UNCLASSIFIED AD NUMBER - Defense Technical ... proposed as a method of solution to the assignment problem. In a properly structured computerized assignment model, all parameters involved

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UNITED STATESNAVAL POSTGRADUATE SCHOOL

THESISA MODEL FOR AJTO•ATION

OF PERSONNEL ASSIGNMENT

by

Russel Neal Blatt

and

Dudley E. Cass

October 1966

This document is subject to special export con-

trols and each Lransmittal Lo foreign governmentor foreign nationals may be made only with prior.ipp -oval of the U. S. Naval Postgraduate School.

A M'ODE~L FOR AUT0311ATIOIT

OF P.LRSOjJ'NEL ASSIGNLET112T

by

Russel Neal BlattLieutenant, United States Navy

B.S., United States Naval Academy, 1958

and

Dudley E. CassLieutenant, United States 11avy

3.5., University of Washington, 1961

Submitted in partial fulfillment

for the degree of

M1ASTiLR OF SCIENCEI IN OPERATIONS RE~SEARCHI

from the

UN~ITED STATE~S NAVAL POSTGRiADUATE~ SCHOOL

October 1966

Signature of Authors Q5? 0-Q 90 s. Research Curriculum, Oct., 19766

Certified by

Accepted by%

Approved by: _______________________Academic Dean

PAGESARE

MISSINGIN

ORIGINALDOCUMENT

ABSTRACT

This thesis demonstrates the feasibility of com-

puterized assignment of Naval enlisted personnel to fleet

units. A model is constructed for determining the utility

of each man for each possible ship assignment. Then

various methods of assignment are investigated to find

one which maximizes the sutxred utilities of assignment.

To illustrate its capabilities, the model is then applied

to several sample sets of men and snips. The authors con-

clude that a model of this type should be implemented in

the Navy's personnel distribution system.

TABLE OF CONTENTS

Section Page

1. Introduction 9

2. Model 12

3. Summary and Conclusions 45

4. Bibliography 49

Appendix A. Description of PersonnelAssignment Deck 51

Appendix B. Codes Used in Assignment Deck 56

Appendix C. Data Input for AUTAM 59

Aý,pendix D. AUTAI Computer Program 67

Appendix E. FORTRAN Listing of AlternateAssignment Methods 102

Appendix F. Sample AUTA1I Printout 107

3

LIST OF TABLES

Table Page

1. Effect of M~odification of(POB-6)/(EDP) Ratio 17

2. Designation of (POB-6)/(EDP) Ratiofor Each Rate 19

3. Illustrative Indifference Comparison 22

+. Sample Data for Comparison ofAssignments 25

5. Weights Determined by Iteration Process 27

6. Utility Matrix for Assignment 30

7. Group and Subgroup Average MarginalUtilities 36

8. Distribution Comparison of Five Methodsof Assignment of 50 B1i's 39

9. Qualitative Parameters for Comparisonof Five Methods of Assignment of 50 BL's 41

5

LIST OF ILLUSTRATIOINS

Figure Page

1. Feed-Back Process of WeightEvolution 28

7

1. Introduction.

The ultimate objective of all administrativesystems concerned with the movement of per-sonnel is to maximize their utilization inthe fleet. The basic aim of all personnelsupport systems, such as selection, classi-fication and training, is to ensure fullutilization of personnel if at all feasible.The medium through which these ends must beattained s the fleet personnel assignmen•t'osystem.3Js

Under the present system of fleet personnel assign-

ment, BUPERS assigns about twenty types of specially

qualified people to fleet units. The remaining assign-

ments are made by the Type Command Representatives

(TYCOMREP) at the Enlisted Personnel Distribution Offices

(EPDO). The TYCOMREP personnel assigners make their

assignments on a one-at-a-time basis, using their best

judgment, various thumb rules, and a number of policy

and concept guidelines. Some of the man-related param-

eters which must be considered include personal prefer-

ences, experience, training, number of dependents,

obligated service remaining, ard present location of

the man and his dependents. These parameters must be

matched in proper sequence with the parameters descriptive

of the units to which the man could be assigned. Some

ship-related parameters are operating schedules, location,

homeport, status of personnel requirements, and requirements

unique to the particular unit. It can be seen that the

task of the personnel assigner in the present system is

a complex and difficult one. •

9

Since the days of "wooden ships and iron men," the

Navy has grown to such magnitude in physical size, number

of different types of operating units, and different skills

required to operate them, that manual means of assignment

are no longer acceptable. Even on a one-at-a-time basis,

it would be difficult and very tV.e consuming for an

assigner to consider all pertinent parameters for each

man in an objective and consistent manner. It is almost

impossible to consider the array of all possible assign-

ments, given a group of men to assign to a number of ships.

But, to make the optimal set of assignments, the array of

all possiblc assignments must be considered.

Given P number of units and a group of men to assign,

it is assumed that the desirability of each possible assign-

ment can be represented by an ordinal utility value which

is useful in relating that assignment to all other possible

assignments. Then, by "optimal" assignment, the available

men are assigned to units in a manner such that the summed

utility of all assignments is maximized. Of course, the

utility of an assignment must consider both the uility of

the man for the ship and the utility of the ship for the

man. Naximum utilizaticn cannot be realized unless both

the ship's needs and the ian's needs are considered in

every case.

The determination of the utility of an assignment is

a particularly difficult problem for the Navy. It might

also be consid.?red a unique problem in that the operating

and d',qploymcnt schedules of fleet units cause the utility

10U

of the assignment of a man to a ship to be time-dependent;

i.e., the benefits a ship can derive from the assignment of

any man is directly dependent upon that ship's state of oper-

ation. For example, all other things being equal, a man

may be more valuable to a ship preparing for deployment

than to a ship returning from deployment, or going into

the shipyard for overhaul. Some time-independent param-

eters affecting the utility of an assignment will be dis-

cussed later in the paper.

The discussion thus far has indicated that the com-

plexity and number of operations required in determining

the utility of each possible assignment and then finding

the optimal set of assignments is beyond the capability of

manual methods. Therefore, the use of computer techniques

is proposed as a method of solution to the assignment

problem.

In a properly structured computerized assignment model,

all parameters involved in all possible assignments can be

considered in making the "optimal" set of assignments.

Thorpe and Conner have postulated that an acceptable com-

puterized assignment model has to meet three basic reouire-

ments: first, it has to determine for which assignments a

man is eligible; second, it has to evaluate the utility

value or "return" fur each man in each billet for which he

is eligible; finally, the assignment model has to select

the set of assignments for which the total value of all men

available for assignment in all vacant billets is maximizedpi

11

I

r

These requirements constitute the basis for AUTAM

(AUTomated Assignment Lodel), which the authors have

developed and analyzed as a demonstration of the feasi-

bility and effectiveness of computerized assignment.

2. Model.

As the name implies, AUTAJ* is a computcrized model

for assignment of personnel on the basis of utility.

AUT"AI is not just a theoretical exercise for computer

fanatics. It is, in fact, a useful assignment model

which can 'e implemented (with few changes) at any level

of personnel administration.

In order to insure understanding at all levels, the

model was kept as simple as possible. For purposes of

assignment, an imaginary Type Command consisting of sixteen

ships was considered. Within this TYCO04 only three ratings

were usedt Boatswain's Kates, Quartermasters, and Signal-

maen. These rates were picked because they qre not sensi-

tive to Naval Phlisted Classification codes (OEC's) and

thus allowed a more compact program.

As previously stated, certain nan and ship parameters

must be matched in proper sequence in order to determine

a utility of assignment of each man for each ship. The

number of parameters used in this model was kept to a

minimum for the sake of simplicity. Significant omissions

from the model are the man's 7NLC, performance evaluation,

and choice of ship type. However, it was felt that the

inclusior of too many parameters would only add unnecessary

complexity to thc model. A few representative parameters

12

were arbitrarily chosen to show how they might be adopted

to the program. Once the reader is familiar with the proc-

essing of the model, AUTAM can easi~y be expanded to include

any parameters that might be required. The parameters con-

sidered in this model were:

Man-related: (1) Rating and pay grade.

(2) Take-up date (predicted date of

reporting on board).

(3) Homeport preferences.

(4) EAOS (expiration of active obligated

service).

Ship-related: (5) POB-6 (predicted on board count

six months from now for a given

rate and pay grade).

(6) EDP (enlisted distribution plan -

number of personnel required).

(7) Homeport.

(8) Overseas deployment date.

(9) Return date from deployment.

The man-related parameters used in this model are

available on the punched-card standard-format assignment

deck for each man. [l] Appendix A gives a detailed descrip-

tion of all the m•an-related data that can be found on these

cards. The ship-related information is readily available

at all personnel distribution centers.

Having chosen the desired parameters, it was necessary

to derive the assignment variables as functions of these

parameters. This was accomplished by performing the

13

man-ship matching operation which was mentioned earlier.

In particular, the following relationships were examined:

(1) Man's rating and pay grade vs. ship's

requirements and POB-6 in that rating and

pay grade, pay grade above and/or b(low.

(2) Man's take-up date vs. ship deployment

dates.

(3) Man's homeport preferences vs. ship's

homeport.

(4) EAOS date vs. ship deployment dates. 4Although the use of these variables in the model

reflects the judgment of the authors, the model is not

restricted to these expressed and implied judgments. The

assignment "ground rules" used by any assigner or group

of assigners can be applied to this model with equal

effectiveness. To show how this might be done, the

"assignment policy" of this model is as follows:

All other things being equal between men and/or

ships, it is desirable to accomplish the following:

(1) "fill",or even "overfill" slightly,a ship

preparing to deploy, in order to insure

that the ship has sufficient manpower to

meet its operational commitments and allow

for normal manpower attrition. This policy

also reduces the cost of transporting ad-

ditional men overseas to the ship.

14

(2) insure that an assigned man has sufficient

obligated service to complete the ship's

next deployment.

(3) assign a man in accordance with his homeport

preference.

(+) assign a man to the ship which has the smallest

(POB-6)/(EDP) ratio for the rating concerned.

This is the most important factor in assign-

ment. In addition, the ratio of (POB-6)/(EDP)

for the pay grade above and/or below the subject

man should be considered. A man in any specific

pay grade has positive utility to the ship which

is short of men in the pay grade above and/or

the pay grade below.

Using these criteria, the assignment variable, Wljk?

was computed for the assignment of the ith man to the jth

ship as follows:

(1) WijI - Is take-up before deployment? (Parameters

2 and 8)1

No - 0

Yes - 1

Yes and 63 months before deployment - 22

1 The parentheses indicate which parameters are com-pared to determine the answer to the question. See page 13for parameter list.

2 The values assigned for each answer are strictlyarbitrary. They reflect only ordinality of preference,not relative magnitude of preference.

15

(2) Wij 2 - Is take-up during deployment? (Paramett-s

2, 8, and 9)

No - 0

Yes - 1

(3) Wij 3 - Is EAOS after return date? (Parameters

4 and 9)

No- 0

Yes i

(4) Wij4 - Is ship homeport one of man's preferences?

(Parameters 3 and 7)

No - 0

2nd choice - 1

lst choice - 2

() ~Wijk (k = 1, ... 1i) takes into account the POB-6

and EDP information. (Parameters 1, 5, and 6).

For the ith man's rating and pay grade, the model

computes for the jth ship:

( POB-6 ++.1aIMP + . 1 j

For the ith man's rating and pay grade above

and below, the following is computed for the

ith ship:

Pay grade above: P + PA +

G "A + .

Pay grade below: (P PB + .)

16+ J

16

ON N 4 *0-

4J4

0'-I4

0

p4 -444

0

'4--4 l.

