LIBRARYTECHNICAl REPORT SECTIONNAVAL POSTGRADUATE SCHOOIMONTEREY* CALIFORNIA 93940

NPS55-77-24

NAVAL POSTGRADUATE SCHOOL

Monterey, California

FORECASTING THE NUMBERS AND TYPES OF

ENLISTED PERSONNEL IN THE UNITED STATES

MARINE CORPS: AN INTERACTIVE COHORT MODEL

by

Kneale T. Marshall

May 1977

Approved for public release; distribution unlimited

spared for

:

dquarters Marine CorpsFEDDOCS e Mpi20D 208.14/2:NPS-55-77-24 hington, DC 20380

NAVAL POSTGRADUATE SCHOOLMonterey, California

Rear Admiral Isham Linder Jack R. BorstingSuperintendent Provost

This work was supported by the Manpower Planning Division(MPI20) of the Marine Corps through the Navy Personnel Researchand Development Lab, San Diego.

Reproduction of all or part of this report is authorized.

Prepared by:

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1. REPORT NUMBER

NPS55-77-24

2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle)

Forecasting the Numbers and Types ofEnlisted Personnel in the United StatesMarine Corps: An Interactive CohortModel

5. TYPE OF REPORT ft PERIOD COVERED

Technical Report6. PERFORMING ORG. REPORT NUMBER

7. AUTHORfs;

Kneale T. Marshall

8. CONTRACT OR GRANT NUMBERfsJ

9. PERFORMING ORGANIZATION NAME AND ADDRESS

Naval Postgraduate SchoolMonterey, CA 9394

10. PROGRAM ELEMENT, PROJECT, TASKAREA ft WORK UNIT NUMBERS

N6822177WR70052

11. CONTROLLING OFFICE NAME AND ADDRESS

Headquarters Marine Corps, Code MPI20Washington, DC 20380

12. REPORT DATE

May 197713. NUMBER OF PAGES31

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Approved for public release; distribution unlimited.

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18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide It neceaaary and Identity by block number)

ManpowerForecasting

PersonnelCohort model

20. ABSTRACT (Continue on reverae aide If neceaaary and Identity by block number)

In this report we develop a model to forecast the total enlistedMarine Corps strength at the end of each quarter for one or twoyears into the future. The method involves a simple cohortmodel. The model is programmed in APL with a number of featureswhich allow the user to interact in the forecasting procedure.He can introduce further projected retention policy changes orchanges in the recruit population which might affect future

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TABLE OF CONTENTS

PAGE

1. Introduction 1

2. The Basic Model 2

3. Continuation Rate Estimation 8

4. Steady State Results , . . 12

5. Interactive Program Illustration 17a. Data Input and Storage 17b. Endstrength Forecasts 20

References 26

Appendix 27

1. Introduction

In this report we develop a model to forecast the total

enlisted Marine Corps strength at the end of each quarter for

one or two years into the future. The method involves a simple

cohort model similar to that described in Zacks and Haber [1975]

The model is programmed in APL with a number of features which

allow the user to interact in the forecasting procedure. He

can introduce further projected retention policy changes or

changes in the recruit population which might affect future

predictions.

In Section 2 we describe the cohort model and present

the equations for forecasting. In Section 3 we discuss a number

of ways of determining the parameters in the model from past

data. In Section 4 we describe how steady state results can

be obtained. In Section 5 we describe the use of the APL

programs which comprise the model, and present illustrative

examples. Detailed and documented APL functions are given

in the appendix.

2 . The Basic Model

It has been shown previously (see, for example, Zacks and

Haber [19 75] that retention behavior patterns of enlisted marines

are reasonably consistent within certain subgroups of the total

population. It has been found that the important characteristics

to be used in forming the subgroups appear to be race, educa-

tional level, and length of first term enlistment (FTE) of new

recruits. For race we take the groups Caucasian (C) and non-

Caucasian (NC) ; for education we take the groups high school

graduate (HS) and non-high school graduate (LHS) ; for FTE we

have 2, 3 and 4 year enlistments. Thus all recruits and current

marines can be uniquely placed into one of the 12 cohorts (groups)

in Table 1.

