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REPORT DOCUMENTATION PAGE
Form Approved
OMB No.
0704-0188
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(Leave
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2 . REPORT
D A T E
Ju ne
1 9 9 8
3 .
REPORT TYPE
A N D
DATES
C O V E R E D
Master's T hes i s
TITLE
A N D
SU BTITLE
FLIGHT
HOURS
TO
ARMY HELICOPTERS
5 .
U N D I N G N U M B E R S
AUTHOR(S)
Bradley W .
PERFORMING
ORGANIZATION
NAM E(S)
A N D
ADDRESS(ES)
Postgraduate S c h o o l
o nt e rey , CA
3 9 4 3 - 5 0 0 0
8 .
PERFORMING
ORGANIZATION R E P O R T
N U M B E R
S P O N S O R I N G
/
M O N I T O R I N G
A G E N C Y
NAM E(S)
A N D
ADDRESS(ES)
10 .
S P O N S O R I N G /
MONITORING
A G E N C Y
REPORT
N U M B E R
. SUPPLEMENTARY
N O T E S
e views ex pres sed in this thes is are those
of
the author and do not re f lect the off ic ia l policy or position of the
Department
of
or
the U . S . G o v e r n m e n t .
DISTRIBUTION / A V A I L A B I L IT Y S T A T E M E N T
for public re lease; distribution is u nl imi t ed .
12b.
DISTRIBUTION
CODE
ABSTRACT
maximum
200 words)
Army
helicopter battalions,
consisting of
2 4
hel icopters valued from $ 2 0 6 . 4 million U H - 6 0 Blackhawk
battalion)
o
million A H - 6 4 Apache
battalion),
l locate
light
hours
o
hel icopters
using
manual
echniques
hat
have
caused
an
decrease
n
battalion
eployabi l i ty .
This
hes i s
odels
he
battalion's
light
hour
llocation
problem
using
it develops
both
a
mixed
integer
linear
program and
a
quadrat ic program.
The
2
nd
Battalion,
4
th
Aviation Regiment
4
th
Mechanized
Division currently u ses
a
spreadshee t implementation of
the
quadratic
program
d e ve lop e d
by the
author cal led
Quadrat ic Flight H o u r Allocation
M o d e l ) ,
hat s vai lab le o other battalions
or use
with existing
o f t ware and
resources .
hemixed integer linear
program,
called
F H A M ( F l i g h t Hour Allocation
M o d e l )
more appropriately mo de ls
problem, but
requires additional
sof tware .
his
thes is validates
the tw o
mo de ls
using
actual
flight
hour
data
from
a U H - 6 0
under
both
typical
training
and
co nt ing ency scenarios . T h e
mo de ls
pro v ide
a
monthly
flight
hour allocation
for the
ircraft
hat
esul t s n
teady-s ta te equ enc ing
f
aircraft
n to
hase
maintenance,
hus
liminating hase
b ack lo g
and providing
a
fixed number of aircraft avai lab le for
d e p loym e n t . This thesis
also
addres se s
the
neg a t iv e
of
current helicopter battalion readiness measu res
o n
deplo y ment and
of fers
al ternat ives .
.
S U B J E C T
T E R M S
Flight
Hour Allo ca t io n , Phase Maintenance
S chedu l ing
15 . N U M B E R O F
P A G E S
56
16 . PRICE
C O D E
. SECURITY CLASSIFICATION O F
18 .
SECURITY
CLASSIFICATION
O F
THIS PAGE
Unclassified
19 . SECURITY
CLASSIF I -CATION
O F
ABSTRACT
Uncla s s i f i ed
2 0 .
I M I T A T I O N
O F
ABSTRACT
U L
N
7540-01-280-5500
Standard
Form
29 8 (Rev.
2-89)
Prescribed by A N S I Std. 239-18
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Approved
fo r
public
release;
distribution
is
unlimited
ALLOCATING
FLIGHT
HOURS
TO
ARMY
HELICOPTERS
Brad ley
W .
Pippin
Capta in ,
Uni ted
States A r m y
B.S . ,
U n i t e d
States
M ili ta ry
A c a d e m y ,
9 8 8
Submit t ed
in partial
ful f i l lment
of the
requ i rements
f o r
th e
degree
of
MASTER O F SCIENCE IN OPERATIONS
RESEARCH
f rom
th e
NAVAL
POSTGRADUATE SCHOOL
June
1998
Author :
A p p r o v e d
b y :
TMam
rr
iin
T ̂
BradleyWJPippin
Robert
F . Dell ,
Thes i s
A d v i s o r
T h o m a s
Halwachs ,
Seco nd
Reader
Richard
E .
Rosenthal ,
C h a i r m a n
D e p a r t m e n t of Operat ions
Research
m
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D I S C L A I M E R
T he
reader
is
cautioned
that
computer
programs
developed
in
this
research
m ay
not
have
been
exercised
fo r
al l cases of
interest.
Whi le every effort w as made, within
th e
time available, to ensure
that
th e
programs ar e free of computational an d
logic
errors,
they cannot
be considered
validated.
ny application of these
programs without
additional
verification
is
at
th e
risk of th e
user.
VI
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TABLE OF
CONTENTS
I . NTRODUCTION
A .
ATTALION O R G A N I Z A T I O N
A N D
M A I N T E N A N C E
B A C K G R O U N D
B .
ISTORIC C A S E S T U D Y
C . ROBLEM D E F I N I T I O N
D . U T L I N E
I I .
ELATED R E S E A R C H
m.
OPTIMIZATION
M O D E L I N G
O F T H E F L I G H T
H O U R
ALLOCATION
P R O B L E M
5
A
MIXED
I N T E G E R L I N E A R
P R O G R A M
F O R M U L A T I O N
5
B .
Q F H A M
F O R M U L A T I O N 0
IV .
O M P U T A T I O N A L
R E S U L T S 1
A .
Y P I C A L T R A I N I N G S C E N A R I O
1
B .
P T I M I Z A T I O N R E S U L T S FOR T Y P I C A L T R A I N I N G
S C E N A R I O 3
C .
FHAM O P T I M I Z A T I O N
R E S U L T S
F O R
T Y P I C A L
TRAINING S C E N A R I O 8
D . F H A M O P T I M I Z A T I O N
O F
C O N T I N G E N C Y S C E N A R I O 1
E . ISCUSSION O F
T H E R E S U L T S 4
V .