0 0A 0q0 4-

0007

where P = POB-6

E = EDP

SUBSCRIPI NOTATION:

A = pay grade above

B = pay grade below

none = pay grade of interest

It is noted that a constant value of 0.1 is added to

both the numerator and denominator in the above ratios. The

0.1 in the denominator prevents division by zero and the

same constant in the numerator allows comparisons in cases

where the POB-6 is zero. Although the addition of this

constant does not alter the ordinal utility of an assign-

ment, it does bias the assignment in favor of the ship with

the larger EDP. Table 1 gives examples of how the addition

of the 0.1 effects the (POB-6)/(EDP) ratio. (In following

these examples, the reader is reminded that a low (POB-6)/

(EDP) ratio corresponds to a high utility.)

First, comparing ships E and F in the table, it is

obvious that (POB-6)/(EDP) ratios cannot be computed

because both ships have EDP's equal to zero. However,

adding the 0.1 constant allows ratios to be determined as

shown in row 4. In this case, ship F is overfilled by two

men and has the higher ratio. Therefore, ship ! has the

higher utility and will be favored for the assignment.

A compirison of ships C and D demonstrates the case where

both ships have a POB-6 equal to zero. Since the ratio is

again indiscriminate, the addition of the constant is needed

to allow the ratios to be formed as shown in row 4.

18

Ship D is favored.

One final example is given to indicate how the addi-

tion of the 0.1 constant tends to bias the ratio in favor

of the larger sbip. In Table 1, ships A and B both have

the same ratio of 0.5. However, after the addition of the

constant, ship B has the lower ratio and is favored for

assignment. Valid arguments can be presented both for

and against this procedure. Therefore, it is hypothesized

in this model that in those cases where the ratios are

equal, it is better to assign to the ship needing the most

number of men. To reverse this hypothesis, a small con-

stant could be subtracted with a slight arithmetic modi-

fication. Before leaving the (POB-6)/(EDP) ratio, two

more facts should be mentioned: (1) AUTAM was arbitrarily

set up to compute the (POB-6)/(EDP) ratio for the ith man's

pay grade, pay grade above and/or pay grade below, in that

order. (2) The Wijk (k = 5,6,7,8,9,10,11) elements are

designated in the model as follows:

TABLE 2

Designation of (POB-6)/(EDP) Ratio for Each Rate

it- Rate For Which WiJk is Computed*ian' s Rate CPO P0I P02 PO-3 STKR

CPO J5 W6Fol 8 ij7 ij9 ---FU2 wiJ8 'UJ7 WiJ9

_______ Ili__ ____ 7___ ___ ijlO

19 ii

19 a

The significance of Table 2 may not be clear at this

point, but it will be useful for reference during che dis-

cussion involving weighting factors for these variables.

Now that the variables have all been defined, it can

be showm how these variables can be used to determine the

utility of assignment of the ith man to the jth ship.

In AUTA14, this utility is11

u =a + akW)ik

where a is an arbitrary intercept point (10 in this0

model) and ak is the weight assigned to each variable,

Wijk. The assumption of linearity was assumed in equation

(1) for ease of computation. It was also considered that

first order approximations were sufficiently accurate for

this model.

The determination of the weight (a,) of each variable

is, obviously, a crucial part of the model. The concept of

an effective assignment model is based on the assumption

that proper weights can be found such that the generated

utility of assignment, uij, reflects accurately the assign-

ment policy desired. Since the assignment policy is based

on the judgment of personnel administrators, the assign- ?

mem t weights must likewise be generated through repeated

subjec.tive judgments which are consistent with the policy

set forth. As an illustration, it will now be shown how

the weights used in this paper were determined.

20

Of all the variables considered in this Liodel, the

(POB-6)/(EDP) ratio is the most important. Therefore, it

was used as the reference variable for determining the first

rough weights. The reader is referred to Table 2 to see

how the (POB-6)/(EDP) ratio for each rate is designated in

the model. From this it can be seen that a good starting

point might be the a5 and a 6 coefficients. These coeffi-

cients represent, respectively, the weight assigned to the

(POB-6)/(EDP) ratio for a Chief Petty Officer and the weight

assigned to a Chief Petty Officer who might be utilized in

a First Class Petty Officer's billet. This assumes that,

other things being equal, a CPO has a greater utility on a

ship which is shor÷ of P01's than a ship which is over-

filled with P01's. This assimption was taken into account

in the derivation of the Wijk vectors for the pay grade

above and the pay grade below. The mathematical formu-

lation of these vectors was shown earlier.

First, a5 was arbitrarily set equal to -5. (The

negative sign is necessary to counterbalance the fact that

an increase in numerical value of Wij5 causes a decrease

in uij.) Then it was assumed that there were two ships,

1 and 2, to which the ith man could be assigned. By use

of an indifference comparison, similar to that used in the

economic study of consumer choice,[5lvalues were found for

Wij5 and Wij6 which caused the authors to be indifferent

between assignment to either Ship 1 or Ship 2. The follow-

ing is an example of this procedure:

21

TABLE 3

Illustrative Indifference Comparison

PreferredTrial Chip (j) Wij5 Wij6 Assignment

1 .7 .71 •Ship 1

2 _,2.9 .91 .7 .7

2 Ship 12 .9 .5

1 .7 .7S3 Indifferent2 .9 .3

On the first trial in Table 3, the Wijk values were

picked arbitrarily. Since Ship 1 has a lower (POB-6)/(EDP)

ratio for both CPO and P01, it has a higher utility of

assignment and is preferred for assignment of a CPU. In

the second trial, the Wij 6 value for Ship 2 was reduced to

•5. However, the authors felt that Ship 1 still had prefer-

ence for assignment of CPO. In the third trial, the greatly

reduced ratio for P01's on Ship 2 caused the authors to

become indecisive as to which ship should be assigned an

additional Chief Petty Officer. Therefore, this was the

indifference point for these two variables, Wij 5 and WiJ6.

It should be noted that this is not a unique set of values.

Using the values froti the third trial aid a 5 = -5, the

Wility of Ship 1 was set equal to the utility of Ship 2

ard solved for a,:

22

Ui =1 ui 2

a Wi +aW a W + aWil5 6Wi16 5 i25 6Wi26

(.7) + a6 (.7) = -5(.9) + a6 (.3)

a 6 = -2.5

With Wij5 as reference and a still equal to -5, the

values of al, a 2 , a3 and a. were determined by the swae

method. The results were: a1 = 0.5, a 2 = -1, a 3 = 1,

a4 = 0.5. Since a7 , a8 , and a9 apply only to rated Petty

Officers (PO1, P02, and P03) and alO and all apply only to

Strikers, they were determined separately.1 In this case

a 7 was set equal to -5 and a 8 and a 9 were found to be -5

and -3.5 respectively. Similarly alO was set equal to -5

and all was found to be -3.5. Thus far, the values obtained

were:

a0 = 10 a4 = 0.5 a8 = -5

a1 = 0.5 a5 = -5 a9 = -3.5

a2 = -i a6 = -2.5 alO = -5

a3 = 1 a 7 = -5 a1 1 = -3.5

For the purpcse of allowing the utilities between

different pay grades to be easily compared, the ak (k =

1.. 11) were rescaled such that

6 112- ak j akW = Y akWij

k= 5ki k =7 k= 0i0 k

iThe reader is referred to Table 2 to verifythis statement.

23

S.

a • ' • h • . " TM . . ... . . r,,,, . . . ,/

This was done by first assuming a utility range,

O&uij&lO. Since OWijkK 2 for all conceivable cases,

akwas scaled such that

6 2_ 11Sa. k a, k a. -

k 5 =7 k 10 l

On this basis the following revised values were

obtained:

a -1-3 -. a =-2.9

a6 -1.7 a8 -1.9 a = -2.1

a9 -1.3

Recalling that a- = -5 was used as a reference to

determine ak (R = 1,2,3,4), it became necessary to rescale

these four coefficients in order to maintain their same

relationship with a5. Doing this: a1 = .3, a2 -. 7,

a= .7, a= .3.

The procedure discussed above could be used to

deterrine the first approximate weights for any number

of variables. However, these are only approximations and

must be checked by using them in the model and analyzing

the results to see if the desired policy guidelines are I

being followed,

In this paper the initial weights were refined as

follows: Using the ak values determined above, assignment

of 40 men to 16 ships was accomplished utilizing the program

shown in Appendix D. This gave a sample of 640 assignments.

~24

TABLE L

Sample Data for Comparison of Assignments

n Wijk, -= :

i j 1 2 3 4 5 6 7v 8 9 10 11 u4

1 10 0 1 1 0 0 0 .05 .09 1.48 0 0 8.86

2 13; 2 0 1 0 0 0 .05 1.00 .52 0 o 8.83

31 13 1 0 1 1 0 0 .26 1.00 .30 0 0 a 8.5

22 11 0 1 1 0 0 0 .05 .52 1.00 0 0 aw4'7' 8.,

2 16 0 1 1 0 0 0 .05 1.00 .09 0 0 8.39

36 16 2 0 1 0 0 0 .51 .51 1.00 0 0 8.31

1 + 0 0 1 0 0 0 .05 1.00 .52 0 0 Bwý S.A

21 2 0 1 1 0 0 0 .05 .52 1.49 0 0 B-027 .BA.

34 8 1 0 1 0 0 0 .63 .80 .50 0 0 7.65

5 O11 0 0 1 0 0 0 .50 .83 .51+ 0 0 7.57

F3 13 1 0 1 1 0 0 .5111.20 .1+4 0 0

25

Since those assignments with extremely high or low

utility values contribute little to the refinement process,

they were eliminated from the sample. Also those assignments

having duplicate W vectors were eliminated. This reduced

the original sample of 640 assignments to a subsample of

85 assignments. The assignment program of Appendix D was

modified to give an output (on standard pu:.2hed cards) of

the assignment identification (number of the man and ship),

the W vector describing this assignment, and the computed

utility of this assignment. These pun, !d cards were tht-n

arranged in order of descending utility 'iTe, sorted by

rate group, and printed as shown in Table 4. The assign-

ments were then compared, two at a time, to see if the

assignment with the higher computed utility vaue was in

fact preferred to the assignment with the lower utility

value. Where this .as not the case, the utility values

were changed to reflect the disagreement with the computed

utility ranking. For example, in Thole 4, it was decided

assignment (22,11) should have a higher utility value than

assignment (34,13) bLcause jhip 11 was lower in the rate

(W22,197 ) and rate above (W2 2 , 1 1 , 8 ) comparisons. This

outweighed the fact that for assignment (34,13), the man

would be picked up before deployment (W3 1 3 , would

receive his second choice homeport (W334, 1 3 ,4), and would

alleviate a shortage in the rate below (W3 1 , 1 3 9 ). When

all assignments had been compared, the corrected utility

values and the original values of the "ijk variable were

26

U)

~ U r~ cf~ N 1-4

o U) 0 m N Nao' t r'- 00 00 00

a, 0' 0 0 .- 1 - -

0 0 N N cok() -4 0 a, 0, 00 00

a, A 0 0 0

-4-4 -

LA(n 0) -4L LA 0

Vr 0' 1-0 N N N

Ai N' N4 N NN

0 n LA r- 0c 0'Vn N 'V0 U) L L Lt)

0 e

Co I Ic I I I

0 LA N N N0 0

oO N %0 L Y fo

27fO CO C

Find first weight estimatesJby indifference comparisos.

Compute assignment utilities. Generate now weight

(Program AUTAM) estimates by multiple

linezr xearessiou.

(Pruram BIHED-03R)

Are computed utility values Re-order inconsistent

consistent with assipment No assipmenPm by cbang-

policy? (AsBiAOent pair- ing their respeotHve

comaisons) utility values.

