€I

LRTP MATHEMATICAL MODE B",OCHU 2,

CAL No. VQ-2044-H-3

Prepared for.

U. S. A"MY MT~ CMNContract DA-49-106 AMC-237(X)

30 October 1965

CLEARINGHOUSE

I

I

COMINUL AErZONAU1CAL LAtVIATC.N, UC.

LRTP MATHEMATICAL MODEL BROCHURE

CORNELL AERONAUTICAL LABORATORY

REPORT NO. VQ-2044-H.3

30 OCTOBER 1965

AppDo dby:, HGVO PROJECTS DPAMENT

Prepared for U.S. ARMY MATERIEL COMMAND

CONTRACT DA-49-186 AMC.237(X)

NI

CONTENTS

Y No.

1. INTRODUTTION 12. MATHEMATICAL DESCRIPTION OF THE 1

LRTP C1.OICI MODEL

2. 1 Strictural Relationships

2. 2 i ,thematical Description

2. 2. I Problem Formation

;2. 2 The MBPA Configuration Set

2.2.3 The Expected Technical Value ofan MBPA Configuration

2.2.4 The Annual Cost of a Configurationfor an MBPA 7

2. 2. 5 The Annual Monetary Quota Co:,t ofa Configuration for an M3IPA 8

2.2.6 The E.cpccted Coot of a Configuc.tioafor an M2,PA 9

2. 3 vfethcd of Approximation

2.3.1 Dczcr;ption 10

2.4 Summary of Sy.nbols 1

2.4. 1 Subscr.pts 11

2.4.2 Inputs 12

2.4.3 Auxilia-y Symbols

2,4.4 Outputs

3. COMPUTER PROGR.A, f FOR LRTP Zv!ODEL -.

3. 1 Description of t) i Program

3.1.1 The Inpt.s -,

3.1.2 The LR':P Program

I

3. Z i of TABL.$ and ITEMS 6ow of L*rTP P:ograrn

333.4 A' ortrzn Li:,ting 4

3 , ' : n L o u - '4. UMhLRI"AL. =,A MPLES

574. Gcnirraon of Hypoth.ical Data 57

4. Z Com, puter .- i ur 59

11- SAMPLE COMPUTER OUTPUT iU-I

[.

1. INTRODUCTION

This brochure contains a technical description of the LRTP Choice

Model derived in Cornell Aeronautical Report No. VQ-2044-H-2, "The

LRTP Process as it Relates to the US. Army Materiel Command".

The brochure is self-contained in that the technical aspects may be read

and understood without referring to the above report.

This brochure is divided into three sections, excluding the Intro-

duction. Section Z gives a mathematical description of the model.

Section 3 contains a description of the computer program which includes

flow charts, a FORTRAN listing and a debugging log. Section 4 contains

several numerical examples of program outputs using hypothetical input

data.

2. MATHEMATICAL DESCRIPTION OF THE LRTP CHOICE MODEL

This section presents a mathematical description of the LRTP Choice

Model to the extent necessary for programming the model.

The description is given in four parts. Section 2. 1 provides a

description of the relationships between the conceptual ele nts generatd

by the LRTP planning process. Section 2. 2 gives a mathematical descrip-

tion of the model and Section 2. 3 gives the procedure used to approximate

solutions. Section 2.4 contains a summary of symbols.

2. 1 Structural Relationships

The choice problem begins with a given set of 'Major 1arrier

Problem Areas (MBPA's) where each MBPA has been derived from 0:ne

or more Research Development Objectives (RDO's). Acccrpanying each

MBPA is a binary statement as to whether or nut a minimum research and

development work effort must be funded. Also, each MBPA has three

numerical values associated with it. The first is the estimated

expected probability that an IRDO will appear at some future date in

the form of a Qualitative Maturiel Development Objective (QMDO) or

a Qualita ive Materiel Require.ment (QMR). The second is the estimated

expected probability that the '.BPA will be encountered in a Technical

Approach given that an RDO c,, -taining the MBPA appears in the formof a QMl or QMR. The third value associated with each MBPA is its

estimated essentiality relative to other MBPA's. The essentiality isassumed to be derived from priorities assigned to RDO's.

In order to overcome the MBPA's, one or more alternativeTasks (TK's) are proposed for each MBPA, any Task proposed for an

IMBPA will overcome it if successful. A Task is defined in terms of

a sequence of annual Work Efforts (WE's), and associated with eachannual Work Effort is an estimated conditional probability of success,

estimated cost and a Monetary Quota to which it is assigned. A Monetary

Quota represents a Field Establishment assigned to conduct the work.

A Task is sr.id to be successful if all of the annual Work EFf&orts asso-

ciated with the Task are successful.

The above relationships are indicated in Figure 2-1.

The problem is to determine possible combinations of Tasksfor funding (and consequently those not to fund) that ma.ximize the

expected Technical Value of the LRTP program and satisfy given mini-

mum costs assigned the Monetary Quotas and MBPA minimum Work

Effort statements,

Henceforth, a combination of Tasks will be ralled a Configiration.

*

Pf11OPOSED SEQUENCES OFMAJOI BARRZER ALTERNATIVE ANNUAL WORKPROELEM AREAS TASKS EFYOR TS

I, Binary statement PROBLEM: 1. Probability ofconcerning mini- Determine comnbi- Successmum iunding nations of Task#for possible funding2. Pro: ability of subject to constraints Z. Cost

z.2 --o anc e inRDO

3. Probability that 3. Monetary Quotait will beencountered

4. Essentiality

TK1 WE 1 2II1 IWE 211...

MBPA I

T ,

1

, -

,,, -9

@KI Z ..

TK22 .. ...MB PA

2

Figure 2-1. Structural Relationshipt

-3-

I

2.2 IMathematical Description

2.Z. 1 Problem Formation

Let R denotv the Configuration set where R is of the form:

aR(r) = rl Rk (r k ) (direct product set)

k= 1

where a Configuration r C R consists of an ordered a-tuple (r 1 , rzo.

rk# .. , r a ) of Configurations, one for each MBPA, Defined on the Confi-

guration set ic x funrction V(r) called the expected Technical Value of a

Configuration. Also defined on the Configuration set are three cost

functions. The first cost function Cr) is called the Annual Cost of a

Configuration and is expressed as a single value. The second cost function

Z(r) is called the Annual Monetary Quota Cost of a Configuration and is

expressed as an ordered b-tuple (ql, qZ ... # q no. aq.) of annual costs,

one for each Monetary Quota, The third cost function E(r) is called the

Expected Cost of a Configuration and is expressed as a single value.

The expected Technical Value and Costs of an LRTP

Configuration are given by:

a(1) V(r) = L Vk(rk)

k I

a(3) C(r) = Z Ck(rk)

k- I

a(3) Q(r)- = Qk(rk)k: 1

(4) E(r)= E Ek(rk)kz 1

-4-

where

Vk(rk) the expected Technical Value of a Configuration

for the k-MBPA

Ck(rl) the Annual Cost of a Configuration for the k-th MBPA

Qk(rk) the Annual Monetary Quota Cost of a Configuration for

the k-th MBPA

E(rk) the Expected Cost of a Configuration for the k-th MBPA.

Given the above relationships and a Monetary Quot.

constraint F, where F is an ordered b-tuple (fI' .. I fn' -''' fb ) of

minimum funds, one for each Monetary Quota and binary statements

hk , one for each MBPA, the problem is to determine

max fV(r) Ir" RIsubject to

Q(r) k F (qn k in for all n)

and the conditions imposed by the binary statements.

Z. 2. 2 The MBPA Configuration Set

A Configuration for the k-th MBPA rk Rk consists of

an ordered dk-tuple of the form (rIk, r 2 k,.., rjk,. , ., rd kk) where

rjk can take on one of two values, say either 1 or 0;

rjk = 1 denotes the j-th Task proposed for the k-th MBPA is repre-

sunted in the rk Configuration

rjk = 0 denotes the j-th Task proposed for the k-th MBPA is not

represented in the rk Configuration.

-5-

0J

Let

hk a binary statement as to whether or not a minimum

research and development work effort for the k-th

MBPA must be fundedwhere

hk=I denotes the k-th MBPA must be funded

hk--O denotes the k-th MBPA does not necessarily have to

oe funded.

O.ven hk = 1, the Configuration set Rk for the

k-th MBPA consists of all Configurations rk that have at least one

Task represented in. them, Given hk = 0, the Configuration set Rk

iot th k-th MBPA consists of all possible combinations where there

are 2 k Lombinations (Configurations) represented in the set.

2. 2. 3 Th 2 Expected Techniczl Vahe of an MBPA Configuration

Let

Pijk estimated conditional probability of success of the i-th WE

of the j-th Task proposed for the k-th MBPA, i=l, 2,.. .mjk

Uk = expected probability that an RDO will appear at some

future date auid contain the k-th MBPA

wk a estimated expected probability that the k-th MBPA will be

encountered in a Technical Approach given that an RDO

containing the MBPA appears at some future date

Uk number of RDO's that the k-th MBPA is aasociated with

s = total number of RDO's.

.6. m m m

Then, the estimated probability Uk is given by

(5) Uk = Uk/ S.

The probability of successP k (r A) of the j-th Task

proposed for the k-th MBPA is given bym

jk(6) P k(r k ) Pijk'

(7) P k (rjk a 0)= 0.

The probability that the j-th Task proposed for the k-th

MBPA fails Njk (r jk) is given by

(8) Njk (rjk) = - Pjk (rjk)

The probability that at least one Task is successful

Sk(rk) in overcoming the k-th MBPA is given by

dk

(9) St r n N3 k (rjk).

Finallt t z! expec *d Technical Value of a Configuration

for the k-th MBPA is given by

(10) Vk(rk) UkwkekSk(rk).

2,2.4 The Annual Cost of a Configuration for an MBPA

Let

Cijkn= estimated cost of the i-th annual Work Effort of the j-th

Task proposed for the k-th MBPA and assigned to the n-th

Monetary Quota.

