figure 16).

In order to determine time interdiction between

ship movements entering/exiting maneuvering

movements are divided in 5 phases:

1 Approach to mouth,

2 Access to the channel,

3 Rotational movement,

4 Approach to the quay,

5 Anchorage.

Figure 16 Typical port layouts subjected to analysis

The carrying capacity of the terminal corresponds

to the maximum number of movements allowed dur-

ing the reference time and it depends mainly upon

the following factors:

− time distribution of entering and exiting move-

ments to/from the port and related assignment to

the docks;

− terminal topology defined by the location of

docks and the mouths.

The model approach is based on a constant prob-

ability for the arrivals i.e. a fixed number of move-

ments for each route in the reference time.

This condition well represents both:

− high frequency of arrivals in peak periods;

− usual data availability in the planning phase,

without detailed information on ship scheduling.

This condition is formally defined by an array P,

with dimensions corresponding to the number of the

239

routes in the terminal and single elements p

defining

the number of movements on each route in the refer-

ence time T.

The analysis of the terminal morphology allows

to define the whole set of routes and their reciprocal

compatibility/incompatibility represented in a square

matrix (compatibility matrix) C = P x P, with each

element c

representing the condition of compatibil-

ity/incompatibility between routes i and j.

The possible relationships are:

− incompatibility between two routes with:

a. common final/initial sections,

b. common middle sections,

c. same path but opposite direction;

− compatibility between two routes without com-

mon sections, allowed to be run contemporarily.

The proposed approach allows to calculate the

mean number of possible simultaneous movements n

by taking into account the compatibility of the routes

and their frequency of utilisation:

∑

(1)

where:

− m

= p

x p

if i and j are incompatible;

− m

= 0 if i and j are compatible.

− N is the total number of movements during refer-

ence time T.

In a similar way the mean terminal utilisation

time can be defined as:

∑

⋅

ijij

(2)

where t

is the time during which the route j may

not be run because a ship is moving on the route i

(interdiction time).

The total occupation time can be calculated as:

×=

(3)

In order to take into account the waiting situa-

tions due to simultaneous arrivals on incompatible

routes it is possible to calculate the delay imposed

by the p

movements on the p

movements because

of the interdiction time t

tpp

ijji

(4)

these parameters allow the comparison between

the total utilisation time of the terminal, including

the delays, and the reference time.

The utilisation degree can be calculated with ref-

erence only to the situation of regular running on

routes, as:

U =

(5)

Or reference to the total time, including the de-

lays, as:

(6)

where:

∑

(7)

3.2 Applications and remarks

The model has been applied to five Italian ports

(Ancona, Bari, Brindisi, Gioia Tauro and Livorno)

characterised by three different morphologies (circu-

lar, channel and tree layout).

The results of the model application are summa-

rised in Table 3.

Table 3 Capacity limit for analysed port [movements/day]

__________________________________________________

Port Ancona Bari Brindisi Gioia T. Livorno

__________________________________________________

Observed 33 23 27 18 41

movement

Maximum 61 70 49 40 53

capacity

__________________________________________________

The port with a circular morphology normally

shows a higher capacity limit than the other ones,

due to shorter routes and shorter interdiction times

between movements.

The channel ports show a lower capacity than

ports with tree layout, due to a lower number of ba-

sins that are able to let an early release of common

sections between entering/exiting route.

For these ports largest capacity are related to

number of quay basins and consequently to their ro-

tation basins as well as to the assignment of docks to

ships characterised by less manoeuvrability (e.g. liq-

uid/solid bulk and container ships) in specific part of

ports.

4 COMPARATIVE MODELS

In order to validate on a comparative basis the pre-

vious model and its results, two alternative models

for the evaluation of port capacity have been identi-

fied; they are based on:

− Channel capacity,

− Minimum spacing.

240

These models are characterised by a fewer input

data and able to analyse the particular basin channel

morphology or a specified part of a port terminal

referable to this specific characteristic (Ricci & al.

2008a).

4.1 Models based on channel capacity

The port system is schematically structured into

three parts (Fig. 17):

− the waiting basin, where ships arrive and wait to

enter the channel;

− the entering area, where only the ship approach-

ing the channel is admitted;

− the channel itself.

Figure 17 Port schematisation for channel capacity method

As soon as the ship in the entering area approach

the channel, the following one enters this area at the

minimum separation distance.

The following hypotheses are considered for the

calculations:

− ship arrivals according to the Poisson distribu-

tion;

− infinite capacity of the waiting basin;

− fixed speed for each ship in the channel;

− deterministic separation distance between ships;

− fixed fleet composition;

− permanent communication between ship and traf-

fic controller;

− ship characteristics known in advance by traffic

controller;

− irrelevant wind effects;

− permanent availability of pilots and tugboats;

− 24 hours/day operation;

− balanced entering and exiting flows.