Yea

Figure IPeed-Back Prooes of Weight Evolution

28

then used as data input to a multiple linear regression

computer program, [21generating new weights, a, as the

regression cocfficients of the linear regression. This

process was repeated until the weights obtained resulted

in satisfactory assignments. For this paper, the weights

were considered satisfactory when the number of utility

values changed were less than 5% of the total number in

the representative sample. The evolution of the weights

which satisfactorily represented the "cssignment policy"

of the authors is shown in Table 5. Seven iterations were

required. Note that 37 of 85 utility values were changed

in the first iteration; none were changea in the final run.

The evolution as described, may be thought of as a

"feedback" process represented as a flow diagram in Fig. 1.

It is evident that much of this process depends on the

judgment of the authors. However, it cannot be too strongly

ermphasized that the same process can be carried out by any

assigner, or group of assigners, using policy guidelines

determined by proper authority. [l

After the weights of all the variables have been

determined, the utility of assignment of the i th man to

the jth ship can be found by using equation (1). All the

utility values can then be arranged in an (n x m) array for

the assignment of n men to m ships. Having set up the array

as in Table 6, the objective is to assign the men such that

the sum of the utilities is maximized. It is obvious that

assignments must be made sequentially because the uij values

29

S.

must be recomputed after each assignment to reflect cor-

rected POB-6 figures; i.e., the assignment of a B111 to a

ship lowers the utility of assignment of any remaining

BM1, BaC, or d612 to be considered for that same ship.

TABLE 6

Utility Matrix for Assignment

sHIP NMMERMAN 1 2 3 4

MUNYON A B1I 8.6 6.8 9.0 10.0

MULTUNAS BI1*2 7.3 5.4 8.3 9.4

STEVEISON B1112 7.0 5.4 8.1 10.2

WHITTLET BM12 7.3 5.1+ 8.3 9.1+

WIMGER R B112 7.3 5.9 9.3 9.4

ANDERSON B3113 6.5 3.1 8.6 5.9

BRAINARD a13 6.5 3.6 8.8 6.6

SA14NICOL B113 6.5 2.6 8.6 5.9

TRUJILLO B113 6.5 3.6 8.6 6.41

COLLINS Bi-13 7.0 2.6 9.6 5.9

GAIRRI DO Q11 6.7 2.8 7.3 8.7

After the utility array has been determined, the

method of assignment from this array will affect whether

or not maximum utility is achieved. The classic linear

programming simplex solution to the personnel assignment

problem was not used because: (1) the ships have no

explicit "quotas" which must be filled or cannot be

30

exceeded, and (2) the men do not have constant utility

values for all ships.

Several otier standard methods exist for obtaining

exact solutions to the classical assignment problem.

However, the problem treated in this paper does not readily

lend itself to these methods. Therefore, the authors con-

sidered methods of assignment which would:

(1) at least approximate a maximum solution.

(2) minimize computer run time.

On this basis, the following five alternative methods

of assignment were investigated.

(1) Row Viaximum

This was the simplest method investigated and was

chosen because it was believed to most nearly simulate the

manual assignment method. The ith man is assigned to the

jth ship where i, j .-re determined by

max u 1 , i = 1, 2, 3, ... , n.j 3j '

This method looks at the first man and assigns him to

the ship with the highest utility. This man is deleted from

the array, the remaining affected u j's are recomputed, and

the next man is assigned in the same manner. This process

is continued until all men are assigned. Using this method

in the array of Table 6, iIUNIYON would be assigned to Ship

4, the ui4 for the remaining Dil's recomputed, then NULTU1TAS

would be assigned to the ship with the highest utility

value.

31

Appendix D shows the basic assignment program used

for all five methods considered in this paper. The appli-

cation of a separate subroutine for each method allows the

different methods to be accomplished by the computer. In

this case (Row Maximum), the subroutine in Part 1 of

Appendix E is used.

(2) Array Maximum

This method is one step of complexity above the Row

Maximum method. Instead of looking at only one row of the

array and picking the maximum, this method makes the assign-

th tment of the p man to the qth ship such that

u pq= max max uj ii

This method makes the assignment having the highestutility in the array. The assigned man is deleted from

the array, all the affected u Is are recomputed, and theij

procedure is repeated until all men are assignea. In the

array in Table 6, STEVENSON B12 would be the first man

assigned, and would be assigned to Ship 4.

For computer purposes, the subroutine in Part 2 of

Appendix E is uscd for this method.

(3) Row-Column Maximum

This method was investigated because of the possible

savings in computer time. Rather than recompute the

affected uij after each assignment, this method assigns

up to m men before recomputing the affected u ij. The pth

man is assigned to the qth ship if

32

U max u maxupq iq pj j

In this method, the first column (first ship) is

looked at to see if the maximum in that column is also

the maximum utility in it's row. If it is, that assign-

rent is mada and the second column. is checked. If there

is no row ard column maximum, no assignment is made and

the program goes to the next column. After all columns

(ships) are checked, and the resulting assignments are

made, the utilities are recomputed, and the process is

reiterated until all men are assigned. In .the array of

Table 6, columns 1 and 2 have no row-column maximum.

However, columns 3 and 4 do, and COLLINS would be assigned

to Ship 3 and STEVENSON to Ship 1+. Then the utilities

would be recomputed before starting over.

The subroutine in Part 3 of Appendix E is used to

perform this operation on the computer.

(4) Mlodified VAR

Vogel's Approximation .1ethod (VAM) is a natural choice

as a possible solution to this type of assignment model

because it assigns sequentially and provides a solution

that is usually quite close to optimum. • It is also a

convenient method to use because it presents little program-

ming difficulty, requires few iterative operations, and

utilizes minimum-time arithmetic operations.

The logic supporting this method is that a near maximum

solution should be obtained if, at each step, the man is

33

S.

assigned who will incur the greatest loss of utility if he

is assigned to the ship having the second highest utility

for him.

The VAM method, as modified for this paper, computes

in each row of the utility array the difference between the

maximum utility and the next highest utility. After this

has been determined for all rows, assignment is made to the

maximum utility in the row with the maximiu difference.

The affected utilities of the remaining men are recomputed

and the above process is repeated until all men are assigned.

As an example, applying this method to the utility array in

Table 6, COLLINS would be assigned to Ship 3.

Appendix D contains the subroutine which pertains to

this method of assignment.

(5) Decision Index

This method of assigning pem. onnel has been proposed

for use by the Air Force and is included for comparison.

It is based on the assumption that only one man will be

assigned to any one job (ship). Ward has shown that the

expected value of the sum of all remaining assignmients is

maximized by making the assignment (p, q) where DI is the

maximum value of the Decision Index array. V

m nDI q= mu -- upj Luiq (2)

J=l i=l

34

where m = number of ships

n = number of men to be assigned

u pq = utility of assignment of pth

man to qth ship

The Decision Index array is computed by use of

equation (2). The assignment is made to the maximum DI,

the utility array is recomputed, DI array is recomputed,

and the procedure is repeated until all assignments are

made. As an example of this process, the first row of

the Decision Index array would be computed from Table 6

as follows:

D11 = 4(8.6) - 34.4 - 77.2 = -77.2

DI1 2 = 4(6.8) - 34.4 - 47.2 = -54.4

DI13 = 4(9.0) -34.4 - 94.5 = -92.9

DI1 4 = 4(lO.0) - 34.4 - 87.8 = -82.2

The entire array must be comp'ted, in the manner il-

lustrated, before any assignments can be made. If DII2 is

the maximum of the array, then the first man would be as-

signed to Ship 2.

This assignment method is accomplishud by use of the

subroutine in Part 4 of Appendix E.

In order to obtain data for the analysis of the five

methods of assignment, each method was applied to the model,

utilizing the weighting factors found earlier in the paper.

First, each method was used to assign the same sample

of 50 men to 16 ships. This sample, designated Group I,

was composed of 50 Boatswain's iates of all pay grades.

35

/

(4) (: mV N t4 w Vo M %O 00IPO ro

en

i- n %D(r- 00N N

g4-b

.14

4 Ln N t- o 0n

1*o 0 7 v ~ .4 V I

4.) - -- n '0 C ' -

00

14 Z 4

0, - en V r-0, I

.0 (

r- tCo

04 U) ) N 36

Then each method was used to assign another sample of 50

men to 16 ships. This sample, designated Group II, was

composed of Boatswain's Mates, Quartermasters, and Signal-

men of all pay grades. Group II was further subdivided

into smaller sets to investigate the effect of sample size

on each method cf assignment. Using these subdivisions,

each method was used to assign the 50 men of Group II to

the 16 ships; but all the men in one subgroup were assigned

before proceeding to the next subgroup. The size, number,

and the results of these subdivisions are shown in Table 7.

The assignments produced by each method of assignment for

each sample cf men were compared on the basis of average

marginal utility of assignment as shown in Table 7.

The assignment utility used in tL.a five processes of

assignment is dependent on the preceding assignments; i.e,

given a set of 5O assignments to make, the utility of the

1 6 th assignment depends on the preceding 15 assignments.

However, the marginal utility of any assignment (as defined

in this paper) depends on all 49 other assignments. This

r, rginal utility can be computed by consider.ng each man

individually after all assignments have been made. The

procedure would be to take the first assignment and subtract

the man from the assigned ship's POB-6 figure. Then recoin-

pute the affected Wijk variables and use these new values

to determine the utility of that assignaent by the procedure

described earlier in the paper. Before goin6 on to the next

assignment, the PO3-k is restored to its initial value.

37

S.

It is obvious that a comparison based on marginal

utility of assignment is preferred because it eliminates

the effects of the order in which the assignments are made.

As an example, assume that three Boatswain's Mates are

assigned to the same ship by different methods of assign-

ment and that they are assigned in different order. This

means that the utility of assignment of each man is dif-

ferent for each method. However, the marginal utility of

each man, as defined above, will be identical for each of

the methods. Therefore, this gives an equal basis on which

to compare the five different methods of assignment.

Since Group I was composed of only one rating, a more

complete set of data was obtained and is presented in

Tables 8 and 9. Table 8 allows a comparison, by pay-

grade, of the distribution of assignment of )U Boatswain's

M1ates to 16 shLps. Table 9 can be used for analysis of the

same set of assignments.

Analysis of the information presented in Tables 7, 8,

and 9 leads to several conclusions about the different

methods of assignment. Referring to Table 7, it can be

noted that the VAI method made assignments which gave the

maximum average margina7. utility in 10 of the 12 sets of

assignments which were made. This obviously accounts for

the fact that the VAM method also had the highest over-all

average marginal utility in both subgroaps.

It can also be seen in Table 7 that the Decision Index

method had the lowest average marginal utility in every case.