Cohort No. FTE Education Race

1 2 LHS C

2 2 LHS NC

3 2 HS C

4 2 HS NC

5 3 LHS C

6 3 LHS NC

7 3 HS C

8 3 HS NC

9 4 LHS C

10 4 LHS NC

11 4 HS C

12 4 HS NC

Table 1: The twelve cohorts of the enlisted Marine Corps

personnel.

Let S. (t;u) be the "stock" of enlisted Marine Corps

personnel in cohort type i at time t with length of service

(LOS) equal to u (for a detailed descripton of cohort models

the reader should see Grinold and Marshall [1977]). The time

periods are taken to be quarters, and the phrase "at time t"

means the last day of quarter t. For consistency the LOS is

also measured in quarters. If a person enters the Marine Corps

in quarter t and is counted as being present at time t,

then we say he has LOS equal to 1. Thus, if he enters in t

and is counted at time t+k , k >_ , then he has LOS equal to

k+1 . Table 2 gives the stocks at the end of March 1976 of

marines who were listed as being still in their first term

enlistment.

Let q. (u) be the fraction of those in cohort type i

with LOS equal to u at some time t who will continue in

service to time t+1 with LOS u+1. The q. (u) are commonly

called "continuation rates." By using this notation we are

assuming that they are independent of the actual time t. This

assumption is modified later. Let g. (t) be the number of

new recruits who enter in cohort type i in period t, and

let m be the maximum number of periods a person can spend

in the Marine Corps. The total stock S(t+1) of marines at

(t+1) is given by

12 m(1) S(t+1) =

I £ S. (t+l;u) ,

i=l u=l

where

(1.1) Si(t+l;l) =

g;.(t+l) q..(0)

(1.2) Si(t+l;u) = S

i(t;u-1) q^u-1), u = 2,3,..., m

In order to use equation (1) to forecast end strength

it is necessary to know (i) the cohort stocks {S. (t;u)}

for all i and all u, (ii) the continuation rates {q. (u)

}

for all i and all u, and (iii) the future recruit inputs

{g. (t+1) } for all i. It is the determination of these

three sets of data to which we now turn.

The new recruit input in future years will be given

to the model by the user and thus we can dispose of (iii)

.

Table 2 shows the stocks of marines who are still in their

first term enlistment at some given t for each cohort i,

but only for u = 1,2,..., 20. Marines can reenlist and

remain in service 30 years; thus m is 4 x 30 = 120. But

as the LOS of a marine increases beyond his FTE period there

is little distinction to be found among the 12 cohorts. These

marines essentially form what is called the "career" force,

and continuation in service of these people is governed by a

different set of factors than those affecting first term

marines. Thus, we modify equation (1) in the following way

to reduce both the size of the model and the number of parameters

to be estimated.

Cohort Number

LOS 1 2 3 4 5 6 7 8 9 10 11 12

1 3 3 2 1706 301 1424 422 2419 410 2982 5882 5 4 14 2 931 134 1256 299 2635 497 3418 7973 48 12 221 33 907 132 1683 387 2441 462 5563 1166J* 165 29 879 117 495 81 1041 236 1749 336 4276 9075 527 92 806 137 928 211 645 147 3143 897 2563 5826 543 154 804 202 672 210 495 187 2372 793 2013 5037 845 235 1926 541 736 247 936 299 2180 697 3841 8168 380 128 899 387 301 108 560 196 1107 356 2685 7009 197 80 248 85 794 200 545 143 1981 583 1433 340

10 83 39 140 51 547 124 436 108 1487 435 1179 33411 43 27 174 34 508 122 876 185 1688 387 2846 62412 23 31 50 21 414 96 460 124 1721 400 1892 40713 26 13 52 22 126 39 123 50 1502 394 1147 35014 20 12 25 11 61 18 70 28 1187 360 1176 40415 30 19 74 24 52 24 123 41 1282 354 2409 53016 31' 20 24 18 40 11 62 28 932 206 1562 28117 22 7 17 9 26 6 25 11 325 70 285 8618 14 4 7 3 19 8 14 4 150 17 186 4419 6 5 14 5 11 33 10 119 17 279 612 4 1 6 4 10 2 19 3 101 32 157 28

Table 2 Stocks of enlisted Marines on 31 March 1976.

Let c(t) be the total number of enlisted marines in

service time t with 21 or more quarters of service.