O N C L U S I O N S
A N D
R E C O M M E N D A T I O N S
5
A .
E A D I N E S S I M P R O V E M E N T 5
B .
E C O M M E N D A T I O N S
7
C . FHAM
I M P L E M E N T A T I O N
9
L I S T O F R E F E R E N C E S
1
I N I T I A L DISTRIBUTION L I S T
3
VI I
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Vlll
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E X E C U T I V E
S U M M A R Y
A r m y
helicopter battalions, consisting of2 4
helicopters valued f rom
$206 .4
million
( U H - 6 0
Blackhawk
battalion) to
$432
million
( A H -6 4
Apache
battalion),
allocate
f l ight hours to
helicopters using
manual techniques
that
have caused an
unnecessary
decrease
in
battalion
deployability.
T he
st
Armored Division
(AD) , currently
assigned
in
Germany, provides an
example
where
th e
lack
of
individual
aircraft
f l ight
ho u r
allocation
management
resulted
in
a
non-deployable
helicopter
battalion.
During
th e
Dayton
Peace
Accord
arbitration
process ,
prior
to th e U . S. implementation
force
( I F O R )
deployment
to Bosnia ,
1
st
Armored
Division's
U H - 6 0
Blackhawk battalion
reported 89%
fully
mission
capable
( F M C ) .
Given th e
Army standard o f 7 5 %
F M C ,
al l reportable indications showed
a
battalion
ready
f or
deployment. However ,
th e
st
A D
trained extensively
f or
its
impending
deployment ,
an d when
th e
Dayton
Peace Accords
were
signed
in
late
N o v ember
1995
an d
st
A D w as ordered
to deploy, it immediately
sent
u p a
red
f lag.
T he
aviation
brigade
commander
directed
that
aircraft
with
less
than
75 f l ight
hours
remaining
until
phase
maintenance, o r
nine
of th e
battalion's
2 4
U H - 6 0
Blackhawks
would
not deploy.
his
problem w as
previously
unnoticed above
th e br igade
level and
w as
directly attributable
to
a
lack of
f l ight
hour
allocation
management
within th e
battalion.
This thesis models th e
battalion's
f l ight
hour
allocation
problem
using
optimization; it develops both a
mixed integer
linear
program and
a
quadratic
program.
T he
2
nd
Battalion,
4
th
Aviation
Regiment
of
4
th
Mechanized
Division
currently
uses
a
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sp readshee t
implementa t ion
of the
quadrat ic program
deve loped b y th e author called
Q F H A M
(Quadrat ic
Flight Hour
Allocat ion
M o d e l) ,
that
is
available to
other bat ta l ions
fo r
u se
with
exist ing
so f tware and
c o m p u t e r resources .
h e m i x e d
integer
l inear
prog ram, called FHAM (F l igh t Hour Allocat ion Model) m o r e
appropria te ly
mode ls
th e
prob lem, b u t
requires addit ional
sof tware .
h is
thesis
val idates th e tw o
m o d e l s
using
actual f l i gh t h o u r
data
f rom a
U H - 6 0
battal ion
under
both typical
training
and
con t ingency
scenarios .
h e
resul t
is a steady-state sequenc ing of aircraf t
into
phase
maintenance
that
el iminates p h a s e
maintenance
backlog and
provides
a f i x e d n u m b e r
of
aircraf t
available
for
dep loyment .
This
thes is
also
addresses
th e
negat ive
i m p a c t
of
cur ren t
hel icopter
battal ion readiness
m e a s u r e s
o n
deployabi l i ty
and of fers
alternatives.
Q F H A M br ings
immedia te results
to a helicopter battalion. F H A M w o u l d
increase th e
n u m b e r
of dep loyab le
ai rcraf t
for
st
AD's
U H - 6 0
bat ta l ion b y 2 0 . 8
%
( 8 3 . 3 %
vs. 6 2 . 5 % )
in
th e
scenario
d iscussed abo v e .
h e init ial m o d e l
set -up is s imple
and
requi res
a
battal ion
less
than
an
hour .
h e output
prov ides f l i gh t c o m p a n y
c o m m a n d e r s
a
by-a i rc ra f t
f l ight
h o u r
al locat ion
f o r
a
planning
cycle.
T h e
al locat ion
proces s
t akes less than 15
minutes
and
can b e
adjus ted
easily
during
the
planning
cyc le
if
m a j o r
c h a n g e s occur . h e aircraf t
f l i gh t
h o u r
al locat ion
planning
process
that
prev ious ly
h as
ei ther
b e e n
i gnored
or est imated us ing t ime-
c o n s u m i n g
m a n u a l
t echniques
can
no w
easily b e
accompl i shed with
an
au tomated
process .
T h e
percent
F M C
m e a s u r e s
th e
battalion's
abil i ty
to
mainta in
hel icopters
operat ional ly
ready,
but
it
provides
very
little
indicat ion
of a battalion's
deployabil i ty .
A n
ai rcraf t
is
dep loyab le
if it is both F M C
and
h as
a
m i n i m u m
n u m b e r
ofhours until
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phase maintenance.
Furthermore,
striving to maintain a high
percent
F M C
can
discourage
proactive
phase maintenance
procedures.
he
additional
readiness
measure
recommended in
this
thesis is a tiered
reporting
ofth e percentage
of
aircraft
above
2 5 ,
50 ,
and 75 hours.
his
report
gives
an
immediate
indication of
th e
actual
nu mber
of
deployable
aircraft, in
terms
of
phase
maintenance
scheduling,
for
th e battalion.
T he bottom
line:
ptimization models such as
Q F H A M improve
A r m y
helicopter
battalion deployability.
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L
NTRODUCTION
Army
helicopter
battalions
allocate
f l ight
hours to
helicopters using
manual
techniques
that have caused
an
unnecessary decrease in battalion
deployability.
his
thesis
models
th e
battalion's f l ight
hour
allocation
problem
using
optimization; it
develops
both
a
mix ed integer
linear
program an d
a quadrat ic program.
he
2
nd
Battalion, 4
th
Aviat ion Reg iment
of 4
th
Mechanized Divis ion currently uses a
spreadsheet
implementat ion
of
th e
quadratic
program
developed
by
th e
author
called Q F H A M
(Quadratic
Fl ight
H o u r
Allocation
M o de l ) , that
is
available to
other
battalions fo r
u se
with
existing
sof tware
an d
computer
resources.
he
mix ed
integer
linear
program,
called
F H A M
(Flight
H ou r
Allocation
M o de l ) more
appropriately models
th e
problem, but
requires additional software. his
thesis
contrasts both programs and shows
that
both
provide
helicopter
battalions
with
a valuable
planning tool fo r allocating
f l ight hours.