38

TABLE 8

Distribution Comparison of Five Methods of Assignment of 50 BM's

4) Q No. Assigned by: No. Assigned by:0-I~ 0_ 0 00

0 H '"0044r. 4,r

Q tic 0) b 0 0tc ()C0, rl 4 0 04 ýH U ý , -

Q 0 010300000 1 0 NO00

1314. 5 133 1 33 78 00 00 0BI112 1 8 10 0 0 0 0 1 9 18 15 1 1 1 1 0B1313 1311 00 1 00 3121 00 00 0BIS 1 20000 0 0200000 IiBMC 10 12 1 11 -1 1 00 1 001311 541+10 1 12 4 3 11 1 103V142 28 90 01 0 110 89 00 0 00B143 13 14 00 0 00 1610 11 11 1

S1 0 1 1 1 1 0 1 0 000I0BIAIC 1 2 00 0 00 10 11 11 11311 5 8 0 0 0oo0 +6 0 00 013,112 3 8 7 00 0 00 11 8 4 4 3 33 1B3143 1312 00 0 00 169 33 33 1B1ŽISN 1 0 11 111 01 00 00 0BhAC 13 0 0 000 11 0 00 01BIU4 52 23 3 22 4 4 10 0 0o0B112 8 622220 12 81100ooo0B143 1382 0 1612 0 00 01+BMSN 1 1 0 0 01 01 1BlIlC 2 20 0 010 11 11 1 11Disiu 6Com o6600000 3v 1 1 1 013112515 132 3 231 13 8 900 001+M I-43 191 1+11 110 16 101+1+ 31+2B•ISN " 0 2 0 00 0 0 0 0 0 0--B31:c 2 13 1 1 11 1 2 0 0 0 00Bl36. 6 0 0 0 00 0 2 20 0 0 0 0BM12 6 8 18i0 0 0 0 0 1 9 1 1 1 1 0B113 3118 2 2 221 6 7 0 0 0 0 0BMSl 1 9 0 0 0 0 00 0 0 000 00BMC 2 11111 1 1 000 0B13 6 5 0 0 10 2 5 30 0 2 1 113142 7 18 15 1 1 1 1 0 15 1+ 3 1 1 1 1 0i3'13 2 0 0 0 6 6 0 0 0 0 00BM3 I 1 000 0 200 0 0 011.N C2 11111 1 1 0 0 0 0

B3MC 6 8 0 0 0 0 0 2 1 1 1 1 1 2B1 8 18 22 0 0 0 0 2 6 0 - 2 2 2

B__2__8_ 70_ 00___ 100000 •3 31

B113 32 21 2 2 2 2 6 6 8 0 0 0 0 0B3 13 80 0 0 0 0 0 1 _00 _00 _

39

The utility t tbe Jor ±.n:nn ui'ee methods varied with the

size of the saLiple to he s ziued; Unfortunately, the

variance was not cL Lstc .. ,coild not be defined by

any the usual ma ca techniques. Therefore, based

on the data in Table 7, the •iughest average marginal utility

was obtained when usi'; tL~e VAM method and the lowest when

using the Decision Inaex method, regardless of the size of

the sample. Although not presented in this paper, the

authors investigated several other sample assignments.

The results of this work tended to substantiate this

relationship between the VAMl and Decision Index methods.Table 8 represents a detailed break-down of the assign-

ment of Group I by each method. It can be seen that the

Row, Array, Row-Column, and VAfl methods effected a similar

pattern of assignment distribution. For seven of the 16

ships the assignments were identical and for six other

ships these four methods disagreed by only one assignment

on each ship. Clearly, on the basis of this data, it is

impossible to choose any one method as better than t'Ve

other three. On the other hand, the pattern of di V•Jbution

produced by the Decision Index method was definitely in-

ferior to the other four methods. Some specific evidence

of this poor distribution can be seen by inspection of the

assignments made to Ships 4, 8, and 12. The Decision Index

method did not assign nearly enough men to Ship 4 while it

overfilled Ships 8 and 12. Of particular note, Ship 8 was

40

TABLE 9

Qualitative Parameters for Comparison ofFive Methods of Assignment of 50 BM's

Quality Parameters Methodof

Assignment Methods Row Array R-C VAM D. I.

(1) Total No. Men Assigned 50 50 50 50 50

(2) No. Men With Take-Up.3 Mos. Before Deploy-ment 12 13 12 18 11

3) No. Men With Take-Upi3 Mos. Before Deploy-ment 9 10 9 7 19

4) No. Men With Take-UpDuring Deployment 12 11 11 9 12

5) No. Men With EAOS AfterDeployment Return 50 50 46 50 49

6) No. Men Receiving 1stHP Choice 6 7 5 7 7

7) No. Men Receiving 2ndHP Choice 4 2 1 2 4

8) No. Men Who Could BeAssigned to HP Pref-erence 11 11 11 11 11

9) Marginal AssignmentUtility (Average) 7. 602 7. 608 7. 465 7. 727 7. 103

10) Assignment Utility(Average) 7. 938 7. 973 7. 763 7. 978 7. 485

11) Computer Run Time(Seconds) 135 135 158 132 143

IF

overmanned by four B112's and the Decision Index method

assigned four more of that same pay grade. Obviously,

this is an undesirable assignment pattern.

The assignment methods described in this paper each

use a different procedure to assign any given group of men.

Because of this fact, it is reasonable to expect that the

order in which these men are assigned will differ with

each assignment method. In order to investigate the effects

of this ordering, Group I was assigned by each method. The

results of these assignments as pertains to specific param-

eters is presented in Table 9.

Looking at rows (2) and (3) in Table 9, it can be seen

that the Decision Index method assigned the men in such a

manner that 30 of the 50 men were sent to ships preparing

to deploy. Of these 30 men, 19 were sent to ships three

months or less before deployment. Recalling that the

authors' policy was to fill all ships preparing to deploy,I

the Decision Index method was the most desirable in this

instance. However, looking down the list to row (4), the

VAM method is favored over the other four methods in the

fact that it assigned the least number of men (9) to ships

which were already on deployment. Again, this is a desirable

feature according to the authors' policy. At this point it

might be noted that rows (2), (3), and (4) under each method

do not sum to the total nuuber of ien assigned. This is due

to the fact that ships which have just returned from a de-

ployuent do not have a firr.. date for their next deployment.

42

Until this date is known and can be entered into the program,

men assigned to this ship do not fit into any of the cate-

gories of rows (2), (3), and (4).

The results in row (5) indicate that the Row-Column

method assigned the men such that four of them were as-

signed tc ships on which they could not couplete the deploy-

ment. Clearly, this is an undesirable feature. Rows (6)

nnd (7T show the number of men who received either their

f•: ,t or second homeport preferences for the ships which

"were oonsidered. Based on homeport preferences, the

Dec'Nion Index method is favored because it assigned all

ii•izn t- a homeport of their choice.

:osed strictly on the assignment parameters of rows

<) t...r:r:h (7), the Decision Index method would probably

:ioz, vored. However, when taking into account the

Slttn• factors and the distribution of assignment

o .arlier, row (9) shows the Decis-on Index method

,- :ivk ;•h -lowest average marginal utility of assignment.

The avt-,-fge a:signment utility was included for the purposes

o~ �v �i-• I.En jow ('Oj and a-so shows the Decision Index

methcd uc !,ave the lowest utility. Both rows (9) and (10)

Indicla- i , i .t the VAIl method is preferred on the basis of

highec; utt.L_,

Anoth<• i-.l.-rtant consideration in comparing these five

methods is thc 2omputer run time. It can be shown that the

number of computer operations required in AUTAII is not a

linear function of the number of ships and men, but rather

43

/,

a polynomiol involving multiplicative terms of higher order.

Therefore, although a difference in run time of five seconds

may be trivial for the assignment of 50 men to 16 ships, a

very significant difference in run time could result when

the number of ships and men is increased for application

in the fleet. In row (11) of Table 9, the VAi method is

shown to have the shortest computer run time. Computer

run times shown in Table 9 include program compiling time,

program listing, and computation of marginal itility. By

eliminating the last two items and using a binary program

deck, run time for VAM was reduced to 69 seconds.

All five assignment methods were capable of performing

the assignment process. However, the Decision Index method

was discounted as a useful procedure because of its poor

assignment distribution. Each of the other four methods was

considered more effective than the manual process of assign-

ment. Since the VAIL method achieved the maximum utility and

required the minimum computer run time, it was chosen for

implementation into the AUTAI• model as shown in Appendix D.

A sample printout of AUTAPI, showing only those items useful

to j'i assigner, is shown in Appendix F. For this printout

a sample of ten ships and 30 men was used.

44$

3. Summary and Conclusions.

Briefly, the development of AUTAI was as follows:

(.) Selected man-related and ship-related parameters were

compared in order to derive a set of assignment variables.

These variables were used to describe the assignment

function.

(2) Weights were determined for these variables in accord-

ance with a prescribed assignment "policy."

(3) The weights and variables were incorporated into a

computer program to compute the relative utility of each

assignment of a given set of assignments.

(1+) Me~hods of assignment were investigated to determine

a method which would make optimal assignments and require

a minimum of computer run time.

AUTAh,! was then derived f1,na the computer program of

step (3) combined with a modified version of the Vogel

Approximation Mlethod as applied in step (1+).

AUTAýi demonstrates the feasibility of computerized

personnel assignment. The authors do not claim that AUTAN

is the only or best method of assignment, or that the

techniques employed are unique. However, it is asserted

that this program is capable of duplicating any "assignment

policy" formu±ated by authoritative sources. In comparison

with the present manual methods of assignment, AUTAM, or a

program similar to it, has several major advantages:

(1) Rapid. The most obvious advantage of a computerized

system is that it is capabl'3 of assigning a given set of

45

/

men in only a fraction of the time required by manual

methods. In addition, it could eliminate time-consuming

accounting and order-writing procedures by proper inte-

gration into a centralized ;or:onnel accounting, distri-

bution, and assignment system.

(2) Objective. A properly programmed computerized

assignment process is much more objective than a qualified

assigner because the computer is not subject to outside

influences and personal feelings. Although it's listed

here as an advantage, this cold objectivity of computerized

assignment is attacked by many pe( le on the grounds that

the benefits of the "human touch" are being denied in the

assignment process. In reality, all the desirable aspects

of the "huiman touch" are included in a good assignment

model. It is only the undesirable features, such as human

boredom and fatigue, which are eliminated in computerized

assignment. This elimination of undesirable human factors

leads to the next advantage.

(3) Consistent. After determining the variables and cor-

responding weights which effectively describe the assign-

ment policy, all assignments made by the computer would be

in strict accordance with that policy. This process requires

that the same qualitative factors be considercQ foi -uh

man for all possible assignLients. In addition, after a

specific weight has been det2rr.lined for each factor, this

weight must be maintained constant for all possible assign-

iients. Certainly this is a consistency which is almost

impossible for a man to accomplish. A man can only attempt

to perform the assignment task through the tedious process

of repetitive subjective judgments. This very often leads

to gross misuse of available manpower.

The above argunments in favor of computerized assign-

ment are not meant to infer that skilled personrel as-

signers would no longer be needed. Although the number

of assigners could be reduced, there would still be a

requirement fur handling special assignment problems.

For example, it must be recognized that computers are not

infallible. Therefore, each assignment should be checked

by an experienced assigner. This would be a rapid spot-

check for any glaring errors that would give evidence of

computer malfunction. Also, tho "additional information"

contained on card(s) 5A of the assignment deck cannot

easily be processed by the computer and may contain infor-

mation which would affect the suitability of a given assign-

ment. To more easily examine this information, it could be

printed out with the computed assignment for further con-

sideration by the assigner.

It is obvious that any assignment policy will change

over a period of time. Linor changes could be reflected

by an adjustrment of the weight for the affected variable.

HIowever, major changes of assignment policy (usually a

result of foreign conflict or otiher emergency) require a

completely revised set of weights. In this case the entire

47

process of the determination of weights would have to be

repeated. Hopefully, this situation will not occur often.

This thesis has attempted to show that computerized

personnel assignment is both a feasible and a highly

desirable process. On the basis of the results obtained

in the use of AUTAI, it is highly recommended that the

Na-ry consider implementation of a program of this sort.

Proper application of this program will permit full

consideration of the preferences of each man to be as.-

signed. Simultaieously, the "needs of the Service" .:ould

be considered and assignments could then be made so that

the utilization of manpower would be greatly increased

while taking into account the preferences of the -adi-

vidual.

BI PTI 0OGRAPHY

1. Enlisted transfer manual. Department of the Navy,B4reau of Naval Personnel, Washington, D.C. NAVPERS15909A. 22 Klarch 1960.

2. Multiple regression with case combinations. HealthSciences Computing Facility, UCLA. Computer ProgramBI•IO3R, 13 August 1964.

3. Proposed five year program piar for perseonel systemsresearch department. U.S. Naval Personnel ResearchActivity. San Diego, California. 1 February 1965.