.7-

The r cot Of the j-th Task C,, (rj ) proposed for the k-th MBPA

is given by

(11) Cjk(r jk ) I jkn'

(1z) cjk(r jk 0) 0

and the Annual Cost Ck (r k) of a Configuration for the k-th MBPA is

given by

dk

(13) Ck(rk)= E C.k(r.k)j=j

2. Z. 5 The Annual Monetary Quota Cost of a ConfigLration for

an MBPA

The annual Monetary Quota Cost Q3k (rjk) of the j-th

Task proposed for the k-th MBPA is given by

(14) jk (r jk=l) = (YI' 2 ... Yz yn ' Yb)

where

'n 6 C1 jkn'

I for n = n'6 =o otherwise

and

5) jk(rJk 0) = 0 (yr- 0 for all n)

The Monetary Quota Cost Qk(rk) of a Configuration for the k-th MBPA

is given by

-B-

d k

(16) Qk(rk) = Q.k (r ;k

2. 2. 6 The Exected Cost of a Configuration for an MBPA

The expected cost E k(r k) of the j-th Task associated

with the k-th MBPA is given by

m jk{17) E k(rjk ) I1 jkn + E Pijk ciJkn

(18) Ejk(rjk 0) = 0.

The expected cost Ek(rk) of a Configuration for the k-th MBPA is given

dk

(19) Ek(rk) - E Ejk(rjk).jl

2.3 M ethodofApproximation

The purpose of this section is to list the steps employed in

determining

max (V(r) I r&-rR)subject to

Q(r) a F

and the MBPA binary work effort statements.

The methodology presented herein is similar to that described

in Cornell Aeronautical Laboratory Report No. VO-i887-H-l, May 19, 1964.

As indicated in the report, the method is one of approximation and the

results are not necessarily true maximums.

-9-

Z, 3.1 Description

The steps employed to approximate the set of Configu-

rations with maximum Expected Technical Value subject to Monetary

Quota Costs and MfBPA binary work effort statements may briefly be

described as follows:4'

I. Set rk a 1. rk = I denotes an MBPA Configuration

consisting of all Tasks proposed for the MBPA.)

2. Compute Vk(rk), Ek(rk).

3. For each Task compute

=Vk Vklrk) - Vk(rkJ)

AEjk Ek(rk) - E (rkJ)

where r k denotes the rk Configuration without the j-th Task

of the k-th MBPA.

4. Rank the Tasks ir. order of increasing

AV jk/AEjk' il' J ' Jx+l .... ;x:istrue.

5. Set r=l (r=l denotes the Configuration consisting

of all proposed Tasks.)

6. Determine if Q(r) k F. If the statement is true,

proceed to the next step. If the statement is false, stop

computation.

7. Set xuO.

-10-

S. Determine if U(r ) 2 F where r denotes

the r-th Configuration with the Jx+I Task removed. If the

statement is true proceed to the next step; if false, go to

step 11.

9. If hk= 1, determine if i.t least one Task for theJx+l

k-th MBPA is represe.:ed in the Configuration r i f

yes, proceed to the next step, if not, go to step I.

jx+1 3x+l10. Set r x - r+l and r = r

11. Set x x x+l and go to step 8.

The above procedure is repeated until all Tasks in

the rank ordering have been considered.

2. 4 Summary of Symbols

2.4. 1 Subscripts

k= identification number of a Major Barrier Problem

Area. ka 1, 2, ... , a.

j= identification number of a Task. j = 1, 2, .... dk.

ix identification number of an Annual Work Effort,i-- 1, 2, ..... ,mjk.

n= identification number of a Monetary Quota.n 1, 2 .... b.

-11 -

2.4.2 Input

FOR EACH MAJOR BARRIER PROBLEM AREA (MBPA)

hk= a binary statement as to whether or not a minimum

research and development work effort for the k-th

MBPA must be funded

where

hk=1 denotes the k-th MBPA must be funded.

hk=0 denotes the k-th MBPA does not necessarily have

to be funded.

Uk= number of Research Development Objectives (RDO's)

that the k-th MBPA is associated with,

Wk= estimated expected probability that the k-th M.BPA

will be encountered in a Technical Approach given

that an RDO containing the MBPA appears at some

future date.

e k- the Technical Essentiality assigned to the k-th MBPA.

FOR EACH ANNUAL WORK EFFORT (WE)

)ijk= estimated conditional probability of success of the

i-th WE of the j-th Task proposed for the k-th MBPA.

Cijkn = estimated cost of the i-th WE of the j-th Task proposedfor the k-th MBPA and assigned to the n-th Monetary

Quota

OTHER INPUTS

5= total number of ADO's

FE minimum amount of funds that must be allocated to

each Monetary Quota where F is an ordered b-tuple

(f# f1, . f I ) funds, one for each Manetary

Quota.

Z,4.3 Auxiliary Symbols

Vk(rk) expected Technical Value of a Configuration for the

k-th MBPA

Ck(rk) the Annual Cost of a Configuration for the k-th MBPA

Qk(rk) = the Annual Monetary Quota Cost of a Configuration

for the k-th MBPA

Ek(rk) = the Expected Cost of a Configuration for the k-th M.BPA

Uk expected probability that an RDO sill appear at some

future date and contain the k-th MBPA

Pik(r k) = probability of success of the j-th Task proposed for

the k-th MBPA

Njk(rik) probability that the j-th Task proposed for the k-th

MBPA fails

Sk(rk) probability that at least one Task included in the rk

Configuration is successful

-13-

C., = annual cost oi the j-th Task proposed for the k-th MBPA

a (rik) z annual Monetary Quota Cost ol the j-th Task proposed

for the k th MBPA

E k (r jk) the expected cost of the J-th Task proposed for the

k-th MBPA.

2. 4.4 Outputs

r identification number of a Configuration. ri 2, ...

(j, k)= identification of Task@ included in the r-th Configuration

V(r)= the expected Technical Value of the r-th Configuration

C(r)- the Annual Cost of the r-th Configuration

AV(r)= the difference between the expected Technical Values of

the r-th and r-l Con..gurations

4C(r)= the difference between the Annual Costs of the V-th

and r-I Configurations

Q(r) = the Annual Monetary Quota Cost of the r-th Configuration.

3. COMPUTER PROGRAM FOR LRTP MODEL

This cction contains a description of the computer program which

pr.,cctes data for the LRTP model. The inputs and the outputs of the

progr.m are illustrated and the method of organizing information which

controls the program's operation is presented.

-14-

The computer program has been written in the FORTRAN IV

Lrngagc. It is prepared for operation under the control of IBSYS,

the operating system used for a-vtezal nAM computers (work on

this project was conducted at a 7090-1401 computing center).

3. 1 Description of the Program

3. 1 ,1 The InguttThere are three categories of inputs that affect the

program, those that control IBSYS, those that control the progran and

those that provide data to the program, Thceac three types of inputs are

provided on four kinds of punched cards: (1) IBSYS Control, (2) Program

Control, (3) Data, and (4) Special. These cards are described in the

ollowlng paragraphs and illustrated in Appendix I and Figures 3-1 through

3-6,

3.1.1.1 IBSYS Control Cards

IBSYS is the system which exercises control

over the operations conducted by the computer and equipment attached

to it. In order for the LRTP Program to operate and to have data for

its computations, LBSLS must do these things: (1) Arrange MBPA and

WE data ir a prescribed order (SORT), (2) establish the arrangement of

equipment for the programs use, (3) prepare the program for operation

Figure 3-1 illustrates those cards which

causa SORT (a subprogram of IBSYS) to place MBPA and WE data cards

in order (aee section 3. 1. 1. 3). (For a complete description of SORT

see IBM Systems Reference Library File No. 7090-33, entitled,

"Generalized Sorting System").

L

pr I - .

ILEP~~- - TUtdfI1 GLC

~.y~~L ,'..ATISs TAG, OCICMgN7T.*COUNT .- *MARK* L ACCL

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444444'44444444i4444444444444444444444444444444444d4444444444444444444444 /4444444 J

*SORT CONTRlOL CARDS

* FLOUR E 3 -1

Soo Appeadix I tor a deacription of thcas fields, on which a coamercial

SORT is ;Iona.

UN~ I TC? C I T09;Aj 01 MWN1U7Ti I IIPUT, BCHOLD -

UN-ct -~t T09 -- - .

I 1 Ii IS 1 II t ill U1ihIJ MiiiW1all11Ila 142 a AN m UamV11641l aUuaamiJ UIaJuumuII WHOPS Wuu m sii amlh uPbIj "114 " ??U

2~ ~ ~ ~~' 2 2222 2?2 22222222 222222222222 22222222222222222221222-222222222222 22

4 ~ 4 4 44444444444 44444444444444 4444 4 444 4 44 4 444444 444414 4 4444* ~ ~ . 5 55 5~ SS SLSSISISSS 15555555555555555555555 S5555155 555 555555 5

b~c" C"

r".I ASSIGNMENT

VlOURE 3-2

-17-

I iORAN L. -I7 ..--.-.. ___3 N E

;;-EX CL; . D .r.. . .

$JOB .- . - - - - - -

S--G PRTO4 4,0ES " .-.--.-.---- ./.....-.--*..W-...-...-.*...-.....- . LA

00 .00 0 001 -0coo.;.;**-- . . . . .d

3 43333333 33 i.3 3 3 3 3 3 3 1 33 3 33i*3 3 3 3 3 33 3 3 3 33 3 .

4 4444444 444 444444 4444444 AAAA44 444444:.

s !~ft si. 55 5 i ssis s5 5_ss__ss_5sss_____

6666 6z 6 66/666666 66 6066 616 i~ 6 &66 6 6 66 64 6

T .L~r ~ NC-DCK I

',!7 ... 1___7_ 1 1_7_1____7 1 1 1 1 1 1 1 . 7?I 7?III 71 11 1? 71 1 1 1 '

"1BJO 9 $349

2 5IiI......9l.C 99999tgggggiggg999tgggggs9L9 9 M O1$~ 21 1 a 0at * 44aw-"NWa a o "0 b* p l! -p

SY WI. OtATI 1

CRSTO CNUC'CVI , 4f~A

2~~OTOLCRSc "C00.0OOMPILE@OANDQOPERATE"OOOO0O0~0JOO

.;2~~~~~~FGUr 3-3iiII11111111111111111 11 il 111ll I iiJl

iiL Q

srt~x 1C i vT ---- L0001 .

