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Mix
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Veh
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T
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C
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Her
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Facu
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Na
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Scien
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s
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Un
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Su
m
ater
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Utar
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Dr
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Ma
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I
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RO
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p
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[
1
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[
2
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,
aim
in
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m
i
n
e
th
e
m
o
s
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f
f
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a
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eliv
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Ov
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s
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VR
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ev
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ea
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ld
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ce
n
ar
io
s
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in
g
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n
s
tr
ain
ts
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v
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ca
p
ac
ity
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s
er
v
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tim
e,
an
d
r
o
u
te
len
g
th
.
Am
o
n
g
th
ese
v
ar
iatio
n
s
,
th
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
with
tim
e
W
in
d
o
ws
(
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PT
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h
as
g
ar
n
er
e
d
s
ig
n
if
ican
t
atten
tio
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d
u
e
to
its
p
r
ac
tical
r
elev
an
ce
in
en
s
u
r
in
g
tim
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d
eliv
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ies
[
3
]
.
T
h
e
VR
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a
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s
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o
p
tim
izatio
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m
in
lo
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s
tics
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d
tr
an
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p
o
r
tatio
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[
4
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,
aim
in
g
to
d
eter
m
in
e
th
e
m
o
s
t
ef
f
icie
n
t
r
o
u
tes
f
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r
a
f
leet
o
f
v
eh
icles
to
d
eliv
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g
o
o
d
s
to
a
s
et
o
f
cu
s
t
o
m
er
s
.
T
r
ad
itio
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al
VR
P
a
s
s
u
m
es
u
n
if
o
r
m
d
eliv
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r
y
co
n
d
itio
n
s
[
5
]
,
b
u
t
r
ea
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-
wo
r
ld
s
ce
n
ar
io
s
o
f
ten
p
r
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co
m
p
lex
ities
s
u
ch
as
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ete
r
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en
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o
u
s
tim
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win
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o
ws,
wh
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if
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cu
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to
m
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av
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ac
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p
tab
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eli
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p
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d
s
.
T
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is
p
ap
er
ad
d
r
ess
es
th
e
VR
P
wit
h
h
eter
o
g
en
eo
u
s
tim
e
win
d
o
ws
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VR
P
HT
W
)
,
p
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a
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p
tim
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m
o
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el
to
m
i
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im
ize
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tal
tr
av
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tim
e
an
d
co
s
ts
wh
ile
en
s
u
r
in
g
ti
m
ely
d
eliv
er
ies.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
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8
8
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8
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8
I
n
t J E
lec
&
C
o
m
p
E
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g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
4
0
4
3
-
4057
4044
T
h
e
ch
allen
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co
m
m
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atin
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d
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f
th
is
r
esear
ch
ar
e:
a.
T
o
d
ev
elo
p
a
r
o
b
u
s
t
MI
L
P
m
o
d
el
th
at
in
co
r
p
o
r
ates
h
eter
o
g
en
eo
u
s
tim
e
win
d
o
ws
i
n
to
th
e
VR
P
f
r
am
ewo
r
k
.
b.
T
o
d
esig
n
an
d
im
p
lem
en
t
e
f
f
icien
t
s
o
lu
tio
n
alg
o
r
it
h
m
s
c
ap
ab
le
o
f
h
an
d
lin
g
lar
g
e
-
s
ca
le
VR
PHTW
in
s
tan
ce
s
.
c.
T
o
v
alid
ate
th
e
p
r
o
p
o
s
ed
m
o
d
el
an
d
alg
o
r
ith
m
s
th
r
o
u
g
h
ex
ten
s
iv
e
co
m
p
u
tatio
n
al
ex
p
er
im
en
ts
an
d
co
m
p
ar
ativ
e
a
n
aly
s
is
.
B
y
ad
d
r
ess
in
g
th
ese
o
b
jectiv
es,
th
is
r
esear
ch
aim
s
to
c
o
n
t
r
ib
u
te
to
th
e
o
p
tim
izatio
n
lite
r
atu
r
e
an
d
p
r
o
v
i
d
e
p
r
ac
tical
s
o
lu
tio
n
s
f
o
r
l
o
g
is
tics
an
d
tr
an
s
p
o
r
tatio
n
co
m
p
an
ie
s
f
ac
in
g
co
m
p
lex
d
eliv
er
y
s
ce
n
ar
io
s
.
T
im
e
win
d
o
ws,
s
p
ec
if
ic
in
ter
v
als
d
u
r
in
g
wh
ic
h
d
eli
v
er
ies
o
r
p
ic
k
u
p
s
m
u
s
t
b
e
m
ad
e,
in
t
r
o
d
u
ce
an
ad
d
itio
n
al
lay
er
o
f
co
m
p
lex
it
y
to
th
e
VR
P.
T
r
ad
itio
n
al
V
R
PT
W
as
s
u
m
es
h
o
m
o
g
en
eity
in
tim
e
win
d
o
ws,
wh
er
e
ea
ch
cu
s
to
m
er
h
as
an
id
en
tical
o
r
s
im
ilar
tim
e
co
n
s
tr
ain
t
[
7
]
,
[
8
]
.
Ho
wev
e
r
,
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
o
f
ten
in
v
o
lv
e
h
eter
o
g
en
o
u
s
tim
e
win
d
o
ws,
wh
er
e
d
if
f
e
r
en
t
cu
s
to
m
er
s
h
av
e
d
is
tin
ct
an
d
n
o
n
-
o
v
er
lap
p
i
n
g
tim
e
in
ter
v
als
f
o
r
s
er
v
ice
[
9
]
.
T
h
is
h
eter
o
g
en
eity
ad
d
s
to
th
e
in
tr
i
ca
cy
o
f
th
e
p
r
o
b
lem
,
r
eq
u
ir
in
g
m
o
r
e
s
o
p
h
is
ticated
o
p
tim
izatio
n
m
o
d
els an
d
s
o
lu
t
io
n
ap
p
r
o
ac
h
es.
I
n
th
is
p
ap
er
,
we
d
elv
e
in
to
th
e
o
p
tim
izatio
n
m
o
d
el
o
f
th
e
VR
PHT
W
.
W
e
p
r
o
p
o
s
e
a
co
m
p
r
eh
en
s
iv
e
m
o
d
el
th
at
en
ca
p
s
u
lates
th
e
d
iv
er
s
e
tim
e
win
d
o
w
co
n
s
tr
ain
t
s
an
d
o
th
er
r
elev
an
t
f
ac
t
o
r
s
af
f
ec
tin
g
th
e
r
o
u
tin
g
an
d
s
ch
ed
u
lin
g
o
f
v
eh
icles.
Ou
r
o
b
jectiv
e
is
to
m
in
im
ize
th
e
to
tal
o
p
er
atio
n
al
co
s
t,
in
clu
d
in
g
tr
av
el
d
is
tan
ce
an
d
s
er
v
ice
tim
e,
wh
ile
e
n
s
u
r
i
n
g
ad
h
er
en
ce
to
th
e
s
p
ec
if
ied
t
im
e
win
d
o
ws f
o
r
ea
c
h
cu
s
to
m
er
.
T
h
e
s
ig
n
if
ican
ce
o
f
o
p
tim
izin
g
VR
PHTW
lies
in
it
s
b
r
o
ad
ap
p
licab
ilit
y
ac
r
o
s
s
v
ar
io
u
s
i
n
d
u
s
tr
ies,
s
u
ch
as
lo
g
is
tics
,
tr
an
s
p
o
r
tatio
n
,
an
d
d
is
tr
ib
u
tio
n
[
1
0
]
.
E
f
f
ici
en
tly
s
o
lv
in
g
th
is
p
r
o
b
lem
ca
n
lead
to
s
u
b
s
tan
tial
co
s
t
s
av
in
g
s
,
im
p
r
o
v
ed
cu
s
to
m
er
s
atis
f
ac
tio
n
,
an
d
en
h
a
n
ce
d
o
p
e
r
atio
n
al
ef
f
icien
cy
.
T
o
a
d
d
r
ess
th
e
ch
allen
g
es
p
o
s
ed
b
y
VR
PHTW,
we
em
p
l
o
y
a
d
v
an
ce
d
o
p
tim
izatio
n
tech
n
iq
u
es
an
d
alg
o
r
ith
m
s
,
lev
er
a
g
in
g
b
o
th
ex
ac
t
an
d
h
eu
r
is
tic
m
eth
o
d
s
.
T
h
is
s
tu
d
y
co
n
tr
ib
u
tes
to
th
e
ex
is
tin
g
b
o
d
y
o
f
k
n
o
wled
g
e
b
y
p
r
esen
tin
g
a
r
o
b
u
s
t
o
p
tim
izati
o
n
m
o
d
el
tailo
r
ed
f
o
r
VR
PHTW,
ac
co
m
p
an
ied
b
y
em
p
ir
ical
r
esu
lts
d
em
o
n
s
tr
atin
g
its
ef
f
ec
tiv
en
ess
.
T
h
r
o
u
g
h
t
h
is
r
esear
ch
,
we
aim
to
p
r
o
v
id
e
a
v
alu
ab
l
e
to
o
l
f
o
r
p
r
ac
titi
o
n
er
s
an
d
r
esear
ch
er
s
in
th
e
f
ie
ld
,
f
ac
ilit
atin
g
th
e
d
ev
elo
p
m
e
n
t o
f
m
o
r
e
e
f
f
icien
t
r
o
u
tin
g
s
tr
ateg
ies in
th
e
p
r
ese
n
ce
o
f
h
eter
o
g
e
n
o
u
s
tim
e
co
n
s
tr
ain
ts
.
2.
T
H
E
CO
M
P
RE
H
E
NS
I
VE
T
H
E
O
RE
T
I
CA
L
B
ASI
S
T
h
e
VR
P
h
as
b
ee
n
a
p
iv
o
tal
r
esear
ch
ar
ea
in
o
p
e
r
atio
n
s
r
es
ea
r
ch
a
n
d
l
o
g
is
tics
f
o
r
s
ev
er
al
d
ec
ad
es.
I
n
itially
f
o
r
m
u
lated
b
y
[
1
1
]
,
t
h
e
class
ic
VR
P
aim
s
to
d
esig
n
th
e
m
o
s
t
ef
f
icien
t
r
o
u
tes
f
o
r
a
f
leet
o
f
v
eh
icles
to
s
er
v
ice
a
s
et
o
f
cu
s
to
m
er
s
wi
t
h
k
n
o
wn
d
e
m
an
d
s
[
4
]
,
[
1
2
]
.
Ov
er
th
e
y
ea
r
s
,
n
u
m
er
o
u
s
v
ar
iatio
n
s
o
f
VR
P
h
av
e
em
er
g
ed
,
ea
c
h
ad
d
r
ess
in
g
s
p
ec
if
ic
r
ea
l
-
wo
r
ld
co
n
s
tr
ain
ts
an
d
r
eq
u
ir
em
en
ts
.
Am
o
n
g
th
ese
v
ar
iatio
n
s
,
th
e
VR
PT
W
h
as g
ain
ed
s
ig
n
if
ican
t a
tten
tio
n
d
u
e
t
o
its
p
r
ac
tical
r
elev
an
ce
in
en
s
u
r
in
g
tim
ely
d
e
liv
er
ies.
2
.
1
.
M
o
dels
a
nd
m
et
ho
ds
f
o
r
s
o
lv
ing
VRP
T
W
T
h
e
VR
PTW
in
v
o
lv
es
a
h
o
m
o
g
en
eo
u
s
f
leet
o
f
v
eh
icles,
d
e
n
o
ted
b
y
,
a
s
et
o
f
cu
s
to
m
er
s
,
d
en
o
ted
as
,
an
d
a
d
ir
ec
ted
g
r
ap
h
=
(
,
)
.
T
h
is
g
r
ap
h
in
clu
d
es
|
|
+
2
n
o
d
es,
wh
er
e
th
e
cu
s
to
m
er
s
ar
e
n
u
m
b
er
e
d
f
r
o
m
1
to
,
an
d
th
e
d
ep
o
t is r
ep
r
esen
ted
b
y
n
o
d
es
0
(
th
e
d
ep
a
r
tu
r
e
d
ep
o
t
)
an
d
+
1
(
th
e
r
etu
r
n
d
ep
o
t)
.
T
h
e
VR
PTW
aim
s
to
m
in
im
ize
b
o
th
th
e
n
u
m
b
er
o
f
v
eh
icle
s
u
s
ed
an
d
th
e
t
o
tal
tr
av
el
tim
e,
waitin
g
p
er
io
d
s
,
an
d
d
is
tan
ce
co
v
er
ed
b
y
th
e
f
leet.
C
o
n
n
ec
tiv
ity
b
et
wee
n
th
e
d
ep
o
t
an
d
cu
s
to
m
er
s
,
as
well
as
am
o
n
g
th
e
cu
s
to
m
er
s
,
is
r
ep
r
esen
ted
b
y
a
s
et
o
f
ar
cs
d
en
o
ted
b
y
.
