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A Lagrangian Relaxation based Heuristic for the Static Berth
Allocation Problem using the Cutting Plane Method
A. S. Simrin, N. N. Alkawaleet and A. H. Diabat
Engineering Systems and Management Program, Masdar Institute of Science and Technology, Abu Dhabi, U.A.E.
Keywords: Container Terminal, Linear Program, Static Berth Allocation, Lagrangian Relaxation, Cutting Plane
Method.
Abstract: One of the important seaside operations problems that received a lot of attention in the literature is the
assignment of quay space and service time to vessels that have to be unloaded and loaded at a terminal. This
problem is commonly referred to as the Berth Allocation Problem (BAP). Different approaches exist in the
literature for the berth allocation problem (BAP). Some of those approaches consider static arrival of
vessels, so called the static berth allocation problem (SBAP), while other approaches consider dynamic
arrival of vessels, called the dynamic berth allocation problem (DBAP). Approaches also differ in the layout
used for the quay. In this paper we study one of the SBAP models presented in literature. Since the SBAP is
a non-deterministic polynomial-time (NP) problem, we applied a Lagrangian Relaxation heuristic technique
with the application of cutting plane method on our problem. We coded the cutting plane method in Matlab,
and ran it on different instances of the problem. In most of the cases that we studied, our solution technique
converged to an optimal solution.
1 INTRODUCTION
We consider the problem of allocating berth space
for vessels in container terminals, which is known as
the berth allocation problem (BAP). The vital need
for efficient berth scheduling is stimulated by the
fact that the cost of constructing a berth is
considered very high compared to the costs of other
facilities in container terminals. Hence, berth is
considered as the most critical source for
determining the capacity of container terminals.
Planners in container terminals usually construct a
Berth schedule which shows the berthing position,
the arrival time, as well as the handling time of each
vessel to be serviced at that berth.
In berth scheduling problem, vessels arrive over
time at a port and the terminal operator assigns them
to berths for unloading and loading of containers
based on several factors and considerations: (i) the
discrete, continuous and hybrid berthing space, and
(ii) the static versus dynamic vessel arrivals. The
Static Berth Allocation Problem (SBAP) is the kind
of problems when it is assumed that vessels arrive
before berth allocation is planned, while in the
Dynamic Berth Allocation Problem (DBAP) vessels
can arrive before or after allocation plan is made.
In discrete layout, the quay is divided into
separated berths, and a berth can be assigned to only
one vessel at a time, while in continuous layout, it’s
assumed that the quay is not divided, and vessels can
berth at any location within the boundary of the
quay. Finally in the hybrid layout, the quay is
divided into berths as in discrete, but the difference
between the two is that small vessels can share one
berth and large vessels may be assigned more than
one berth.
Imai et al. (1997) studied the discrete SBAP
(Imai et al., 1997). Berth allocation was planned
with respect to minimum waiting and handling time
of the vessels in addition to the deviation between
the arrival order of vessels and the service order. It
was also assumed that the handling time of a vessel
depends on the berth i.e. a vessel has different
handling times on different berths. The problem is
then reduced to a classical assignment problem. Imai
et al. (2001) (Imai et al., 2001) presented another
formulation of discrete SBAP where planning was
done only with respect to waiting and handling time
of vessels. They presented a Lagrangian relaxation
based heuristic to solve the problem.
Hansen and Oguz (2003) (Hansen and Oguz,
2003) presented a more compact Mixed Integer
565
S. Simrin A., N. Alkawaleet N. and H. Diabat A..
A Lagrangian Relaxation based Heuristic for the Static Berth Allocation Problem using the Cutting Plane Method.
DOI: 10.5220/0004628105650569
In Proceedings of the 15th International Conference on Enterprise Information Systems (SSOS-2013), pages 565-569
ISBN: 978-989-8565-59-4
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)