ST X L01T I ___L T__________

j: a4l _ _N96 Ap(poQonO1

,Qi -0.000A9

$41 dL4 400900 __________ _______________ o0000o00o"000

_____________H11E1ECUTA1 I1DJ111B m iP

.2 2 2 22 12213 3 _ _ _ _ 331311

~QB~ .74444L4-44444

4 1 w Il m[ I

A& PIaANa11 0

I 1~I1I1111 II111111111111111111111111 iATIi 11111

z~~~2 ? 12Iz2 O CARDS?*2 ?222222llu~l~lz2l23?lZ TO2"LOADAND

FIGURE 3.

~ ~~ ~~ 33333333333333333333333)333333)3

A program (using the MAP language) is

used to add FILE 09 to the dictionary of files that is maintained in

IBSYS. This input file (on a ragnetic tape) is the sorted MBPA/WEdata. Figure 3-2 - illustrate& this routine.

'4

The FORTRAN IV statements which make

up the program are prepared for use by an XBSYS routine called a

comp-.1er. The compiler, when the program is free of error#, works

in conjunction with another IBSYS routine, called the loader, which

organizes the LRTP program and lets it conduct its operations, (see

Figure 3-3). NOTE: error free FORTRAN IV statements need not

be compiled repeatedly. Once prepared, the "Loader" can use the

LRTP program in its prepared form (a binary deck), and compiling

need not be done; see Figure 3-4.

A "DATA" card is used to signal the point

at which the IBSYS control system shall transfer operatioas to program

,..RTP. When LRTP has completed its computations, it relinquishes

control to IBSYS (IBJOB Processor) which is directed to cease operations

by the "STOP" card.

File No. 7090-27 of the IBM Systems

Reference Library, entitled "1IBJ0B Processor" explains in detail

the routines and cards mentioned above.

3.1.1. 2 Program Control Cards

Three types of cards influence the operationof the LRTP program. One of them, the "END LRTP" card denotes

the end of data on FILE 05, the IBSYS input file. After finding this card,

the LRTP prugram will not seek any more data from FILE 05. For

structure of the deck that contains this card see Figure 3-5.

-20-

The second kind of control card is the

"WE END" card which signifies the end of data on the MBPA/WE

file (FILE 09). The sorting process, mentioned in 3. 1.1.1, makes

thit. card the last one in the file. The recognition of this card signi-

fits to the program that all data and control cards have been read in.

For structure of the deck that contains this card see Figure 3-6.

The third control card may or may not beused. It is th% "PRINT" card and contains 1 to 16 numbers which

specify coordinates, Use it to indicate the Configuration summaries

tho user wishes to see. A Configuration summn ry lists the tasks and

their costs, by monetary quota, for a coordinate. When used, the

card must be placed on FILE 05, somewhere ahead of the "END LRTP"

card. For structure of the deck that contains this card see Figure 3-5.

The formats of these three control cards

re described 'n Appendix I.

3.1.1.3 Data Cards

Three kinds of data cards are provided theLRTP program. They contain information about (1) Monetary Quotas(2) Work Efforts and (3) Major Barrier Problem Areas. This informa-

tion is described in Appendix I. The placement of the MQ cards is

illustrated-in Figure 3-5, and Figure 3-6 depicts the MBPA and WE

cards as they appear in FILE 09 after the operation of SORT. These

serve only to provide data to the LRTP program.

ASee Appendix I for the formats of theseIcards.

-21 -

I AT

02 2

41 -444 4' ,4444444444444 444444444444444444444444444444444444444444444444444444444444

no11 gi117711 box1o 1111117110wo7ms 4066N 11111111111114111111;7777777 71777711111s1aa111 m

CONTROL AND DATA cARDs WOR rILE,05

FIGURE 3-5

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007

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AT

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I43

3.1.1.4 Special Cards

It is necessary that three special cards beused. The first of them, the '"LRTP" card serves to identify a run ofthe program, and it also provides one item of information to the program,that item being a count of Research and Development Objectives. See

Figure 3-5 for the structure of the deck that contains this card.

A second card, the "BCT) Image" card,contains letters, digits and special characters which the program useswhen making comparisons. This card must always follow the "$DATA"

card. (See Figure 3-5)

Special card three is called the "HEADER"card. It must precede the MBPA/WE cards before they are sorted.The SORT program expects a card of this kind to head the data to besort';d, see Figure 3-6. The sorted MBPA/WE data has the "HEADER"

as the first file on the magnetic tape, with the data making u-' the secondfile. When processing this file, the LRTP program skips the "HEADER"

file.

See Appendix I for the formats of these cards.

3.1.2 The LRTP Program

This section describes how the program reads and usesthe control, data and special input cards, makes the calculations specified

in the discussion of the model, and provides outputs which reflect theresults of its calculations. The flow diagram in Section 3. 3 illustratesthe movement within the program and the FORTRAN statements in Section3.4 provide a dercription of the details in each area of the program. Forthis section the LRTP program will be discussed from the standpoint ofits inputs, its computations and its outputs.

-24-

T..o categories of lJes exist: those that contain data

for computations :nd those that ar/.As baffers (storage of input or output

images). The -ables of comput.Tinal data are organized so that there is

a relationse'p between the re;Is',.rs of different tabler that pertain to the

same subject, i. ot., the farst ,gisters of MQID, QUOT and BUDG respec-

tively. contain identiicati',', quota and budget for the "MQ" with the

lowest ID. Data about "1.. .PA's" is kept in tables MBNO, MBCD, FREQ,VALU and NODR; anl ".rblos NUTE, TECH. PSTZ, COST, CSPS, MQNO

and DVAL contain ... ormation on "TASK's". The MBPA znd TASK tables

are organized in , .e same fashion as the MQ tables. Tables IXTE and

NOTE are us s storage for indexing data; i. e., data which enables the

program to -elate a TASK to its MBPA.

Input buffers, tables LPHA, INPT and sometimes IXTE,

wi.; contain the code for one card column or one priit character per

register. Output buffers are set up by the comapiler for IOCS, the Input/

Output Control System, The LRT" program in its "WRITE" statement

specifies the data to be transferred from ITEMS and/or TABLES to the

output bulf, re.

Further detailed explanation may be secured by exami-

nation of the FORTRAN listing in Section 3.4.

3. 1. 2. 1 iput Proeessing

The LRTP program reads in the nine kindsof cards described in Appendix I. With the exception of the "BCD

IMAGE" card and the "HEADER" card, field one is tested to ascertainthe routine which is to be used to process the card. Once this selection

has been made, (if unable to make a selection, see section 3.1.2. 1. 10)

the processing goes as follows:

~-25-

3. 1,2.1.1 "LRTP" Card

(a) Fields 2 and 4 are converted to integers,

(b) Field 2 is saved in register LRTP.

(c) Field 4 is saved in register RDOS.

(d) The contents of the card are written on

output FILE 06 (to identify the run of the program

for the user).

(e) U an error is found during the convorsion,

the program transfers to the error routine described

in section 3. 1. Z. 1. 10, below.

3.1.2.1.2 "PRINT" Card

(a) Up to 16 numbers will be converted to integer

form and stored in registers of TABLE IOUT. The

numbers must start in Column 7 and be separated by

one blank column. Consecutive blank columns are

interpreted as signalling the end of the control informa-

tion. The last column that may be used is number 72.

(b) Errors in converting cause the program to

execute the error routine; see section 3. 1. 2. 1. 10,

below.

3. 1. 2.1. 3 "Monetary Quota" Card

(a) Field 2 is converted to integer and stored in

a register of TABLE MQID.

(b) Field 3 is converted to a floating point

number and saved in a register ot TABLE QUOT.

(c) Errors in converting these fields cause the

program to execute the error routine; see section

3. 1.2.1.10, below.

-26-

3.1.Z.1.4 "END Card

There is no data on this card, Its recognition,

hwevcr, cau-es the progra-. to arrange the MQID and QUOT tables in

ascunzding order of MQ identification. In addition, an indicator, MBTK, is

set which iniorri the program that all card reading is now to be done from

FILE 09. Several items and tables are cleared in preparation for informra-

tion, frorm the data cards,

3. 1.2.1.5 "MBPA" Card

(a) Field 2 is converted to integer and stored

in a register of TABLE MBNO,

(b) Field 3 is converted from a BCD percentage

to a floating point decimal and stored in a register of

FREQ.(c) Field 4 is converted to a floating point

number, divided by item RDOS, multiplied by the

contents of a register of FREQ (from field 3) and

this product stored in this register of FREQ.

(d) Field 5 is converted to a floating point

number, multiplied by the contents of FREQ (from (c)

above) and the product stored in this register ofFREQ,

(e) Field 6 is tested for a blank; if it contains

a blank, a register of MBCD is set to blanks; other-

wise, the register is set to an asterisk(C).

(f) For errors in fields 2, 3, 4 or 5, see

section 3. 1.2.1.10, below.

-27-

3.1.Z. 1.6 'WE" Card

(a) Fields Z, 3, 4 and 5 are converted to

integers and stored in 1MB, LDTE, lDWE and

IDMQ respectively.

(b) Fields 6 and 7 are converted to floating

point and stored in PSTK and CSWE respectively.

U the annual Work Effort is for the first year, the

contents of field 7 are stored in CSTK, also.

(c) The program now uses the iniormation

in the items listed in (a) and (b), above, to place

the following data in their proper locations in

these tables.

(1) NOTE = Count of TASKS in a MBPA

(2) IXTE z index to TASK information for

a MBPA

(3) NUTE w TASK Id

(4) PSTE w Product of the probabilities of

success of the WORK EFFORTS

in a TASK

(5) COST = First year cost of a TASK

(6) CSPS = Expected cost of a TASK

(7) MQNO = MONETARY QUOTA which

contains cost of TASK

Id) For errors in fields 2 through 7, see

section 3. 1. Z. 1. 10, below.