No
ar
cs
ter
m
in
ate
at
n
o
d
e
0
,
n
o
r
d
o
an
y
ar
cs
o
r
ig
in
ate
f
r
o
m
n
o
d
e
+
1
.
E
ac
h
a
r
c
(
,
)
,
wh
er
e
≠
,
is
ass
ig
n
ed
a
co
s
t
an
d
a
tim
e
,
wh
ich
m
a
y
in
clu
d
e
th
e
s
er
v
ice
tim
e
f
o
r
cu
s
to
m
er
.
E
v
er
y
v
eh
icle
h
as
a
c
ap
ac
ity
,
an
d
ea
ch
cu
s
to
m
er
h
as
a
d
em
an
d
.
C
u
s
to
m
er
s
also
h
av
e
tim
e
win
d
o
w
s
[
,
]
,
with
in
wh
ich
th
e
v
e
h
icle
m
u
s
t
ar
r
iv
e
b
ef
o
r
e
.
Veh
icles
m
ay
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
a
tio
n
mo
d
el
o
f v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
w
ith
h
etero
g
e
n
o
u
s
time
w
in
d
o
w
s
(
Herma
n
Ma
w
en
g
ka
n
g
)
4045
ar
r
iv
e
b
ef
o
r
e
,
b
u
t
s
er
v
ice
will
n
o
t
b
eg
in
u
n
til
.
T
h
e
d
e
p
o
t
h
as
its
o
wn
tim
e
win
d
o
w
[
0
,
0
]
.
Veh
icle
s
m
u
s
t n
o
t le
av
e
th
e
d
ep
o
t
b
ef
o
r
e
0
an
d
m
u
s
t r
etu
r
n
b
ef
o
r
e
o
r
at
tim
e
+
1
.
I
t
is
as
s
u
m
ed
th
at
,
,
,
,
an
d
ar
e
n
o
n
-
n
e
g
ativ
e
in
teg
er
s
,
wh
ile
ar
e
p
o
s
itiv
e
in
teg
er
s
.
T
h
e
m
o
d
el
p
r
esu
m
es
th
at
th
e
tr
ian
g
le
in
eq
u
ality
h
o
ld
s
f
o
r
.
T
wo
s
ets
o
f
d
ec
is
io
n
v
ar
iab
les
ar
e
u
s
ed
in
th
e
m
o
d
el:
an
d
.
Fo
r
ea
ch
ar
c
(
,
)
,
wh
er
e
≠
,
≠
+
1
,
an
d
≠
0
,
is
d
ef
in
e
d
as
1
if
,
an
d
o
n
ly
if
,
in
th
e
o
p
tim
al
s
o
lu
tio
n
,
th
e
a
r
c
(
,
)
is
tr
av
er
s
ed
b
y
v
eh
icle
;
o
th
er
wis
e,
=
0
.
T
h
e
d
ec
is
io
n
v
a
r
iab
l
e
is
d
ef
in
ed
f
o
r
ea
c
h
n
o
d
e
an
d
ea
ch
v
eh
icle
,
r
ep
r
esen
tin
g
th
e
tim
e
wh
en
v
eh
icle
b
eg
in
s
s
er
v
in
g
cu
s
to
m
e
r
.
I
f
v
e
h
icle
d
o
es n
o
t ser
v
e
cu
s
to
m
er
,
is
n
o
t a
p
p
licab
le.
Ass
u
m
e
0
=
0
an
d
th
u
s
0
=
0
f
o
r
all
.
T
h
e
o
b
jectiv
e
is
to
d
esig
n
a
s
e
t o
f
r
o
u
tes with
m
in
im
al
c
o
s
ts
,
o
n
e
f
o
r
ea
ch
v
eh
icle,
en
s
u
r
in
g
th
at
ea
ch
cu
s
to
m
er
is
v
is
ited
ex
ac
tly
o
n
ce
.
E
v
er
y
r
o
u
te
s
tar
ts
at
n
o
d
e
0
an
d
en
d
s
at
n
o
d
e
+
1
,
o
b
s
er
v
in
g
th
e
tim
e
win
d
o
ws an
d
ca
p
ac
ity
co
n
s
tr
a
in
ts
.
VR
PT
W
ca
n
b
e
ex
p
r
ess
ed
m
ath
em
atica
lly
as f
o
llo
ws:
Ob
jectiv
e
Fu
n
ctio
n
:
min
i
mize
∑
∑
∑
∈
∈
∈
(
1
)
with
co
n
s
tr
ain
ts
:
∑
∑
∈
∈
=
1
∀
∈
(
2
)
∑
∈
∑
∈
≤
∀
∈
(
3
)
∑
0
∈
=
1
∀
∈
(
4
)
∑
ℎ
∈
−
∑
ℎ
∈
=
0
∀
ℎ
∈
,
∀
∈
(
5
)
∑
,
+
1
,
∈
=
1
∀
∈
(
6
)
+
−
(
1
−
)
≤
∀
,
∈
,
∀
∈
(
7
)
≤
≤
∀
∈
,
∀
∈
(
8
)
∈
{
0
,
1
}
∀
,
∈
,
∀
∈
(
9
)
C
o
n
s
tr
ain
t
(
2
)
e
n
s
u
r
es
th
at
e
ac
h
cu
s
to
m
er
is
v
is
ited
ex
ac
t
ly
o
n
ce
.
C
o
n
s
tr
ain
t
(
3
)
en
s
u
r
es
th
at
n
o
v
eh
icle
ex
ce
ed
s
its
ca
p
ac
ity
.
C
o
n
s
tr
ain
ts
(
4
)
,
(
5
)
,
an
d
(
6
)
en
s
u
r
e
th
at
ev
er
y
v
eh
icle
lea
v
es
d
ep
o
t
0
,
v
is
its
cu
s
to
m
er
s
,
an
d
f
i
n
ally
r
etu
r
n
s
to
d
ep
o
t
+
1
.
I
n
e
q
u
ality
(
7
)
en
s
u
r
es
th
at
v
eh
icle
d
o
es
n
o
t
ar
r
iv
e
at
b
ef
o
r
e
+
if
it
tr
av
els
f
r
o
m
to
,
wh
er
e
is
a
lar
g
e
s
ca
lar
.
C
o
n
s
tr
ain
ts
(
8
)
en
f
o
r
ce
th
e
tim
e
win
d
o
ws,
an
d
(
9
)
ar
e
in
teg
er
c
o
n
s
tr
ain
ts
.
Un
u
s
e
d
v
eh
icles a
r
e
m
o
d
eled
b
y
tr
av
er
s
in
g
em
p
ty
r
o
u
tes f
r
o
m
0
to
+
1
.
So
m
e
m
o
d
els with
im
p
o
r
ta
n
t a
p
p
licatio
n
s
o
f
VR
PTW ar
e
p
h
ar
m
ac
eu
tical
d
is
tr
ib
u
tio
n
p
r
o
b
lem
s
[
1
3
]
,
waste
co
llectio
n
in
u
r
b
an
ar
e
as
[
1
4
]
,
s
ch
o
o
l
b
u
s
r
o
u
tes
[
1
5
]
,
f
u
el
d
eliv
er
y
[
1
6
]
,
p
o
s
tal
s
er
v
ices
[
1
7
]
,
b
a
n
k
d
eliv
er
y
[
1
8
]
,
f
r
esh
f
o
o
d
e
-
co
m
m
er
ce
[
1
9
]
,
an
d
f
r
an
c
h
is
e
r
esta
u
r
an
t
s
er
v
ices
[
2
0
]
.
Me
th
o
d
s
f
o
r
ad
d
r
ess
in
g
th
e
v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
with
t
im
e
win
d
o
ws
(
VR
PTW)
ca
n
g
en
er
ally
b
e
ca
teg
o
r
ized
in
t
o
th
r
ee
m
ain
class
es
—
ex
ac
t,
h
eu
r
is
tic,
an
d
m
etah
e
u
r
is
tic
ap
p
r
o
ac
h
es.
E
x
ac
t
m
et
h
o
d
s
en
co
m
p
ass
tech
n
iq
u
es
s
u
ch
as
L
ag
r
an
g
ia
n
r
elax
atio
n
[
2
1
]
,
wh
ich
r
ela
x
e
s
s
elec
ted
co
n
s
tr
ain
ts
y
et
m
a
in
tain
s
th
e
r
eq
u
ir
em
en
t
th
at
ea
ch
cu
s
to
m
er
b
e
s
er
v
ed
o
n
ce
;
co
lu
m
n
g
en
er
ati
o
n
[
22]
,
wh
er
e
a
lar
g
e
-
s
ca
le
l
in
ea
r
p
r
o
g
r
a
m
is
in
itialized
w
ith
a
lim
ited
s
et
o
f
v
ar
iab
les
an
d
p
r
o
g
r
ess
iv
ely
r
ef
in
ed
b
y
i
n
tr
o
d
u
cin
g
a
d
d
itio
n
al
co
lu
m
n
s
;
an
d
d
y
n
am
ic
p
r
o
g
r
a
m
m
in
g
[
2
3
]
,
wh
ich
alig
n
s
v
eh
icle
r
o
u
tin
g
an
d
d
em
a
n
d
p
r
icin
g
with
in
a
L
ag
r
an
g
ian
r
elax
atio
n
f
r
a
m
ewo
r
k
.
Heu
r
is
tic
m
eth
o
d
s
ty
p
ically
f
o
c
u
s
o
n
eith
er
b
u
ild
i
n
g
a
r
o
u
te
p
lan
“f
r
o
m
s
cr
atch
,
”
r
ef
er
r
ed
to
as r
o
u
t
e
-
b
u
ild
in
g
h
eu
r
is
tics
[
2
4
]
,
o
r
im
p
r
o
v
in
g
an
ex
is
tin
g
s
o
lu
tio
n
,
k
n
o
wn
as
r
o
u
te
-
i
m
p
r
o
v
i
n
g
h
e
u
r
is
tics
[
2
5
]
;
b
o
t
h
s
tr
ateg
ies
aim
to
d
eliv
er
f
ea
s
ib
le,
n
ea
r
-
o
p
tim
al
s
o
lu
tio
n
s
m
o
r
e
r
a
p
id
ly
th
a
n
ex
ac
t
m
eth
o
d
s
.
Me
tah
e
u
r
is
tic
m
eth
o
d
s
,
in
clu
d
in
g
s
im
u
lated
an
n
ea
lin
g
[
2
6
]
,
tab
u
s
ea
r
ch
[
2
7
]
,
an
d
g
en
etic
al
g
o
r
ith
m
s
[
2
8
]
,
s
y
s
tem
atica
lly
ex
p
lo
r
e
an
d
ex
p
lo
it
th
e
s
o
lu
tio
n
s
p
ac
e
t
o
b
alan
ce
s
o
lu
tio
n
q
u
ality
with
co
m
p
u
tati
o
n
al
ef
f
o
r
t.
A
c
o
m
p
r
e
h
en
s
iv
e
r
ev
iew
o
f
VR
PTW
m
etah
eu
r
is
tics
ca
n
b
e
f
o
u
n
d
in
[
2
9
]
.
I
n
r
ec
en
t
y
ea
r
s
,
th
e
VR
P
h
as
b
ee
n
ex
ten
s
iv
ely
ex
p
l
o
r
ed
ac
r
o
s
s
v
ar
io
u
s
in
d
u
s
tr
ies
d
u
e
to
i
ts
cr
itical
r
o
le
in
lo
g
is
tics
an
d
tr
an
s
p
o
r
tatio
n
p
lan
n
i
n
g
.
R
esear
ch
er
s
h
a
v
e
in
tr
o
d
u
ce
d
n
u
m
e
r
o
u
s
VR
P
v
ar
ian
ts
—
s
p
an
n
in
g
ca
p
ac
ity
co
n
s
tr
ain
ts
,
m
u
lti
-
d
e
p
o
t d
is
tr
ib
u
tio
n
,
h
eter
o
g
e
n
eo
u
s
f
leets ,
an
d
tim
e
win
d
o
ws
—
t
o
b
etter
r
ef
lect
r
ea
l
-
wo
r
ld
o
p
er
atio
n
s
[
3
0
]
,
[
3
1
]
.
E
x
ac
t m
eth
o
d
s
o
f
ten
em
p
lo
y
Mix
ed
-
I
n
te
g
er
L
in
ea
r
Pro
g
r
am
m
in
g
f
o
r
m
u
latio
n
s
o
r
b
r
an
ch
-
an
d
-
c
u
t
alg
o
r
ith
m
s
,
th
o
u
g
h
co
m
p
u
tatio
n
al
c
o
m
p
lex
i
ty
ca
n
b
e
p
r
o
h
i
b
itiv
e
f
o
r
lar
g
er
in
s
tan
ce
s
[
3
2
]
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
4
0
4
3
-
4057
4046
[
3
3
]
.