Thus

12 mc(t) =

I I S. (t;u)

.

i=l u=21

Now assume that q.(u) = q for all u >_ 20 and i = 1,2,..., 12

Using (1.2) it is easy to show that

12(2) c(t+l) = [c(t) + I S. (t;20)]q .

i=lX

Equations (1) and (2) are now combined to give the forecasting

equation

12 20(3) S(t+1) =11 S. (t+l

;u) + c(t+l)

i=l u=l

where

(3.1) Si(t+l;l) = g i

(t+l) qi (0)

(3.2) S. (t+l;u) = S.(t;u-1) q.(u-l), u = 2,3,.. .,20

12(3.3) c(t+l) = [c(t) + I S. (t;20)]q.

i=l

Equation (3) requires only 241 continuation rates com-

pared to 1452 in (1). This gives a considerable saving in data,

computation, and storage requirements. Figure 1 illustrates

the flows assumed in (3).

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3. Continuation Rate Estimation

Before (3) can be used for forecasting we must obtain

values of q^Cu), u = 0,1,. ..,19, i = 1,2,. ..,12, and q.

These values are determined from historical data on past

stocks.

Assume that t = is the most recent time for which

stocks are available. By using these and the stocks at

t = -1, let

S. (0;u+l)(4) V U) = sV^u) '

u = 0,1,..., 19; i = 1,2,..., 12 ,

and

(5) q = c(0)12

c(-l) +I S. (-1;20)

i=lX

Thus all the parameters can be estimated from the data of two

consecutive periods.

If data from more than two periods is available

we can use it to obtain smoother estimates, ones less susceptible

to random fluctuations in the stocks. Assume that data is

available for periods 0,-1,-2, ... ,-k. Then we modify (4) and

(5) to be

(6) q, (u) =

-(k-1)

I Si(j;u+1)

-k

I Si(j;u)

u = 0,1,... ,19; i = 1,2,... ,12

and

(7) q =

-(k-1)

I c.(j)

JJlP_-k 12

I (c(j) + J Si(j;20)}

j=-l i=l

The values obtained using (6) and (7) for any given k

are said to be determined using rate method k.

Recruit attrition in the first six months of service

is measured by (l-q.(0)) and (l-q.(l)), and is considered

controllable by the Marine Corps. Estimates from past data

have little meaning. In the interactive APL model described

in detail in Section 4, recruit attrition is entered directly

by the user at the computer terminal. The six month attrition

of LHS and HS recruits is normally about 20% and 10% respec-

tively. The conversion of these into q. (0) and q. (1)

is illustrated for some cohort i if a six month rate r is

entered. They are calculated by

(8) q..(0) =qi

(l) = /l - (r/100) ,

which spreads attrition evenly over the six month period.

Table 3 gives the continuation rates q.(u) obtained

using rate method 2 with t = equal to 3-31-1976, and re-

cruit attrition for LHS and HS equal to 15% and 12%, respec-

tively. The value obtained for q was 0.980.

The reader will notice that some of the q. (u) in

Table 3 exceed 1.0. Although this could be in part due to

errors in the data base, it is also in part due to the return

from unauthorized absences. Note that this phenomenon occurs

most frequently when the LOS is 2 and 3. This is a period

immediately following the end of basic training, when many

Marines return after being AWOL. Thus they are counted in

the numerator of (4) or (6) but are not present to be counted

in the denominator.

10

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4 . Steady State Results

The model summarized mathematically in equation (3)

is used for short-term forecasting (1 or 2 years) under a

given recruitment policy. The basic model can also be used to

show the long-run, or steady-state, effects of a fixed recruit-

ment policy. Although it is unlikely that the system parameters

will remain constant over many periods or that recruitment

policies will remain unchanged, the long run behavior of the

system under a given policy is often useful in showing trends.

These trends can act as warning signals of future problems.

Let L. be the random lifetime of an individual of

cohort type i. Let Q.(£) = P[L. > £] ; then

9) Q. U) = n q. (u) , I = 0,1,2,.. . ,m .