-28-

3, 1, 2. 1. 7 "WE END" Card

When the program finds this card, it transfers

its operations from reading input data to doing the computations stated in

the discussion of the LRTP MODEL in Section 2,

3. 1. 2. 1. 8 "BCD IMAGE" Card

The program must have this card prlir to

operating on any other input. Therefore, this card must follow the

"$DATA" card (see Figure 3-5). The first 48 characters are stored in

TABLE LPHA. The data on this card must be correct and in the pre-scribed order, as tests for the correctness of other input data are made

using "BCD IMAGE" information as the criterion.

3.1.2.1.9 "HEADER" Card

When the program begins to read from FILE 09,it executes two "read" instructions, one is to by-pass this card; the second

to by-pass the "END-OF-FILE" mark. The only purpose this card serves

is to satisfy the rules by which the SORT program operates.

3.1.2.1.10 Errors

An error in a piece of input information results

in no computations. The program, however, prints the card which contains

the error and examines all input data for illegalities, printing the cards with

erroneous data.

3.1.2.2 The Calculations

There are two major areas of computation in

the LRTP program. The first calculates the Technical Value of each Task

and, using this TV and the Expected Cost of the Task, establishes their

order of elimination. The second takes each Task, in the order that has

-29-

mam i m m m i m m m m m m m i m m

been sct, and examines it in relation to the constraints (MBPA and

MQ) that are to apply for this run of the program. When a Task is

to be eliminated, the program enters -iutpu se!ction (see

Section 3. 1. 2. 3, below). After reco" g \ 'at is required in the

output section, the program returns amine the next Task in line'4

against the con-,raints.

The details of ne two areas of computa-

tion are as follows.

3.1.2.2.1 Technical Value

The LRTP program cornputec first the

cost of the program being considered and then its Technical Value.

Cost is the sum of the first year costs of all Ta.As; Technical Value

is the sum of the Technical Values of all MBPA's.

Secondly, t number which signifiea relative

i.nportance is attached to each Task by compw.ing its TV and dividing

that figure by its Expected Cost (CSPS). The results are saved in the

Table TECH.

3.1.2.2.2 Constraints

The Task with the least importance attached

to it is examined according to rules that pertain to MBPA elimination and

satisfaction of Monetary Quotas. If the Task can be eliminated without

violating any M.PA or MQ rules, it is removed from the list of Tasks9;

and appropriate action is taken in the Output section. Whether a Task

is remuved or not, the next Task considered for removal is the one wi'h

the next lowest ratio of Technical Value to Expected Cost; and so on,

through all Tasks.

-30-

QI

The rulej which the program contains

have to do with setting a value on each Monetary Quota and not permitting

the elimination of a Task to reduce a Quota below this value; and, itating

whether or not all the Tasks in a MBPA may be eliminated.

3.1.2. 3 The Outputs

When the LRTP program sel*cts a Task to be

eliminated, it enters the area of the prograrr which will record for the

user the pertinent information about the removal of the Task.

3.1.2.3.1 Run Information

However, three kinds of information have been

written on the output file (FILE 06) prior to selecting Tasks for removal.

The first of these is the Run Identification which is merely writing on the

outpu Lie, the contents of the LRTP card. The second kind of information

i a list of MBPA's, by ID, together with the indication of whether a VMPA

can be eliminated. The third is a list of Monetary Quotas, by ID, with the

number of dollars assigned to each.

The formats of these three types of output are

illustrated in Figure 3-7.

3.1.2.3.2 Run Results

Illustrated in Figure 3-8 is the chart produced

by the LRTP program as Tasks are eliminated. As each Task is removed,

the charges in Technical Value and in Cost are printed, as well as the dat"which identifies the MBPA, TASK and Coordinate.

-31-

a j

IN M -' f oC3-

IN 0. .. " % ----

6da

4 I

Au.ry F-c ' yA

LU V)

* .) 0. 1

w* LA fl -- - aO a N a

CCU - - - - --- - - - - -,

a - -- - - - - - ---

-I t .

UN .4 S r

%ri in CQ Vc

* ~-4- N~m.O'.NI-4

CO hi. Q-

'0 -4 Tin.. 'r u 0

"4 tv z.. o ,

IN %r In- -0

0. . LI..

,**o* o no- noO o0c 0 o0000 - c

C- .4 M j0 N 0% O MQM4).4(' 'IC D-C C 0 C .j- 3C -L 07" I

0~~~~I 04 '.0 a 0 0

CO <" M 0) I.NG %C '0r.V4C '4W f-"C C - 0 . %% \CO W i9 f0 %0 9 O a 0 .'0 69 7 07 m m4 M 9, 0 0 0 C7. C% 07 w w 0- (. 0 0 0-*

61 c - % Q Q cI rIC < - mC " "11 NQ % 07 44 I- ILCiC 4- 4 - 1 Nt) 4) % <'0.IZ< Q l0 r- a 1 CO0 0 -,-

09.0 . 0) 9 00 09 1 C) 0 I000C9.~ ~ 0 0 0 4 0 0 S 4 0 4

4.;.4

- . -t-i- ~.3N C -i-.. AC ~1 CO 0. C.- k.3 kC? CDl -- LA L.- N J 3 G -- L N co- C% 0N N -I_: . --- -- -l .s - - -D o -- - -- ,0 Nv , -r

V, V. V) -n '. 61 V'- M. M.. r- P- Q. 6- %r % ~ m Mm N ~T Co -0

C.I en ene 'Ie4 n c .Ic

1 I Io- o ca

L' v ,IiI

3.1. 2. 3. 3 Coordinate Configuration

W1,,n the "PRINT" card is an input, the data

liluitriaed in Figure 3-9 will result. This lists, according to Monetary

Quota, those TASKS which make up the R&D program at the coordinate(s)

specified on the "PRINT" card.

In operation, the program examines Table

1OUT each time a Task is removee. When it finds that a summary has been

requested for a coordinate, the program writes the information on FILE 08.

Upon completing the examination of all Tasks, the Configuration summaries

are transferred from FILE 08 to FILE 06 so that all information produced

by the LRTP program can be printed from one magnetic tape.

3.1.2.4 Using the LRTP Prograis

Listed below are the steps to be taken in using

the program. The list shows all steps. Steps that cannot be by-')assed are

flagged by an asterisk.

(a) SORT MBPA/WE Cards

*(b) Load program decks,control cards and data

cards on Tape

*(c) Place MBEPA/WE tape on FILE 09

*(d) Place tape from (b) on FILE 05

*(e) Place blank tape on FILE 06

(f) Place blank tape on FILE 08

(g) Compile "FILE ASSIGNMENT" subroutine deck

(h) Compile "LRTP" program deck

(i) Compile "BCDINT" subroutine deck

(j) Compile "SKFIL1t subroutine deck

-34-

00 LA4 0.

C; C. Id 0J ~J4

*4'* 0 0* m

a. b.

0- -L C, ,i a

.~~r 0C Cj C 4 C ~u~I. fn en co (n 0. 0 ( d '

IA A ', A 'A 0

I r- #4 - j kU'4 ... 0 0 'o OD N)14* m w %r w M- d% wmo- n4:4 1% 4A .. 0

4

o :0

ea .0 6 AC- N fn Q

'IAIA A ?4 A 4A

N -4 OD 4

X *p

'IA &A A --4

M : AAIP C

~ ~ Q .4

V. : . mvk-

40 U

'At hA

*(k) Load "FILE ASSIGNMENT" deck

*(1) Load "LRTP" dcck

*(m) Load "BCDINT" deck

*(n) Load "SKFL2" deck

*(o) At this point, whatever course has bcen

followed above, the LRTP progiram operates on data from

FILES 05 and 09, recording information on FILES 06 and 08

(if requested), according to control information on FILES 05and 09. Upon completion of program operation:

*(p) Print FILE 06

3. Z Definition of TABLES and ITEMS

Listed below are terms used in the LRTP program. The

definitions attached to these terms reflect, where appropriate, the

symbols used in Section 2, Mathematical Description of LRTP Model.

VALU w table of technical values of MBPA's, Vk( rk)

COST = table of first year costs of TASKS, C

NUTE a table of identiflcato i numbers of TASKS, (j)

CSPS x table of expected costs of TASKS, Ejk(rk)

PSTE a table of probabilities of success of TASKS,

or table of probabilities of failureof TASKS NA (rjk

TECH = table of ratios V k/Ejk

DVAL a table of values of Vjk

MQNO a table of the Monetary Quota number of the

first WE of the TASK

TCST z annual cost C(r) of a Configuration

TVAL z technical value V(r) of a Configuration

MBNO a table of Identification numbers of MBPA's

k-l, 2, ... , a 9999

-36-

FR EQ x table of values of wkekU k

MBCD w table of values of hk where;

h C: denotes the MBPA cannot be dropped;

hk blank: denotes the MBPA can be dropped

NOTE w table of count of TASKS in each MBPA. dk

QUOT z table of minimurn funds that must be allocated

to each Monetary Quota F i (fI) fV ... ' fnP

. b) where b < 1000 and number of MQ's 3 100

MQID a table of identification numbers of Monetary

Quotas N t (n x , ny ,.., nz) where x, y, Z r 999

and number of N(s) s 100; and no n equals another

BUDO a table of Monetary Quota Cost of a Configuration,

Q(r) - (ql, q2 , qb)

IXTE - Table of factors for setting indexes in tables that

contain information about Tasks

NODR - Table where a count is maintained of the Tasks

eliminated from a MBPA

LPHA - Table of the representations of letters, digits

and special characters

INPT - Table into which card images are read

IOUT - Table in which coordinate numbers are stored.

-37-

I

3.3 Ylow of LRTP Prograin.

END ORTP

*DNTACARDSDATA CARDS

CONV22

AIM -38-

READ BCD L.'AOECARD~, Ff FGHtAT,

~STORE IN TABLE

- -I

2C

HEAD CONTBQI/DATACARD.tRTPuOO TO 3AKQ -GO TO 3BPRInT-OO TO 3CMMD m0 TO 4A

FROR-GO TO 5A

2B

i=A DATA CARD.MBPA - GO TO 4BWE - GO TO 5B

ERROR- 5A

-39-

a

Com Bfl Fit=~ (21 ) EWWlD PIL 08TOZTORAND REAL ()coW1EiT BCD co-RE - (1)m nr INRP ORDLW'E S TOR(2) # OF RO 11 WO'S aTZE,

O)WRTE APD WE(3) STORE INf TABLE01 F=L 06 !OUT

2±) 2C

'I

W M BOV~ CD FU= ILLODSTO flT r REAL CONFI GURATIO N 0

(2)# OF rWLLAF.5 M?MR EACH XD)

(1)WARrEZ "'FMIS" ONFrnL 08.