4. Tri-Service conference on new approaches to personnel-systems research. Office of Naval Research. Depart-ment of the Navy, Washington, D.C. ONR SymposiumReport ACR-76. 23, 24 hay 1962.

5. Baur~ol W 3. .Economics Theory and Operations Analysis.Prentice-Hall, Inc., New Jersey, 1961.

6. Bottenberg, R. A. and J. H. Ward Jr. Applied multiplelinear regression. 6570th Personnel Research Labora-tory, Aerospace Ledical Division. Air Force SystemsCommand, Lackland Air Force Base, Texas. TechnicalDocumentary Report PRL-TDR-63-6. March, 1963.

7. Gulliksen, II. and L. R. Tucker. A general procedurefor obtaining paired comparisonf from multiple rankorders. Psychometrika, V. 26, No. 2. June, 1961.

8. Jackson J. E. and L. Fleckenstein. An evaluation ofsome statistical tecihniques used in the analysis ofpairud comparison data. Biometrics, March, 1957.

9. King W. R. Personnel evaluation and optixmal assign-ment Operations Research Grou Case Institute ofTechtnology. 01lOU Project - NONRI-1141+(.I). April,1964.

10. Kossack, C. F. and R. E. Beckwith. The mathematics ofpersonnel utilization models. Pe".-sorinel Laboratý,y,Wright Air Development CenterAir Research and De-velopment Command, United StatesiirJForce, LacklandAir Force Base, Texas. Technical Report W'ADC-T,.-5q-359. November, 1959.

4 c.

i

BIBLIOGRAPHY

11. Reinfeld, 11. V. and W. R. Vogel. Miathematical Pro-gramming. Prentice-Hall, Inc., 1958.

12. Thorpe, R. P. and R. D. Conner. A computerized modelof the fleet personnel distribution system. U.S.Naval Personnel Research Activity, SanDiego- Call-fornia. Research Report S R66-13. February, 15766.

13. Votaw, D. F., Jr. Functional tests of solutions ofpersonnel assignment problems. Persontel Laboratory,Wright Air Development Center, Air Researcb and De-velopment Command, United States Air Force, LacklandAir Force Base, Texas. Technical Report WADC-TR-59-3578, ASTIA Document No. AD 229 881. August, 1959.

14. Walkup, D. W. and 11. D. NacLaren. A multiple assign-ment problem. Mathematics Research Laboratory,Boeing Scientific Research Laboratories. Mathe-matical Note No. 347, Dl-82-0346. April, 1964.

15. Ward, J. H., Jr. The counseling assignment problem.Psychometrika, V. 23, No. 1. 1arch, 1958.

16. Ward, J. H., Jr. Use of a decision index in assign-ing Air Force personnel. Personnel Laboratory,Wright Air Development Center, Air Research andDevelopment Command. United States Air Force,Lackland Air Force Base. Texas. Technical ReportWADC-TN-59-38, ASTIA Document No. AD 214 600.April, 1959.

17. Ward, J. H., Jr. and K. Davis. Teaching a digitalcomputer to assist in making decisions. 6570thPersonnel Research Laboratory. Aerospace MedicalDivision, Air Force Systems Command, Lackland Airiorce Base, Texas. Technical Docunentary ReportP•3L-TDMi-63-16. June, 1963.

18. Wolfe, J. 11. Personnel applications of operationsresearch. U. S. Naval Personnel Research Activity,San Diego. California. PRASD Report No. 200.December, 1962.

APPEDIX A

pERsoNNE ASSIGUNT DBM

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APPENDIX A

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uWla to US(NY r 15,6,Pa (WI) Partt todi" rarer 25 MtAr broa1 Lee x) t Code. for~ ClomeZO.

* Priat poeltim 10. Print PWeeltign h this 57.

(6) Priary sadURC claus S Gfsvyu O&. (38) * Pourcl dtchife aOW stweooeleaverarer to 110111 (11AvMM 15,t2, Pont %ulook sh o~atrt (ActXW)) faCor :s."e fodr a Cob .1Prist post~am 121. P(int plaraveetiftahathis Cod.

()Primvat Dlspemasce statua ss. () pSafe 'toPUU 103138, othaivesa s.?Atuu to 3(1 (RAVYW I615,412 PWAt Pbltp&LQo h., 11 (AMriM)) cu ob"ta.Prnpoita .

()purom"% ldsotlt ictior t Clus.le

alter to qq" (KAVPM I5433 Fors Pir.5% Ipoletufss &9 this. 63.1 (wCTr)) far coft.Prim% poettic 116. (31) Aeh sodyoo of dsatz oft tuanm

MA least ind a lollt ?AM "a eoo

(9) Teow of birth. Nothjing lastallatims.nust poeltuisa is thira x.6. Phit positiwe 6(A %lb" 68.

(10) *44twlsti Of tha IsIvidusl 66 #t~tastm (83) Maestavibisr tbst m is belmsbry thi cqam~in *.iicear "A Boutais soam sibli seveable. Rsfuor to C4timpafive Witcoils as patlinad is e epter at. 24 for sodeis.Print peatUina 17 thru 21. PrInt p"Wseii 69 this 71.

(1&3) Iducacsol.1 feislvmanit. * (t) ecis Mtopq C011A. Ifthr feePAITe to Charter at for soda. CWr Its far eoase*.Print postUm." 22 thais 23. Prime posuiias To.

(lit) Active iluty aobbgatims. bsalefiv (85) vsate Cods. ear low by PUU ma"?4s&ieumt NAd al1 eatsatmeos. veter slackift IaattallstiooaPrim% peslimal "1 thi 11,. v.1s pmoaim 73 tuft 77.

(13) haUI, 111111 bees 41111s (Yoor). (Mi) Osoet aid ar~iauIl vuhtte4Prial poesitimes 3 tbru 27. tol Una. SetS, to Ob"" 314

for cob.I(116) Prinary Navy Uolited Clne"Itiitiio. Paint psabtini is "min 77.

oism appielmnle. Prott to 1W Merma(SAYMS 15105) Camrlioi'. (a7) outsaller c.Pait as "otmal #A thrw l. pnut Value IM.

CARD 2A

52

11CG8~4 4GGCP 3UGUTH 04GOTH APWGIDI 83

004, .S00009eSoooo ,So ,ge '666 eeeooe606oSOSSeoSSSeeeooooeoeoeeeeeeoe 0 6e 6o 0.CPV _ _ -. NI O T AC @ AT 3

r!- K 's-

blanka UI5~r al_

and otermchneustllt.os

()Tepasrir yaso dt it positions 13 thru 7. eerCatr.5 u

( jacket. C ord~ed lacorane Print positions 72.hm79with postrutions cotane (6in.Cd.Po s yP

Cndaoterr24.hi(e)iCaarla-ro3.Prin po sitions9earuofdu.' Print Position 00. i'7

(4) Distributor to id~ch individu&alI.is been made &vai]~ble. Asefrto Chapter 24 for Codes.Print positions 69 thru, 71.

S3

APPM11 A

soeosseeeoesesoeessssssseeoossoeesee W000 0000

• IC

Pi "sto I 7i c* :i

~i

(1J Service number. (5) Special Categor-v Code,Print positions i thria 7. if applicable. Itefer t~o

Chapter 24 for special

(2) Sex. "4" for Aaves, leAve category codes.blank for sale. Print position 72.Print position 8.

(6) Rate Code. For use by PAMI andU) Schools attended. List In other rachine ihstallations.

Inverse order of attendance. Print position 73 thru 77.Naer to Chpter 25 for Codes.Print position 9 thru 68. (7) Leave bWank.Pint poltion 76 thr 79.

(4) Distributor to which an Individual

has been ma•e available. L"er to (S) Card mber *4Chapter 24 for Codes. YrUA position 60.Prl•t positiom 69 uhrA 71.

CARD 4D

5"4

APPENDIX A

4.104C 0 REQ SEA O=SR STAIT - CMa543Ce .

"N s.VICE ' *Avg&OPTIONAL *F0u*M6T rV OWt

N I.

II I.

(1) Service nu, ber. ( Secial Category Code. (,, ferPrint polition 1 thru 7. to Chapter 25 for Co, a).'

Print Position 72.(2) SMx. "N" for Wvy, 0a ve.S

blank for males. (6) rate Code. For use by PAW andPrint position 8. other aschins Ingtwlation..Pilo t petiooT thin 77,

(3) Additional inormation

Additional cosents. (7). Consecut ie card am& r.Print positions 9 thru 61. Pri potto 78 thn79.

(,4) Distributor to h',.. an lndividual (a) Cart sawer 65 'has been made available. (Rotor Print Poo-IDS 60,to Chapter 24 for d1str*lbnAioCodes) ' •

r-14 pouitions 69 thza 71.

CARD 5A

APPENDIX B

CODES USED IN ASSIGNI•ENT DECK

Month Codes

Month Code

Jaiuary 1

February 2

March 3 jApril 4

I-lay5

June 6

July 7

August 8

September 9

October 0 (zero)

November 5

December B

Mate Codes

Rate Code

BMC 01001

B1.11 01002

B1,12 01003

Bi.,3 01004

"B1.1,SI-11 01005

56

IAPP1!2IDIX B

Rate Codes

Rate Code

QI4C 02001

QN1 02002

Q12 02003

QM3 02004

QMLSN 02005

siC 02501

SNl. 02502

SM2 02503

S113 02501+

SIISN 02505

57

APPEDIX B

Rome Port Codes

A..... .......... ANT PORT, ATLANTIC L•ET.B... ..... ... ... jN CONSTRUCTION, LANTIC FIT.C .............. ITOMN, UASS. IICLtDES PORTSMOJU4, N.H.D .............. NEW LONDON, COllN.

B............. 110T, R. I., INCLUDES ONO*ISIT ?OINT, ft. I., DAVISVILLZ, Re I.,PROVIDENCE, R. I., FAIL RIVER, MASS.

XW TYORK, N. Y., DNLUES JAMAICA, N. I., FVWSCUYI•ER•, N I.,FlRTH AMBOY, N. J. PORT IWARK, It. J.

09..... ...*ooo.o. PiiILADLPHIIA, Pelts INCLUDES ATILANT1C CITY, Me. J., TmIONTI, No J.,

LAKEHURST, N. J.H ........... ,.... WASHINGTON, D. C., INCLUDSS PATNJENT RIM, MD., B&TI0MR, 1D.,I ................ NORFOLK, VA., DICIJ., S NWPORT NMS, VA., DAM NECK, VA., LITUJX

CREEK, VA., OCEANA, VA., FORT STOREY, VA.JO .............. YORKTOWN, VA., INCLUDES CHINCOTEAGUE, VA.K................ CHARLESTON, S. C. INCLUDES MAUFORT, S. C., WILRMN , N. C.,

CHR POINT, N. C.L .............. JACKSONVILIE, FLA., INLUDES MAYPORT, FLA., 0 COVE SPRIN ,

FLA., SANFORD, FLA., GLYNCO, GA.Mo............... BRUNSXCK, US., INCLUDES PORTLAND, IS.

.W ORLZAJLS, LA., I1NCLUDBS PENSACOLA, FLA., ST. PII!5SUIM , FLA.PANAMA CITY, FLA., MOBILE, ALA., HOUSTON, =., GALVZSTCI,

1EX., PASCAGOULA, HISS.PM................ MIAI, FLA., INCLUDES PORT EVERGLADRS, FLA., KEIY S,FL rA.Q............... CHICAOO, ILL., INCLUDES GREAT LA5S, IUL., MILNAUm, WISC.,

SHEBOYGAN, WISC., DETROIT, MICH., EWNTON HARBOR, MICH.,TOLEDO, OHIO, CLEVELANDOH•0IO, FOCMU N. Y.R ............... OVERSEAS ATLANTIC, ICLtIDES ANY HOllPORT OVERSES IN Ma

ATLANTIC OCEAN OR MEDflSRRA)KAN SEA.0............Poo. NO Pt• FKREE, EITHER FLEET, ANY PORT.S............... OVMAS PACIFIC, INCLU= ANT HiiEPOT OVEMEa IN THE PACIFIC

OCEAN OR INDIAN OCEAN.T .............. ANY PORT, PAC.IFIC FLZET.U ... ......... NEW CONSTRUCTION, PACIFIC rFZLT.