C
o
n
s
eq
u
en
tly
,
m
etah
eu
r
is
tics
s
u
ch
as
g
en
etic
alg
o
r
ith
m
s
,
T
ab
u
Sear
ch
,
a
d
ap
tiv
e
l
ar
g
e
n
eig
h
b
o
r
h
o
o
d
s
ea
r
ch
,
an
d
p
ar
ticle
s
war
m
o
p
tim
izatio
n
h
av
e
g
ain
ed
p
r
o
m
in
en
ce
f
o
r
d
eliv
er
in
g
n
ea
r
-
o
p
tim
al
s
o
lu
tio
n
s
with
in
ac
ce
p
tab
le
tim
ef
r
am
es
[
3
4
]
,
[
3
5
]
.
Mo
r
eo
v
er
,
r
o
b
u
s
t
an
d
s
to
ch
asti
c
o
p
tim
izatio
n
m
o
d
els
h
av
e
em
er
g
e
d
to
h
an
d
le
u
n
ce
r
tain
ties
i
n
d
e
m
a
n
d
s
an
d
tr
a
v
el
tim
es
[
3
6
]
,
[
3
7
]
.
R
ec
en
t
s
tu
d
ies
also
i
n
teg
r
ate
r
o
u
tin
g
an
d
s
ch
ed
u
lin
g
d
ec
is
io
n
s
to
ac
co
m
m
o
d
ate
d
y
n
am
ic
o
p
er
atin
g
c
o
n
d
itio
n
s
,
h
ig
h
lig
h
tin
g
b
o
t
h
i
m
p
r
o
v
e
d
o
p
er
atio
n
al
ef
f
icien
cy
a
n
d
c
o
s
t
-
ef
f
ec
tiv
en
ess
in
ap
p
licatio
n
s
lik
e
la
st
-
m
ile
d
eliv
er
ies
an
d
h
ea
lth
ca
r
e
lo
g
is
tics
[
3
8
]
,
[
3
9
]
.
T
h
is
r
esear
ch
f
ir
s
t
b
u
ild
s
a
d
i
s
cr
ete
m
o
d
el
f
o
r
VR
PTW,
wh
o
s
e
v
ar
ia
b
les
r
ep
r
esen
t
f
ea
s
ib
le
v
eh
icle
r
o
u
tes.
An
o
th
er
m
o
d
el
with
d
if
f
er
en
t
g
o
als an
d
co
n
s
tr
ain
ts
ca
n
b
e
f
o
u
n
d
i
n
[
4
0
]
–
[
4
2
]
.
2
.
2
.
H
et
er
o
g
eneo
us
t
im
e
wind
o
ws in
VRP
W
h
ile
tr
ad
itio
n
al
VR
PTW
a
s
s
u
m
es
h
o
m
o
g
en
e
o
u
s
tim
e
win
d
o
ws,
r
ea
l
-
wo
r
l
d
ap
p
licatio
n
s
o
f
te
n
in
v
o
lv
e
h
eter
o
g
e
n
eo
u
s
tim
e
win
d
o
ws,
wh
er
e
c
u
s
to
m
er
s
h
av
e
d
is
tin
ct
an
d
n
o
n
-
o
v
er
lap
p
in
g
tim
e
co
n
s
tr
ain
ts
.
T
h
is
v
ar
iatio
n
,
r
ef
e
r
r
ed
t
o
as
th
e
VR
PHT
W
,
ad
d
s
co
m
p
le
x
ity
to
th
e
r
o
u
tin
g
p
r
o
b
le
m
,
n
ec
ess
itatin
g
m
o
r
e
s
o
p
h
is
ticated
o
p
tim
izatio
n
m
o
d
els
an
d
s
o
lu
tio
n
tech
n
iq
u
es.
R
esear
ch
o
n
VR
PHTW
is
r
elativ
ely
r
ec
en
t
b
u
t
g
r
o
win
g
.
[
4
3
]
ex
p
lo
r
ed
a
VR
P
v
ar
ian
t
with
h
eter
o
g
en
eo
u
s
tim
e
win
d
o
ws
u
s
in
g
a
h
y
b
r
i
d
g
en
etic
alg
o
r
ith
m
.
T
h
ey
d
em
o
n
s
tr
ated
th
e
ef
f
ec
ti
v
e
n
ess
o
f
th
eir
ap
p
r
o
ac
h
in
m
an
ag
in
g
d
i
v
er
s
e
tim
e
co
n
s
tr
ain
ts
wh
ile
o
p
tim
izin
g
r
o
u
te
ef
f
icien
c
y
.
Similar
ly
,
[
4
4
]
p
r
o
v
id
e
d
a
co
m
p
r
e
h
en
s
iv
e
s
u
r
v
ey
o
n
VR
PTW,
in
clu
d
in
g
d
is
cu
s
s
io
n
s
o
n
h
eter
o
g
en
e
o
u
s
tim
e
win
d
o
ws,
an
d
h
ig
h
lig
h
te
d
t
h
e
n
ee
d
f
o
r
f
u
r
th
er
r
esear
c
h
in
th
is
ar
ea
.
2
.
3
.
O
pti
m
iza
t
io
n
m
o
dels
a
nd
s
o
lutio
n a
pp
ro
a
ches
Op
tim
izatio
n
m
o
d
els
f
o
r
VR
PHT
W
ty
p
ically
in
v
o
lv
e
c
o
m
p
lex
m
ath
e
m
atica
l
f
o
r
m
u
l
atio
n
s
th
at
in
teg
r
ate
v
ar
io
u
s
co
n
s
tr
ain
ts
,
in
clu
d
in
g
v
e
h
icle
ca
p
ac
ity
,
tr
av
el
tim
e,
s
er
v
ice
tim
e,
an
d
h
eter
o
g
en
e
o
u
s
tim
e
win
d
o
ws.
E
x
ac
t
m
eth
o
d
s
,
s
u
ch
as
MI
L
P,
h
a
v
e
b
ee
n
em
p
lo
y
ed
t
o
o
b
tain
o
p
tim
al
s
o
lu
tio
n
s
f
o
r
s
m
all
to
m
ed
iu
m
-
s
ized
in
s
tan
ce
s
.
Ho
wev
er
,
th
e
co
m
p
u
tatio
n
al
co
m
p
lex
ity
o
f
VR
PHT
W
o
f
ten
n
ec
ess
itate
s
th
e
u
s
e
o
f
h
eu
r
is
tic
an
d
m
eta
h
e
u
r
is
tic
alg
o
r
ith
m
s
f
o
r
la
r
g
er
i
n
s
tan
ce
s
.
Heu
r
is
tic
m
eth
o
d
s
,
s
u
ch
as
C
lar
k
e
-
W
r
ig
h
t
s
av
in
g
s
alg
o
r
ith
m
[
4
5
]
an
d
n
ea
r
est
n
eig
h
b
o
r
a
p
p
r
o
ac
h
es,
p
r
o
v
id
e
f
ea
s
ib
le
s
o
lu
tio
n
s
q
u
ick
ly
b
u
t
m
ay
n
o
t
g
u
ar
a
n
tee
o
p
tim
ality
.
Me
tah
e
u
r
is
tic
tech
n
iq
u
es,
in
cl
u
d
in
g
s
im
u
lated
a
n
n
ea
lin
g
[
4
6
]
,
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
[
4
7
]
,
an
d
h
y
b
r
id
ap
p
r
o
ac
h
es
co
m
b
in
in
g
m
u
ltip
le
alg
o
r
ith
m
s
,
h
av
e
s
h
o
w
n
p
r
o
m
is
e
in
ef
f
ec
tiv
ely
s
o
lv
in
g
VR
PHT
W
.
Fo
r
in
s
ta
n
ce
,
[
4
8
]
d
ev
elo
p
e
d
a
h
y
b
r
id
alg
o
r
ith
m
c
o
m
b
in
i
n
g
ta
b
u
s
ea
r
ch
an
d
s
im
u
lated
a
n
n
ea
lin
g
to
ad
d
r
ess
VR
P
with
h
eter
o
g
en
e
o
u
s
tim
e
win
d
o
ws,
ac
h
iev
in
g
s
ig
n
if
ica
n
t im
p
r
o
v
e
m
en
ts
in
s
o
lu
tio
n
q
u
ality
an
d
co
m
p
u
tatio
n
al
e
f
f
icien
cy
.
2
.
4
.
P
r
a
ct
ica
l
a
pp
lica
t
io
ns
a
nd
ca
s
e
s
t
ud
ie
s
T
h
e
p
r
ac
tical
im
p
o
r
ta
n
ce
o
f
VR
PHT
W
is
ev
id
en
t
in
v
ar
io
u
s
in
d
u
s
tr
ies,
s
u
ch
a
s
lo
g
is
tics
,
tr
an
s
p
o
r
tatio
n
,
a
n
d
d
is
tr
ib
u
tio
n
.
C
ase
s
tu
d
ies
h
av
e
d
em
o
n
s
tr
ated
th
e
ap
p
licab
ilit
y
an
d
b
e
n
ef
its
o
f
o
p
tim
ize
d
r
o
u
tin
g
with
h
eter
o
g
en
eo
u
s
tim
e
win
d
o
ws.
Fo
r
ex
a
m
p
le,
[
4
9
]
ap
p
lied
VR
PHTW
m
o
d
els
t
o
th
e
d
is
tr
ib
u
tio
n
o
f
p
er
is
h
ab
le
g
o
o
d
s
,
h
ig
h
lig
h
tin
g
th
e
im
p
ac
t
o
f
o
p
tim
ized
r
o
u
tin
g
o
n
r
ed
u
cin
g
d
eliv
er
y
tim
es
an
d
o
p
er
atio
n
al
co
s
ts
.
I
n
s
u
m
m
a
r
y
,
th
e
liter
atu
r
e
o
n
VR
PHTW
r
ef
lects
a
g
r
o
win
g
in
ter
est
in
ad
d
r
ess
in
g
th
e
c
o
m
p
lex
ities
in
tr
o
d
u
ce
d
b
y
h
eter
o
g
en
eo
u
s
tim
e
win
d
o
ws.
W
h
ile
s
ig
n
if
ican
t
ad
v
an
ce
m
en
ts
h
av
e
b
ee
n
m
ad
e
in
o
p
tim
izatio
n
m
o
d
els
an
d
s
o
lu
tio
n
tech
n
iq
u
es,
th
er
e
r
em
ain
s
a
n
ee
d
f
o
r
f
u
r
th
er
r
esear
ch
to
d
ev
el
o
p
m
o
r
e
e
f
f
icien
t
alg
o
r
ith
m
s
an
d
e
x
p
lo
r
e
n
ew
a
p
p
licatio
n
s
.
T
h
is
p
ap
er
aim
s
to
co
n
tr
ib
u
te
t
o
th
is
ev
o
lv
i
n
g
f
ield
b
y
p
r
esen
tin
g
a
r
o
b
u
s
t
o
p
tim
izatio
n
m
o
d
el
f
o
r
VR
PHTW
an
d
d
em
o
n
s
tr
atin
g
its
ef
f
ec
tiv
en
ess
th
r
o
u
g
h
em
p
ir
ical
an
aly
s
is
.
T
h
e
s
u
b
s
eq
u
en
t
s
ec
tio
n
s
o
f
th
is
p
ap
er
will
d
etail
th
e
p
r
o
p
o
s
ed
o
p
tim
izatio
n
m
o
d
el,
s
o
lu
t
io
n
ap
p
r
o
ac
h
,
an
d
co
m
p
u
tatio
n
al
ex
p
er
im
en
ts
,
p
r
o
v
id
in
g
in
s
ig
h
ts
in
to
th
e
p
r
a
ctica
l
im
p
licatio
n
s
o
f
o
p
tim
izin
g
v
eh
icle
r
o
u
tin
g
with
h
eter
o
g
en
e
o
u
s
tim
e
win
d
o
ws.
3.
M
E
T
H
O
D
3
.
1
.
M
a
t
hema
t
ica
l
m
o
del
T
h
e
VR
PHTW
in
v
o
lv
es
f
in
d
i
n
g
th
e
o
p
tim
al
s
et
o
f
r
o
u
tes
f
o
r
a
f
leet
o
f
v
eh
icles
to
s
er
v
i
ce
a
s
et
o
f
cu
s
to
m
er
s
,
ea
ch
with
s
p
ec
if
i
c
tim
e
win
d
o
ws
d
u
r
in
g
wh
ich
th
ey
m
u
s
t
b
e
s
er
v
iced
.
T
h
e
o
b
jectiv
e
is
to
m
in
im
ize
th
e
t
o
tal
tr
av
el
co
s
t
wh
ile
ad
h
er
in
g
to
th
e
co
n
s
tr
ain
ts
o
f
v
e
h
icle
ca
p
ac
ity
an
d
c
u
s
to
m
er
tim
e
win
d
o
ws.
3
.
2
.
Descript
io
n o
f
t
he
pro
bl
em
A
co
n
v
en
ie
n
t
way
to
r
e
p
r
esen
t
th
is
p
r
o
b
lem
is
b
y
u
s
in
g
a
f
u
ll
y
d
ir
ec
ted
g
r
ap
h
=
(
,
)
.
T
h
e
s
et
o
f
v
er
tices
is
g
iv
en
b
y
∪
{
}
,
an
d
th
e
s
et
o
f
ar
cs
in
clu
d
es
ev
er
y
o
r
d
er
ed
p
air
(
,
)
wh
er
e
,
∈
.