A. BATTALION ORGANIZATION AND MAINTENANCE BACKGROUND
U n d e r th e
Aviation
Restructuring Initiative ( ARI )
th e
A r m y
is reorganizing
helicopter
battalions
(Robinson, 998) .
T he new
organizat ion
consists of five
companies:
a
headquarters
company, three f l ight companies,
an d a
maintenance company.
he
headquarters
company
performs
th e
battalion's administrative activities
and
maintains
th e
battalion's
ground vehicles.
E a c h
of
th e
three
f l ight
companies operates its
eight
aircraft
an d
performs
scheduled
maintenance.
he maintenance company coordinates
al l
maintenance
activities
for
th e
battalion's
f leet of2 4
aircraft
valued at
approximately
$206 .4
million for
a U H - 6 0 Blackhawk battalion
an d $432 million fo r
a n A H -6 4 Apache
battalion
(Jackson,
1997) .
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The
Depar tment
of
th e
A r m y
(DA)
schedules
maintenance
requirements fo r
helicopters
on
a
phase
maintenance
scheduling
program
( D A
1 9 9 5 )
where
aircraft
undergo
extensive maintenance
procedures after
a f ixed number
of
f l ight
hours.
F o r
th e
U H - 6 0
Blackhawk,
A H - 6 4 Apache , an d C H - 4 7 Chinook , th e
primary
helicopters
of th e
Army
fleet, phase maintenance occurs every 5 0 0 hours
(DA,
1996) , 2 5 0 hours
(DA,
1998) ,
an d
30 0 hours (DA
9 8 9 )
respectively. Phase
maintenance is
t ime an d m a n p o w e r
intensive
requiring anywhere
f rom
30
to 30 0 days.
he length of
th e
phase
maintenance
can
translate
into lack of deployability with
no quick
f ix
for battalions
that
do not
properly
manage
their
aircraft.
D A
( 1 9 9 5 ) advocates
using
th e Sliding
Scale
M et ho d
to
help
manage
th e f low
of
aircraft
into
phase maintenance.
he
sliding
scale method
has
battalions sequentially
plot
th e aircraft 's remaining f l ight hours
until
phase maintenance
from
most hours
remaining to
least
hours remaining (Figure 1 ) .
hey
then
compare
this
plot versus
th e
Army goal ,
referred
to as th e D A go a l line, a
line drawn
from
zero
to th e
m a xi m um
hours
remaining until
phase
maintenance.
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Battalion Flow Chart
6 0 0
500 - -
I
4 0 0
to
x :
a.
o
300
|
200
1 0 0
lßg>CMOCMQ--0
ocsoh-oocüinooŵoôT-oj
Tail
Figure
1
Sample
Battalion
Flow
Chart
for
a
UH-60
Battalion
The
graph
shows
th e
relationship
between
flight hours for
sequentially
sorted aircraft
an d
the
D A
goal
(shown
as
line).
The D A
goal line establishes a
steady-state
flow
of
aircraft into phase
maintenance.
When
f l i gh t
h o u r s
remain ing unt i l
p h a s e
main tenance
are
ke p t
o n
the
DA g o a l
l ine,
th e
times between the
aircraf t phase main tenance du e dates
are
equal between the
aircraft .
or
instance , if the
n e x t
aircraf t
du e
phase main tenance h as
3 0
h o u r s
remain ing ,
and
the unit's opera t iona l
tempo ( O P T E M P O ) av erages 15
f l i gh t hours /per ai rcraf t /per
month ,
then the
n e x t
phase
maintenance
beg ins
in
a b o u t 2
m o n t h s
(6 0
days) . By
keeping
th e
ai rcraf t
on the DA g o a l line
(or parallel to
it ) th e
sequenc ing
of aircraf t into phase
maintenance is equal .
h is prevents a b a c k l o g
of aircraft wait ing
fo r
phase main tenance .
Many battal ions
i gnore DA guidance and do
not m a n a g e their ai rcraf t f l ow since
cur ren t
helicopter battal ion
measures
of ef fect iveness ( M O E s )
do
no t requi re
report ing
of
ind iv idua l
aircraft
f l i gh t
hour
( t ime
remain ing
unt i l
phase
maintenance) .
T h e
pr imary
MOE
for
a
helicopter
battal ion
is
th e
percen tage
of
aircraft
that
are
Ful ly Mission
C a p a b l e
( F M C ) with a DA goal of7 5 %
F M C .
F M C
is
th e
percen tage
of time within the
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previous m o n t h tha t an
aircraf t
is
able to per f o rm
it s
füll
wartime
miss ion
( D A ,
9 9 2 ) .
T h e
battal ions
m u s t
repor t
percen t F M C
to h i g h e r
headquar te rs
o n
th e
15
th
of
each
month .
T h e percent
F M C
measures th e battalion's
ability to
mainta in helicopters
operat ional ly ready, b u t
it
provides
very
little
indicat ion
of
a
battalion's deploy ability.
A n
aircraf t is
deployable
if it is
both F M C
and
h as
a m i n i m u m
n u m b e r
ofhours unt i l
phase maintenance . t
is easy to see
that
a
battal ion
could
report 9 0 %
F M C
for a g iven
m o n t h
and have several aircraf t with
only
a few
f l i gh t
h o u r s
remain ing unt i l
phase
main tenance .
s long as
those
aircraf t
a re operat ional , they
a re repor ted
as
F M C ,
however ,
they
are
no t
considered
dep loyab le
unt i l
phase
maintenance
is
comple te .
This
si tuat ion w o u l d
no t be visib le
o n th e
battalion's
m o n t h l y
report .
Battal ions that
do
m a n a g e aircraf t f low tend to
do
so
o n
a
daily
basis , with th e
battal ion main tenance
of f ice r (ma in tenance c o m p a n y
c o m m a n d e r )
dictating
o n
a b y-
miss ion
bas i s
w h i c h
ai rcraf t
to
f ly . h is
leads
to
react ive
micro-management
of
th e
company's aircraf t f l i gh t h o u r s b y
th e
battal ion
rather than
proact ive
management b y th e
f l i gh t
c o m p a n y c o m m a n d e r .