By adopting the Permanent International Associa-

tion of Navigation Congress (PIANC) expression for

the stopping distance is:

2.5

4LD

0.75













×=

(8)

This distance is increased to take into account ad-

verse weather conditions (+50%), approximation in

speed measurement (+40%) and additional safety

rate (+20%):

( )

1.8V0.235

0.75

+××=

(9)

The minimum separation time S

between a cou-

ple of ships I and J further depends upon the speed

strategy adopted in the channel (single speed or mul-

ti-speed) and is calculated at the generic ship I dock,

whose distance from the channel entering is LC

























−×−+

= ;0

MAX)D(LC

)L(D

(10)

The probability P

that the generic arriving ship

has a separation time S

from the following one is

the product P

x P

of the corresponding probability

of arrival of ships I and J.

Therefore the mean service time is:

∑ ∑∑ ∑

I J

JIIJ

I J

IJIJ

PPSPSE(S)

(11)

and the maximum arrival rate, corresponding to

the capacity of the system, according to this method,

may be calculated as:

E(S)

μλ

MAX

(12)

The whole methodology is represented in Figure

18 flowchart.

Figure 18 Channel capacity methodology

4.2 Models based on minimum spacing

The capacity corresponds to the maximum amount

of movements possible within defined time interval

under continuous demand service, corresponding to

saturation conditions.

The input required by this model is limited to ar-

rival delays, which can be easily calculated or esti-

mated for any port.

Moreover the definition of operational rules, fol-

lowed by the ships under saturation conditions, is

required taking into account that port basin and ap-

proaching zones are considered as a whole.

Arrivals always have priority on departures,

moreover an exiting ship may be authorised to move

only the minimum spacing from the previous

movements is reached.

Two possibilities exist (Fig. 19):

241

− if the second ship is faster than the first one the

minimum spacing d will be located at the port

mouth;

− if the first ship is faster than the second one the

minimum spacing d will be located at the pilot

point (where the ship is manoeuvred by personal

of The Port Authority).

Figure 19 Minimum spacing location

The perfect coordination of arrivals is obviously

impossible, therefore the spacing is normally higher:

BdD +=

(13)

where B is a buffer depending upon the traffic

regularity level, which is normally possible to define

according to a standard normal distribution.

Moreover a departure may be allowed only if the

crossing with the first arriving ship is located at a

spacing D.

Therefore, if a departure (ship 1) is followed by

an arrival (ship 2) the time interval between two de-

partures (ships 1 and 3) is defined as:

e2u

u113

tΔt +++=

(14)

where:

- V

and V

are the speeds of the ships outside the

port mouth;

- t

and t

are the mean exiting and entering

times for the ships, calculated according to traf-

fic mix and dock location;

The whole methodology is represented in

flowchart Figure. 20.

4.3 Applications of the two models and remarks

The capacity values have been estimated:

− for the port of Gioia Tauro on the basis of the

overall number of entering/exiting daily move-

ments (19);

− For the port of Livorno on the basis of the enter-

ing/exiting number daily movements in the sec-

tion before Darsena n°1, Canale Industriale and

Calata Gondar basins that is possible to assimilate

to a channel.

Figure 20 Minimum spacing methodology

The key results of the comparison between the

model based on the mean number of movements and

the alternative models are reported in Table 4.

Table 4 Comparison of model results [movements/day]

__________________________________________________

Model Gioia Tauro Livorno

__________________________________________________

Channel 35 64

capacity

Minimum 29 29

Spacing

Mean number 40 53

of movements

__________________________________________________

For the channel port of Gioia Tauro the results are

similar.

In the case study of the port of Livorno (tree lay-

out) relevant differences exist, particularly for the

minimum spacing model, which seem unsuitable for

the application to tree lay-out ports.

The original model based on the calculation of

mean number of movements seems well reproducing

the average capacity volumes for the analysed typi-

cal port lay-outs.

5 CONCLUSIONS

A stepwise approach is presented allowing:

− to dimension a harbour terminal (container termi-

nal) in terms of optimal storage capacity, geomet-

rical and operational characteristics, starting from

freight handled in a reference time interval;

− to estimate terminal capacity expressed by the

number of ships able to use the port equipments

in addition to regular and daily traffic inside the

port in defined service regularity conditions (un-

der the influence of considered additional move-

ments);

− to identify a qualitative correspondence between

analysed different port lay-outs and respective

manoeuvring capacity.

242

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