It............E.. TTLEYI, WASH.s, INCLUDES PUGST SOUND), WASH., Z;VZRSTLT, WASH.,BREMERTON, WASH., WHIDBEY ISLA%, WASH., ASTORIA, M.,PORTLANDI, ORE., TONGUE POINT, ORE.

............... SAN FIRANISCO, CALIF., INCLtI)I MM ISLAND, CALIF., VALLEJO,CALIF., ALAWA, CALIF., CONCORD, CALIF., HOPTT YFIL,CALIF., STOCKTON, CALIF.

X.... . ... LONG SACH, CALIF., INCLUDES SAN MDBI, CALIF., FOIT MUGU,CALIF., PORT " ", CALIF., LOS ALAMITOS, CALIF.

......... ..... SAN 0I1GO, CALIF., DCLtS XORTH I LA#, CALIF., sMIRMA, CALIF*.,um r=D, CAL?, mm FED, CALIF.

Z.............. . P IARL KADB lANAlZ DICLA SAISM POITs, L•AAfL.

58

APPUNDIX C

DATA DECK ORDER AND FOR1.AT DESCRIPTIOQI

FieldColumn No. Speci-

Card No. Description (Inclusive) fication

1 Control Card

No. sets of data (NSET) 9,10 110

No. of ships (NSHIP) 19,20 IN1

2 Ship Information (KS)

Hull no., name 1-16 A8

Deploy month (code) 21 A8

Deploy year " 22 Il

Return month " 31 Al

Return year I 32 I1

Homeport f 41 Al

Ship identity no. 44-45 12

(one card for each ship)

3 EDP-POD Information

(a) EDP- BI3C 1-4 F4.0

1311 5-8"

B112 9-12

B13"3 13-16

B11SN 17-20

QI :C 21-241

QN1 25-28

59

,LT I n7~ DIX C

FieldColumn ITo. Speci-

Card No. Description (Inclusive) fication

3 EDP- Q112 29-32 F4.0

QI1-3 33-36 " >1QIISN 37-40"

SIC 41-44"

S 45-48 "

SI, 2 49-52 "

S143 53-56 "

SI.ISN 57-60 o1

Ship identity no. 69-76 A8

(one card for each ship)

(b) POB - exactly same format as above

(one card for each ship)

4 Wptzhts - a 0 1-5 F5.2

a1 6-10 "

a 2 Ul-15 "I

a 3 16-20 "

a 4 21-25

a, 26-30

a6 31-35

a7 36-40

a 8 41-45

a9 46-50 "

alO 51-55

all 56-60 "

60

APPenDIX C

FieldColumn No. Speci-

Card No. Description (Inclusive) fication

No. of men in set 9,10 110

6 Assignment cards 1A and 2A for

each man. Format ii, accordance

with Appendix A.

Repeat 5 and 6 for each set of men to

"be assigned.

61

i P,-,oi n Or- ,rn I r-K

I or-~r 1 a rI NVý0 I I ~-0 I

I COO I -O 'Oio- I o0-

LIccI I tnO'-lI 'O'OI nI o I4

I OtA1 I .On I

I t"OMI I 00M II LON I I ~o~n)I

I .O~r) I 4,-cI

I *Pn I 4riV r4)co 00471xMD

mo*-I m I0.I XI Zrn*0I Iu.r*41O r-I-o-O6I DMI) I I =rl."-O I

0 IZ ~ ~OAW IZ~A

N-I eli N'IO I~gU

I ) Oo I'CIa

.-r--

::, a -r) I r- lz -eJ I IcJ

< 04p1 00 tZ.aXJa- 00 or . ot 0(7%1 W 044 wc-1

44 I 440 1 0401 Odw0..4-Zu.om

o 0 o*i 4 I I 0* niw0f'n I I 000I V90#~VI1ONI go'

62

APPUDIZ C

w-L I

Onj OQI

I 0*1O

I OmN I

NO~~NJ~i5 OO O -t OCI

I Lfl") I

*f

I MCII4 0.I

'-Q~~OO e-NOO IN ~f U.3Cw--coC coo- I ONCOI

g ýjvo I

o~tI ry!I

'Q00 OONOC NO eI

0 r-ý Cy I'O

I -tn I

Ci i F,.,1ýCODO

63

APPENDIX C

co I

.0 r~- *I

.01

:r ~ I tn001

* ICON I

I I LA- I

is I ULnIA

* ~ U..* 0h1xmLANI

I 50,)N*I II-*'OI

0' ~ N I *I

km I NNf I

I 140 1

z I r'CLO I

tA Ir~I

I x ;N'I

0' g~r~61+

APPENDIX C

tin m I0io 0 r -

O Oen( I I-tf

-- N ~jNNN,- Ir-*m

I I-NDY

O'QOL(Oj n 0U I-O0. L3OLJQ 0 I 0

N"WO 0% 0"luNcificuo"I 0 1 10-1

N It) O-N. N 01~10iI .- ) 0 NN t 2C

Ln P-CJ-%'4 Z O r- =0 N Noa a i0 < .0 1 U.>4

f)- 4N Ait. ; NI i0- . ii t

IO Uu 11 4n I rU -)< 0 !" <-U :b 4 OO*om

.0u.~ N .3 W0 y .0 10- -, a uJi0^ -z ac'ni.Cj f f U.c-r 0.;I)- W VU 0 - C <.: 4 -0 _j i<L

rCd0U-OC 14 -I' rt-t

c0O>0 OZ 4~c0-ft.:0 cuo ý OWzo(A 1~ o0 1. <- U C

WbO U> X ntt)Z 1 No.*

im of-im)'.fr- 0 Ijý M Ln 4 n X I0

iN~ n thO- ,0-nWC)r)-'.0' t I..- I 0I*

an I N1ODGU -r r C0001Cf-CC '~a 0IC e a)(65-

CNJ ! Pin ,4'S

APP2ENDIX C

N! NJeN N.N -N, NN V-N 1 0-'3

0 o0 oo0oo0ooc 0 ooooociooo , I -C

rr~ -.--

an IA '0'00oO=.Q'IA aj4LI ~ UKII JLIA Ua~(~,A'IA ~ IC-1I -.

w -~0CI 00

.0 a - :- 00 f'- I

I - r- f-fl N f- N . 1 1

0 4 < %t .CL 4 -d 0. 1 OON-C0~ 10 ox"o0 i r-),onU Lno-id.ýov(3i win-C

- -0ca 04 c II C-0 r"Ot MI-0uco~-00I4wen0

* U ~- >000001 4A001-04o00,0 ý-0U0Lzfl-< ,'ZO%

.00<Coo- c ,1--Or. 00-JtJJI 4 ,W4U-4 4

* OU.0 -J cL'Wv..j00u>o> Wi I-Womuxc1: -14Tn$4's..-dn n7 9E*quj<-X)- 11 11 qd 'ae -Vara 'reztrmi

M ý-. L.LWWQ 4N3Ojw- 0 )-V4( MZ>W3CCL-Za- 10*.-

u)X40 C0. 1 ppý 0 p CI 0.0 ) 0 I nOrv

0. U.0 mC x 44'a1> C-I W<Z03004 Zooac40o0 04000- hWo Z1n~.

00 C)- 00C5 0 Q0 11 OJ(N0zo 0 0:0 n 010 0 0 O010 0 0Ij0CNJ

CN LL rn N N r - - V , 7N~10 T- 0) .- N IV-a*I0 I Irn I.- N-

Wir* N3tJ M'0(*~ ro M ~ rfl ~rII 0) .Z 5 -I M I, pn 0lCa NA ?Ett Ii I. 41 .!a

.:t X-CN'a4NINWN0-m-I'0(3O4mZNrrl Moon

W 0 ad 4 0. 3 '3 (3 x I- d 3 XMIO I' 00'

zr-t * NNINa mo **0l)(00'0' a** * U 44 mVVf(Y'4M1)I. ON'

COC 0 0* tt1p- -~**00'0'*~a-o~W~e-,-nin co-~

~~'0a.-*~~NFP,..*4O'7AG.OI '%

~ 066

APPI-IDIX D

DESCBIPTIOI OF PROGRAI AUTAII

AUTAL was written in FORTRAII-63 for use on the CDC-1604

computer at the Naval Postgraduate School, Monterey. AUTAM

consists of the main program, PROGRAI': AUTAM; one function

subprogram, FUqICTION IDA; and two subroutine subprograms,

SUBROUTINE RATIO and SUBROUTINE ASSIGN. The interrelation

of the main program and the subprograms is shown in the

plain-language generalized flow chart in Part 1 of this

appendix.

In Pat-t 2 of this appendix, each part of the complete

program is described in more detail by:

(1) Table of Variables Used,

(2) Detailed Pla'n-language Flow Chart,

(3) FORTRAI,1-63 Program Listing.

67

APPEDIX D

Part 1. AUTAM General± od Block Dianaz

Read program control parameters,ship information, weights., •

Read ith, man's, assignment cards,•

Convert month-year codes to

numerical value. (FUNCTION IDA)

Compute time-dependent assigmentiva~riables. ,Wjk=19293) 1

Cmuevalue for homeport pref-

erence variable. (WiJ4) I,Strate index for

it man'sr~ate code.

13 1 th manlatmniseN

05

63

A P-I X ID

Compute POB/EDP ratios fo• all

men in set. (Wijk, k 5-11.

SUBROUTIN RATIO)

Compute Utility for anl i

possible assignments,f opt tiit fo i l

Make one assignment from

utility army. (SUBROUTINELASSI )

yoNoAr•e all men in set asaned?9

yen

69

APPEITDIX D

TABLE OF VARIABLES AIND CONSTANTS IN PROGRPAM AUTA1A

1. A(K) Weight vector for assignment variable.

(Constant) E2. GR(K) Dummy variable used in conjunction with

computation of marginal utility. Contains

sum of W(I,J,K) elements.

3. I Row subscript. Usually refers to Ith man.

4. IDA Function subprogram used to convert alpha-

numeric date code to number of months from

base date (January 65).

5. ID(J) Identifies tz which ship the set of 15 EDP

values belong.

6. IK(U,) The sequential order of assignments. (Used

in comparing assignment methods, in con-

junction with marginal utility.

7. Ii.(I) The number of the ship to which the Ith man

was assigned. Zoro value indicates man has

not yet been assigned in assignment process.

Set to 99 if Ith man has rate code error.

8. IP(J) Relates POB values to proper ship. (ID(J)

and IP(J) "-ed to insure proper or ordering

of data deck.)

70

APPENDIX D

9. IR(I) A rate code index for Ith man. Relates his

rate code to proper columni in (EDP)/(POB)

array.

10. I23 Iteration index for number of sets of men

to be assigned.

11. 12 Iteration index for number of assignments

made.

12. ISD Numerical conversion (by IDA) of ship's

deployment date code.

13. ISR Numerical conversion (by IDA) of ship's

return from deployment date code.

14. ITU Numerical conversion (by IDA) of man's take-

up date code.

i5. IXE Numerical conversion (by IDA) of man's EAOS

date code.

16. J Column subscript - usually refers to Jth

ship.

17. JAJB Control indices for computation and recom-

p:ation of (POB)/(1DP) ratio and utility.