1u=0

Now let X . be the average time spent in the Marine Corps

of an individual in cohort type i, and let g. be the

fixed quarterly recruit input into this cohort. The stocks

S(t) converge to a constant stock level S, where

12(10) S = I X g

i=l

and

m(11) X. = I Q. U)

1 1=0

12

Recall that we assumed that for u _> 20 and all

i = 1,2,..., 12, q. (u) = q, a constant. Recall also that m

m-19 99is 120 so that q = q is negligible for values of q

of interest. From (9) we have

£

Q. (£) = n q. (u) , £ = 0,1,. .. ,19u=0

£-19= Q

i(19) q* ., £ > 19

Using these with (11) and (10) gives for the steady state

stock level

12 i-18 Q. (19) -,

(12) S =I I Q (£) + -i—— g

i=i L £=0 J- -l q j i

To illustrate the use of (12) , Table 4 gives the life

distributions Q.

(u ) for the continuation rates in Table 3i

for £ <_ 19. Using the constant recruitment policy shown in

Table 5 and q = 0.980, the steady state stocks will become

163,149.

In addition to calculating S, many more steady state

calculations of interest can be made. For example, the steady

state fraction with less than high school education is given

by

(A 1^1 + A2 g 2

+ A5 g 5

+ A6 g 6

+ A9 g 9

+ A10g 10

)/S*

13

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Cohort No. Number of Recruits

1

2

3

4

5 1428

6 252

7 2142

8 378

9 2652

10 468

11 3978

12 702

TOTAL 12,000

Table 5 : Quarterly input of recruits into each cohort

15

Similarly, the steady state fraction of non-Caucasions in the

force is given by

(A2 g 2

+ A4g 4

+ A6 g 6

+ A8 g 8

+ A10g10

+ A12 g 12

)/S*

16

5 . Interactive Program Illustration

In this section we describe the use of a set of inter-

active APL functions for both data input and enlisted end-strength

forecasting. These functions are available in Scientific Time

Sharing* s APL + system in a workspace called ENLISTED . Listings

and documentation of the functions are given in the Appendix.

a) Data Input and Storage

There are 3 functions used to input, display and correct

the stocks {S. (t;u)} for any given time period t. These are

(i) INPUTSTK

(ii) DISPLAYSTK

(iii) CORRECTSTK

INPUTSTK is a function that requires no arguments. It asks the

user for the time period t, and for each cohort 1=1,2,... 12 it

asks for the 20 numbers {S. (t?u) , u=l , 2 , . . . , 20 . } . After these

are entered it asks for the remainder of the force, c(t) . A

sample use of INPUTSTK is shown in Figure 2. The data is stored

in a file called '4894733 STOCKS' ; details of the file format

can be found in the Appendix.

DISPLAYSTK is a monadic function which takes as its right

hand argument a 2 element vector of month and year, and displays

the stocks for that time period with suitable headings. Table 6

demonstrates the use of DISPLAYSTK for data on 31 March 1976.

CORRECTSTK is a monadic function which takes as its right

hand argument a 2 element vector of month and year. After using

DISPLAYSTK to observe the stocks on file, CORRECTSTK can be used

to make any necessary corrections. A sample use of CORRECTSTK

17

cr> <r> u"> ct>

t-« to ^-4 «-(

CO ^-H 00

r^ cm c^ r- r-*-H CM *-l ,~l

i_0 t-h (X) C CD

LO O lO C"> lO

jt o .zr cm jr-i CM i-< tH ^H

co co co co co,-1 cm ,_| ,_| ^

t-< CMCO *—

CO

Oh

Hmo

r-t ro <-<

CO *- fO «-l

o-H4-1

in

3

CO O CO CM CD

Eh

a-

o

os

lo r- ro t-

LO CM LD CN LO

ld zj- en ^r

CN

u

Hfa

CO CO CO CM CO

CJ

^a^E-, CM. CM CM i* CMto Q LOE-, Q=5 "-H LDO, as f-

=S fa3 IS »H IS <n i 1-1

>-h a. ro ro ^ ofe3 to <0 to

«u a; a: as|-i kfl 1-0 >J CO toE-t o • • o • o

cm lJ cm kjQ r\i >-3

18

Oj«-<^3-cf\'cr ro t-< cm r- cc*-• *—« o ro i/) (\

CT> LO U0 -3" Lf> «-• co o^h i-> r- a>

COJJhn^CDJ-J o r- i£>

l/l *-» cc

f"- CN r- t** cniDiDiOni^omiD

'X *-4 o * cc o «H c^ CC cn lO CM fHfO r^ cn »H CT Uj CN o

CN IT)