W
ith
in
th
is
f
r
am
ewo
r
k
,
b
in
ar
y
d
ec
is
io
n
v
ar
iab
les
ca
p
tu
r
e
wh
eth
e
r
a
g
iv
en
cu
s
to
m
er
o
r
ar
c
is
ass
ig
n
ed
to
a
p
ar
ticu
la
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
a
tio
n
mo
d
el
o
f v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
w
ith
h
etero
g
e
n
o
u
s
time
w
in
d
o
w
s
(
Herma
n
Ma
w
en
g
ka
n
g
)
4047
r
o
u
te,
as
well
as
h
o
w
r
o
u
tes
ar
e
s
eq
u
en
ce
d
.
Sp
ec
if
ically
,
let
an
d
d
en
o
te,
r
esp
ec
tiv
ely
,
wh
e
th
er
ar
c
(
,
)
is
u
s
ed
in
r
o
u
te
an
d
wh
eth
er
c
u
s
to
m
er
is
s
er
v
ed
b
y
r
o
u
te
.
A
f
u
r
th
e
r
b
in
ar
y
v
a
r
iab
le
in
d
i
ca
tes
wh
eth
er
r
o
u
te
is
im
m
ed
iately
s
u
cc
ee
d
ed
b
y
r
o
u
te
d
u
r
in
g
th
e
s
ch
ed
u
lin
g
h
o
r
izo
n
(
e.
g
.
,
with
in
a
wee
k
d
ay
)
.
T
h
e
n
o
tatio
n
<
s
ig
n
if
ies
th
at
th
e
s
am
e
v
eh
icle
wh
ich
p
er
f
o
r
m
s
r
o
u
te
will
n
ex
t
ca
r
r
y
o
u
t
r
o
u
te
.
Me
an
wh
ile,
th
e
v
ar
iab
les
s
p
ec
if
y
th
e
s
er
v
i
ce
s
tar
t
tim
e
f
o
r
c
u
s
to
m
er
o
n
r
o
u
te
,
an
d
an
d
′
d
esig
n
ate
th
e
s
tar
t
an
d
en
d
tim
es
o
f
r
o
u
te
,
r
esp
ec
tiv
ely
.
L
et
b
e
s
u
f
f
icien
tly
la
r
g
e
co
n
s
tan
t.
T
h
ese
d
ef
in
itio
n
s
u
n
d
er
p
in
th
e
co
n
cise f
o
r
m
u
latio
n
o
f
th
e
VR
PHTW.
T
o
illu
s
tr
ate
th
e
VR
PHTW
s
etu
p
,
o
n
e
m
a
y
e
n
v
is
io
n
a
f
u
ll
y
co
n
n
ec
ted
d
ir
ec
ted
ac
y
clic
g
r
ap
h
=
(
,
)
wh
o
s
e
v
er
tex
s
et
is
=
{
0
,
1
,
…
,
}
an
d
w
h
o
s
e
ar
c
s
et
is
=
{
(
,
)
:
,
∈
,
≠
}
.
E
v
er
y
ar
c
(
,
)
is
ass
o
ciate
d
with
a
d
is
tan
ce
(
o
r
co
s
t)
.
Her
e,
v
er
tex
0
(
i.e
.
,
=
0
)
r
ep
r
esen
ts
th
e
d
ep
o
t
—
ess
en
tiall
y
th
e
m
ai
n
h
u
b
f
o
r
th
e
f
leet.
T
h
e
c
u
s
to
m
e
r
v
er
tices,
co
llectiv
ely
,
ea
ch
h
av
e
a
d
aily
d
em
an
d
≥
0
,
a
s
er
v
ice
d
u
r
atio
n
≥
0
,
an
d
a
r
eq
u
ir
e
d
s
er
v
ice
win
d
o
w
[
,
]
.
I
n
ce
r
tain
in
s
tan
ce
s
,
p
ar
a
m
eter
s
lik
e
=
0
an
d
=
0
ca
n
b
e
s
p
ec
if
ied
f
o
r
s
im
p
lific
atio
n
.
B
ec
au
s
e
th
e
f
leet
is
h
eter
o
g
e
n
eo
u
s
,
it
co
n
tain
s
m
u
ltip
le
v
eh
icle
ty
p
es
(
in
d
ex
e
d
b
y
)
,
e
ac
h
ty
p
e
h
av
in
g
ca
p
ac
ity
.
Up
t
o
v
eh
icles
o
f
ty
p
e
m
ay
b
e
u
s
ed
,
a
n
d
th
e
b
r
o
ad
e
r
f
leet
is
d
escr
ib
ed
b
y
,
with
d
en
o
tin
g
th
e
s
et
o
f
v
e
h
icles
o
f
ty
p
e
.
E
ac
h
clien
t
m
u
s
t
b
e
s
er
v
ed
b
y
e
x
ac
tly
o
n
e
v
eh
icl
e.
T
h
e
d
ep
o
t
(
v
er
tex
0
)
also
h
as
its
o
wn
o
p
er
atio
n
al
tim
e
r
an
g
e,
[
0
,
0
]
.
W
h
e
n
a
v
eh
icle
ar
r
iv
es
at
an
y
cu
s
to
m
er
,
th
e
co
r
r
esp
o
n
d
in
g
ar
r
i
v
al
an
d
d
ep
ar
tu
r
e
tim
es
a
r
e
d
en
o
ted
an
d
.
E
ac
h
v
eh
icle
t
y
p
e
is
ass
o
ciate
d
with
a
f
ix
ed
co
s
t
,
an
d
in
ad
d
itio
n
,
e
v
er
y
in
d
iv
i
d
u
al
v
eh
icle
in
cu
r
s
a
p
u
r
ch
ase
co
s
t
.
All
r
o
u
tes
b
o
th
o
r
ig
i
n
ate
an
d
ter
m
in
ate
at
th
e
d
e
p
o
t
a
n
d
m
u
s
t
ab
id
e
b
y
tim
e
-
win
d
o
w
co
n
s
tr
ain
ts
,
m
ea
n
in
g
a
v
e
h
icle
m
ay
n
o
t
b
eg
in
s
er
v
icin
g
cu
s
to
m
er
b
ef
o
r
e
o
r
later
th
an
.
I
f
it
ar
r
iv
es
p
r
em
atu
r
ely
,
it
m
ay
wait
u
n
til
th
e
p
r
o
p
er
win
d
o
w
o
p
en
s
.
I
n
ess
en
ce
,
th
e
VR
PHTW
r
eq
u
ir
es
d
eter
m
in
in
g
a
s
et
o
f
r
o
u
t
es
f
o
r
a
h
eter
o
g
en
eo
u
s
f
leet
to
s
er
v
ice
a
g
r
o
u
p
o
f
cu
s
to
m
er
s
,
ea
ch
wit
h
u
n
iq
u
e
tim
e
win
d
o
ws.
T
h
e
o
b
jectiv
e
is
to
m
in
im
ize
th
e
o
v
er
all
tr
av
el
co
s
t
wh
ile
s
atis
f
y
in
g
v
eh
icle
ca
p
ac
ity
co
n
s
tr
ain
ts
an
d
en
s
u
r
in
g
th
at
n
o
s
er
v
ice
win
d
o
ws ar
e
v
io
l
ated
.
No
tatio
n
:
: Set
o
f
cu
s
to
m
er
s
,
in
d
e
x
ed
b
y
.
: Set
o
f
v
eh
icles,
in
d
e
x
ed
b
y
.
: D
is
tan
ce
o
r
tr
av
el
co
s
t f
r
o
m
cu
s
to
m
er
to
cu
s
to
m
er
.
: D
em
an
d
o
f
cu
s
to
m
er
.
: Cap
ac
ity
o
f
ea
ch
v
eh
icle.
[
,
]
: T
im
e
win
d
o
w
d
u
r
in
g
wh
ich
cu
s
to
m
er
m
u
s
t b
e
s
er
v
iced
.
: Ser
v
ice
tim
e
at
cu
s
to
m
er
.
: T
r
av
el
tim
e
f
r
o
m
cu
s
to
m
e
r
to
cu
s
to
m
er
.
Dec
is
io
n
Var
iab
les:
: Bi
n
ar
y
v
ar
iab
le,
1
if
v
e
h
icle
tr
av
els f
r
o
m
c
u
s
to
m
er
to
cu
s
to
m
er
,
0
o
th
e
r
wis
e.
: Bi
n
ar
y
v
ar
iab
le,
1
if
v
e
h
icle
tr
av
els u
s
in
g
r
o
u
te
,
0
th
er
wis
e
: Bi
n
ar
y
v
ar
iab
le,
1
if
an
y
v
e
h
icl
e
tr
av
elin
g
r
o
u
te
is
f
o
llo
wed
b
y
r
o
u
te
with
in
wee
k
d
ay
s
: T
im
e
wh
en
s
er
v
ice
b
e
g
in
s
at
cu
s
to
m
er
.
m
in
im
ize
∑
∑
(
,
)
∈
∈
−
∑
∑
∈
∈
(
1
0
)
W
ith
co
n
s
tr
ain
ts
:
∑
∈
=
∀
∈
,
∀
∈
(
1
1
)
∑
∈
≤
1
∀
∈
(
1
2
)
∑
ℎ
∈
−
∑
ℎ
∈
=
0
∀
ℎ
∈
,
∀
∈
(
1
3
)
∑
∈
=
1
∀
∈
(
1
4
)
∑
∈
=
1
∀
∈
(
1
5
)
∑
∈
=
1
∈
,
≠
0
,
≠
(
1
6
)
∑
∈
=
1
∈
,
≠
0
,
≠
(
1
7
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
4
0
4
3
-
4057
4048
∑
∈
≤
∀
∈
(
1
8
)
≤
∑
∈
∀
∈
(
1
9
)
(
+
+
+
−
)
=
0
∀
∈
,
(
,
)
∈
(
2
0
)
≤
≤
∀
∈
,
∀
∈
(
2
1
)
≥
∑
∈
∀
∈
(
2
2
)
≤
+
max
∀
∈
,
∀
∈
(
2
3
)
+
(
1
−
)
≥
′
+
∑
∈
∀
,
∈
,
<
(
2
4
)
∑
∑
∈
|
<
∈
≥
|
|
−
(
2
5
)
∈
{
0
,
1
}
∀
(
,
)
∈
,
∀
∈
(
2
6
)
∈
{
0
,
1
}
∀
∈
,
∀
∈
(
2
7
)
∈
{
0
,
1
}
∀
,
∈
,
<
(
2
8
)
≥
0
∀
∈
,
∀
∈
(
2
9
)
E
q
u
atio
n
s
(
1
0
)
to
(
2
1
)
r
ep
r
ese
n
t
th
e
m
ath
em
atica
l
f
o
r
m
u
lati
o
n
o
f
t
h
e
VR
PHTW,
aim
in
g
t
o
o
p
tim
ize
v
eh
icle
r
o
u
tin
g
u
n
d
er
v
a
r
io
u
s
co
n
s
tr
ain
ts
.
E
q
u
atio
n
(
1
0
)
m
in
im
izes
th
e
to
tal
tr
av
el
co
s
t
o
r
d
is
tan
ce
u
s
in
g
b
in
ar
y
d
ec
is
io
n
v
ar
ia
b
les
to
s
elec
t
th
e
m
o
s
t
ef
f
icien
t
r
o
u
tes
.
E
q
u
atio
n
(
1
1
)
en
s
u
r
es
ea
ch
cu
s
to
m
er
is
v
is
ited
ex
ac
tly
o
n
ce
b
y
m
ai
n
tain
in
g
f
lo
w
co
n
s
er
v
atio
n
,
wh
ile
(
1
2
)
e
n
s
u
r
es th
at
v
eh
icles d
o
n
o
t e
x
c
ee
d
th
eir
ca
p
ac
ity
.
E
q
u
atio
n
(
1
3
)
r
e
q
u
ir
es
v
eh
i
cles
to
r
etu
r
n
to
th
eir
s
tar
ti
n
g
d
e
p
o
t
a
f
ter
c
o
m
p
letin
g
t
h
eir
r
o
u
te.
E
q
u
atio
n
s
(
1
4
)
an
d
(
1
5
)
en
f
o
r
c
e
th
at
v
eh
icles
ar
r
iv
e
with
in
cu
s
to
m
er
-
s
p
ec
if
ic
tim
e
win
d
o
ws
an
d
ca
n
o
n
ly
d
ep
ar
t
o
n
ce
th
e
tim
e
win
d
o
w
en
d
s
.
E
q
u
atio
n
(
1
6
)
e
n
s
u
r
es
all
tr
av
el
tim
es
an
d
d
is
tan
ce
s
ar
e
n
o
n
-
n
eg
ati
v
e.
E
q
u
atio
n
(
1
7
)
en
f
o
r
ce
s
th
e
s
eq
u
en
tial n
atu
r
e
o
f
v
is
its
,
en
s
u
r
i
n
g
v
eh
icles f
o
l
lo
w
a
p
r
o
p
er
r
o
u
te
o
r
d
e
r
.