After an assignment utility and (POB)/(EDP)

ratio recomputed only for ship just assigned

to.

18. K Element index for WJijk vector describing

assignment of ith man to jth ship.

71

APPENDIX D

19. KS(IJ) Hull no., name, deployment dates, homeport

and identification number corresponding to

ID(J), IP(J) for Jth ship.

20. NA(I,J) Data vector, for Ith man, taken from assign-

ment deck. (Name, serial no., rate, rate

code, etc.)

21. HR(I) Rate code table which is compared to man's

rate code to find rate code index IR(I).

22. N Number of men in set to be assigned.

23. NSHIP Number of ships to be assigned to.

21. SA(IJ) Array of (POB)/(EDP) values for ships.

(IISHIP X 30)

First 15 cols: EDP Next 15 cols: POB

25 W(IJ,K) N X NSHIP array of vectors describing

assignment of Ith man to jth ship.

72

)V

APPENDIX D

D.tailed Plain-LanMma• ?low-Chart for AUTAIL

Rlead:number sets of me-. nimber of ships; ships'identification, deploy dates, homeport;ships" EDP, POB; w.;igment veights

Read uumber of men in 'this setStSe mamne*

j Read assioumet-card deck for it ai

Convert .LOS and takeup date-code to numberof months from JAK 65. (FUNC'TION IDA)

Convert 3 ship' deploy and return date-code to number of months from JAY 65,..(FUNCTION IDA)

,73

73i

APPENDIX D

4

S man's takeup date

before deployment date of3h ship?

yes

Isi man's takeup date

'within 3 months before deploy-

,mont date of 3 thiSP?

yes

Wi~l m 2I T

x INS

APPMDIX D

h thIs jh ship's homeport i

Maznts first homeport choice? .Is J ship's homeport iman's second homeport choice?

Have all sBps been pro-.

P'ind rate index for i*

man's rate-code.

Have all men in this setbeen processed? (ia-N?) i

Yves

Set shipdex limits forcomputation of assigaant.' • .

U..ptility &avray(J.L6,1 9 3BNH )Cu'A. __________ _ .75

APPDIX D

Set assigment counte(12=1) ..

" S.'.-' ISet man index.

(•1)

Has ith man already beonass~igned? (mO?)

Set shi~p index. (=A

Compute POB/EDP-ratios forI •. man to d•ship. \

(SUBROUTIM RL¶TIO)

Compute assignmnt utilty Of1ih man to j'~ ship. ,."

Have all necessary cooputa-tions (or- recomputations)• of J-6- =•1

assignment utilities for iP

,m=an been done? (,J-•,7

76

APPENDIX D

Have all men in this set No

jbeen processed? (i 0N?)

Assign one man. (SUBROUTINEASSIGN. L••h man is astsined

to %MIMt ship.)j

Set ship index Uits for

reoomputation of affeoot"

assinment utilities.

(JA JB DIM~)

Have all men in the setbee Nobassigned? (I2 MN) '

Yes

rHave all sets of mon been NAassiged? ( NSET?, )

77

APPENDIX- D

Vý 000000000

*0 W.. z U

0 UL.I-00

0 *- 0~P 0W

-i ~oz*4 *0~ ' z

0U .-. ) M )

*.- ~ ~ U 0- 00 AJ4

0-NO 39 cLD-'A 1.. 0.I IL IL. -O0 .- N.40 N: C0 D I---.-4a

0c 0 . I.0L-I V)-10 04 xDI' 1 -> L) 0 0

0 N< 0i -' 9- 1)2W

.uCK 0A 1: 0 41'- 0 *-4N 3: x0- 0' It oz I in 7: U))

N.4 0( ...0 Lf j) a U)kn '.0 In - %00 U) 0. z0. ; &L 9- 02 OZW 0 "4:A 'Nt -Z :-) 0o, 0 4P40 X 2 in 0 b

:;- 0 'iI 10- - . - 3:0 0:

**ON ZL. 49-WV) x(.0 W *w- '-40 z 0. Ix ~ m: x 4<'A 0.

00~ inr No .- I 00 -Z IE 11 4- .4-4 *N W r-4 3:O I-- V-0 - 11 0

D 0.mU ) 7r OU. mAn~ MZo a .- 40 . V) ý-0-L 0 -'W .4. ai <4

3:~0 v-4 0'-X -- W 0 LU c'o slI-LA)u4 0 1.- I-0 2Z Z z &4-4

N .9& u-N "N r-U)-x 'N 4:4 O.ZU .As-V'. 9-.-I~ ~ C0C V) 0~1) 0. *--9-4

Idr4z1.Z- 0 "1.sP4 X 9 ai~dV) W0&%o 0 00 IU.0. 0WWII-' IWU a -0.4 a .

<r4 ON 0"'' 0W N 6.4 - S-- Z.-~4c ZIIN 3 J9 *- : .4 W 0

)t-390 4 0- ILW a W sI--4V Z 2 3k Z-. 4a o'-0 W W W 9 -431L-M 0n-- a * 0 ao

< -- Z40 0 ') 0 0 41 0old-ZZ--- IkMZP4 U) 0V- Orq R V-4Oi1W N N Lj. wr4 a W * 0U v- S-'4 0 N LU 11 H- 4

IX - 0 a oZ>- 0 X.-n0XQ)%0-41-40 Q.%" I- "Iuz-. N4n a Xa ) '20 00' '-.-2 0 - 4 -I-.404 V""4:1 t o

ce Z0 0 M Z a- LU'- 0 0% 0" VJ -1N93 W 0x <0 --- 041X12 Z00 0,00 a'ý0C co. W" c c a- <:0 X-xl-O N ýj n Z3B4 Z 4 4 4 4:4 A) < 0- r-M '- 40 4 N (L '0. a 4.0* x UJWWW~hJ z K 00-0m. 0X%.00 ll-'-%" J'-'ý11 ow w w u &" -0 Ci390 a

z4g414 4 4-0-Z 0 0

78

APPENDIX D

00 44I 0 000 00 In 00n 000 00 00 %0 t 0%00 000to0%0 f

-I

1-4 0.

0.u w zI-4 -- i

4. D- - z)

z- z ij V

0 0 xWLL <-

Z1 Z I W 00c.wiI- I-0: % N z Z a

OZ4 It% 0 N1. W I-I-. 0 - N I- N C.C t 4

I-' p-. aNoV yV4I-w 0 0 VZ 0 -VU g 0 ty W o I

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79

L2PENDIX D

r4 N l r- r-t~ PI- 00r 0'. N 0" 4 A '0 -0 a C 00ý 0.A 0t% 40, '0 0 040% Cu-i 0 E 4 0 00

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APPENIX D

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jPPMEIX D

r-4-

c00

r-4

US

APPENDIX D

Part 2

Function Subprogram IDA

Subroutine Subprogram RATIO

Subprogram Subroutine ASSIGN

83

APPENDIX D

TABLE OF VARIABLES AND CONSTANTS USED IN FUNCTION IDA

1. IM Alpha-numeric month code.

2. IY Numeric year code.

3. KII(I) Table of month codes for decoding IM.

4. U-1 No. of months from January.

5. LY No. of years from 1965.

6. IDA No. of months from January 1965.

81+

APPEDIX D

Plain-languaiM 'loow-Char for Funtioa Suhro" IDA

PUNCTION IDA converts month-year code (IM,IY) to nmber of'months from January 1965. All date codes are assumed to beincluded in period January 1965-D•o•mbir 1974

Set 12 elements of month

code in X11 array. .(KM =(1g2,v,4,5,,6,7g8,,9j,

Initialize iteration

counter. (i I]

Is month-code same as :i Have all &Is-

element of'larray? Oments o•n

Maxi?)array been coon-

espared? (i"1?

•TNumber months from Jan. ,e

equals number iterations P•Plnt "]*ROR IN

85

' 'S

APDIX D

Is erods k5? Y1(IY~ 5?) ______

?lumber years from 1965 Number of years from

equals year-code plus 1965 equals yea-code

five years. (L,-IY+5) minus five years.

L (Lys IT - 5)

Number wrnths from Jan 1965

equals nmnber months from

Jan. plus 12 times number

years from 1965.

(InA=uL.N+2(LY)1

86

APPENDIX D.

--- %or -- 0 % 0-4-N ---- M

'0

r-

0 -

o lx> IX, -

X- 0o -4

Z 0 $,43 U

N- V4 M%00

W a

0 '087

APPI9nDIX D

TABLE OF VARIABLES AND CONSTANTS

USED IN SUBROUTINE RATIO

1. S(LIM) EDP-POB values for ship 14. Same as

SA(LM).

2. XE EDP for rate or rate above or rate below

that of Ith man on Mth ship.

3. XEE EDP for rate of Ith man on M th ship + .1.

4. XP POB for rate or rate above or rate below

that of Ith man on Mth ship.

XPP POB + .1 for rate of Ith man on Mth ship.

6. W5 Dummy variable for temporary storage of

(POB)/(EDP) ratio.

7. L Subscript corresponding to rate code index

for Ith man. Varies to include rate above

and/or below values.

8. K Iteration counter used to place W5 value in

proper element of Wijk array and to terminate

ratio process.

88

APPENDIX D

Elain-l0An-u~ rPloW-char for Silbrutin Subrmem RATIO

BEIGIN

Set iteration index.

Set variable rate inde. to

i man's rate-code index.

Compute PO/EDP ratio for~th *-ih man.,..

POBIR POB +JPIR,M*"•LM .4

[ i man CPO?2

(IR=t,6, or 11?)

__________No

Is ± man a striker? at

NO,

891o1

89

APPEIX D

Set variable rate index to

rate below. (L=L"I)

Assign W5 value to proper

element in W a~rray.¢Wi,M,K+ 4-7 )

Advance tterat~on index.I

Has POB/EDP-ratio for rat.e

below been computed? No

(K)-2?) ____ _J9yes"

RETURN

go

APPMIX D

Set variable rate index to

rate above. (L=L-1)1Assig W5 value to proper

element in W array.

(€I,M,K+ 6w15)

Advance iteration index.

j(K= K++)

Has POB/EDP ratio for rate

above been computed?

(K> 2)? .

91

APPMIX D

Set variable rate index to

rate above (first iteration)

or rate below (seoond iter-

atioA) ih man's rate.(L=L+K(-I) )

SAssig W5 value to proper

element in arr.

C~i,,K +90 5)

Advance iteration 1• =

]C= +÷

Has POB/EDP ratio for rate

above and below been

computed?

(K>3•?

es

C pw=

92

APPENDIX D

DIA 0%~0 Ni4 mA'O- f '- F-f.*eI' wow- 0 Owww .-4 N

39

%00

- w* 0

NOt

Go w

w V4

0 W

i-W av. ++ 0 M0. zO w A +O aW

N) OZ2: a ic 0 adIC I.1..

m > 00 ( o- 1 +w

00v~ V Ln LIV CIV - LInvV

0.0 a.- 94 . w ob 'X93I

APP11nDIX D

TABLE OF VARIABLES AND CONSTANTS

USED IN SUBROUTINE ASSIGN

1. %1 Maximum utility of Ith man.

2. RN Next highest utility of Ith man.

3. DM Maximum difference between R1 and RN for

all unassigned men.

4. JK Temporary storage for number of ship which

has highest utility for Ith man.

5. LI Number of man (utility array row) which is

to be assigned.

6. JS Number of ship (utility array column) to

which LIth man is to be assigned.

7. IT Dummy variable which defines column in

POB array to be corrected when man is

assigned.

94

APPENDIX D

Plain-languaae Flow-chart fgr Sub&rm . Subrotine ASIG

Set difference variable to

zero. (DuO••

Set man index. (i± I)!

H ith man already been ye

assigned? ( d 0?)