B .
HISTORIC CASE STUDY
T h e 1
st
A r m o r e d Divi s ion ( A D ) ,
current ly
ass igned in
G e r m a n y , provides an
e x a m p l e where th e lack
of individual aircraf t
f l i gh t
h o u r al locat ion resul ted in
a non-
deployable
hel icopter battalion. During th e Dayton P e a c e A c c o r d arbi trat ion proces s ,
prior
to
the
U . S .
implementa t ion
force
( I F O R )
d e p l o y m e n t
to
Bosn ia ,
st
AD's
UH-60
B l a c k h a w k
bat ta l ion
repor ted
8 9 %
F M C . G i v e n
the
DA g o a l of 7 5 % , al l reportable
indicat ions
s h o w e d
th e
battal ion w a s ready
fo r
dep loyment . Upon notification
of it s
impending
dep loyment , the
s
t
A D t ra ined
ex tens ive ly
fo r
th e
mission. h e
Dayton
-
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Peace A c c o r d s w e r e s igned
in late November 1 9 9 5 ,
and 1
st
A D was
ordered to
dep loy to
th e
f o r m e r
Y u g o s l a v
Republ i c
(Bosn ia ) .
mmedia te ly
th e U H - 6 0
Battalion
s e n t
u p
a red
f lag . h e
aviat ion br igade
c o m m a n d e r directed that
aircraf t
with
less
than
7 5
f l i gh t
hours remain ing unt i l p h a s e maintenance w o u l d
not deploy. h is
a f f ec ted nine
of th e
battalion's 2 4
U H - 6 0
B l a c k h a w k s . h is
prob lem w as
previous ly
unnoticed
above
the
br igade
level
and w as
directly attr ibutable to a lack off l i gh t hour al locat ion m a n a g e m e n t
within
th e battalion.
h e
prob lem
w as
f u r the r
ace rba ted
b y the
high
O P T E M P O of the
required
training
prior
to
thei r
dep loyment .
F i g u r e
2
s h o w s
an
e x a m p l e
of
this
type
of
main tenance
f low
prob lem.
Battalion Flow
Chart
60 0
50 0
OOJCMCOCMOr-OCDCOCNOr̂OOCNOOOCOTroOT-T-CD
o
4-coo)r>̂ rcMc»̂r
-
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deployments,
battalions
can
achieve
higher
deployability
by deviating
f rom
th e
D A
goal
line,
however ,
for
long
term
planning
under
conditions
ofuncertainty,
th e
D A goa l
line
provides
th e
best
solution
fo r max imu m deployability at an y
time.
his
thesis allocates
f l ight
hours to g et as close to
th e
D A goal line
as
possible. hapter
V
addresses
intentional deviat ion
from th e D A goa l line
fo r k no wn deployments .
C.
PROBLEM
DEFINITION
A n
A r m y
helicopter
battalion
must
be
prepared
fo r
missions
that can vary
daily.
T he
A r m y
organizes
aviation
maintenance activities
to
provide
th e
battlefield c o mmander
with
th e
max imu m
nu mber
of
safe,
mission-capable
aircraft
to
meet
its
missions
(DA,
1995 ) .
iven
th e
vas t array
of
mission
profiles
for the
combat
aviation unit, from
direct,
high
intensity
conflict
to operations other
than
war, battalions can
expec t
to deploy as
either
a
battalion assigned
to
an
aviation
brigade
level task
force o r
as
smaller
sized
(company
and
below) support
packages .
herefore,
th e
battalion must be
prepared
fo r
any
cont ingency.
large
part
ofthat
preparation is
a
well-established
battalion
phase
maintenance
f low
( D A ,
1995 ) .
In
order to
maintain
an
effective
phase maintenance f low, th e battalion
c o mmander
mu st
balance
his operation
an d
training
requirements
against
his maintenance
effort .
he
battalion
staff
and
th e
f l ight
company
commanders
ar e
responsible
fo r
th e
operational
an d
training aspects. he
battalion maintenance off icer
is
responsible
fo r th e
maintenance
effort .
he
battalion
c o mmander
manages
resources
through
f l ight
hour
allocation
an d
maintenance management
within
a
planning
cycle
(Planning
cycles
are
typically
monthly and
this
thesis
uses
only monthly
planning cycles
fo r
computat ional
studies,
although
F H A M
an d Q F H A M
are
appropriate
fo r
an y
planning cycle length).
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T he
battalion
maintenance off icer
mu st
recommend
th e
f l ight
h o u r
allocation
fo r
each
aircraft
assigned to th e battalion
at th e beginning ofeach
planning
cycle. Prior to
making
this
recommendat ion,
he
mu st
k no w th e
fo l lowing
information:
•
attalion
commander ' s
f l ight
hour goa l
fo r
planning
cycle.
•
u mber
of f l ight hours
remaining until
phase
maintenance
f o r each aircraft in
th e
battalion.
• inimum
percentage of
battalion
f l ight
hours
each
company
receives.
•
ost probable
status ofan y on-going phase
maintenance
at
th e en d
of
th e
planning
cycle.
•
inimum
and m a xi m um
f l ight
hours
each
aircraft flies
during
th e planning
cycle.
T he A r m y
can benef i t
from an
optimization program to
help
hel icopter battalions
allocate
f l ight hours. chieving
an d
maintaining
a steady-state f low
of aircraft into phase
maintenance
guarantees
a constant
nu mber
ofaircraft available
f or
deployment without
a
phase
maintenance
backlog .
F H A M
can help
th e
battalion
maintenance off icer
determine
an optimal
f l ight h o ur
distribution
between
individual
aircraft . he
battalion
maintenance off icer
applies
current mission
criteria
and aircraft limitations
while
setting
up
th e
constraints
within
Q F H A M . Having solved
for
th e optimal
f l ight
h o ur
allocation,
th e
battalion
maintenance
officer then
issues
f l ight
hour
allocation
goa ls
fo r th e
f l ight
company
commanders
fo r
th e
planning
cycle.
This
thesis
analyzes
th e
stated
optimization
problem
with F H A M
and Q F H A M .
F H A M
validates th e
exportable
( to
battalions)
Q F H A M .