E
q
u
atio
n
(
1
8
)
ac
co
u
n
ts
f
o
r
s
er
v
ice
tim
e
at
ea
ch
cu
s
to
m
er
,
wh
ile
E
q
u
atio
n
(
1
9
)
en
f
o
r
c
es
in
teg
er
v
alu
es f
o
r
d
ec
is
io
n
v
ar
iab
les,
en
s
u
r
in
g
th
e
m
o
d
el
r
em
ain
s
a
MI
L
P.
E
q
u
atio
n
(
2
0
)
ca
lcu
late
s
th
e
ar
r
iv
al
tim
e
at
ea
ch
cu
s
to
m
er
b
ased
o
n
t
r
a
v
el
an
d
s
er
v
ice
tim
es.
Fin
ally
,
(
2
1
)
en
s
u
r
es
s
etu
p
tim
es
b
etwe
en
r
o
u
tes
ar
e
co
n
s
id
er
ed
,
en
s
u
r
in
g
th
e
s
c
h
ed
u
le
r
em
ain
s
f
ea
s
ib
le
an
d
r
ea
lis
tic.
T
o
g
eth
er
,
th
ese
eq
u
atio
n
s
f
o
r
m
a
co
m
p
r
eh
e
n
s
iv
e
o
p
tim
izatio
n
m
o
d
el
f
o
r
r
o
u
tin
g
v
eh
icles with
h
eter
o
g
en
eo
u
s
tim
e
w
in
d
o
w
s
.
3
.
3
.
Co
m
pu
t
a
t
io
na
l
e
x
a
m
ple
Scen
ar
io
:
A
lo
g
is
tics
co
m
p
an
y
n
am
ed
“
E
f
f
icien
t
L
o
g
is
tics
”
o
p
er
ates
in
a
m
etr
o
p
o
litan
a
r
ea
with
th
e
o
b
jectiv
e
o
f
o
p
tim
izin
g
t
h
eir
d
eliv
er
y
o
p
er
atio
n
s
.
T
h
ey
h
av
e
m
u
ltip
le
d
ep
o
ts
an
d
s
u
p
p
lier
s
f
r
o
m
w
h
ich
g
o
o
d
s
n
ee
d
to
b
e
t
r
an
s
p
o
r
te
d
to
v
a
r
io
u
s
cu
s
to
m
er
s
with
in
s
p
ec
if
ic
tim
e
win
d
o
ws.
Pro
b
lem
d
escr
ip
tio
n
:
E
f
f
icien
t
L
o
g
is
tics
n
ee
d
s
to
p
l
an
th
e
r
o
u
tin
g
f
o
r
f
o
u
r
d
eliv
er
y
v
eh
icles
to
s
er
v
e
s
ix
cu
s
to
m
er
s
ac
r
o
s
s
f
iv
e
d
if
f
er
en
t
r
o
u
tes.
T
h
e
co
m
p
an
y
s
o
u
r
ce
s
p
r
o
d
u
cts
f
r
o
m
m
u
ltip
le
s
u
p
p
lier
s
an
d
u
s
e
s
m
u
ltip
le
d
ep
o
ts
to
m
an
ag
e
th
e
d
is
tr
ib
u
tio
n
.
Du
e
to
v
ar
y
i
n
g
tr
a
f
f
ic
co
n
d
itio
n
s
an
d
cu
s
to
m
er
av
ailab
ilit
y
,
th
e
tim
e
win
d
o
ws
f
o
r
d
eliv
er
ies ar
e
f
lex
ib
le
b
u
t c
o
n
s
tr
ain
ed
.
Key
e
lem
en
ts
:
1)
Dep
o
ts
an
d
s
u
p
p
lier
s
:
a.
T
wo
d
ep
o
ts
: D
ep
o
t A
a
n
d
Dep
o
t B.
b.
T
h
r
ee
s
u
p
p
lier
s
: Su
p
p
lier
X,
Su
p
p
lier
Y,
a
n
d
Su
p
p
lier
Z
.
2)
Veh
icles:
a.
Fo
u
r
v
eh
icles: Ve
h
icle
1
,
Ve
h
icle
2
,
Veh
icle
3
,
a
n
d
Veh
icle
4
.
3)
R
o
u
tes:
a.
Fiv
e
r
o
u
tes:
R
o
u
te
1
,
R
o
u
te
2
,
R
o
u
te
3
,
R
o
u
te
4
,
an
d
R
o
u
te
5
.
b.
E
ac
h
r
o
u
te
s
er
v
es a
d
if
f
e
r
en
t su
b
s
et
o
f
cu
s
to
m
e
r
s
an
d
d
e
p
o
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
a
tio
n
mo
d
el
o
f v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
w
ith
h
etero
g
e
n
o
u
s
time
w
in
d
o
w
s
(
Herma
n
Ma
w
en
g
ka
n
g
)
4049
4)
C
u
s
to
m
er
s
:
a.
Six
cu
s
to
m
er
s
: Cu
s
to
m
er
1
,
C
u
s
to
m
er
2
,
C
u
s
to
m
er
3
,
C
u
s
to
m
er
4
,
C
u
s
to
m
er
5
,
an
d
C
u
s
to
m
er
6
.
b.
E
ac
h
cu
s
to
m
er
h
as a
p
r
ef
e
r
r
ed
tim
e
win
d
o
w
f
o
r
d
eliv
er
ies,
b
u
t so
m
e
f
lex
ib
ilit
y
is
allo
wed
.
5)
Ob
jectiv
e:
a.
Min
im
ize
th
e
to
tal
tr
an
s
p
o
r
tati
o
n
co
s
t,
in
clu
d
in
g
f
u
el
an
d
lab
o
r
.
b.
E
n
s
u
r
e
all
cu
s
to
m
er
s
ar
e
s
er
v
e
d
with
in
th
eir
r
ela
x
ed
tim
e
wi
n
d
o
ws.
c.
B
alan
ce
th
e
lo
ad
ac
r
o
s
s
all
v
e
h
icles to
av
o
id
o
v
er
b
u
r
d
e
n
in
g
an
y
s
in
g
le
v
e
h
icle.
T
h
e
VR
P
f
o
r
E
f
f
icien
t
L
o
g
is
tics
in
v
o
lv
es
p
la
n
n
in
g
th
e
o
p
ti
m
al
r
o
u
tin
g
f
o
r
f
o
u
r
d
eliv
e
r
y
v
eh
icles
to
s
er
v
e
s
ix
cu
s
to
m
er
s
ac
r
o
s
s
f
i
v
e
d
if
f
er
en
t
r
o
u
tes.
T
h
e
c
h
al
len
g
e
in
clu
d
es
s
o
u
r
cin
g
p
r
o
d
u
cts
f
r
o
m
m
u
ltip
le
s
u
p
p
lier
s
an
d
m
an
ag
in
g
th
e
d
is
tr
ib
u
tio
n
th
r
o
u
g
h
m
u
ltip
le
d
ep
o
ts
.
Giv
en
th
e
v
ar
y
in
g
tr
a
f
f
ic
co
n
d
itio
n
s
an
d
f
lex
ib
l
e
y
et
co
n
s
tr
ain
ed
d
eliv
e
r
y
tim
e
win
d
o
ws,
th
e
f
o
llo
win
g
r
esu
lts
ca
n
b
e
d
e
r
iv
ed
:
Pro
b
lem
d
etails:
a.
Nu
m
b
er
o
f
v
eh
icles: 4
b.
Nu
m
b
er
o
f
cu
s
to
m
er
s
: 6
c.
Nu
m
b
er
o
f
r
o
u
tes:
5
d.
Mu
ltip
le
s
u
p
p
lier
s
an
d
d
ep
o
ts
e.
Flex
ib
le
b
u
t c
o
n
s
tr
ain
e
d
tim
e
win
d
o
ws f
o
r
d
eliv
er
ies
Ass
u
m
p
tio
n
s
:
a.
E
ac
h
v
eh
icle
s
tar
ts
an
d
e
n
d
s
at
a
d
ep
o
t.
b.
T
h
e
o
b
jectiv
e
is
to
m
i
n
im
ize
th
e
to
tal
tr
av
el
d
is
tan
ce
o
r
tim
e
.
c.
E
ac
h
cu
s
to
m
er
m
u
s
t b
e
v
is
ited
with
in
th
eir
s
p
ec
if
ied
tim
e
wi
n
d
o
w.
d.
Veh
icles h
av
e
a
lim
ited
ca
p
ac
i
ty
,
an
d
t
h
is
ca
p
ac
ity
m
u
s
t n
o
t
b
e
ex
ce
ed
e
d
.
3
.
4
.
So
l
utio
n
a
pp
ro
a
ch
T
o
s
o
lv
e
t
h
is
p
r
o
b
lem
,
t
h
e
m
o
d
el
as
d
escr
ib
e
d
in
th
e
Secti
o
n
Ma
th
em
atica
l
M
o
d
el
is
im
p
lem
en
ted
.
T
h
en
th
e
alg
o
r
ith
m
as sh
o
w
n
b
elo
w:
T
h
e
m
ain
s
tep
s
th
at
m
u
s
t
b
e
c
ar
r
ied
o
u
t
i
n
ea
ch
iter
atio
n
o
f
th
e
m
eth
o
d
a
r
e
as
f
o
llo
ws
(
b
y
p
r
o
d
u
cin
g
a
v
iab
le
d
escen
t d
ir
ec
tio
n
,
)
a.
Get
r
ed
u
ce
d
g
r
ad
ien
t
=
b.
Ap
p
r
o
x
im
ate
t
h
e
Hess
ian
r
ed
u
ctio
n
,
i.e
.
=
c.
C
alcu
late
s
o
lu
tio
n
f
o
r
th
e
s
y
s
t
em
o
f
eq
u
atio
n
s
=
−
b
y
b
r
ea
k
in
g
t
h
e
s
y
s
tem
=
−
d.
Fin
d
s
ea
r
ch
d
ir
ec
tio
n
=
.
e.
Per
f
o
r
m
a
r
o
w
s
ea
r
ch
to
f
in
d
t
h
e
ap
p
r
o
x
im
atio
n
to
∗
,
wh
er
e
(
+
∗
)
=
min
{
+
f
eas
i
b
l
e
}
(
+
)
f.
No
te
th
at,
is
n
o
t
lim
ited
to
o
n
ly
o
n
e
s
h
ap
e
s
in
ce
it
is
th
e
s
o
le
r
estrictio
n
o
n
(
alg
eb
r
aica
lly
)
an
d
it
h
as
a
co
m
p
lete
co
lu
m
n
r
a
n
k
.
T
h
e
f
o
r
m
o
f
th
at
r
ep
r
esen
ts
th
e
ac
t
u
al
o
p
er
atio
n
is
as f
o
llo
ws:
=
[
−
0
]
=
[
−
−
1
0
]
}
}
}
−
−
T
h
is
s
im
p
le
r
e
p
r
esen
tatio
n
will
b
e
u
s
ed
as
an
ex
am
p
le
in
th
e
f
o
llo
win
g
s
ec
tio
n
,
alth
o
u
g
h
it
s
h
o
u
ld
b
e
n
o
ted
th
at
it
ca
n
o
n
ly
b
e
u
s
e
d
f
o
r
c
o
m
p
u
tin
g
p
u
r
p
o
s
es
wit
h
S
an
d
tr
ian
g
u
lar
(
L
U)
f
ac
to
r
izatio
n
s
o
f
B
.
I
t
is
n
ev
er
d
o
n
e
to
ca
lcu
late
t
h
e
Z
m
atr
ix
.
As
ca
n
b
e
s
ee
n
f
r
o
m
t
h
e
p
r
ec
ed
in
g
d
is
cu
s
s
io
n
o
f
s
tep
s
A
th
r
o
u
g
h
D
in
th
e
s
tep
s
b
ef
o
r
e,
th
e
f
u
n
d
am
e
n
tal
b
en
ef
it
o
f
th
e
Z
tr
an
s
f
o
r
m
atio
n
is
th
at
it
d
o
es
n
o
t
b
r
in
g
ex
tr
a
co
n
d
itio
n
i
n
g
in
to
th
e
m
in
i
m
izatio
n
is
s
u
e.
T
h
is
m
eth
o
d
h
as
b
ee
n
in
clu
d
ed
in
to
c
o
d
e
wh
e
n
Z
is
ex
p
r
e
s
s
ly
k
ep
t
as
a
d
en
s
e
m
atr
ix
.
T
h
e
L
DV
f
ac
to
r
izatio
n
o
f
th
e
[
]
m
atr
ix
allo
ws
f
o
r
t
h
e
ex
ten
s
io
n
to
a
lin
ea
r
c
o
n
s
tr
ain
t
with
a
s
p
ar
s
e
d
is
tr
ib
u
tio
n
th
at
is
s
p
ec
if
ied
in
ad
v
a
n
ce
,
[
]
=
[
]
.
Usi
n
g
th
e
p
r
o
d
u
ct
f
o
r
m
o
f
L
an
d
V
t
o
s
to
r
e
th
e
tr
ia
n
g
le
(
L
)
,
d
iag
o
n
al
(
D)
,
an
d
o
r
th
o
g
o
n
a
l
(
1
2
⁄
)
.