CDCN

lO c en a- 3- CN 3" re ,-, CM cr Ol o** CO ^ r- CM in cn CM 3 CC

CM1/1

COo F5

1/5

zr o cm lo i-< *-* opr1 (N H fv r< ID H

o co r- o u) j

c2rocNCNi£icx>cr>c>CN.3-r^oMHiTfMfNPOfNinOC^^l^

*—

'

«—

<

m CO ^ o

oj n «- o hh cv< n m ex

(X) o j- «-» o cm r-CJl tO C\ CN O C71 O

a- *h r- j cc j

^- no r*- .3- J«-» a- csi r* ro

co <n l£> m CD t^o cm r-* oo co colo «—

< co *-* id co

O CO 0> O r<H CO r) 3- iTl

a- v£> co r- to & stcm co o co co r* cor< ^ r* J J r- O

c?>r»-ocoi-c>.3-oi/">fOi-icocoCfiCO?O0CnC3'^CDC0fO*-• cn r- cm to *m ex> u-> .=r

Cocoocccnp^*-tcoo<x>r^tDLOOO coCNC^coootDCTOmcoo>0 coT-tcorr)OOT-iLO*-''»-tco(£>r^

ininioniDh-ioCDOl^HiojncNjn^ncncocrijtHCOCNOT>iDr*-CNCJ»CNtr-'i£}C0CO

Ehto>H

ft,

COH

M-l

coH+J

(d

M-PCO

cod-a-CNCMOmr^CM(r>cocn3'Lnoot~'-'cnocr~ai^oLO^-HCCCM^CM3^HCOC^Oi/>

r~CMtor^cD«-<Lnr~cor^cocMWCflOCKNrlJJJffiaO)

(DCMt-- ^ncT'CO^-co.rrcor- o,-i x h j o cm r~ ro cm cn

CJHcd

En

cooocMTHfnr^CMfnr^^-tCMCoir)

CM tTHiDrOJ^lft^r-» CM lT> *-t

CMLO^-jCMt-ts-tocrimc^cor^«-* corou")cncocn*-<cn

CTi«-lCMCMtD33-p~•H CM CO

OOCMtNHHCOCOr^oa-d-a-a-cni/).H »H CM CM

% 5£ * 3; =S *

Eh

0*-<cNcr>;ru">t£>r-~cocno*-iCN

19

is shown in Figure 3.

b) Endstrength Forecasts

The function ENDSTR is used to calculate end-strengths for

given recruitment policies using equation (3). It requires no

arguments, but interactively asks the user for the following

data

:

(i) Number of periods to project (call this n)

(ii) Base Period

After these it asks for the following data for recruits for each

of the next n periods:

(iii) Percent Caucasian

(iv) Percent 3-Year Enlistments (it is currently assumed

that there are no 2-Year Enlistments)

(v) Percent of high school graduates in Caucasian recruits

(vi) Percent of high school graduates in non-caucasian

recruits

(vii) Total recruits in each period

(viii) First 6-month attrition percent for high school

graduates

(ix) First 6-month attrition percent for those without

high school education

The answers to (iii) through (ix) are used to spread the recruits

in each period over the 12 cohorts. The next input required is

(x) Continuation rate method (see section 3)

(xi) Does the user wish to change the continuation rates.

If the answer to (xi) is yes, the user is asked for

(xi-a) High school graduate factor

(xi-b) Non high school graduate factor

20

CORRECTSTK 3 76TO END, ENTER COHORT NO. 0. TO CHANGE >20, USE COHORT NO. 1, LOS 2 1

COHORT NO.?Q:

12LOS?D:

6

CURRENT: -5 5 3

D:503

COHORT NO.?Q:

1

LOS?D:

21CURRENT: -4815 2

A/£W?

D:48049

COHORT NO.?D:

Figure 3. Demonstration of CORRECTSTK

21

These factors are used to multiply all the continuation rates

for the given cohort type. This approach is used rather than

asking the user for changes in each of the 241 rates.

After answers have been given to questions (i) through

(xi) the end-strengths are calculated using equation (3) and

stored on a temporary file. When the calculations are completed

a report is printed showing the recruit policies used and the

end-strengths obtained. Following this printed report the user

is asked if he wishes to continue. If the answer is yes, the

user can then pick a subset or all of the questions (i) through

(xi) to enter different data and rerun the model. An example

run follows in Figure 4.