F H A M
is
a
m ixe d
integer
linear
program
with penalties
per hour
deviation
that
increase
as
th e
f l ight
hours
f rom th e
-
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desired
D A
goa l
line increase. he
resulting aircraft
f low
should be as
parallel as
possible
to
th e
D A go a l
line
an d
thereby
provide
a
steady-state
f low
of aircraft
into
phase
maintenance.
F H A M
changes
th e
methodology
of
th e
battalions from reactive
micro-
management
to
proact ive management . onducting th e flight h o ur
allocation
on
a
periodic
basis
rather
than
managing
on
a
miss ion-by-miss ion basis,
gives
th e
f l ight
company c o mmander
th e
f lexibility
to manage his ow n aircraft assets
within
a
planning
cycle
rather than
having
th e
choice
of aircraft for
missions dictated
on
a
daily
basis.
D. OUTLINE
Chapter
I I
describes
related
research.
hapter
m
formulates
both
th e
mixed
integer
linear program an d
th e
quadrat ic
program.
hapter IV
provides
results
from
both
programs
using
data
f rom
a U H - 6 0 battalion's annual flying
h o ur
program.
nalysis
includes
both typical
training
an d
contingency
scenarios. hapter V discusses th e
implementat ion
of
Q F H A M
and
th e
ramif icat ions
of current
helicopter
battalion M O E 's
an d
possible alternative
M O E ' s .
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H.
RELATED
RESEARCH
A literature review
revealed
several examples of similar work . However ,
previous models
addressing
issues of scheduled maintenance on
repairable
systems are
no t
directly adaptable
to
th e
problem
addressed
by
this
thesis.
he
bulk
o f th e
w o r k done
fo r
aircraft scheduling
addresses mission
ass ignment
to
specific
aircraft with
no
consideration
given
to major scheduled maintenance
procedures. n
models
addressing
major scheduled maintenance
procedures,
systems are
grouped
by
ag e
of device
with
no
consideration to
individual
sys tems
(e.g. ,
aircraft). he only
model found
that
specifically
addresses
necessary
issues
contained
in
F H A M
and
Q F H A M
is
developed
by
D A .
he
fo l lowing
contains
a
brie f
discussion of
related
models an d their
relevance
to
th e
problem addressed
in
this
thesis.
D A
prescribes
a
technique fo r
establishing
a
steady-state
flow
of
aircraft
into
phase
maintenance
called
th e sliding scale scheduling
method ( S S S M )
(DA,
1995) .
U n d e r th e
A R I
organized battalions, th e S S S M requires th e battalion maintenance off icer
perform
th e fo l lowing
steps:
•
lo t
th e actual
f l ight
hours an d
manually
draw
a
linear
approximation
of this
plot;
•
ivide
th e
number
of
f l ight
hours
available
for
th e nex t
planning
cycle
(given b y
battalion
commander )
by
th e
nu mber
of
aircraft
assigned to
th e
battalion;
•
ubtract
th e average
f l ight
hours
per aircraft
f rom
th e
Y-ax is
intercept
ofth e
linear
approx imat ion
of th e battalion's current
aircraft
flow;
an d
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•
Draw a l ine (ad justed
g o a l l ine)
parallel
to
th e
DA g o a l line such that it
in tercepts th e
Y - a x i s
at
th e adjusted
Y- in te rcept ( F i g u r e 3 ) .
T h e
battal ion
main tenance
of f ice r then
de te rmines
th e
r e c o m m e n d e d f l i gh t
hours
b y calculat ing th e dif ference
be tween
actual
f l i gh t
h o u r s
and
th e
adjusted
g o a l
line.
f
an
aircraf t is
below th e
adjusted line,
then
that
aircraf t
is
no t
f lo wn.
Example
of SSSM
-D A Goal Line
ea r Approximation
Figure
3 -
An example of the
DA sliding
scale scheduling method
(SSSM).
F or simplicity, SSSM
is
shown
for
a
flight
company.
The
DA goal line
shows
th e
desired
position
of
the
aircraft.
The
linear
approximation
shows
the
battalion
maintenance
officer's
estimate
of
a
linear
f it
to
th e
actual
flight
hours.
The adjusted goal line shows the line
parallel
to
the DA goal
line
with
a Y-intercept determined by
subtracting
the
average
number of
flight
hours for the
aircraft
for this
planning
cycle from
the
Y-intercept
of the
linear
approximation F or
example,
aircraft
2 ca n f ly
400
37 5
= 2 5
hours,
while Aircraft
5
is
allocated
zero
hours.
The
adjusted
goal line i s
the
desired
end-state after the
planning
cycle.
T h r o u g h o u t
a ten
yea r
aviation
career , the
au thor h as never
obse rved
n o r
heard of
any
aviat ion
battal ion
using S S S M . W h a t e v e r
shor tcomings
kept S S S M f rom
being
used ,
it
is
less appropriate for today's A R I
o rganized
battal ions
as
it
is des igned fo r u se
a t a
c o m p a n y
level.
rev ious
battal ion
organizat ions
( p r e - A R I )
h ad
m u c h
l a rger
f l i gh t
c o m p a n i e s
with
their
o w n
main tenance sect ions
a l lowing
p h a s e
maintenance
m a n a g e m e n t
a t
th e
c o m p a n y level .
owever , with res tructuring
of
th e
bat ta l ion ,
all
phase
maintenance
is n o w
m a n a g e d
at
th e battal ion level.
t th e battal ion level, S S S M
10
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does
n o t
ensure
any type of
equitable
distribution
of
f l i gh t
time
between
th e
compan ies .
Als o ,
when aircraf t fall below th e adjusted g o a l l ine,
then as s i gned f l i gh t h o u r s fall
below
th e
al located f l i gh t hours for th e planning
cycle .
n
general ,
the sliding
scale
schedu l ing
m e t h o d
provides
a generic planning tool , b u t it s
lack of
f lex ibi l i ty
and s impl ic i ty m a k e it
unusab le
at
th e
battalion
level .
Other m o r e
sophist icated
methods
w e r e
f ound
in the literature. Bargeron ( 1 9 9 5 )
addresses
readiness
issues
f rom schedul ing d e p o t level
maintenance
ofMarine
C o r p s
Ml Al m a i n battle tanks . e
dev elo ps a
linear integer
p r o g r a m
with an i m b e d d e d
mult i -
c o m m o d i t y
network
structure
to
so lve
the
tank
maintenance
prob lem.