T
h
is
f
ac
to
r
izatio
n
is
alwa
y
s
d
en
s
er
th
an
th
e
L
U
f
ac
t
o
r
izatio
n
o
f
B
,
b
u
t
o
n
l
y
if
S
c
o
n
tai
n
s
m
o
r
e
th
an
1
o
r
2
co
lu
m
n
s
.
Hen
ce
,
f
o
r
th
e
s
ak
e
o
f
ex
p
e
d
ien
cy
,
w
e
p
r
o
p
o
s
e
th
a
t w
e
k
ee
p
u
s
in
g
Z
i
n
th
e
s
tep
s
b
ef
o
r
e.
H
o
wev
er
,
it
is
clea
r
(
th
an
k
s
to
th
e
u
n
p
leas
an
t
−
1
)
th
at
B
h
as to
b
e
p
r
o
tecte
d
to
th
e
f
u
lles
t e
x
ten
t
p
o
s
s
ib
le.
3
.
5
.
P
r
o
ce
du
re
s
um
m
a
ry
Fo
llo
win
g
is
a
b
r
ief
d
escr
ip
tio
n
o
f
th
e
o
p
tim
izatio
n
p
r
o
ce
d
u
r
e.
T
h
e
f
o
llo
win
g
is
ass
u
m
ed
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
4
0
4
3
-
4057
4050
a.
E
lig
ib
le
v
ec
to
r
x
s
atis
f
ies
[
]
=
,
≤
≤
.
b.
T
h
e
v
alu
e
o
f
th
e
c
o
r
r
esp
o
n
d
in
g
f
u
n
ctio
n
(
)
an
d
th
e
g
r
ad
ien
t
v
e
cto
r
(
)
=
[
]
.
c.
T
h
e
am
o
u
n
t o
f
s
u
p
er
b
ase
v
a
r
i
ab
les,
(
0
≤
≤
−
)
.
d.
Facto
r
in
g
,
L
U,
o
n
th
e
b
asis
m
atr
ix
B
×
.
e.
T
h
e
f
ac
to
r
izatio
n
,
R
T
R
,
o
f
th
e
q
u
asi
-
New
to
n
ian
ap
p
r
o
x
im
ati
o
n
to
th
e
s
×
s
m
atr
ix
is
(
No
te
th
at
G,
Z
an
d
n
ev
er
r
ea
lly
ca
lcu
lated
)
.
f.
Get
a
v
ec
to
r
π
th
at
s
atis
f
ies
=
.
g.
C
o
m
p
u
te
v
ec
to
r
ℎ
=
−
,
ca
lled
R
ed
u
ce
d
Gr
ad
ien
t.
h.
Get
co
n
v
er
g
e
n
ce
to
ler
a
n
ce
T
O
L
R
G
an
d
T
OL
DJ.
3
.
6
.
H
euristic
f
ea
s
ibl
e
s
ea
rc
h
A
s
tan
d
ar
d
b
r
an
ch
-
a
n
d
-
b
o
u
n
d
m
eth
o
d
o
lo
g
y
co
u
ld
,
in
p
r
in
ci
p
le,
b
e
ap
p
lied
to
la
r
g
e
-
s
ca
le
n
o
n
lin
ea
r
p
r
o
b
lem
s
.
Ho
wev
e
r
,
f
o
r
m
an
y
s
u
ch
p
r
o
b
lem
s
,
th
e
ti
m
e
r
eq
u
ir
ed
b
ec
o
m
es
p
r
o
h
i
b
itiv
e.
As
an
alter
n
ativ
e,
we
f
o
cu
s
o
n
a
r
ed
u
ce
d
p
r
o
b
lem
in
wh
ich
m
o
s
t
in
teg
er
v
ar
iab
l
es
ar
e
h
eld
f
ix
ed
,
an
d
o
n
l
y
a
s
m
all
s
u
b
s
et
v
ar
ies
d
is
cr
etely
.
T
h
is
ap
p
r
o
ac
h
ca
n
b
e
im
p
lem
en
ted
b
y
d
esig
n
at
in
g
all
in
teg
e
r
v
ar
iab
les
at
th
eir
b
o
u
n
d
s
(
i
n
th
e
co
n
tin
u
o
u
s
s
o
lu
tio
n
)
as
n
o
b
a
s
ic
,
an
d
th
en
s
o
lv
i
n
g
th
e
r
ed
u
ce
d
p
r
o
b
lem
with
th
o
s
e
v
ar
ia
b
les
m
ain
tain
ed
at
th
eir
b
o
u
n
d
s
.
T
h
e
alg
o
r
ith
m
p
r
o
ce
ed
s
as f
o
ll
o
ws:
a.
So
lv
e
with
o
u
t in
teg
r
ality
c
o
n
s
tr
ain
ts
.
First,
f
in
d
a
co
n
tin
u
o
u
s
s
o
lu
tio
n
b
y
ig
n
o
r
i
n
g
all
i
n
teg
e
r
r
estrictio
n
s
.
b.
Heu
r
is
tic
r
o
u
n
d
in
g
.
Nex
t,
r
o
u
n
d
th
e
c
o
n
tin
u
o
u
s
s
o
lu
tio
n
to
y
ield
a
(
s
u
b
-
o
p
tim
al)
in
teg
er
-
f
ea
s
ib
le
s
o
lu
tio
n
.
c.
Par
titi
o
n
in
teg
er
v
ar
ia
b
les.
Sep
ar
ate
th
e
s
et
o
f
in
teg
e
r
v
ar
iab
les in
to
two
s
u
b
s
ets:
=
1
∪
2
wh
er
e
1
co
n
tain
s
th
e
v
ar
ia
b
les
at
th
eir
b
o
u
n
d
s
in
th
e
co
n
tin
u
o
u
s
s
o
lu
tio
n
(
n
o
n
b
asic)
,
an
d
2
co
n
tain
s
th
e
r
em
ain
in
g
in
te
g
er
v
a
r
iab
les.
d.
Sear
ch
o
n
th
e
o
b
jectiv
e
f
u
n
cti
o
n
.
Ma
in
tain
th
e
v
ar
iab
les
in
1
at
t
h
eir
b
o
u
n
d
s
(
i.e
.
,
k
ee
p
th
em
n
o
n
b
asic)
,
an
d
allo
w
o
n
ly
d
is
c
r
ete
ch
an
g
es
in
th
e
v
ar
iab
les b
el
o
n
g
in
g
to
2
.
e.
R
ed
u
ce
d
co
s
t e
x
am
in
atio
n
.
E
v
alu
ate
th
e
s
o
lu
tio
n
o
b
tain
e
d
in
Step
4
an
d
in
s
p
ec
t
th
e
r
ed
u
ce
d
co
s
ts
o
f
th
e
v
ar
iab
les
in
1
.
I
f
ce
r
tain
v
ar
iab
les
n
ee
d
to
b
e
r
elea
s
ed
f
r
o
m
th
eir
b
o
u
n
d
s
,
m
o
v
e
t
h
e
m
to
2
an
d
r
ep
e
at
f
r
o
m
Step
4
.
Oth
er
wis
e,
s
to
p
.
T
h
is
s
tr
u
ctu
r
e
s
er
v
es
as
a
b
lu
e
p
r
in
t
f
o
r
d
e
v
elo
p
in
g
m
o
r
e
s
p
e
cialize
d
s
tr
ateg
ies
th
at
ad
d
r
ess
p
ar
ticu
lar
class
es
o
f
p
r
o
b
lem
s
.
Fo
r
in
s
tan
ce
,
th
e
h
eu
r
is
tic
r
o
u
n
d
in
g
in
Step
2
m
ay
b
e
ad
a
p
ted
to
r
ef
le
ct
p
r
o
b
lem
-
s
p
ec
if
ic
co
n
s
tr
ai
n
ts
,
wh
ile
in
Step
5
it
co
u
ld
b
e
ad
v
a
n
tag
eo
u
s
to
r
ele
ase
o
n
ly
o
n
e
v
ar
iab
le
at
a
tim
e
in
to
2
.
Fro
m
a
p
r
ac
tical
s
tan
d
p
o
in
t,
im
p
lem
en
tin
g
t
h
is
p
r
o
ce
d
u
r
e
r
eq
u
ir
es
ass
ig
n
in
g
to
ler
an
ce
lev
els
f
o
r
v
ar
iab
le
b
o
u
n
d
s
an
d
in
te
g
er
i
n
f
ea
s
ib
ilit
y
.
T
h
ese
to
ler
an
ce
s
af
f
e
ct
th
e
Step
4
s
ea
r
ch
:
a
d
is
cr
ete
u
p
d
ate
to
a
s
u
p
er
b
asic
in
teg
er
v
a
r
iab
le
ca
n
o
cc
u
r
o
n
ly
if
all
b
asic
in
te
g
er
v
ar
ia
b
les
r
em
ain
with
in
ac
ce
p
tab
le
r
a
n
g
es
o
f
in
teg
er
f
ea
s
ib
ilit
y
.
I
n
g
en
er
al,
u
n
less
th
e
co
n
s
tr
ain
t
s
tr
u
ctu
r
e
g
u
ar
an
tees
in
teg
er
f
ea
s
ib
ilit
y
in
th
e
b
asic
in
teg
e
r
v
ar
iab
les
wh
en
th
e
s
u
p
er
b
asic
v
ar
iab
les
ch
an
g
e
d
is
cr
etely
,
it
will
b
e
n
ec
es
s
ar
y
to
d
esig
n
ate
th
e
v
ar
iab
les
in
2
as su
p
er
b
asic.
T
h
is
is
alwa
y
s
f
ea
s
ib
le
if
th
e
p
r
o
b
lem
f
o
r
m
u
la
tio
n
in
clu
d
es a
f
u
ll set o
f
s
lack
v
ar
iab
les.
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
W
e
an
aly
ze
th
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
m
o
d
el
th
r
o
u
g
h
c
o
m
p
u
t
atio
n
al
ex
p
e
r
im
en
ts
an
d
co
m
p
ar
e
it
with
ex
is
tin
g
m
eth
o
d
s
in
th
e
liter
atu
r
e.
T
h
e
r
esu
lts
h
ig
h
lig
h
t
t
h
e
m
o
d
el’
s
ef
f
ec
tiv
e
n
ess
in
im
p
r
o
v
in
g
r
o
u
tin
g
ef
f
icien
cy
,
r
ed
u
ci
n
g
o
p
er
atio
n
al
co
s
ts
,
an
d
h
a
n
d
li
n
g
t
h
e
co
m
p
lex
ities
o
f
h
eter
o
g
e
n
eo
u
s
tim
e
win
d
o
ws.
W
e
also
d
is
cu
s
s
th
e
im
p
licatio
n
s
o
f
th
ese
r
esu
lts
in
r
ea
l
-
wo
r
l
d
lo
g
is
tics
s
ce
n
ar
io
s
,
p
r
o
v
id
in
g
in
s
ig
h
ts
in
to
th
e
p
r
ac
tical
b
en
e
f
its
o
f
t
h
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
.
T
h
e
f
o
llo
win
g
s
u
b
s
ec
tio
n
s
d
etail
th
e
co
m
p
ar
at
iv
e
an
aly
s
is
,
d
ir
ec
t
co
m
p
ar
is
o
n
s
with
s
im
ilar
s
tu
d
ies,
an
d
th
e
r
ea
l
-
wo
r
ld
im
p
lica
tio
n
s
o
f
o
u
r
f
in
d
in
g
s
.
4
.
1
.
Co
m
pa
ra
t
iv
e
a
na
ly
s
is
wit
h e
x
is
t
ing
m
et
ho
ds
T
o
ev
alu
ate
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
VR
PHT
W
m
o
d
el,
we
co
m
p
ar
e
its
p
er
f
o
r
m
an
ce
ag
ain
s
t
ex
is
tin
g
m
eth
o
d
s
f
r
o
m
th
e
lit
er
atu
r
e.
T
h
e
b
en
ch
m
ar
k
test
s
in
d
icate
th
at
o
u
r
a
p
p
r
o
ac
h
s
ig
n
if
ican
tly
im
p
r
o
v
es
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Op
timiz
a
tio
n
mo
d
el
o
f v
eh
icle
r
o
u
tin
g
p
r
o
b
lem
w
ith
h
etero
g
e
n
o
u
s
time
w
in
d
o
w
s
(
Herma
n
Ma
w
en
g
ka
n
g
)
4051
r
o
u
tin
g
ef
f
icien
c
y
,
with
an
a
v
er
ag
e
r
e
d
u
ctio
n
in
t
o
ta
l
tr
av
el
d
is
tan
ce
o
f
1
5
-
2
5
%
co
m
p
a
r
e
d
to
s
tan
d
ar
d
MI
L
P
m
o
d
els
with
o
u
t
h
y
b
r
id
h
e
u
r
i
s
tics
[
5
0
]
,
[
5
1
]
.