(2 REW'D 08(35 CON FIL 08 o:oFILE 06.

4r.- 09

STOP

-40-

j4UOA 1(5)WJLTIPY FREQ(I)sowR YONETARY JV~IM RDO FACTORQTJOA TAIM MAND STORE 12 F!REQ

(6)STOM~ vlop()oID. ' yfDICATOR

MBPA AN~D WEDATIA CARD

PROCEssniNo--

20D

4B (I)CONVERT BCD FIELDSTO REAL AND flJTUGE

(2)STORE FIRST YEARCOST .ADD EXPECTED

T CCST TO CSP3.ADD(1)CO:WERT BCD FIELDS COST TO BUDG.[ TO REAL AN~D fITGE (3)STc2E PROBABILIT'Y(2)STORE MPA D fI OF SUCCESS OF TASK

.- M~oDn PSTE.(3)ST0oaE FEQUEUCY (4)CcMPUT: AND STO.RE

PER RDO IN~ FREQ A DEXI:%G FACTORS(4)muinu~Y F=E rl MlCE AND NOTE.

TBI4S RATIO OF (5)STORE ID OF TACSROSFOR THIS AND INtT= AND ID

RW O TTA OF MONEMARY QUOTAl.,-E OFi ?DOSNMoo

L AN STREEMNFMV E

-41-

(2)FRT CARD WHICH STOPCONTAINS ERROR(S) (2)CC:.LTE TECFNICAL

(3)sLT EROR mlVECATOR VALL OF ;HTASK AND EACHIMPA

(3)CO.TUTE TOTALTECHE41CAL VALUEAND TOTAL COST OFPROGRAM

()ca.uTE RATIO OF'ASK T.V. TO TASK

COST(5)cosPUTE ORDER IN

WHICH TASKS ARE

TO BE M~l~lATD

NO

-42-

PR OC ES S L Tv O

1M1PA' S_______________(2)Pn,*T LIST OF

(3.)SRLECT TASK OF. MOi'ETAFR QUOTASLOIWEST RATIO OFT.V. TO MCST

(2)TMT F0.1~ CON-STRAINT: NOT SATIS-

(FID,RrURN TO Wi3TEST FOR I4BPA

MROP CO*:ISTRAINT: 6cP~OT SAbTISFIED,RETURII TO (1.)

(4) cc:.:Pu'rE: (a) IMTOTAL COST,(b)NEWTOTAL T.V.,(C)THE46COST 7OR THIS PRINT ONE 1,11M OFTASK, (d) THE A TV COORDINATE SU101AM.OR THIS T.ASK, (e)THE COORDINATE

NIIMRAD()HID OF THE TASK(AND MBPA, IFAPPLICABLE) BEflIDROPPZ.

-43-

7A

(1) PRINT MONETARYQUOTAS

(2) CoapUxE TASKS ANDTHIR~ COSTS,By M1Q,WHICH MAKE UP THISCONFZMtRATION

(3)PRN~T TASK ID ANDCOST. XED RUNNflMTOTAL OF COSTS BYMq

( 4 )PRINT TOTAL OFTASK COSTS By Vq.

-44-

3.4 17raa ILti

EXT RNAL FORMULA NUMBER - SrflU'qCE STATEMENT

COlVMON LPHA(4.'),INPT(D72),INCHNOCHINTGIERR,INTICOM'MON 1ITE5 .1,IPTI,i'PCHN4PCHIPTG,IPRRDIMENSION BtDf')*9QO10,U11r)FE10)MN(C)

2MBCP)(5 , NOOJ,( 5C ,NOTE( 500),VALU(50(o) ,COST( 1500) ,CSPS( 1500),3NLII:( 1500),PSTE( L50O),TECH( 1500)tOVALtI5C0) , IUT(16),4MQNO(l5C0I),C8U~tI0)tCMQT(1O).oK8IIF(10).MBUF(10)

RFWINQ q~

Ml3TKxDLRCD = .00 WU4 J 1*100MQID(J) 0QUOT(J) 18'JDG(J)

104 CONTINUE

100 RFAD (5,191) (INPT(N),N*l,7?)IF (INPT(1).EO*LPHA(13)) GO TO 140IF (INP7(1)*EQ.LPHA(121) GO TO 130IF IINPT(l)oEQ.LPHA(16)) GO TO 500IF (INPT(l).EOLPHA(5)) GO TO 200

GO TO 1130102 REAO (9t191) (INPTlNbpNz1,72)

CALL SKF Il.

IF (INPr(I1.E0.LPHIA(23)) GO TO 110IF (INPT(l)oEQ.LPHA(13)) GO TO 120GO TO 18n

110 IF lINPT(4).EQ.LPHA15)) GO TO 300INCH =6NOCH =4CALL BCDINTIF (IERR.EC.l) GD TO 180I0MB =INTGINCH =11NOCH- 3CALL BCDINTIF (IERR.EC.1) GO TO 180TOTE = INTGINCH - 15NOCH = 3CALL BCOINTIF (IERR .EQ. 1) GO TO 180IDWE = INTGINCH = 19NOCH =3CALL SCOINTIF (IERR&EO.L) GOI TO 18010MG aINTGINCH =23NOCH =3C A L 1, TIF IlLXRA.EC.1)G0f TO 180PSTK a INTG

-45-

EXTERNAL FORMULA NUMBER - SOURCE STATEMENT

PSTK =PSTK/1C'G.INCH a27NOCH -CALL BCOINTIF (IERA~.EC.1) GO TO 180CSWE m INTOIF (lOWE .GT. 1) GO TO 103CSTK a CSWEDO 30 JK = 1,tIENTIF 9400D(JK).NETDMQ) GO TO 30BLJOG(JK) = UD(IJK) + CSTKGO TO 1039

30 CONTI NUEGO TO 1.8'

103 CSTK = L0.109 IF (LMID.EQ.IOMB.ANDLTIO*EQ.IDTE) GO TO III

IF (LMID.EQ.IOM0.AND.LTIO.NE.lOTE) GO TO 112K aK + I00 31 V= 19JENTIFCM8Nfl(M).NE.IDMBl GO TO 31NOTE(M) -IXTE(M) K30 To 1G6

31 CONTINUEGO TO 100

1.06 LMID TOMB113 LTID = ITE

NUTE!K) x TOTEPSTE(K) PSTKCOSTIK) =CSTKCSPS(K) xCSWEIAONOW = IDMOGO TO I.Vt

1.12 K = K + I.NOTE(M) a NO.TE(M) I

GO TO 113111 PSTEWK = PSTE(K).PSTK

CSPS(K) a CSWE*PSTK + CSPS(K)CO TO 1Li

120 INCH =6riOCH =4CALL 6CnINTIF (IERR.EC.11 GO TO 180j = j IJENT =J

?M2NO(J) = INTO,INCH = 11N~OCH- = 3CALL HCDINTIF (IERR.EQ.1) GO TO 18C-

FEJ)= INTGFRE(Q(J) =FREO(J)/100.iNCH = 15NOCh z3CALL 3CDINTIF (IERR.EC..) GO TO 130

-46-

EXTERNAL .FURMULA NUMBER - SOURCE STATEMENT

PARD a INTGFREQIJ) a IPARDiRDOS)*FREO(J)INCH a 19NOCH 4CALL OCOINIIF (tERR.EQ.°) GO TO 1SOTEMP mINTGFREQ(Jl w FREQ(J)OTEMPIF (INPTIZ4|.EQ.LPHAI48)) GO TO 121MBCDtJ) = LPHA(44)GO TO 101

121 MBCD(J) * LPHA(48)GO TO 101

130 INCH a 6NOCH a 2CALL BCOINTIF (IERR.EQ.1) GO TO 180LRTP a INTGINCH u 17NOCH a 3CALL BCDINTIF (IERREQ4*) GO TO 180ROOS a INTGWRITE (6#194)WRITE (6,195)WRITE (6s193) (INPTIN),NsIt2)WRITE (6,195)LINE a 58

GO TO 100140 1I I

INCH a 4NOCH = 3CALL BCDINTIF (IERREQ.1) GO TO 180MQI('(I) a INTOINC, .6 BNOCH 8CALL BCOINTIF (IERR.ECol) GO TO 180QUOTt1) a INTGIENT a IGO TO 100

180 IF (INER.EC.1) GO TO 181INER a IWRITE (6,192)LINE a LINE -2

181 WRITE (6,193) (INPT(I),lul72)__LINE v LINE - 2IF (LINEGT.6) GO TO 183WRITE (6p194)WRITE (6,195)WRITE (6,195)LINE a 60

183 IF (MRTK.EQ.1) GO TO 101GO TO 101

200 IJNT m IENT - 1

-47.--

EXTERNAL FORMULA NUMBER - SOURCE STATEMENT

00 40 IJ w iJtINTi1 m IJ + 1IF (MQID(IJ),LEMOIO(Jl)| GO TO 40KEMP w MOIC(JI)TEMP - QUOT(J)?MQID(JI) * MolO(I.J)QUOT(JI) * QUOT(IJ)M0O0J( 1) KEMPQUOTIIJ) u TEMPIF (IJ*E6.11 GO TO 40IK s IJ

41 IK a IK - IKI a 1K + 1IF (IK .EOa 0) GO TO 40IF (MOID(IK) .LE. MQID(KI)) GO TO 40KEMP a MQIO(IK)TEMP a OUOT1IK)MQIO(IK) a MOIDKI)QUOT(IK) a QUOTIKI)MQID(KII a KEMP(QUCT(KI) u TEMPGO TO 41

