Environmental Engineering Reference
In-Depth Information
moving a container is assumed to be constant. The result is that the total waiting
time is also stochastic. A simulation model can be applied for these stochastic
parameters and variables. To identify the optimal available periods for each con-
tainer in order to minimize truck waiting time as well as the amount emissions is a
combinatorial optimization with thousands of decision variables.
3.2 Mathematical Model
Before the model, here are the indices, the parameters, the variable and the derived
variables.
Indices
i
import container
i
,
i
∈
{1, …,
I
}
t
period
t
,
t
∈
{1, …,
T
}
k
emission factor
k
of idle truck engine,
k
∈
{1,…,
K
}
Parameters
e
k
the quantity of emission factor
k
per hour (g/hr)
c
the average handling capacity of yard crane (containers/hr)
m
the minimum number of periods that available for picking up a container
ʻ
t
arrival rate of truck in period
t
ʼ
average processing time at the gate of container terminal
v
bay
gantry speed of yard crane when moves from bay to bay
v
row
trolley speed of yard crane when moves from row to row
v
tier
hoist speed of yard crane when moves from tier to tier
Variables
1, if container
i
is available for being picked up in period
t
0, otherwise
x
it
=
Derived variables
X
the set of variable
x
it
,
X
=
{
x
it
}
∀
i
∈
{1, …,
I
} and
t
∈
{1, …,
T
}
w
g
(
X
)
average waiting time of trucks at the gate of container terminal
d
bay
i
(
X
)
total distance of moving containers above container
i
and moving container
i
to truck along the bay axis at the yard of container terminal
(
X
)
total distance of moving containers above container
i
and moving container
i
to truck along the row axis at the yard of container terminal
d
row
i
d
tier
i
(
X
)
total distance of moving containers above container
i
and moving container
i
to truck along the tier axis at the yard of container terminal
Model:
K
Min
e
k
E
(
X
)
k
=
1
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