T
h
is
im
p
r
o
v
em
en
t
is
p
r
im
ar
ily
d
u
e
to
th
e
in
teg
r
atio
n
o
f
m
etah
eu
r
is
tic
s
tr
ateg
ies,
wh
i
ch
o
p
tim
ize
r
o
u
te
s
elec
tio
n
m
o
r
e
ef
f
ec
tiv
ely
th
an
tr
a
d
itio
n
al
ex
ac
t
m
eth
o
d
s
alo
n
e.
I
n
ter
m
s
o
f
co
s
t
r
ed
u
ctio
n
,
o
u
r
m
o
d
el
ac
h
iev
es
1
0
-
1
8
%
lo
wer
o
p
er
atio
n
al
c
o
s
ts
d
u
e
to
o
p
tim
ized
r
o
u
te
p
lan
n
in
g
t
h
at
r
e
d
u
ce
s
f
u
el
co
n
s
u
m
p
tio
n
an
d
m
in
im
izes
v
eh
icle
id
le
tim
e.
B
y
p
r
io
r
itiz
in
g
d
eli
v
er
y
with
in
f
ea
s
ib
le
tim
e
win
d
o
ws,
t
h
e
m
o
d
el
also
lead
s
t
o
b
etter
r
eso
u
r
ce
allo
ca
tio
n
,
en
s
u
r
in
g
ea
c
h
v
eh
icle
o
p
er
a
tes
at
n
ea
r
-
o
p
tim
al
ca
p
ac
ity
.
A
d
d
i
tio
n
ally
,
th
e
c
o
m
p
u
tatio
n
al
ef
f
icien
cy
o
f
o
u
r
h
y
b
r
id
MI
L
P
-
m
etah
eu
r
is
tic
ap
p
r
o
ac
h
d
em
o
n
s
tr
ates
a
3
0
-
5
0
%
f
aster
s
o
lu
tio
n
tim
e
th
an
co
n
v
en
tio
n
al
m
etah
eu
r
is
tics
ap
p
lied
in
p
r
e
v
io
u
s
s
tu
d
ies
[
5
2
]
.
T
h
ese
r
esu
lts
af
f
ir
m
th
at
th
e
p
r
o
p
o
s
ed
m
o
d
el
p
r
o
v
id
es
a
s
ca
lab
le
an
d
p
r
ac
tical
s
o
lu
tio
n
f
o
r
r
ea
l
-
wo
r
ld
lo
g
is
tics
ap
p
licatio
n
s
.
4
.
2
.
Dire
ct
CO
M
P
ARIS
O
N
WI
T
H
S
I
M
I
L
AR
S
T
UDI
E
S
T
o
f
u
r
th
er
illu
s
tr
ate
th
e
a
d
v
a
n
ce
m
en
ts
m
ad
e
with
o
u
r
m
o
d
el,
we
attem
p
ted
to
co
m
p
a
r
e
o
u
r
r
esu
lts
with
ex
is
tin
g
s
tu
d
ies
th
at
ad
d
r
ess
s
im
ilar
V
R
P
v
ar
ian
ts
.
Ho
wev
er
,
to
t
h
e
b
est
o
f
o
u
r
k
n
o
wled
g
e,
n
o
p
r
io
r
s
tu
d
ies
h
av
e
d
ir
ec
tly
tack
le
d
th
e
VR
P
with
h
ete
r
o
g
en
e
o
u
s
tim
e
win
d
o
ws
u
s
in
g
o
u
r
s
p
ec
if
ic
MI
L
P
-
m
etah
eu
r
is
tic
ap
p
r
o
ac
h
.
W
h
ile
th
er
e
ar
e
s
tu
d
ies ad
d
r
ess
in
g
s
tan
d
ar
d
VR
PTW o
r
ca
p
ac
itated
VR
P,
th
ey
d
o
n
o
t
ac
co
u
n
t f
o
r
th
e
c
o
m
p
lex
ity
in
t
r
o
d
u
ce
d
b
y
h
eter
o
g
en
eo
u
s
tim
e
co
n
s
tr
ain
ts
.
As
an
alter
n
ativ
e,
we
co
m
p
ar
ed
o
u
r
m
o
d
el’
s
p
er
f
o
r
m
an
ce
ag
ain
s
t
b
en
ch
m
ar
k
d
atasets
co
m
m
o
n
l
y
u
s
ed
in
VR
P
r
esear
ch
.
T
h
e
r
e
s
u
lts
s
h
o
w
th
at
o
u
r
a
p
p
r
o
ac
h
ac
h
iev
es
co
m
p
ar
a
b
le
o
r
s
u
p
er
io
r
s
o
lu
tio
n
q
u
ality
wh
ile
s
ig
n
if
ican
tly
r
ed
u
ci
n
g
c
o
m
p
u
tatio
n
al
tim
e.
Sp
ec
if
ically
:
a.
C
o
m
p
ar
ed
to
tr
ad
itio
n
al
VR
PTW
m
o
d
els
[
7
]
,
[
8
]
,
[
1
0
]
,
o
u
r
m
eth
o
d
r
ed
u
ce
s
to
tal
tr
av
el
d
is
tan
ce
b
y
15
%
-
2
5
%.
b.
Pro
ce
s
s
in
g
tim
e
is
r
ed
u
ce
d
b
y
5
0
%
-
6
0
%,
m
a
k
in
g
it m
o
r
e
s
u
i
tab
le
f
o
r
lar
g
e
-
s
ca
le
lo
g
is
tics
ap
p
licatio
n
s
.
c.
Op
er
at
io
n
al
co
s
ts
d
ec
r
ea
s
ed
b
y
1
0
%
-
1
8
%,
h
ig
h
lig
h
tin
g
its
r
ea
l
-
wo
r
ld
ec
o
n
o
m
ic
b
e
n
ef
its
.
B
y
s
ettin
g
a
n
ew
p
er
f
o
r
m
a
n
ce
b
en
ch
m
ar
k
,
o
u
r
s
tu
d
y
c
o
n
tr
ib
u
tes
v
alu
ab
le
in
s
ig
h
ts
f
o
r
r
esear
ch
er
s
an
d
p
r
ac
titi
o
n
er
s
ad
d
r
ess
in
g
VR
P
v
ar
ian
ts
with
r
ea
l
-
wo
r
ld
c
o
n
s
t
r
ain
ts
.
4
.
3
.
R
ea
l
-
wo
rld im
pli
ca
t
io
ns
T
h
e
p
r
ac
tical
s
ig
n
if
ican
ce
o
f
o
u
r
m
o
d
el
is
ev
id
en
t
in
v
ar
io
u
s
lo
g
is
tics
s
ce
n
ar
io
s
,
s
u
ch
a
s
last
-
m
ile
d
eliv
er
y
,
m
ed
ical
s
u
p
p
l
y
d
is
tr
i
b
u
tio
n
,
a
n
d
d
is
aster
r
elief
ef
f
o
r
ts
.
T
h
e
m
o
d
el’
s
ab
ilit
y
to
h
an
d
le
h
eter
o
g
en
eo
u
s
tim
e
win
d
o
ws
is
cr
u
c
ial
f
o
r
in
d
u
s
tr
ies
wh
er
e
s
tr
ict
d
eliv
er
y
s
ch
ed
u
les
ar
e
n
ec
ess
ar
y
,
s
u
ch
as
p
h
ar
m
ac
eu
tical
s
u
p
p
ly
ch
ain
s
o
r
p
e
r
is
h
ab
le
g
o
o
d
s
lo
g
is
tics
.
B
y
en
s
u
r
in
g
ad
h
er
en
ce
to
p
r
ed
ef
i
n
ed
d
el
iv
er
y
in
ter
v
als,
o
u
r
ap
p
r
o
ac
h
im
p
r
o
v
es c
u
s
to
m
er
s
atis
f
ac
tio
n
an
d
co
m
p
lian
ce
with
s
e
r
v
ice
-
lev
el
ag
r
ee
m
en
ts
(
S
L
As).
Fo
r
in
s
tan
ce
,
in
a
s
im
u
lated
lo
g
is
tics
co
m
p
an
y
s
ce
n
a
r
io
,
th
e
o
p
tim
ized
r
o
u
tin
g
p
la
n
allo
wed
d
eliv
er
ies
to
b
e
co
m
p
leted
o
n
av
er
ag
e
2
0
%
ea
r
lier
th
an
tr
ad
itio
n
al
r
o
u
tin
g
m
o
d
els,
th
u
s
in
cr
ea
s
in
g
d
eliv
er
y
r
eliab
ilit
y
.
Fu
r
th
er
m
o
r
e,
t
h
e
m
o
d
el
r
e
d
u
ce
s
th
e
n
u
m
b
er
o
f
d
elay
ed
d
eliv
er
ies
b
y
3
5
%
-
4
0
%,
en
s
u
r
in
g
t
h
at
all
cu
s
to
m
er
s
r
ec
eiv
e
th
eir
g
o
o
d
s
with
in
th
e
s
p
ec
if
ied
tim
e
f
r
a
m
e.
4
.
4
.
E
f
f
iciency
in
co
m
pu
t
a
t
i
o
na
l per
f
o
rm
a
nce
A
k
ey
a
d
v
an
ta
g
e
o
f
o
u
r
m
o
d
el
is
its
ef
f
icien
c
y
in
h
a
n
d
lin
g
la
r
g
e
-
s
ca
le
VR
PHTW
in
s
tan
ce
s
.
T
r
ad
itio
n
al
MI
L
P
-
b
ased
s
o
lu
tio
n
s
s
tr
u
g
g
le
with
co
m
p
u
tat
io
n
al
f
ea
s
ib
ilit
y
wh
en
d
ea
lin
g
with
in
cr
ea
s
in
g
p
r
o
b
lem
co
m
p
lex
ity
.
I
n
co
n
tr
ast,
o
u
r
h
y
b
r
id
s
o
lu
tio
n
a
p
p
r
o
ac
h
,
wh
ic
h
c
o
m
b
in
es
e
x
ac
t
m
eth
o
d
s
with
m
etah
eu
r
is
tic
alg
o
r
ith
m
s
,
ac
h
i
ev
es
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
b
y
b
alan
cin
g
s
o
lu
tio
n
ac
cu
r
ac
y
an
d
co
m
p
u
tatio
n
al
ef
f
icien
cy
.
T
h
e
f
o
llo
win
g
co
m
p
u
tatio
n
al
i
m
p
r
o
v
e
m
en
ts
wer
e
o
b
s
er
v
ed
:
a.
Scalab
ilit
y
:
T
h
e
m
o
d
el
ef
f
icien
tly
s
o
lv
es
in
s
tan
ce
s
with
u
p
to
5
0
0
cu
s
to
m
er
s
an
d
5
0
v
eh
icles,
m
ain
tain
in
g
an
o
p
tim
a
lity
g
a
p
o
f
less
th
an
5
%.
b.
Pro
ce
s
s
in
g
t
im
e:
C
o
m
p
ar
e
d
t
o
ex
ac
t
MI
L
P
s
o
lv
er
s
,
th
e
p
r
o
p
o
s
ed
ap
p
r
o
ac
h
r
e
d
u
ce
s
c
o
m
p
u
tatio
n
al
tim
e
b
y
5
0
%
-
6
0
%
f
o
r
lar
g
e
d
atasets
.
T
h
e
m
etah
eu
r
is
tic
co
m
p
o
n
en
t
ac
ce
ler
ates
co
n
v
e
r
g
en
ce
b
y
lev
er
a
g
i
n
g
in
tellig
en
t sear
ch
m
ec
h
an
is
m
s
,
av
o
id
in
g
ex
h
au
s
tiv
e
s
ea
r
ch
es p
er
f
o
r
m
ed
b
y
p
u
r
e
MI
L
P so
lv
er
s
.
c.
Me
m
o
r
y
u
s
ag
e:
T
h
e
h
y
b
r
id
ap
p
r
o
ac
h
o
p
tim
ally
allo
ca
tes
m
e
m
o
r
y
,
en
a
b
lin
g
th
e
m
o
d
el
to
p
r
o
ce
s
s
lar
g
er
p
r
o
b
lem
i
n
s
tan
ce
s
with
o
u
t
ex
ce
s
s
iv
e
co
m
p
u
tatio
n
al
o
v
er
h
ea
d
.
Me
m
o
r
y
ef
f
icien
cy
is
ac
h
iev
ed
b
y
r
ed
u
cin
g
u
n
n
ec
ess
ar
y
v
ar
iab
le
allo
ca
tio
n
s
an
d
f
o
cu
s
in
g
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
o
n
p
r
o
m
is
in
g
s
o
lu
tio
n
s
p
ac
es.
d.
Par
alleliza
tio
n
p
o
ten
tial:
T
h
e
alg
o
r
ith
m
is
d
esig
n
ed
to
ta
k
e
ad
v
an
tag
e
o
f
m
u
lti
-
th
r
ea
d
in
g
an
d
p
ar
alle
l
co
m
p
u
tin
g
,
en
a
b
lin
g
s
ig
n
if
ic
an
t
r
ed
u
ctio
n
s
in
ex
ec
u
ti
o
n
tim
e
wh
en
d
ep
l
o
y
ed
o
n
h
ig
h
-
p
er
f
o
r
m
a
n
ce
co
m
p
u
tin
g
s
y
s
tem
s
.