Bargeron'
s
l inear
in teger p r o g r a m contained 3 6 , 2 8 4
variables and 1 2 , 7 0 5
constra ints .
h e
l inear
integer
prog ram
solves
in 6 7 4 . 2 9
C P U
seco nds
o n
an IBM
R S / 6 0 0 0 Model 5 9 0 H
compute r .
Bargeron's
l inear
in teger
prog ram
h as
s o m e
similarit ies,
s u c h
as
scheduled
maintenance
based
on u s a g e
and
a t ime in tensive
maintenance
procedure . o w e v e r ,
there are
s o m e
basic
dif ferences
be tween
h is
l inear
integer
prog ram
and the
problem addres sed in
this
thesis: Bargeron g r o u p s
t anks
within a
battal ion
based o n
ag e
g r o u p s
in
order to avo id
t racking
individual t anks
and
h is
pr imary
object ive is to
minimize
th e
c o s t of a viab le
maintenance
scheduling
plan.
Sgas l ik
descr ibes
a decis ion suppor t
system
des igned
to
assis t
with
maintenance
planning
and
miss ion
ass ignment fo r a G e r m a n UH-1H ( H u e y )
Helicopter
Regiment
(Sgas l ik ,
9 9 4 ) .
n
order
to
so lve this
prob lem,
Sgas l ik
deve lops an
elastic,
m i x e d
integer
l inear p r o g r a m . gas l ik 's m i x e d
in teger l inear program conta ined 2 , 6 0 0 variables ,
9 , 0 0 0
non- ze ro
e lement s , and 1 , 2 0 0
constraints.
h e m i x e d
i n teger l inear
p r o g r a m so lves
in
less
than
15
minutes
o n
an
I B M
compat ib le
4 8 6 / 3 3 compute r .
l t hough
this problem
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deals
with
scheduled
maintenance
i ssues ,
th e
pr imary
ob jec t ive is
the a s s i g n m e n t
of
miss ions to individual
aircraft .
n
this
situation, the
miss ions
and the
miss ion length are
k n o w n
fo r
each
planning
cycle.
F a b r y c k y
and Blanchard
( 1 9 8 4 )
address
the
issue of mode l ing
repai rable
e q u i p m e n t popu la t i on sys tems ( R E P S ) . h e R E P S m o d e l uses f inite queuing theory to
evaluate
the costs as
wel l as des ign
of
a service
facility.
a b r y c k y and
Blanchard t rack
i tems based o n a
dev ice
ag e
grouping
and
m o d e l s parts
requ i rements
and
repairs us ing
nested Markov
chains .
h is
R E P S
m o d e l
deals not
only
in scheduled main tenance , b u t
also
in
th e
s tochas t ic
nature
of
unschedu led
maintenance
whi l e
this
thes is
does
n o t
address unschedu led
main tenance . h e
R E P S
m o d e l
g r o u p s
sys t ems
of similar ag e
characteri s t ics whi l e this
thesis
requ i res
individual aircraft
t racking .
A f inal
m o d e l
that
deals
with
A r m y
helicopters
is
the
P h o e n i x
m o d e l ( B r o w n ,
C l e m e n c e ,
Teufert ,
and
W o o d ,
9 9 1 ) .
h e
Phoenix
m o d e l
schedules
p r o c u r e m e n t
and
re t i rement for the Army's
helicopter fleet .
h e m o d e l
handles
16
di f f e ren t
hel icopter
p la t f o rms
spann ing
a
planning
cyc le
of
2 5
years .
h e
modern iza t ion op t ions
cons ide red
in
Phoenix
mo del :
• rocuring
new
aircraf t
through
comple te ly
new produc t ion
campa igns ;
•
rocu r ing
aircraf t through
b lock
modi f i ca t i on
in
w h i c h act ive produc t ion
c a m p a i g n s
are altered
to
i ncorpora te
enhancements ;
•
ervice
life
ex tens ion
p r o g r a m s
( S L E P s ) ;
and
•
etirement
of obso le te
aircraft .
1 2
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Although
Phoenix
does
not
address issues
involved
with
th e
problem
addressed
in
this
thesis, Phoenix
shows A r m y
Aviat ion will ingness
to use
optimization planning systems.
1 3
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m.
OPTIMIZATION
MODELING
OF
THE
FLIGHT HOUR ALLOCATION
PROBLEM
T he
mixed integer linear program
( F H A M ) and th e quadratic program
( Q F H A M )
use
th e
fol lowing information:
•
attalion
Commander ' s f l ight
ho u r
goal for
th e
planning
cycle
expressed
as
th e minimum
an d
max imu m
number
ofhours .
•
u mber of
f l ight
hours
remaining until
phase
maintenance
fo r
each
aircraft
in
th e
battalion.
• inimum
f l ight hours
fo r
each
company.
•
ost probable status
ofan y
on-going
phase
maintenance at th e
en d
of
th e
planning
cycle.
• inimum
an d
m a xi m um
f l ight
hours each
aircraft flies during th e planning
cycle.
F H A M bases al l
penalties
on
a least squares approximation.
This approximation
thus
penalizes
more
heavily
fo r
larger
relative
f l ight
h o ur
deviation
f rom
th e
D A
goal
line.
A.
MIXED
INTEGER
LINEAR
PROGRAM FORMULATION
This
thesis
uses a
standard
U H - 6 0
Blackhawk
A ir
Assaul t Battalion
( 5 0 0
f l ight
hours between
phase
maintenance)
fo r demonstrat ion purposes:
F H A M
and Q F H A M
can
also
be
easily
adapted fo r A H - 6 4
or
C H-4 7 bat tal ions.
he total hours f lown meets
th e
constraint
given by
th e
battalion commander ' s f l igh t hour goal .
he distribution
of
f l ight hours between th e
f l ight
companies is
held equitable based on
th e
desired
allocation
between
th e
companies. Finally, th e
objective
is
to
minimize
th e
sum
of th e
individual
penalized
f l ight
hours
from
th e
D A
goal
line.
he
outputs
f rom F H A M
are th e
1 5
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al located f l i gh t
h o u r s
p er aircraf t
per planning
cycle. T h e
f o l lowing s h o w s FHAM's
formula t ion in N a v a l Postgraduate
S c h o o l
( N P S )
format :
Indices:
i
nterva l
f rom
th e DAg o a l
l ine
(e .g . , 1,2,...,10);
p
osition
of aircraf t
o n th e battal ion
f low
cha r t (e .g . ,
st
,2
nd
.
