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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

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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


3/55


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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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6/55


7/55

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

IX


11/55

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


12/55

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.

XI


13/55

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) .


14/55

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.


15/55

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


16/55

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


17/55

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


18/55

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).


19/55

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


determine

an optimal

f l ight h o ur

distribution

between

individual

aircraft . he

battalion


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


20/55

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 .


21/55

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


22/55

•

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


23/55

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

11


24/55

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


25/55

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


26/55

14


27/55

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


28/55

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


29/55

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.

17


30/55

FORMULATION

Minimize

th e

Objective

Function...

]T £

[POSPEN,

*

devpos

T

.

+

NEGPEN ,

* devneg

zi

]

Objective

Subject

to .

HTP

t

fy

t

̂ AG, x

tt


31/55

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


32/55

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


33/55

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

21


34/55

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.

22


35/55

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.

23


36/55

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^


37/55

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 .

25


38/55

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

stagger chart

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