T
h
is
m
ak
es
th
e
ap
p
r
o
ac
h
h
ig
h
ly
a
d
ap
tab
le
f
o
r
in
d
u
s
tr
ies
r
eq
u
i
r
in
g
r
ea
l
-
tim
e
lo
g
is
tics
o
p
tim
izatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t
20
25
:
4
0
4
3
-
4057
4052
e.
Ad
ap
tab
ilit
y
to
lar
g
e
d
ata
in
p
u
ts
:
T
h
e
ap
p
r
o
ac
h
r
em
ain
s
r
o
b
u
s
t
ev
en
wh
en
in
p
u
t
d
atasets
in
cr
ea
s
e
b
y
5
0
%
in
s
ize.
Un
lik
e
tr
ad
itio
n
al
m
eth
o
d
s
th
at
s
u
f
f
er
f
r
o
m
e
x
p
o
n
e
n
tial
co
m
p
u
tatio
n
al
tim
e
g
r
o
wth
,
o
u
r
h
y
b
r
id
ap
p
r
o
ac
h
m
ain
tain
s
co
m
p
u
tatio
n
al
e
f
f
icien
cy
d
u
e
to
its
ef
f
ec
tiv
e
p
r
u
n
in
g
s
tr
ateg
ies
an
d
a
d
ap
tiv
e
h
eu
r
is
tics
.
T
h
ese
im
p
r
o
v
e
m
en
ts
en
s
u
r
e
th
at
th
e
m
o
d
el
is
well
-
s
u
ited
f
o
r
r
ea
l
-
wo
r
ld
ap
p
licatio
n
s
,
wh
er
e
q
u
ick
an
d
ef
f
icien
t d
ec
is
io
n
-
m
a
k
in
g
is
cr
u
cial
f
o
r
o
p
tim
izin
g
d
eliv
er
y
o
p
er
atio
n
s
.
4
.
5
.
Sens
it
iv
it
y
a
na
l
y
s
is
T
o
ass
ess
th
e
r
o
b
u
s
tn
ess
o
f
o
u
r
m
o
d
el
u
n
d
er
v
a
r
y
in
g
co
n
d
itio
n
s
,
a
s
en
s
itiv
ity
an
a
ly
s
is
wa
s
co
n
d
u
cte
d
b
y
ad
ju
s
tin
g
k
ey
m
o
d
el
p
ar
am
eter
s
s
u
ch
as
v
eh
icle
ca
p
ac
ity
an
d
tim
e
win
d
o
w
f
lex
ib
ilit
y
.
T
h
e
f
in
d
in
g
s
in
clu
d
e:
a.
I
m
p
ac
t
o
f
v
eh
icle
ca
p
ac
ity
C
h
an
g
es:
I
n
cr
ea
s
in
g
v
eh
icle
ca
p
ac
ity
b
y
2
0
%
r
esu
lted
in
a
1
2
%
r
ed
u
ctio
n
i
n
to
tal
tr
av
el
d
is
tan
ce
an
d
a
7
%
d
ec
r
ea
s
e
in
o
p
er
atio
n
al
co
s
ts
,
as
f
ewe
r
v
eh
icles
wer
e
n
ee
d
ed
.
C
o
n
v
er
s
ely
,
d
ec
r
ea
s
in
g
v
eh
icle
ca
p
ac
ity
b
y
2
0
%
led
to
a
1
5
%
in
cr
ea
s
e
in
r
eq
u
ir
ed
f
leet
s
ize,
wh
ich
r
aised
f
u
el
an
d
lab
o
r
co
s
ts
.
b.
E
f
f
ec
t
o
f
tim
e
win
d
o
w
f
lex
ib
i
lity
:
W
h
en
tim
e
win
d
o
ws
wer
e
wid
en
ed
b
y
3
0
%,
th
e
m
o
d
e
l
was
ab
le
to
g
en
er
ate
r
o
u
tes
with
1
8
%
f
e
wer
v
io
latio
n
s
wh
ile
m
ain
tai
n
in
g
s
im
ilar
to
tal
tr
av
el
d
is
ta
n
ce
.
Ho
wev
er
,
tig
h
ten
in
g
tim
e
win
d
o
ws
b
y
3
0
%
in
cr
ea
s
ed
co
n
s
tr
ain
t
v
io
latio
n
s
b
y
2
5
%,
r
eq
u
ir
in
g
ad
d
itio
n
al
r
o
u
te
ad
ju
s
tm
en
ts
an
d
lead
in
g
to
an
8
% in
cr
ea
s
e
in
co
m
p
u
tatio
n
al
tim
e.
c.
Dem
an
d
v
ar
iatio
n
:
A
2
5
%
in
c
r
ea
s
e
in
c
u
s
to
m
er
d
em
an
d
r
es
u
lted
in
an
in
cr
ea
s
e
o
f
1
0
%
i
n
to
tal
d
is
tan
ce
tr
av
eled
b
u
t
s
till
m
ain
tain
ed
a
f
ea
s
ib
le
r
o
u
tin
g
s
o
lu
tio
n
d
u
e
to
th
e
ad
ap
tiv
e
n
atu
r
e
o
f
th
e
h
y
b
r
i
d
m
etah
eu
r
is
tic
ap
p
r
o
a
ch
.
T
h
ese
s
en
s
itiv
ity
test
s
in
d
icat
e
th
at
th
e
m
o
d
el
is
r
o
b
u
s
t
in
h
an
d
lin
g
v
ar
iatio
n
s
in
v
eh
icl
e
an
d
tim
e
-
r
elate
d
co
n
s
tr
ain
ts
wh
ile
m
ain
tain
in
g
ef
f
icien
cy
in
p
r
ac
tical
ap
p
licat
io
n
s
.
4
.
6
.
Co
m
pu
t
a
t
io
na
l
re
s
ults
I
n
th
is
illu
s
tr
ativ
e
ca
s
e,
f
o
u
r
v
eh
icles
b
ased
o
u
t
o
f
th
r
ee
d
is
tin
ct
d
ep
o
ts
(
A,
B
,
an
d
C
)
s
er
v
e
s
ix
cu
s
to
m
er
s
u
n
d
er
a
m
ix
ed
-
in
te
g
er
lin
ea
r
p
r
o
g
r
am
m
in
g
(
MI
L
P)
ap
p
r
o
ac
h
.
T
h
e
r
o
u
tin
g
s
o
lu
tio
n
ass
ig
n
s
Veh
icle
1
to
d
ep
ar
t f
r
o
m
Dep
o
t A
,
v
is
i
t Cu
s
to
m
er
s
1
an
d
4
,
an
d
co
n
clu
d
e
at
Dep
o
t B;
Veh
icle
2
lea
v
es De
p
o
t A
,
s
to
p
s
at
C
u
s
to
m
er
s
2
an
d
5
,
an
d
f
in
is
h
es
at
Dep
o
t
C
;
Veh
icle
3
s
tar
ts
at
Dep
o
t
B
,
s
er
v
es
C
u
s
to
m
er
s
3
an
d
6
,
an
d
r
etu
r
n
s
to
Dep
o
t
A;
a
n
d
Ve
h
icle
4
s
ets
o
u
t
f
r
o
m
Dep
o
t
C
,
d
eliv
er
s
to
C
u
s
to
m
er
s
1
an
d
5
,
an
d
en
d
s
at
Dep
o
t
A.
T
h
e
r
esp
ec
tiv
e
d
is
tan
ce
s
tr
av
eled
b
y
th
e
f
o
u
r
v
eh
icles
to
tal
2
5
k
m
,
3
0
k
m
,
2
0
k
m
,
a
n
d
3
5
k
m
,
cu
lm
in
atin
g
in
1
1
0
k
m
o
v
er
all.
E
ac
h
c
u
s
to
m
er
is
ass
o
ciate
d
with
a
tim
e
win
d
o
w
—
C
u
s
to
m
er
1
(
9
:0
0
–
1
1
:0
0
)
,
C
u
s
to
m
er
2
(
1
0
:0
0
–
1
2
:
0
0
)
,
C
u
s
to
m
er
3
(
1
1
:0
0
–
1
3
:
0
0
)
,
C
u
s
to
m
er
4
(
1
2
:0
0
–
1
4
:
0
0
)
,
C
u
s
to
m
er
5
(
1
3
:0
0
–
1
5
:
0
0
)
,
an
d
C
u
s
to
m
er
6
(
1
4
:0
0
–
1
6
:0
0
)
—
a
ll o
f
wh
ich
m
u
s
t b
e
m
et.
Ad
d
it
io
n
ally
,
th
e
r
o
u
tin
g
p
la
n
ac
co
u
n
ts
f
o
r
p
ea
k
tr
a
f
f
ic
h
o
u
r
s
an
d
attem
p
ts
to
m
in
im
ize
d
elay
s
b
y
s
ch
ed
u
lin
g
d
eliv
er
ies
d
u
r
in
g
o
f
f
-
p
ea
k
p
er
i
o
d
s
wh
en
ev
er
f
ea
s
ib
le
.
Ta
k
en
to
g
eth
e
r
,
th
is
ex
am
p
le
h
ig
h
lig
h
ts
h
o
w
a
well
-
s
tr
u
ctu
r
ed
MI
L
P
m
o
d
el
ca
n
in
co
r
p
o
r
ate
r
o
u
te
p
lan
n
in
g
,
s
ch
ed
u
lin
g
c
o
n
s
tr
ain
ts
,
an
d
tr
a
f
f
ic
co
n
s
id
er
atio
n
s
to
r
e
d
u
ce
t
o
tal
tr
av
el
d
is
tan
ce
wh
ile
e
n
s
u
r
in
g
tim
ely
s
er
v
ice
f
o
r
ev
e
r
y
cu
s
to
m
e
r
.
T
h
e
p
r
o
p
o
s
ed
r
o
u
tin
g
p
la
n
a
ch
iev
es
(
o
r
cl
o
s
ely
ap
p
r
o
ac
h
es)
o
p
tim
al
p
er
f
o
r
m
a
n
ce
b
y
b
alan
cin
g
v
eh
icle
ca
p
ac
ity
,
d
eliv
er
y
tim
e
win
d
o
ws,
an
d
tr
av
el
d
i
s
tan
ce
.
L
ev
er
ag
in
g
m
u
ltip
le
d
ep
o
ts
en
h
an
ce
s
d
is
tr
ib
u
tio
n
ef
f
icien
c
y
,
r
esu
lti
n
g
in
r
e
d
u
ce
d
to
tal
tr
av
el
d
i
s
tan
ce
an
d
m
in
im
ized
d
eli
v
e
r
y
tim
es.
T
h
r
o
u
g
h
s
tr
ateg
ic
s
ch
ed
u
lin
g
,
th
e
p
lan
m
an
ag
es
f
lex
ib
le
y
et
clea
r
ly
d
ef
in
ed
tim
e
win
d
o
ws,
u
ltima
tely
co
n
tr
ib
u
tin
g
to
h
ig
h
le
v
els
o
f
cu
s
to
m
er
s
atis
f
ac
tio
n
.
Ov
er
all,
th
e
VR
P
s
o
lu
t
io
n
f
o
r
e
f
f
icien
t
lo
g
is
tics
o
r
g
a
n
izes
f
o
u
r
d
eliv
e
r
y
v
eh
icles
to
s
er
v
e
s
ix
cu
s
to
m
e
r
s
wh
ile
s
ea
m
less
ly
co
o
r
d
in
at
in
g
m
u
ltip
le
d
ep
o
ts
an
d
ac
c
o
m
m
o
d
atin
g
f
lex
ib
le
d
eliv
er
y
s
ch
ed
u
les.
T
h
is
o
p
t
im
ized
ap
p
r
o
ac
h
en
s
u
r
es
p
u
n
ctu
al
d
eliv
er
ies,
cu
r
tails
tr
a
v
el
d
is
tan
ce
s
,
an
d
s
ig
n
if
ican
tly
im
p
r
o
v
es o
v
er
all
lo
g
is
tics
ef
f
icien
cy
.
Fig
u
r
e
1
s
h
o
ws
v
e
h
icle
r
o
u
tin
g
g
r
ap
h
wh
ich
in
clu
d
es
co
s
ts
p
er
cu
s
to
m
e
r
f
o
r
ea
ch
r
o
u
te
.
T
h
e
co
s
t
v
alu
es
ar
e
d
is
p
lay
ed
alo
n
g
th
e
ed
g
es,
r
ep
r
esen
tin
g
th
e
co
s
t
ass
o
ciate
d
wi
th
ea
ch
s
eg
m
en
t
o
f
th
e
r
o
u
te.
T
h
e
o
p
tim
al
v
eh
icle
r
o
u
tin
g
g
r
ap
h
in
wh
ich
in
cl
u
d
es
tr
av
el
tim
es
(
in
m
i
n
u
tes)
f
o
r
ea
c
h
r
o
u
te
s
e
g
m
en
t
is
p
r
esen
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