40 CONTINUE00 202 a It 50ONOTE(J) a 0NODR(J) a 0VALU(J) = 0.MBNO(J) a 0

202 CONTINUE00 201 K 1, 1500NUTE(K) a 0MONO(K) aTECK(K) u 0.

COST(K) a O.F C 1CSPS(K) T OsRPSTE(K) a 13

56 ITVALEKa 06 ,2 E CONTINU

j =0K 0

LSOLMID a-4

. , LTID a 0: MGTK a 1': i GO TO 1:32

280 IF (LRCD ,NE, 1) GO TO 281WRITE (Bv1903)

) REWIND 8', GO TO 505

506 WRITE (6,1902) (IXTEIN)t N019120)505 READ (8,1902} (IXTEIN)o N"ltI20!

IF (IXTE(2) ,NE* LPHA(6)} GO TO 506REWIND 8

281 REWIND 9STOP

-48-

EXTERNAL FORMULA NUMBEK - SOURCE STATEMENT

301 IF (INER.EQ.1) GO TO 280KENT a KNUMB aOTCST a 0.TVAL w 0.DO 2 J = 1, JENTNUMB a NOTE(J) + NUMBKIND a IXTE(J)PFTE = 1.DO 1 K a KtNn. NUMBTCST m COST(KI + TCSTPSTE(K) = 1. - PSTE(K)PFTE a PFTE*PSTEIK)

I CONTINUEPFTE a I* - PFTEVALUIJ) = FREQIJIOPFTETVAL = VALU(J) + TVAL

2 CONTINUETEMP = G.00 6 NOTK a 1t KENTNUMB = 0DO 3 I a lJENTNUMB = NOTE(I) + NUMBKIND 2 IXTE1)DO 4 J u KIND, NUMBIF (PSTE(J) .EQ.,) GO TO 4PSUB a PSTE(J)PSTE(JI * 1.

. PFTE - 1.DO 5 K a KINDNUMBPFTE a PFTE * PSTE(K)

5 CONTINUETVUB = (1. - PFTE) 4 FREQII)DVAL(J) a VALU(I) - TVUB

... . TECH(J) a OVAL(J). / CSPSIJ)PSTE(J) a PSUB

4 CONTINUE3 CONTINUE

VEMP a 1.DO 7 L a It KENT

... IF ITECHIL) ,GEe VEMP). GO TO 7VEMP a TECH(L)LIND a L

7 CONTINUEL - LINDTEMP = TEMP + 1.TECH(L) a TEMPPSTE(L) a 1.DO 8 M = I, JENTIF (L oGE. IXTE(M) NOTE(M)) GO TO 8IF (L .LT. IXTEIM)) GO TO 8VALU{M) - VALU(M) - DVAL(L)GO TO 6

8 CONTINUE6 CONTINUE

VEMP De

-49-- .

EXTERNAL FORMULA NUMBER - SOURCE STATEMENT

GO TO 4,3310 VEMP - VEMP + I.

DO 35C K a 1 KENTIF iTECHIK) .NE. VEMP) GO TO 350GO TO 355 ..

350 CONTINUEGO TO ZBO

355 IDMQ u 000 352 1 - 19IENTIF (MQID(I).NE.MQNO(K)) GO TO 352IDMO - 1IF (BUDGII)-COST(K).LT.QUOT(I)) GO TO 310GO TO 351

352 CONTINUEIF (10MO .EQ* C) GO TO 310

351 DO 353 M = 1, JENTIF (K .GE* IXTE(M) + NOTEWM)) GO TO 353IF (K .LT, IXTE(MU) GO TO 353IF (NOTE(M) -NCDR(M).GTol) GO TO 354IF (MtiCl(M)oEQ.LPHA(44)) GO TO 310"F (NOTE(M)-NOOR(MI.EQ,|) GO TO 354GO TO 310

353 CONTINUEGO TO 310

354 IOMB - MBNOIM)IDTE a NUTEIK)TCST = TCST - COSTIK)OELC - COST(K)NODR(M) = NOOR(M) 4 1IF INOTE(M) - NODR(M) ,NE. 0) GO TO 356MBTK a MBNO(M)

356 KORO = KORO + IMQNOCK) a MQNO(K) - 1000BUDG(I) = BUDG(I) - COSTIK)

COST(K) = 3.DELV aOVALIK)TVAL - TVAL - OELVGO TO 45'

400 KLIN = JENT/13 + 4IF (LINE - KLIN.GE.51 GO TO 409WRITE (6,194) -..

WRITE (6P195)WRITE (64195)LINE - 62

409 WRITE (6,196)LINE a LINE - 2

WRITE (6,197) IMBCO(J)*MBNO(J)tJsl#JENT)LINE a LINE - (JENT/13)KLIN - IENT/% + 3IF (LINE - KLIN.GE.3) GO TO 403WRITE (6,194)WRITE (6,195)WRITE (6,195)

403 WRITE (6,198)WRITE (6,199) (MQID(I),QUOT(I)tImIIENTlLINE a 6

-50-

.XTERNAL FORMULA NUMBER " SOURCE STATEMENT

MaTK a450 IF ILINE.T,6) GO TO 451

WRITE (6,194)WRITE (6,195)

t WRITE 16# 1190)

WRITE (6,1191)WRITE (6#1197)LINE u 51IF (KORD.GT.) GO TO 451WRITE (6,1193) TVAL, TCSTGO TO 470 "

451 WRITE 16,1194) KORD#IDMBIDTEpTVALDELVTCSTDELCMBTKHBTK a 0

470 IF (LRCD.NE,l) GO TO 310IF (KORD@GT.1) GO TO 471WRITE 18,19C,0) LRTPWRITE (8.195) .....

471 DO 477 L a 1, LENTIF (KORD -EO, IOUT(L)) GO TO 478

477 CONTINUEGO TO )10

478 WRITE (8919CI) KORD.DO 60 L a IKENTPSTEIL) a 0.

60 CONTINUEII a I[IENT-1)/10) * IM * -9

DO 90 I a 1, IIM = M + 10N * N + 10IF lN.LE.IENT) GO TO 91N I IENT

91 WRITE (8,119E) (MOID(MM)IMM a, MpN)WRITE (8,I196) (QUOT(MM),MM a M#N)WRITE (8,1,97)WRITE (8,1198)WRITE (8,1197)00 472 LL = 1,10KBUF(LL)

MBUF(LL) G CCBUF(LL) m0.CMQT(LL) -0.

472 CONTINUE92 MQGO a

00 80 L u 1tKENTIF lMQNOtL).LTMOIO(M)) GO TO 80IF (MQNO(L).GT.MQIOIN)) GO TO 80IF IPSTE(L) *EQ. -1.) GO TO 80MQGO - 1DO 70 K a MNIF (MQIDIK).NEMQNDIL)) GO TO 70J K

88 IF (JLT,1) GO TO 87

- -51----

F0

EXTERNAL FORMULA NUMBER - 'SOURCE STATEMENT

GO TO 8987 IF lCUF(J).NE.j-,.) GO TO 80

CBuF(J) - COST(L)CMQOT(J) - CMOT(J) . COST(L)KBUF(J) = NUTE(L)00 50 JJ 1 ,JENTIF IL ,GC IXTE(JJ) * NOTE(JJ)) GO TO 50IF (L ,LT, IXTE(JJ)i GO TO SOMBUF(J) - MBNO(JJ)PSTE(L) I -1.GO TO 8D-

50 CONTINUE7; CONTINUE80 CONTINUE

00 474 LL a lplC,IF (MBUF(LL) .NE. 0) GO TO 475

474 CONTINUEGO TO 476

475 WRITE (8*1199) (MBUFILL)9KBUF(LL)#LL ,1tO)WRITE (61196) (CBUF(LL)oLL a 1,1O)O0 473 LL * 1,10K3UF(LL) " 0:'8UF(LL) f oC5UF(LL) =I.

473 CONTINUEIF (MQGO.NE*I)) GO TO 92

476 WRITE (8,1197)WRITE (8,120.j)WRITE (8,1196) ICMQT4LL)PLLa 1910)..WRITE (8,1197)WRITE (8,195)

90 CONTINUEWRITE (8,201) KORDWRITE 48,94)GO TO 310

500 REWIND 800 508 J =1t 16IOUT(J) a.)

508 CONTINUELRCD x ILENT - CINCH a 7NOCH =KL6MP =

00 507 J = I, 16501 "F (KEMP.GT.I) GO TO 100

INCH = INCH + NOCH '> KEMPNOCH =

O D03 N z INCH,72IF (INPT(N).EO.LPHA(48)) GO TO 502IF (KEMP.EC.1) GO TO 504NOCH - NOCH + IGO TO 5D3

502 KEMP z KEMP + 1IF (KEMP.GTol) GO TO 504

EXTERNAL FORMULA NUMBER . - SOURCE STATEMENT

.503 CONTINUEIF lNOCH.EC.)-GO TO 100

504 CALL BCDINTIF (IERR.ECo.) GO TO 180IOUT(J) i INTGLENT = J

507 CONTINUEGO 10 ID)

l.;O FORMAT (44AI)191 FORMAT (72A1)192 FURMAT (lHIt, 97HTHE FOLLOWING CARD(S) CONTAIN(S) ERRORIS) THAT MUS

ZT BE CORRECTED BEFORE COMPUTATIONS CAN BE MADE.;193 FORMAT (lHltT2A1)194 PORMAT (lHl,119X)195 FORMAT (1H'3)119X)195 FORMAT (19H FOLLOWING IS A LIST OF MOPA(S) FOR TIHIS RUN OF THIS

ZPROGRAM. THOSE PRECEDED BY ASTERISKS CANNOT BE DROPPED.)197 FORMAT (13(3H llAlvH)t'f))198 FORMAT (76H FOLLOWING IS A L!ST OF MONETARY QUOTAS WITH THE NUMBE

2R OF DOLLARS IN EACH.)199 FORMAT (8(1392H $tF9.90ille))

