Information Technology Reference
In-Depth Information
σ
s
∈
V
Starting visitation of vessel
s
∈
S
.
V
t
+
Set of visitations with an equipment surplus of type
t
.
V
t−
Set of visitations with an equipment deficit of type
t
.
V
t
∗
Set of visitations with an equipment surplus or deficit of type
t
(
V
t
∗
=
V
t
+
V
t
−
).
∪
V
In
(
i
)
⊆
Set of visitations with an arc connecting to visitation
i
∈
V
.
V
Set of visitations receiving an arc from
i
Out
(
i
)
⊆
∈
V
.
c
Mv
i
+
V
.
∈
R
Cost of a TEU move at visitation
i
∈
f
Port
s,i
V
.
∈
R
Port fee associated with vessel
s
at visitation
i
∈
r
Eqp
t
+
∈
R
Revenue for each TEU of equipment of type
t ∈ T
delivered.
u
s
∈
R
+
Capacity of vessel
s
for cargo type
t ∈ T
.Notethat
u
dc
s
is
the capacity of all slots on the vessel, including reefer slots.
A
V
.
Set of arcs (
i,j
)
∈
A
,where
i,j
∈
c
i,j
A
.
Fixed cost of vessel
s
utilizing arc (
i,j
)
∈
V
,d
V
and
t
(
o, d, t
)
∈
Θ
A demand triplet, where
o
T
are the
origin visitation, destination visitations and the cargo type,
respectively.
∈
⊆
∈
a
(
o,d,t
)
+
∈
R
Amount of demand available for the demand triplet.
r
(
o,d,t
)
+
∈
R
Amount of revenue gained per TEU for the demand triplet.
Variables
x
(
o,d,t
)
i,j
∈
[0
,a
(
o,d,t
)
]
Amount of flow of demand triplet (
o, d, t
)
∈ Θ
on (
i,j
)
∈ A
.
x
i,j
∈
[0
,
max
s∈S
u
d
s
] Amount of equipment of type
t
A
.
∈
T
flowing on (
i,j
)
∈
y
i,j
∈{
0
,
1
}
Indicates whether vessel
s
is sailing on arc (
i,j
)
∈ A
.
Objective and Constraints
max
−
s∈S
c
i,j
y
i,j
−
j∈V
f
Port
s,j
y
i,j
(1)
(
i,j
)
∈A
s∈S
i∈In
(
j
)
⎛
⎝
j∈d
⎞
⎠
r
(
o,d,t
)
− c
Mv
o
x
(
o,d,t
)
i,j
+
(
o,d,t
)
∈Θ
− c
Mv
j
(2)
i∈In
(
j
)
⎛
⎝
i∈V
t
+
⎞
⎠
r
Eqp
t
x
i,j
−
i∈V
t−
+
t∈T
− c
Mv
i
c
Mv
i
x
j,i
(3)
j∈Out
(
i
)
j∈In
(
i
)
s
.
t
.
s∈S
y
i,j
≤
1
∀j ∈ V
(4)
i∈In
(
j
)
y
σ
s
,i
=1
∀s ∈ S
(5)
i∈Out
(
σ
s
)
y
i,τ
=
|S|
(6)
i∈In
(
τ
)
s∈S
y
i,j
−
i∈Out
(
j
)
∀j ∈{V
\
s∈S
y
j,i
=0
σ
s
},s∈ S
(7)
i∈In
(
j
)
