10th European Simulation Symposium and Exhibition, Simulation in Industry, pp. 520-528, October 26-28, 1998, Nottingham, United Kingdom.
RESOURCE ALLOCATION AND SCHEDULING OF OPERATIONS IN
AN INTERMODAL TERMINAL
Marco Zaffalon, Andrea E. Rizzoli, Luca Maria Gambardella, Monaldo Mastrolilli
IDSIA Istituto Dalle Molle di Studi sull Intelligenza Artificiale
Lugano Switzerland
E-mail: {zaffalon,andrea,luca,monaldo}@idsia.ch
KEYWORDS
Intermodal terminal simulation, flexible job-shop
scheduling, resource allocation, network flow
problem.
ABSTRACT
An approach to the problem of deciding which
equipment and manpower must be allocated over a
sequence of work shifts is presented. Once these
resources are given, a feasible and near-optimal
sequence of operations to load and unload a set of
ships harboured in an Intermodal Container
Terminal is found. The solution of the resource
allocation problem is based on a network design
formulation that assumes that the loading and
unloading processes can be modelled as a network
of container flows between the ships and the
terminal yard for all the work shifts. The solution
of the scheduling problem is thus fundamental to
ensure that these flows are sustained in each work
shift, by detailing for each container, the path to
follow from its origin to its destination. A discrete-
event simulation model with a resolution down to
the single container unit is used to validate the
resource allocation and the scheduling policies.
INTRODUCTION
The management of an intermodal container
terminal is a complex process that involves a vast
number of decisions to be taken. Containers arrive
and leave on various transportation means such as
trucks, trains and vessels. An intermodal container
terminal plays a fundamental role in routing goods
to and from their origins and destinations. It is a
basic node in a transportation network, where
thousand of daily decisions are taken to manage
this sustained flow of containers.
The advent of management information services
and data processing greatly improved the ability of
terminal managers to control the whole process,
but yet raw data has to be analysed and treated to
provide some insight on the performance of
terminal operations. Simulation models and
Operations Research techniques have proven to be
a reliable and convenient tool to support the
decision-makers in the daily operations in many
cases (Hayuth et al. 1994, Bl mel, 1997, Bruzzone
and Signorile, 1997).
Storing containers on the yard, allocating
resources in the terminal, and scheduling vessel
loading and unloading operations (L/U
operations, for brevity) are major problems in an
intermodal container terminal (Gambardella et al,
1998). In the last two years IDSIA has been
working on the case study of La Spezia Container
Terminal (LSCT), located in the Tyrrhenian Sea in
Italy.
The system architecture proposed to solve these
problems is composed of three different but
strictly connected modules (see Figure 1):
the simulation model of the terminal, described
in terms of entities (work force, transport
means, storage areas, etc.) and processes
(vessel load/unload, shuttle truck movements,
crane operations, etc.);
a set of forecasting models to analyse historical
data and to predict future events (Box et al.,
Forecasting
Simulation
Planning
Figure 1. The modular system
architecture.

1994; Vemuri and Rogers, 1993), thus
providing estimates of the expected import and
export flows;
the planning system which solves the problem
of the optimisation of L/U operations (L/U
problem), the problem of resource allocation
(RA problem), and the problem of the planning
and management of yard storage areas (space
problem).
This architecture supports the terminal managers
in the evaluation of:
vessels loading and unloading sequences in
terms of time and costs;
resource allocations procedures;
policies for container storage both in terms of
space and cost of operations.
This allows terminal managers to assess what-if
scenarios; for instance, what happens if the
terminal undergoes an increased input/output
throughput, or even if structural changes are made
(e.g.: new berths are built, new cranes are added).
As the forecasting module is described in previous
papers (Gambardella et al., 1996, Bontempi et al.,
1997), in the following sections we introduce the
other two modules of our architecture: the planner
and the terminal simulator. In the planning module
the attention is focused on the problem of resource
allocation and scheduling of L/U operations, while
the planning and management of terminal yard
storage areas is out of the scope of the present
paper. For each topic, we present the major
problems, the resolution methodologies and the
experimental results obtained at the current state of
the project.
RESOURCE ALLOCATION
The LSCT is a terminal characterised by sustained
container traffic on a small yard area. The usual
state of the terminal is such that there are up to 4
large-sized ships, served in parallel by means of
(possibly) more than one quay crane each.
Containers for different ships share the space on
the yard, and as a consequence, yard resources
(gantry cranes, straddle cranes, fork lifters and
carts) are not pre-assigned to a ship, i.e. yard
resources are shared too. The role of the resource
allocation (RA) module is to determine the best
allocation of resources for vessel loading and
unloading operations, with the objective of
maximising the profit, given by the difference
between income and expenses (Zaffalon and
Gambardella, 1998). The income is a term
proportional to the number of moved container,
whereas the expenses are a linear function of the
allocated resources. Since more resources produce
a greater movement capacity, it is clear that the
RA problem corresponds to find the right balance
between moving containers while saving resource
costs. For what above, this can be achieved by
searching for the best way of sharing resources.
As far as RA is concerned, the terminal can be
interpreted as a mechanism which routes the
container flows from their sources to the proper
destinations. This view models the terminal as a
network of flow (Papadimitriou and Steiglitz,
1982). In such a network, the transport capacities
of the arcs are functions of the number of
resources that are allocated: hence, the focus is on
dimensioning arc capacities to maximise the profit.
The latter problem is a particular case of the so-
called network design (Magnanti and Wong, 1984,
Ahuja et al., 1993). In the terminal case, the graph
of the network is also extended along the different
work shifts (1 shift = 6 hours) in order to represent
time (thus allowing the allocations to be computed
over all the period under study).
In Figure 2 we report a diagram showing a
graphical representation of an example problem.
Ship S is served by quay crane QC during a
Ship S
1
QC
1
CA
1
CB
1
CC
1
R
1
10
15
30
45
Shift 1
Ship S
2
QC
2
CA
2
CB
2
CC
2
R
2
Shift 2
Figure 2. The network flow problem over multiple
shifts.