Tabu search in maritime transportation
International trade depends heavily on maritime transportation and more than 7 million tons of
goods are carried by ships every year. A ship involves a major capital investment, and its daily
operating costs often amounts to several thousand dollars. On the other hand, the revenues that can
be made by lifting cargoes can be substantial. Therefore, proper routing and scheduling of the ship
fleets is crucial, as a modest improvement in fleet utilization can result in large profit improvements.
Korsvik et al. (2010a) studies an important routing and scheduling problem faced by many tramp
shipping companies transporting bulk products. A shipping company operating in the tramp market
usually has a set of mandatory contract cargoes it is committed to carry, while trying to derive
additional revenue by accepting optional spot cargoes. Each cargo (both contract and spot) consists
of a given quantity of product that must be picked up at its loading port, transported and then
delivered to its discharge port. There are given time windows during which the loading of the cargoes
must start, and there may also be time windows for discharging. To transport the cargoes available in
the following planning horizon the shipping company controls a fixed heterogeneous fleet of ships,
where the ships may have different capacities, speed and cost structures.
Korsvik et al. (2010) propose a tabu search heuristic for solving the tramp ship routing and scheduling
problem. Such problems are often tightly constrained and an important feature of the approach is
the possibility of exploring solutions that are infeasible regarding time windows and ship capacity
during the search. The search neighborhood is simple and consists of moving one cargo from one
ship route to another, possibly also to or from a list of rejected cargoes (cargoes that are not yet in
the solution). For each move, a large number of cargo insertions into a ship route is evaluated. To
speed up the algorithm, they therefore apply neighborhood reduction, where the cargo’s pickup
node’s position in the ship route is fixed before determining the position of the corresponding
delivery node. To diversify the search, any non-improving solution is penalized based on the number
of times an attribute
has been added to the solution during the search, where
and
represent the cargo and ship, respectively. Korsvik et al. (2010) show that their tabu search heuristic
provides very competitive results for real problems.
Korsvik and Fagerholt (2010) study an important real life extension of the above tramp ship routing
and scheduling problem. Here, the quantities of the cargoes are not fixed but flexible within an
interval, e.g. 10 000 tons
15%. Therefore, interwoven with the routing and scheduling decisions,
the planner must also decide optimal cargo quantities. A tabu search heuristic embedding a separate
method for determining optimal cargo quantities for given ship routes is proposed. In contrast to
(Korsvik et al., 2010), this tabu search heuristic does not allow infeasible solutions during the search.
Therefore, they extend the search neighborhood by also including a swap operator, which swaps two
cargoes between two different ship routes, i.e. the attributes
and
is replaced by
and
. They also use a periodic diversification, which proved to be efficient. For every
iteration, they select the attribute
that has been part of the solution for the largest number of
consecutive iterations, and replace it with the best non-tabu attribute
, where
. The
attribute
is then tabu for a given number of iterations. Computational tests show that the
proposed tabu search heuristic provides good solutions for real life problems. The tests also show
that utilizing flexible cargo quantities in the planning can be of great value as the shipping companies
can use the flexibility to transport additional spot cargoes.
Versions of both the methods by Korsvik et al. (2010) and Korsvik and Fagerholt (2010) have been
implemented in TurboRouter, which is a decision support system for ship routing and scheduling
developed by MARINTEK in cooperation with the Norwegian University of Science and Technology
(see for instance (Fagerholt, 2004) and (Fagerholt and Lindstad, 2007)).
References:
J. E. Korsvik and K. Fagerholt (2010) “A tabu search heuristic for ship routing and scheduling with
flexible cargo quantities”. Journal of Heuristics 16(2), 117-137.
J. E. Korsvik, K. Fagerholt and G. Laporte (2010) “A tabu search heuristic for ship routing and
scheduling”. Journal of the Operational Research Society 61, 594-603.
K. Fagerholt and H. Lindstad (2007) “TurboRouter: An interactive optimisation-based decision
support system for ship routing and scheduling”. Maritime Economics and Logistics 9, 214-233.
K. Fagerholt (2004) ”A computer-based decision support system for vessel fleet scheduling –
Experience and future research”. Decision Support Systems 37(1), 35-47.