22

CN.

CO05COEh05"^

COOf

a-CN.

Eh ^>< Q>Co N 05^ O

OEhH Eh

COST 3 J" Zt it CO CO =f LO =t O 05 * in Q

cn. LO IT) CO <_o IT) Q rH CN. T-i Eh T-Hfe!

COEh o 00 *H 05 EhCo cn. 03 Eh "^co CN CO Co O Ehhe xH Eh CN. <=C O *^ Eho H Eh CO U") S;ftj Ci as CO * cn co CN. CO CN :=» ro 00 CO tH Eh co CO co l>

CD

to

D0, CO > oo CO En LD CO LO co r-4 £» T-< CO tH

5£ CO Eh CO 05Co cn. Eh CO 05 H CO COEh cs s» CO CO =3 O 05 o.

a£(0

Q> CO 05 CL, 05 O COCO H Co CO CO CM o. 33

G> ftj 05 cm CO CN. CN r~ a. CM LT> C5 CN O CO CM *-H CN CN Eh CM COCO CO C*3 oo Eh CO m ^ UD 05 <-H 02 tH 5; r-\

Cfc; H O, cu H C> 05 Eh CoEh i*; ^ ^ CO ^ O ^; ^CO r

-Q CO LO Sh o. 05 ^ O COC5 Qu CO C" H co C3 CO Eh O S| <£>

S{» *c =3 u-> m CO 32 O Q CN CN O-^M • J- QQ CO 05 tH oo 05 <H co CO t-t I_T> r-l lO Eh tH vH UD H t-H CO ^H CM

<o Co !>H 03 3t 33CD

Uas do =5 >-q

05 co 5. CO03

• •• • •• • • • • • • ••HPh

T* CN CO :* LO a to r- CO en

23

3- or lO to

«-h lo o ocC3 J- <N r-l

Eh

Eh

ft;nsi HioomS-Nlfl ID o oi olomiD no s dJ {*) O Ql O^ CO

Cs r- r- r- id 10 mfe TH *-* T-< T-< TH *-H

CO

CO o O o oEh o o o oi-i o CM in lT

5i cm *— rH rH

Q: T-H ^< rH rH

CotaCc

•"^ o CO t— 1/5

0= CM "-1 T-t i-*

co

>o

T3Q)

C•H

Cou

to

5:

Co

CM CM O O

CO O O CD CC:— ID ID Lfi l^

co in cm om m ^d to

a:EhCi=aca CC LO t- TO 3-

CC >H to TO TO TOEh ro

coQ Coa: ccca ca

to1 ca"-1 E-

co:a

COto 3- inCO CO CO

c^. t CoCj I CO ID CC

O Col ca r- caa: •SI <C a.Eh CO to CM

ca Cn. c-. r-l

s: COCO Co Q a

^ca E-. 5: O CO 0= Cs 1-1 CN CO 3-

Eh •^ CO i-i * cc Co"5: cc =3 a: Eh O 6-H >-(

cc CN ca ca 61 Co ccca CL, 5: co 1 toCo •^ tt. a,Si ca [a c^

• •^ CO E-, COo .. a= •"*: =c CO =c~ c_> oa a; * u.

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C2-

col

talc*.

ca >-J •

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>-. Eh caco. 2s =5

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to

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0)

WD

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en

EhCoEh *h

24

toEh cc ro lO WEh r- in ,— CMi in in o CO

<H co o cto T—

1

*H »— *-l

**

EhQe~

EC co in r-v U3 — r-

Eh c^ a- en [» irt st

to CD CM cc C »— rr

:r to m a to cc

=5 1— r- r~ r~ [»> 01-5

to

to o o O oEh o o o o>-h o O c oi CN CM CM CNto TH «— *H t-t

to

m3

a:

to

*to

a:

10

o co r~ inN n th h

CM CM O O

O O CO COto ir> in in

-aOJ

13

C•H4-)

Cou

E-,

<to

M-l

co in cm o\S> lT> t£> l£>

CD

wDCD

col

wHt̂o

c-. oCO Ehto to C-.

