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(
construction
). These two steps are then iterated until some termination criterion,
in our case a time limit. An outline of the search procedure is presented in Algo-
rithm 1. Details of the initial solution generation (line 2), and the neighborhood
selection (line 4), are explained further in Sections 4.1 and 4.2. Notice, that line
7 forces the re-optimization to find only, equal, or improving solutions, and line 8
re-optimizes the model.
Algorithm 1:
LNS
1
M=IPmodel;
2
π
= find initial solution;
3
while
there is time
do
4
V
= select variables from
π
;
forall the
variable v ∈ V
do
5
fix variable
v
with the corresponding value from
π
;
6
post objective of M
≥
objective of
π
;
7
solve M;
8
This work is based on the IP model presented in [13], which is also used during
the re-optimization procedure. We briefly introduce the decision variables used
in the model, and point the reader to [13] for a more in-depth description of
the model. Let
P
be the number of ports in the route,
L
the locations in the
vessel and
T
the supported container types. The decision variable
x
tl
∈
Z
+
defines the number of container of type
τ
∈
T
to be loaded in location
l
∈
L
during transport
t
is the set of
origin destination pairs defined by the loadlist. The container types include 20',
40' and reefer containers, considering two weight classes (light and heavy). A
different average weight for each of the types at each transport is calculated.
We model the weight and capacity limits of the locations and the handling of
release containers. All stability constraints are modelled including shear forces
as an example of stress moments. The model minimizes a weighted sum of cost
variables
∈
TR
,where
TR
=
{
o, d
|
o, d
∈
P,o < d
}
P
y
pl
+
C
O
y
pl
+
T
y
p
C
p∈P
C
(1)
p∈P
l∈L
where
y
pl
is the hatch-overstowage of location
l ∈ L
at port
p ∈ P
,
y
lp
is an
indication of possible overstowage within location
l
P
,and
y
p
is
∈
L
at port
p
∈
T
) have been derived
from the deployed system of our industrial partner and thus reflect a refined
adjustment to the economy of stowage planning and the preferences of stowage
coordinators.
O
,
P
,
the crane makespan at port
p
∈
P
.Theweights(
C
C
C
4.1 Initial Solution
Having an initial solution is essential for the use of LNS, however, it is not
trivial to devise a heuristic procedure that can guarantee feasible solutions to