Set row-max variable (MM)

and row.-next-hi:ghet

variable to e•o.=L (W= RN=0)-

{Set abl index to one

U= 0

95

APPWIZZD

Is utility of ith man toth ship greater than or ye

equal to value of MI?

(U? •Rm?) Replace RN value withii Value of EM. (RNa RU)

No Replace EM value with

1value of U13 . (m-=U13 )Isutility of ih Un to Store ship lndex in 3K.

th

3h ship greater than or Za,(jK3)equal to value of RN?

NO Replace RN valuewith Ujj value.

(RN= U13)

Have all ships bean pro-

cessed for ith man? No O341 3

(_j NsaP)'?______

Yea

Is val•'j of d--foronoo

variable greater than or

equal to difference between o0

maximm utility and next-

highest utility of ith mnA?

(DU (1w-RN)?)

9696

APPENDIX D

Replace value of DU with

value of IM - RN.

(DM= RM - RN)

Set man-assignment index

to value of man-index.(I•=i)

Set ship-assignment index

to value of ,K.

(Js =3K)

Have all men in not been

processed?

Yes

Assign LM man to JSh

ship. (Print assignment

information.)

Correct POB of ship JS forthI

LXh man's rate. Set assign-

ment index to refleot assign-

meont of man to JSth

ship. (I•.. is),

97

/

APPF2IDX D__

000%O 000% Nc 00 c ca00.4. ". 004 00 00 000 00000

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APPENDIX D

do

Go *

V-4

v-4,-4

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0. 0

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-10 0>

APPENDIX D

Modification to Ptoam AM1X for Rlowolm 10tbW of Awugut

JA m IDO 90 12=19N

CC EXECUTE THIS LOOP FOR ASSIGNMENTC

DO 88 Inl9NGR(II)O. :

IF(IM(l))8698608686 DO 189 J=1lNSHIP

CALL RATIO(IR(I1)l1J)U(IJ)=A(1)DO 189 KnlollU(I9J)wU(I9J)+W(I*J9K)*A(K+1)

189 CONTINUE88 CONTINUE

CALL ASSIGN(N9IRIMsJAIK)

*Statements shown above replace card m•l•b 0100-0115(inclusive) in Pz'ograa oUny.

100

.4

APPEN2DIX D

Modifioation to Propsa WAZXl for Minwgna~ UtLitY GONOquMIos

SU.SRU=TN=0.DO 168 Iul)NIFi IM( I)-99)1719168, 166

171 J a IMMIIRANIR( I)+15SAC IRA9J)=SA( IRA9J)-1.CALL RATIO(IR(I)9I.J)T-A(l)DO 188 Kulo11GR(K)-GR(K)+W( IJK)

188 T=T+W(ItJ#K)*A(K+1)SU-SU+U( I J)SRU=SRU+TSAC IRA#J)nSA( IRA#J)+1.PRINT 170,IJU(1,J),TIK(IhP(W(IJK),tK1,1l)TN. TN+l*

168 CONTINUEPRINT 1729SUSRU,(GR(Kh9K1.11)SUwSU,/TI S SRU=SRUfTNDO 173 K*1.11

173 GR(K)nGR(K)/TNPRINT 172pSU*SRU9(GR(K)9K1.lfll

170 FORMAT H %,215*2FlO*3*5Xp 1392X,1lF7*2)172 FORMAT(11X92F~o.39.1OX.11F7*3)

*The above statemenst foflow card number 0124 In Pro,&= AUTAM.

101ý

APPUD1IZ

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103

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APPENIDIX E

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105

APPENDIX Z

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APPEIDIX 7

WEJ-1GHT-S--USEC -IN ASS IGN1ENT

A( 65))-3 500-A( ý7)-1 9

At 8)nu-z.790)

A(1O)u! -.880

-S I P-IS-T-0-GE--AS S-1G"IE-TO 0 -

1 USS GCLF 05 66 V 72 USS KILC 85 36 x 113- ---- SS--ECI-C-- 96 147- w - 5

4 USS CSCAR 85 .66 y 155 USS LIPA .6 17 X 126 USS JULIET 16 6 x 1

--- 7 -USS-HCTEL- --- 5k 37 - Y8 ~8 USS FOXTRCT B 96 W 69 USj DELTA H _ y5

10 US BRAVO J5 2

108

APPEN~DIX 7

0- inl in) N 0 a q0 it Nr- -4 In WW.- MPe- 0"m 0 1a.' '-a. a. "a.L P-a. PWI. CL 0. 0.U4 We- Uip" We- We- We- Wp- W69- We- ULIf

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ui

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2109

APPMHDIX 7

0 %

N

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110

APPENDIX F

I inl 0f IN 0 O %0 it Nr- Fmw LA U10i- Np- 0ý £) to * N

UJ Wjr LUJ UIJ Uip Wjp W.P- Wj- M.- Mip.-

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cm V-4- 111

__ _ _ _ _ COS.,na At - e m 04D a%

INITIAL DISTRIBUITiON LIST

No. Copies

1. Defense Dooomentation Center 20

Cameron StationAlexandria, Virginia 22311+

2. LibraryU. S. Naval Postgraduate SchoolMonterey, California

3. Assistant Professor Sam H. Parry(Thesis Advisor)Department of Operations ResearchU. S. Naval postgraduate SchoolMonterey, California

.. Chief of Naval Personnel (PERS-A3) 1

Navy DepartmentWashington, D. C. 20370

5. U. S. Naval Personnel Research Activity 2

San Diego, California 92152

6. Lt. Russel N. Blatt, USN 1

2623 Whittier AvenueMidvale ManorReading, Pennsylvania

7. Lt. Dudley E. Cass, USN 1

811C 261+5U. S. Naval Postgraduate SchoolMonterey, California 93940

112

UllCLASSI11i,'DSgcudity ClmificationSecrit 0iDOCUMENT

CONTROL DATA - R&D(Naeurity cisetificartal o t"ldo, body of abosftrt ,d lndexin4 annotation nu4t be entered whien te overall rlport Is cbmsiiedf)

I. ORIGINATING ACTIVITY (Corporate auth.,) 2a. REPORT SECURITY C LASSIFICATION

UNCLASSIFIEDU. S. Naval Postgraduate School 2b. ,oupM4onterey, .California 93910

S. REPORT TITLE

A MODEL FOR AUTOJ1ATION OF PERSONMEL ASSIGNMENT

4. DESCRIPTIVE NOTES (7Type oet upm and/ nchuiv.e det*.)

ThesisI. AUTHOR(S) (Lose name. irat haee, initial)

Blatt, Russel N. and Cass, Dudley E.

R Em P O R T D A T E7 a T O A N O O F P G SF M E ̀October, 1966 18

So. CONTRACT OR GRANT NO. to. OCRSINATOR5I REPORT NUMR[IM'S)

II PROJECT NO.

c. S~lb. jTHER %JPORT NO(S) (Any 0etbrnimlamMi @WN he Moist

J.

I& A'V A IL ABILITY/LIMITATION NOTICES

Distribution of this document is unlimited

11 SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY

iS. AGSTR•CT

This thesis demonstrates the feasibility of com-puterized assignment of Naval enlisted personnel to fleettunits. A model is constructed for determining the utilityof each man for each possible ship assignment. Then-7,'rious methods of assignment are investigated to findone which maximizes the summed utilities of assignment.To illustrate its capabilities, the raodel is then appliedto `;everal sample s;,ts of men and ships. The authors con-clude that a model of this type should be implemented inthe Navy's personnel distribution system.

DD I 1473 113 UNCLASSIFIUDSecurity Classlfication

Seculzi Cleumlflcation _____ ____

1.LINK A LINK S LINK CKEY WORDS ROLE WT ROLE WT ROLE WT

Personnel AssignmentUtilityComputer M~odel

INSTRUCTIONS1. ORIGINATING ACTIVITY: Enter the unsmsandw edi.. im oed by security classification, using standard statementsof the contractor, subcontractor, grant*e, Department of Do- suc .sfonse activity or other Organisation (cotporate author) issuing (1) "Qualified requesters may obtain copies of thisthe report. report from DDC."2a. REPORT SECUETY CLASSIFICATION: Enter the over. (2) "Foreign announcement and dissemination of thisall security ciassification of the report. Indicate whether rpr yDCi o uhrzd"Restricted Data" is included. Marking is to be in aceocoyrd-i otathrze.anc with appropriate security regulations. (3) "U. S. Government agencies may obtain copies of

2b. GROUP: Automatic downgrading is specified in DoD Di- thsreprs dillreuetl fhromuDgh te qaiie Drective 520010 and Armed Forces Industrial Manual. Enterthe group number. Also, when applicable, G1.ow that optionalmarkings have been used for Group 3 end Group 4 as author- (4) "U. S. military agencies may obtain copies of this

3z~. RPR I ~Etrtecmlt eotttei report directly from DDC. Other qualified users

capital letters. Titles In ell cases should be unclassified.If a meaningful title cannot be selected without claseifica-tion., show title classification In all capitals in parenthesis (5) "ALl distribution of this report is controlled. Qoal-immedately following the title. ifiad DDC users shell request through

4. DZCR13PTIVE NOTES: If appropriate, enter the type of_______________ ,

report. e~g.. interim, progress. summery, annual, or final. If the report has been furnished to the Office of TechmicalGive the inclusive dates when a specific reporting period is Services. Deprmenut of Commerce, for sale to the public, ei-&covered. Cate thus fact and enter the price, if known.5. AUTHDR(8)X Enter the name(s) of author(s) as shown on I L SUPPLEMNTARY NOTUM Use for additional explena.or in the report. Enter last name, first name, middle initiaL, tory notes.If military, show took and branch of service. The name ofthe principal a~uthor is an absolute minimum requirement. 12. SPONSORING MILITARY ACTIVITY: Enter the name of

the departmental project office or laboratory sponeorinig (par-.REPORT DATE. Enter the date of the report as day, ing for) the research sad development. Include aidreag

month, year. or month. Year. If mor* than one date appears 13AsTAT Enrsoatacgingabifm fculon the report, use date of publicat ion.13ABTATRoo abtctgvnabresdfcse

PAGE Th totl pge cunt summary of the document indicative ot the report, eve though7s. TOTAL NUMBER OF PAE h oa aecut it may also appear elsewhere in the body of the technical re-should follow normal pagination procedures, Le.. enter the port. If additional spaeis1 required, a continuation sheet shall'mamber of pages containing L-formation. bie atahd7ý NUMME OF RZPERRENCIS Enter the total macher of It to hil deslivblo that the abetract of classified repeotref~teaces cited in the qw~t. be unclassified. Each paragraph of the abstract shell sad with"o CONTRCT Oft GRANT NUMBER: If appropriate, enter an Indication of the military security classeification of the in-the #"picable masbe of the contract or grent under which formation In the paagraph, represented as (TT), (3), (C). or (U).the report was mritterA. There is no limaitation en tha length of the abstract. How-Sb a, &. &d. PROJECT NUMBER Enter the appropriate ever, the suggested length is from I to 253 words.military department Identification. such as pro~ject munher, 14KE OD: eywrsaetcucl enngltemsubpiroject nmbcer, system numbers, task number, etc. or. hoY WhRaSe tat characers am reorticall meayinheuusedrm.

go. ORIGINATOR'S REPORT NUMBER(S): Ente the offi- index entries for cataloging the report Key words meset hecia report manoier by which the document will be identified selected so that so security classification Is required. Ideati-sad contolled by the originating activity. Thib number must flare. such as equipment mode designation, trade mmss, militarybe unique to this report. project code name, Weographc location, may he med as bey96. OTHER REPORT NUMBER(S): If the report has bee words buit will be followed by an indication of techicaol cea- '

DD IFJ.0. 11473(ACK 14 M C LASS IFI LDSecurity CiNelficatlo.