. , 24
th
);
x
i rc raf t tail number
(e .g . , 8 0 ,
2 5 4 , ;
and
c
o m p a n y (e .g . ,
, B ,
o r
C ).
Se t s :
A I R C R A F T c
S et
of
al l
ai rcraf t
in
C o m p a n y
c.
Given Data:
BFH
i n imum
f l i gh t
h o u r
al locat ion
f o r th e
battal ion
during
planning
cyc le
(hours ) ;
BFH
a x i m u m
f l i gh t
h o u r
al locat ion
fo r th e battal ion
during
planning
cycle
(hours ) ;
D A G p
A
g o a l
for
aircraf t
ass igned
posi t ion
p
o n
th e
D A
g o a l
line
(hours ) ;
FfTPx
light h o u r s remain ing unt i l
p h a s e
maintenance
du e f o r
aircraf t
x
(hours ) ;
INTERVAL^
A l l o w e d
deviat ion
within
the
I
th
interval
for
aircraf t
x
(hours ) ;
M A X F L Y x
M a x i m u m
f l i gh t
h o u r s for aircraf t
x
(hours ) ;
M T N C O c
M i n i m u m
battalion
f l i gh t
h o u r s
fo r
c o m p a n y
c
(hours ) ;
M T N F L Y x M i n i m u m flight h o u r s fo r
aircraf t
x (hours ) ;
NEGPEN
r
Penal ty per
flight hour
b e l o w
th e
DA
g o a l line
within
th e
r*
in terval for
ai rcraf t
x ( e .g . ,
0,10,30,...,
1 7 0 )
(penalty
uni ts /
ho ur ) ;
1 6
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P O S P E N
r
T A H
X
Decision
Variables:
devneg
x
devposx,,
f ly ,
X x, p
Penalty per f l ight hour
above th e D A
goal
line within
th e
i
th
interval fo r
aircraft
x
(e.g. ,
0 ,10 ,30 ,
. . . ,170) (penalty units/
hour ) ;
an d
Total
f l ight
hours fo r
aircraft
x (hours) .
T he
f l igh t hours aircraft
x is below th e D A goa l
line
within
th e
i* interval
(hours) ;
T he
f l igh t
hours
aircraft
x exceeds
th e
D A goal line
within th e
I
th
interval (hours) ;
Fl igh t
hours
fo r
aircraft x during planning
cycle
(hours) ; an d
O ne
if
aircraft
x
is
assigned
to
th e
p
th
position,
zero
otherwise.
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FORMULATION
Minimize
th e
Objective
Function...
]T £
[POSPEN,
*
devpos
T
.
+
NEGPEN ,
* devneg
zi
]
Objective
Subject
to .
HTP
t
fy
t
̂ AG, x
tt
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T he objective
function
is
th e
sum
of
th e
penalized f l ight
h o ur
deviation
ofth e
battalion's
aircraft
f rom th e D A
goa l line.
he f l ight
hour
deviation
penalty
p er
unit is
dif ferent
depending on the deviation
interval.
F o r
example,
assume aircraft
# 2 5 4
is
assigned
to
th e 5
th
position
an d is
2 3 hours
above
th e D A goa l
line.
E a c h
interval allows
only
10
hours
( I N T E R V A L ^ , ,
=
1 0
V i)
an d
th e
penalties
fo r
th e
first three
intervals
are:
POSPEN^,;
=
0,
P O S P E N 2 5 4
2
=
1 0 ,
P O S P E N
2 5
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B .
QFHAM
FORMULATION
QFHAM's
object ive
func t ion
is
th e
sum ofthe squared
f l i gh t
hours a b o v e
or
be low th e DA g o a l
l ine,
Objective
=
Min̂
HTP
ß
t
ÂG
p
*
x
^
w h e r e posi t ions
of
th e
aircraf t within the battal ion flow
char t
(x
T > p
)
are
f i xed .
pre-
process ing
step
f i x e s aircraf t posi t ion based o n
current f l ight
hours remain ing
unt i l
phase
maintenance
( H T P
T
)
and
the
m i n i m u m
f l i gh t
hours
for
each
aircraf t during th e
planning
cycle
( M I N F L Y , ) .
A
V i s u a l
Basic
M a c r o
( E x c e l ,
1 9 9 6 )
subtracts
MINFLY
X
f rom
H T P
X
,
sorts
th e
ai rcraf t
based o n the
result , and
f i xe s
the
ai rcraf t
to
their sorted order .
With the posi t ion
f i xed , there
are
only
three constraints:
Y f̂ly*
>MINCO
c
V c Cons t ra in t
# 5
reAIRCRAFTc
BFH
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IV . COMPUTATIONAL
RESULTS
This chapter
describes
th e
validation
of
F H A M
an d Q F H A M within both typical
training and contingency planning
scenarios.
he
validation
determines
th e extent
to
which
th e
system
accurately
represents
th e
intended
real
wor ld
phenomenon f rom th e
perspective of th e customer
of th e
mo de l (the
aviation battalion) (DA,
1993) .
F H A M
contains
6 2 0
continuous
variables,
115
discrete
variables, 2 ,013
non-zero
elements,
and
6 30
equations.
F H A M
solves
using
G A M S ,
Release
2 .25
(Brooke,
Kendrick,
Meeraus ,
1 9 9 6 ) on
a
16 6
M H z
PC
within 6 2 seconds using th e G A M S XA
solver
(Brooke ,
Kendrick, Meeraus , 1996) . F H A M is
implemented using a Microso f t
version
97
E x c e l
spreadsheet.
he
basic E x c e l
9 7
solver limits any
model to
no
more
than
2 0 0 variables
(Person,
1997) ,
prohibiting solution
o f F H A M
but
not
Q F H A M ' s
2 4
continuous
variable model.
he ru n
t ime
for
th e
E x c e l
solver with
Q F H A M ' s
quadratic
objective
funct ion
is
approximately
8
seconds. Frontline Systems
Inc. offers
tw o
upgrades fo r
th e
E x c e l solver.
he
Premium Solver
($495)
increases
th e variable
capacity
to
800 .
he L arge Scale
L P
Solver f o r Microso f t E x c e l 97 ($1 ,495) also allows
80 0
variables,
but decreases solution
t ime
significantly
and
simplif ies
sparse
matrices
input
(only
requires non-zero element
input)(Frontline, 1998) .