E-c ^ rH Cc"S to o Oto • Eh

Cl «H C>CO T "a:

» cc; to=*: 15"a: toC~ to •• a: ..

is sea -a

toa:EhC3%to to in r- co a-c= ^ pi n o nEh r>toto to* toto to

tototoEh :* in m a mto CO CO CO CO1 toto ID toto r- CM tocc r* o toto <T> h O •

toM # . ^

rH

to ea to

it o o • • to to HMD Jto H * to o to

=3 a: Eh to Eh >-H

to to E-. to toto 5: to 1

tototo

to to toto Eh to^: ^ to toto to * to

ae

to SSI

Eh•a: cv,

Eh toto ft*

• to

>H Ehto ^Eh oto ro

25

References

Zacks, S. and Haber, S. E. , "A Procedure for Forecasting theSize of a Force Subject to Random Withdrawal," Report No.T-312, Institute of Man. Sci., George Washington University,Washington, D.C. 20037 (1975)

.

Grinold, R. C. and Marshall, K. T., "Manpower Planning Models ,"

North-Holland Press, New York (1977) .

26

Appendix

1. Files

The forecast model requires 2 files for execution. The

file '4894733 STOCKS 1 contains historical data on enlisted Marines

(for details of file creation, manipulation and security, see

the booklet on the APL+ file subsystem from Scientific Time Share

Corp.) component 1 of this file contains data for 30 June 1975,

component 2 the data for 30 September 1975, etc. The format of

the data is shown in Table 6 of the main report.

The file '4894733 FORECAST' is used to store the forecasted

force and attrition whenever the function ENDSTR is used. It

is used to facilitate the printing of various statistics on

the forecasted force and attrition. Its use will greatly

simplify satisfying any future request and allow the user to

display many kinds of data without re-running ENDSTR.

The format of each component of this file is shown in

Table 7. Each component is a 24 x 21 matrix. Rows 1-12 of

component 1 give the base period stocks as in Table 6 with

column 21 having the stock with LOS > 20 in the top row,

followed by 11 zeros. Rows 13-24 of component 1 contain

zeros. Component i (i >_ 2) contains the forecasted stocks

and attrition for (i-1) periods after the base period. Rows

1-12 contain the forecasted stocks in the same format as com-

ponent 1. Rows 13-24 contain the forecasted attrition from

each cohort-LOS cell in the given period.

2

.

Functions

The use of the main functions is discussed in section

5 of the main report. This appendix contains detailed listings

of the functions.

27

e

rHOU

/T^

oCM

I

ou

N/ 4

x:XI pP •H•H O & o5 CN CN)

en a ________ o A O ----- - - - oM •Ho w P C/3

o •H O-P J M hH"

c/) PP<

en

«ao

en •HT3 ~ ^

-H <D

•H aM II

0) ^-^

a -h r-l

|

^^ •HrH 4-1

—1 -H *—

%

•H C rHv—

(fl

,* •H II

Kl'O O p ^dr* -H -HO -H -P 5-1 -H

U t/l P 5-1

P CD P CD 4H

w a^ fd a-H

T3 (D-H tj <u en

<d en 5h cd en o-P rd <D P fd >-i

CO ,Q Q-: W £1 <u

fd fd nU 5-1 CD U H(DOM cu a) .h

S-i 4-> rd 5-1 P rH

O 4-1 CO 4-i <fa fd — fa fd ^

• • ,,

•H •rH

P -P

C C<D 0)

C c

a ag e

u u

<r

W CN

O I

Pi «H

-> <"m rj*

I

Si>

28

in

>

X

+

t> .-

I I

EhCOEh33CL,

Ho

m O cot- Sten -tH cm o

tH CNCm

CO 1*3

cn toen St

^-i 33Eh to r-

>*3 St O ^H O co tH +Eh ;s 4 mto 1*3 N ^O - O(*< Ct< CQ Q. CtJ

CD co th O ^ Co -^1 ^ ft; Sh-csfcoo «• u.

to 35 33 cl 4. t*, 35

Co O Cl f*,

co ct; - 33 cn 11 q fe;

Eh <o . Eh o to S;to 1*4 Co St cn cn Ct; Cq St \

>< OQrl w C0SC0 +•» n 10 9; .^ f Q S) «\^> co r- 4 :=. £. ,_, +•«> r- cn :§: o h • «>

^.^cn O s; E»o ta -

O cn Q O o ?!S;0 1

• «« CO • Ct3 CN CN t] o <q; ..