1190 FORMAT (103HO COORDINATE a TASK ELIMINATED * TECHNICAL VALUE2 a COSl * MBPA ELIMINATED)

1191 FORMAT (97H NUMBER * ABPA TASK * TOTAL DELTA2 * T.TAL DELTA * MBPA)

1192 FORMAT (120X)1193 FORMAT (37H I NONE NONE tF9.3*15H NONE

2 S@F11.)p25H I NONE NONE)1194 FORMAT (5X,4tlXT4,t4Xtl3,TXF9.3,2XtFT.3o6XFllo0,2XtF9,09X14)1195 FORMAT (14 p,91H MQ tl3t4Xbt5H MO s13,3X)1196 FORMAT (IH ,9llH$*F9.,2X)lHSvF9.O*lX)1197 FORMAT (10(12H ***** )l1198 FORMAT (12HO MOPA TASK 9(12H MBPA TASK ))1199 FORMAT (10(2Xti4,tX#It2X1l1200 FORMAT (10(3X,5HTOTAL,4X))1201 FORMAT (19Hj END OF COORDINATE, 1497X)1900 FORMAT (lOHO LRTP 012#108X)1901 eORMAT (30HOCONFIGURATION OF COORDINATE 914986X)1902 FORMAT (120A1)1903 FORMAT (bH FINISoI14X)

ND.........................-........

l l -53 -- - -m m

SU~3RCUTINE BCOINCC____________C A.-(LP 8.)'t. INPT10O72) #INCHoNOCH, IN TGt;ERRLLNTI

* COIM'ON IXTE(500),IPTIIPCHNPCKIPTGIPRR_________NTI 0

IF (NOCH*EC.0) GO TO05__________O 1 J~lphOCH ________________

K J+ NI-I00 2 1 1,10L =1 *26

_______IF (NPT(K)EQ..PA(L)) GO TO 32 CONTIN"UE-

_________IF (IN,)T(K).EQ.LPHA(48)) GO TO 45 I'RRa SW =_ _ _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _

6 PETURN _________________________________ ___

4 IF- (INTNE.0)-GO 10 5._____ GO? O 71 .

3INTG ITO*0______ 1-c CNfl N u r;

* RETURN1 F(I-1NTJ.EMI0GO TO I

____ ___GO TO 5

0 .V

I j.JjIL,

1v T . L- - - . . -- - -

7k, - -.. ~--.--.------~.--.-..-.--I ~~~F'I.. j

St UL. *I CAIMIDPS.NG CC4MNION EAA AE

D 0 .L LI. 01 .tj 1,4 f0 1 1 5 1 M1111 1 16 $1 61 6 1 .V W10. I'l A s- H1

I Li;2 222 1222 222_ _ _ _227 21 22_2 _ _ _ __2_ 222 222 222 222

3 ~ ~ ~ ~ _________ 3i_______3!_______________3___33___3___33___33__ 33 3 33 33 33 33 . 33 133 33

a a^1 11 A1 :11 aIf IlI Ii is I I&Sia61&I' 1 6 I I I I a l1iiB i aaaa I&at 9111 i :iAI s S a9 1s 9 9999991999999 999999 99999$9 9999999 9 9 09fr 66 ii 1 oo sNA s5 ?awAo vaa4 a [4 Wv " M1 u o v "4 r, 4A1 1A "

3.5 D ,-irr-1' r

In the cou,-Gc of gett ig a computer program to operate correctly,

olie attempts to follow a process which will achieve cne's cbjective most

quickly and most economically. Computer operating systems contain routines

to aid in this checkout process. The IBSYS system provides the PDUMP

routine, and this was the means used to verify the correctness of the

program's operationa.

The "Debugging" wen, -&. follows:

(a) Check out card reading processes -- Use as input

the cards described in Sections 3.1. 1. 2, 3. 1.1. 3 and 3. 1. 1.4.

Verify their correct reading by PDUMP of Tables BUDG, MQID,

QUOT, FREQ, MBNO, MBCD, IXTE, NOTE, NUTE, PSTE,

COST, CSPS, MQNO, IOU" and LPHA.

(b) Check out error routine -- Introduce cards with

erroneous data in each field. Examine Item INER (input error

indicator) as well as output messages which specified the

card(s) in eiror.

(c) Check out computations -- Using input data that had

been checked in the course of (a) above, record, via PDUMP.

Tables PSTE, TECH, VALU and DVAL as the computations

are being made. Check enough cases to ascertan the correct-

ness of the re..ults.

(d) Cher'k output -- With data from (c) as criteria,

verify that sarne information that is in tables is printed.

Examine outputs themselves for correctness of format.

-56-

Upon cornpletion of these tests, the program war operated

to produce the information deacribed in Section 4., entitlud, "Nurnerl,.al

Examples of Model Outputs".

4. NUMkERICAL EXAMPLES

The purpose of this section is to illustrate compL er program outputs

for several sets of input constraints by making use c; hy'pothetical data,

The volume of data, esLimated by personnel at Headquarters, AMC, is

believed to be representative of the amount of data that nna; be e..countered

in actual operation. No further significance should be attached to the

hypothetical data, or computer outputs, presented herein.

4. 1 Generaticn of Hypothetical Data

4. 1. 1 Generation of MBPA-TK-WE Struccure

The generation of the hypothetical input dz.ta w:; bscd

on the assumption that Headquarters, AMC, received descriptions of 55

Research Development Objectives (RDO's); the number 55 was chosen

because there are 35 RDO's in the I October 1964 issue of the Researci

and Development Long Range Plan (RDLRP). It was further assumed

that the 55 RDO's resulted in tl-e identification of 150 Major Barrier

Problem Areas (MBPA's).

The number of Tasks associated with each MBPA was

assumed to be uniformly distributed between I and 4 with a mean of 2. 5.

The distribution was sampled to determine the number of Tasks (TK's)

associated with each MBPA. This sarnplinz resulted in a total of 388 TK's.

-57-

4. 1.2 XIBPA Parameters

The number of RDO's that each MBPA is associated with

was derived by sampling a Poission distribution with a mean of 10.

Given that an MBPA was associated with an RDO, auniform distribution between I and 5 with mean of 3 was sampled to deter-mine the frequency of appearance of an MBPA within an EDO. Furthermore,it was assumed that the numoer of Technical Approaches associated with anR ,C was equal to the sum of the frequencies of appearance of MBPA's withinRDO's. The above generated values (frequencies and number of TechnicalApproaches) were then utilized to determine the expected probability thateach MBPA will be encountered in a Technical Approich.

4. 1. 3 Annual Work Effort Parameters

The ensts of the Annual Work Elforts (WE's) were assumedto be uniformly distributed between $30, 000 and $50, 000 with mean of$40, 000, The cost of eicrh WE was determined by sampling this distribution.

The probability of success of each WE was determined byassigning ce of six values (.05 , .0, .40, .50, .8r , .95). Thesc values

were assumed to be binomially distributed with a mean . 5.

After determining the cost and probability of success ofeach WE, the WE's associated with each Task were sequenced in order ofincreasing value of cost/I -Probability of Success.

Furthermore, it was also assumed that a total of 10Field Establishments (Monetary Quotas) proposed the Tasks and theassignments of Tasks were assumed to be randomiy distributed among

the Field Establishments.

-58-

M

N

4. 2 Computer Runs

Using the hypothetical MBPA and WE parameters previously

discussed seven computer runs were made varying the MBPA and Monetary

Quota (MQ) cost constraints from run to run. These runs were made

utilizing the IBM 7090 computer at the U.S. Army Strategy Tactics and

Analysis Group, Bethesda, Maryland. The print out of one of the runs is

given in Appendix II.

The outputs of the seven runs are given in Figures 4-1 and 4-2.

All of the Configurations produced by each run have not been plotted because

of the limited size of each figure, but a sufficient number points are given

to clearly portray the shape and characteristics of the curves.

4. 2. 1 Outputs Varying MBPA Work Effort Constraints

The curves in Figure 4-1 illustrate the effect of varying

the MBPA constraints without any MQ constraints (zero funds for each MQ).

Curve A depicts the Configurations of maximum expected

technical value in which no MBPA need be funded. Since the 150 MBPA's

comprise 388 TK's, the total number of possible Configurations (or pointson the curve) is 389. Appendix II conzains a complete listing of all these

Configurations. Of this number, 389, the first (the Configuration consisting

of 388 TK's), the last (the Configuration consisting of 0 TK's), and every

tenth one were plotted. For Curve A (as well as the other curves), the cost

intervals between points (i. e. , the change al. ng the abscissa) is quite

uniform. This is a consequence of the fact that the cost of a WE was postu-

lated in the relatively narrow range of $30, 000 - $50, 000. Thus, the cost

interval between any pair of plotted points is around $400, 000 (10 x $40, 000).

The expected technical value intervals between points (i. e. , the chanrge

along the ordinate), however, increases as one progresses along the curve

from right to left as expected.

-59-

LLIrA

~ fn

0~ 0~ 0IP" U 9 ) I C) ..

At - - or

00

c r

40 M

H *.i

-c~ ~co- -

iIn

**;-4~. f-

~~jci2~a iv 7vixiat ciio x m----------------------------------

Curve C depicts the Configuratiuns of maximum

expected technical value in which all MBPA's must be Iunded. Since

there are 150 MBPA's, the total number of possible Configurat ons is

239 (388-150+1) and ranges from the Configuration consisting of 388

TK's to one of 150 TK's (i.e., one for each MBPA). The curve stops

at point 239 since none of the remaining TK's can be eliminated

without viola~ing the requirement that every MBP.A must be funded.

The last point and every tenth one commencing with No. 50 are plotted.

Incidentally, the first 40 points on Curve C are identical with those of

Curve A.

Curve B depicts Configurations of maximum expected

technical value in which 30 MBPA's (randomly selected) were required

to be funded. The total number of such Configurations is 359, of which

the last cne and every tenth one commencing with No. Z00 are plotted.

The poiats to the right of No. ZOO are not plotted since they fall between

Curves A and B roughly between the plotted points.

4. 2. 2 Outputs Varying M13PA Work Efforts and MQ Cost

Constraints

In Figure 4-2, Curves A 1, B 1 , C 1 correspond to

Curves A, B. C of Figure 4-1 insofar as MBPA constraints are concerned;

however, a common set of MO constraints, as defined below, were applied.