A.
TYPICAL
TRAINING
SCENARIO
T he
data
used
fo r
th e
typical
training
scenario
ar e th e
f l ight
hours f lown by
a
Mechanized
Infantry
Division's U H - 6 0
battalion
(validation
battalion)
fo r
calendar
year
1997 (Based on
actual
f l ight hours
fo r
th e
2
nd
Battalion, 4
th
Aviat ion
Regiment
as
reported
fo r
their
Annual
Flying
H o u r Report) .
he
author performed
this
analysis
using
a typical training scenario.
F o r
example, there were no aircraft deployed for
high
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intensity
miss ions .
attal ions
operate
u n d e r
this
genera l
scenario
w h e n
bas ing
o u t of
their h o m e station with no
ex terna l
suppor t miss ions .
h e
yea r
consis ts of
month ly
planning
cycles .
H A M
uses
the
allocated total
month ly
hours for th e p u r p o s e
of
analys is
( T a b l e
1)
with
an
a l lowed
deviat ion
above
(BFH )
o r
b e l o w
(BFH
often
percent .
Jan Feb
Mar
Apr
May
Jun
Jul
Aug
ep
Oct N ov
Dec
471
4 27
234
23 6 38 9
1 7 7
5 02
267
27 3
28 2
22 6 4 58
Table
1 :
Actual
hours
f lown pe r
month
for th e validation battalion
The start
point of the
analysis
is 1 5 January 1 9 9 7 . able 2 and
Figure
4
show
the
initial
hours
until phase maintenance
for
the
battalion's aircraft.
Aircraft
Hours to Phase
Aircraft
Hours
to Phase
Aircraft
Hours
to
Phase
A422
1 4 9
B401
25 4
C 1 4 0
12
A427
4 94
B430
441
C 1 63
4 4 3
A428
298
B 4 9 0
0
C392
4 4 6
A431
20 0
B593
1 7 2
C432 1 53
A442
39 8
B 7 5 0
4 36
C437
4 1 4
A446
4 92
B 8 4 3
23 0
C 4 9 5
30 6
A749
1 7 0
B888
198
C 505
1 0 2
A066
25 0
B084
231
C 600
500
Table
2:Initial state o f
th e
validation
battalion
hown ar e aircraft b y company, tail n umber , an d
th e
hours
remaining
until
phase
maintenance.
F or
example,
aircraft
B 5 9 3
belongs
to
B
Comp an y
an d
has
172
hours
remaining
until phase
maintenance.
Validation
Battalion
nitial State
Aircraft
Figu re
4:
Initial state o f
validation
battalion
on
1 5
January
1 9 9 7 .
Notice that
th e
initial
state
shows
very
little adherence to
th e D A
goal
line.
This
is
typical
for Army
helicopter
battalions.
ls o note
that th e sequencing
of aircraft
into phase is no t steady-state
(parallel
to D A
goal
line). This ca n lead to a
back log o f
aircraft awaiting phase maintenance.
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F H A M
f ixes each
aircraft's
max imu m monthly
f l ight
hours as
th e
minimum
of
30
or
its
f l ight
hours
remaining
until
phase.
F o r
instance,
if
an aircraft
is due
phase
maintenance in 2 8
hours ,
th e
max imu m allocated
fo r that
aircraft
in a planning cycle
is 28
hours.
H A M
f ixes
an aircraft's
minimum f l ight
hours as th e minimum
of 3 o r
its
f l ight
hours
remaining
until
phase. F H A M
allocated each
f l ight
company
at
least
2 0 %
of
th e
total
f l ight
t ime
fo r
th e
planning
cycle.
F H A M
analyzed
each
month
based on
th e
initial
conditions
of 1 5
January
1997 ,
and
th e
f l ight
hours
f lown in each
month.
B
OPTIMIZATION
RESULTS
FOR
TYPICAL TRAINING SCENARIO
Figure 5
shows
th e
results
of th e
F H A M f l ight
hour allocation
as
th e
battalion's
phase
maintenance f low approaches
steady-state. F H A M uses
the
end
condition ofone
month
as
th e
initial condit ion
for
th e nex t
month. igures
6
an d
7
show
a
comparison of
F H A M results
an d
th e
actual
hours
f lown b y
th e
battalion
af ter f ive
months.
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15
February
1 9 9 7
15 M a r c h
1 9 9 7
500 j .̂
5
April
1997
400
-
r̂
i -
- *^
300
^^^
200
100
-
-**,
«jr^
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soo
FHAM Results
as
of
15 June 1997
to
JH
400
°-
30 0
O
2
3
1
O
^̂ ^̂ ŝ ̂
*̂^̂̂
^̂-*̂
̂ ̂
**-̂^
_t ° •
CAACBBCBCCACABABBABBACAC
144344671444440084957445
424939056349206843894320
07620000372S816431839225
Aircraft
Figure 6 :
Th e resulting flow
after
5
months
of FHAM
allocation.
FHAM
establishes a phase
maintenance
flow in
adherence
to
the
D A goal line.
Validation
Battalion
15
June
1997
Aircraft
Figure
7 : The
actual flow for
the
battalion as
of 1 5
June
1 9 9 7 .
The
battalion
flow for th e
validation battalion
is
no t as
close
to
the DA
goal
line
as the
FHAM allocation.
FHAM's
resul t ing
f low
of
aircraf t
into
phase
main tenance
now
beg ins
to
parallel
the
DA
g o a l
l ine.
h e
actual data
f rom
th e val idat ion battal ion
is
not
as
close to
the
DA
goal
l ine
as
the
F H A M
results .
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A n
essent ia l
prob lem
handled b y F H A M
is
th e sequenc ing
of
low- t ime
ai rcraf t
into
phase main tenance . A k ey problem with the
Army's
current
sys tem
of
M O E
report ing
is
that th e only m e a s u r e
reported
is
F M C
percen tage .
eaders
f ace
a
d i l e m m a
w h e n
aircraf t approach
p h a s e
main tenance .
f
an ai rcraf t ready now
for phase
main tenance
(e .g . , less
than
10
h o u r s
remain ing
top related