^5 *OE«]^m " It; - tO. 33•»- ijs; af- Eh •- Cl, Eh

.-s- ~ ^ t o 53 0^0•«0^' CO(—14-Ctj O c« =£St QO+ CS^D CO 1*4 1*3

Co Co O r—il_i rosace;H ID H ^ O * ^Q. Ehh^^^u X in Q^^lO

•'^; Cc QEh Ji—1 H '-^n>HhCtjUj^^ + .» vH » .<_ C3.

• tXi^H * ^ + 4 CN StSiCj [Jg m —„ + 1—1 . { k| !^ H tt]

E-nCjCJ^ + THvHg:-!—

I

{ a. •>

to H H En 11 I 1*3 Co •» H " 5* ^hEHEHQO + ^IOHAIHjX33 St n ^ 3t Eh >-3 1—i cm ^ § ^ft, S3 • CN + Co Eh - SH t^Q3t f*. •• w w .... EhHQH + a3CNcoj-LOf t-- co -

iO, i-^to.^k^i-ci i-3 tO,

t> t>1—1

1—1 1—

1

1—1 r—11—1 r-ip-11—it—ir—11—10 rH cnH CN CO J Ul ID > CO Ol rlrl H

CO•I.

1—1 S3

1—1 +

25 +

+

COCo

rH CO1 » 3j

* «•

tH US EhEh cc

Q Co Os; 33cm- ci Occ; 35 COCm Cc

cm-

* ^ co§: s: 35* EhO k tH

r-{ Ph ^T-\ 1 - r-i CN

At

CO O O 1*3 O^-s H H £*3

Ctj Eh Eh 1*4 Eh cjj rj>h CO s: ^ &h Co m st im Cm Cm §2 Cm r- s: 1—

1

33 <> 1 33 *&Eh t*3 r-i Co • *>

3t — - 1—

1

5^ CN H5: c/ LO tH H Co 1—1 <o 1 1

**•*

Co^M CN Eh^>hEh

co 5: CNs:

>H O CN - rH ct; x l-J OS Eh

COt-> •> 1 1

Eh 32 5!<o Eh J" •

1*4 Co + OQ.

GJ §: 1*3 •« y—

\

c^.

CO Cm ^ - Co co co • 4- ^H CO Eh S«2 co .i« co H 1*3

05 r- Eh » co r- 1—1 st 11 ^to 3r •- - .. S3 C •-

CL, en LO '-v O • «> Eh CD i_i Eh n '

00 H CN CN ^ to co Xi ft; t Ocq 3- - xH A •« *• 5^ OO - « ^ Co H St - — 33 O 1—1 StCm ^ Eh Co • #« H + CO ^) CoO • 5: ^i a: Onto — • * «t

t> 5: CO - Cm CO s; 1 B>>. H vH1—1 .«> ^ CO - 33 1—

1

• #» Eh co 4- Ct; • 1 1

£h Eh 5! CO Eh ^H s; S St f*3 CO s: i*3

1—1 3* CO ^ H 1 1 ^ C3 33 Co Eh st r .«Co^ 3t t-3. 1*3 m ^t i< St - St 4 - stj

Eh ^ SH Cm -- Cl, h Eh Sxj Eh Cm th &3 Eh ^ » t-3

CO Eh s: r >H - • CO Eh Co cc .. cl,

>h Co ^ *—* Eh-0- O Eh CO 1*3 C3 • O O Eh i*3

^C t>H cl, i*3 * /-^ 3; Co Eh ctj 1*3 s; cj 33 St ctj

kO. S3 CO H CO »- 1*3 CO ct; H 1*3 st <o - 1*3 1*4

Cm ^ H Eh - a cc; :*3 CO Eh Cq 1*3 CO C--. 0=CO CL, CJ 35 Cl . CN O cq 05 Co St Em CO ftj

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t> Q> Eh a w O Co Eh S - tH - - CN

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29

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to tol E-to tol to=C X tom rr to

+ to^~. torr> to

to cr> ^ cr.

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to O ao

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^ toto Q. 3-

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•r-i to 4 to^ to '—'to4 - s» to

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