Normally, Curvt.. Al, B 1 , C1 , would have been included on Figure 4-1;

however, they fall %o closely to the curves .Llready plotted on Figure 4-1

that Curves A I . 5 1 , C1 would all qtart with Point No. I and end within

circle X. Thus they were plotted separately in Figure 4-Z on an enlarged

zc;,lc. Curve C2 can be associated with Curve C1 as discussed below.

-61-

Figure .2

CC,~tZc,7l -: AxT?,rt7-i np-CTFT T TC.'(,AT. VAT.Urp.UMDER VAR:OUS M3PA CaiSTRAMrS AND MQ CO:1STAraM

I I -* '/64-,_ - -I

644o/- /

~) 6430 -. le /_

[-4 6420 L--641o -

,-,

o 6390o 6380

6370

636o

631-3 0 I 12 13 14 15

COIrrIGURATION ANNUAL COST (millions of dollars)

Curve Ai: I1o ,.SPA need be funded; MQ constraints as defined in 4.2.2

Curve B : Fund 30 selected KBPA's; MQ constraints as defined in 4.2.2

Curve C1: Fund all !MPA's; M'Q constraints as defined in 4.2.2

Curve C2 : Fund all WBPA's; MQ constraints as defined in 4.2.2

-6Z-

Curve A. depicts Confiburatioros f rnaxim")urn vXPC tud

v ,ie in which no MBPA need be funded arnc with MQ constra;rt.

that represent 75% of the number of the ist fiscal year WE's chargeabJe

to each MQ times the avi,ge cost uf each WE ($40, U0W). The number of

possible Configuratiuns is 89. None of the remaining TK'I, of the last

Configuration can be eliminated since a violation of onc of Lhe .! straints

would then occur, The first, la.t and every tenth Cvnfiguration are plotted.

The most significant feature to be noticed upon comparing

curves A and A 1 is that Curve A l , Ithroughout its length, corresnon is

very closely to Curve A. In fact, the first 49 Configurations are identical,

While not exactl,, true, it can be stated that the result of imposing the

stated MQ constraints upon Curve A is a shortening of Curve A (and thus a

reduction in the number of possible Configurations). This ensues because

of the relatively narrow and comparatively uniform WE cost figures, i. e.,

$50 - $50, 000. For example, commencing with the Configuration consisting

of all TK's, each TK is considered for elimination in the same order as

that for Curve A. The procedure is to eliminate it if a MDPA cons'raint

or an MQ constraint is not violated. In this case, there are no MBPA con-

straints so the only consideration is the individual IQ constraints. Since

each MQ represents an amount of money that is large in comparison to an

individual WE cost and all WE costs are quite uniform, then a considerable

number of the TK's to be considered for elimination will be eliminated in

their original order. It is re-emphasized that in determining the original

order of TK's to be considered for elimination that expected costs were

utilized in the calculations; however, once this order is established and

MO constraints are considered cnly the first fiscal year TK (i. e. ,7r)_

cost is involved,

-63-

I.I

i~i"

LI

Curve C1 depicts Configurations of maximum expected

technical value in awhich al1 MBPA's must be funded and with the catne

MQ constraints as for Curve A 1 . There are a total of 89 possible Confi-

gurations. The last and every tenth one, commencing with No. 50, are

plotted. The curve stops at point 89 since elimination of any of the

remaining TK's would violate either an MBPA or an MO constraint. The

first 40 Configurations are identical to the first 40 of Curve A,; the number

of such occurrences being less in this case than the number (49) in the

case of Curves A and A 1 as might be expected because of the inclusion of

the MBPA constraints. The discussion in 4. 3. 3. 1 regarding curve length

also applies to curve C1 .

Curve B 1 depicts Configurations of maximum expected

military value in which 30 randomly selected MBPA's must be funded and

which meet the same MO constraints as does Curve A 1 . It consists of 89

possible Configurations; the first 40 of which are identical to those of

Curve A I. The remaining points have not been plotted since they fall

between Curves A1 and C1 ; merely the position of the curve has been

labeled. The discussion in 4. 3. 3.1 is also applicable herein.

Curve C 2 depicts Configurations of maximum expected

technical value in which every MBPA must be funded and which meet MO

constraints defined as follows. The overall amount available in all MO'u

was estaiolished as $11, 640, 000, the same as that for the total of MQ's

for curve C I. However, the distribution of moneys between MQ's was

r.ancomnly made and varied from about 50% to 95% of the number of I st

fiscal year WE' , chargeabLe to each MQ times the average cost of each

WE ($40, 000) instead of a constant 75% for all MQ's as done for curve C 1 .

Expressed in another fashion, the distribution of moneys for the curve

C1 MQ's was such that each AMC R&D Field Establishment was assumed

-64-

to have proposed a lot of TK's so that the costs chargeable to the appro-

pyiat: iLVQ exceeded the ii"nit ;n in it by 100% whceat another A-C

R&D Field Establishment may have proposed only a few TK's so that

the costs chargeable to the appropriate MQ barely exceeded the minimum

available in that MQ.

This curve consists of 88 possible Configuraticns of

which every tenth one commencing with No. 30 and the last one are plotted.

The last point of this curve falls approximately within the Circle Y indicated

in Figure 4-1. No Configuration other than the first is identical Io any an

curve A I. As expected, the shape of this curve departs considerably from

those of curves Al, B i, C1 ; curve C, dropping in expected technical value

more rapidly as cost decreases. This results from the fact that the mini-

mum amounts in some MQ's are close to the sums of the costs of all this

chargeable to those MO's; thus few TK's can be dropped which means less

desirable TK's may be required to be maintained while more desirable

TK's chargeable to other MQ's are eliminated.

-65-

APPENDIX I

INPUT CARD DESCRIPTION

-AP-Z?-NfIX I - INPUT CARD DESCRIPTION

-IELD I- COLU.MNS CONTENTS 1 DESCRIPTION

1-4 Letters" Identification of Card

z 6-7 Digits ID of Program Run

3 9-15 I./D Date

4 17-19, D Cou.nt of RDOs

5 Z1-7Z Letters Comments•4.; " Digits

Special

8 TPS..- 8SP 15 055:: "NO' MBPA OR.- MQ: CONSTRAI NTS

I ORT N. STA:M: I.T _,_,.,,,,,_,

- --- ' a- - -- -'0--o'd 00 0 0 0 0 0 oo" '0 0 0

22'' 2 2 22222222222222222221222222222222 .222222 22222222222222222 22222 2222222

3 3;3333"33333333333333333333333333333 3 3333333'3333333333333333333 3 3 3333333

i , 4444444444444444444444 4444444 444444444444444444444444444444444 444444444

5"5 S5 5 5 5555555 5555 5555555555 55555. 55555555 5555555555SS55 5 5555555

, .. 3 ,W.,o , ,,,, G E6a666 6a6 665666 6 66$6 66 66 66 666 5,6666 6 666666666 6636 665,," ,7.77;'777 777777777777777777 77 7 7 7 7 7 "7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7

6 9 0 96 S5599S9699B66s9 9 S 9 0 9 9 9 S0991BZC,57 EAC 3030

|'LRTP" CARD

1-2Z

, L•UT CA,, DESCRIPTION

ECOLU S t CO.TENTS . DESCRIPTION N

1-26 Letters The Alphabet

z 27-36 Digits ModuloAO I13 37-4 Specil Other Chracters

49-72 Not Used

V. Q 11 11 3xIl $' I"PRQ. 'OO,.Ta. C iuN(OU?---- &ARS 1~

, I.

" 2 2 22 212 2 22Z22222 2 2222222222Z2222222222 222222 222 ' 22222 222.222222

3333 33 33:3333 33333333 3333 3 3 3 3333 31333333 33 333 3 33 33 33 ,3 3 3

44 4 4 4444 4 44 44 4 44 4 . 4444 4 .444 4 4 44 444 4 44 4 44 4 4 4 4 4 4 4 4 45 53 5 S5S5 S~SS S I SS5

:. 77 7 7 77711 177777 ? 7 7 777777 7 777 7 7 777777 77 7 7 7 77 277, 177 17 7 17777

"BCD IMAG CARD

.APPNDIC I -INPUT CAR~D DESCRIPTION

FILD COLMMS ICNET * DESCRIPTION

1-5 Letters Car~d MD

'a 7-72 Digits 1 - 16 Numn'bers. w ith a'Blanks. Blan~k between Numrbers

FORRA STTEEN*rfI---or .0

23 is2 1U 4U; 7UXQ44 34 4 &4 14 3I 3$ S IL

.1;. 1. .'o 3333)j3')3 3333 31. )3 3333 333 3,j 3333 333 333 3333 333333 333

4 4 , 44 44 414 44 44 4 4 4 4 44 44 44;4 4 4 4

1R~ 77 73 7 7777777777777777777777 1

1:1;1.. 1 lao1 t 4i ' : 1 .2.haI 412333b9W 4ISQ44. 461044 .1)L ,U5?1U66 ?636I 1361V1 11 4 .7 16U*~~~~A . ORRA;TAEMN

oV"PIT CADB s v ia l'C

A??~NDI I - IPUT CARD DESCRIPTION

-! IZL COLU"NOS ICONTMNTS 1DESCRIPTION

14Latters Card IM

z 2 4-6 'Digits ' m~l

3 8-15 Digits * Ntimber of Dollars

;e* ,,1J.0 5 0 . ........

SYM30L OPERATION 'ADDRESS. TAG.DECEMNTCON -. IhCMARKS AE

0 0 0 0 10 0 00 0 0 O 0O 0 0 0 0O O 0 OO 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0J,14167S11 11 13l i t: j2 : 4nni 4) 3 4aX3 A 4 t4 4 14 64 44 t . 31 4i tQ 1Q6 44 )U( A u1 Ii 1n6

.2 22 22 22 22 :22 22 22 22 22 22 22 22 22 22 22 22 22 2.12 22 2 22 22 2 22 22 2 22 221-. j3- 3 3- 3 31.3113 :3 3 3 31 3I 3 33 33I33 33 33 33 33 33 33 33 331 33 33 31I3 3 3 3 3 3 3 3 31 31 3 11131

4 !14 44 " 44422 44444 222442422222 44444 44444 4444 44444

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