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UNCLASSIFIED
AD NUMBER
AD489885
NEW LIMITATION CHANGE
TOApproved for public release, distributionunlimited
FROMDistribution authorized to U.S. Gov't.agencies and their contractors;Administrative/Operational Use; Oct 1966.Other requests shall be referred to NavalPostgraduate School, Monterrey, CA.
AUTHORITY
USNPS ltr, 15 Feb 1968
THIS PAGE IS UNCLASSIFIED
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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* 51
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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w I.-'i x -V )I U. -~ - 'I ) -L "I ) L '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
C CC 0a0 00 0 000 00 000 00a0 0 0 a0 0000 0 00 00000
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APPENIX D
ol.0 W' O %0 06.4 N 014 0 o '.0 I - 00".0.IN VM4 IM .0 - w 0'. a WO, C f .O-0'C C ccPN4 NN" NNNN NNNoimql(V1.M COM
- .4'. .4- . '4 . v4 .4p4p4p '4 4'. '4'..4'4 .1'4 '4 . '4 . '4 .4p4'3v4 .
C 0 0 00 0 0 0 00 000000 000 00 000 0X
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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
u akNZ Go
0. 0
ELL I--lz & -
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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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APPENDX E
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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
NO r'lN '-0 00 "O0 WKN NYO NV- Ne- "10
Iq V--0e-- @--.W Vf e-e- e---N e-Q Cy" -e- -
V-VlP-- -e- 00 e-e- raw=- 0 -10 09' 00
ui
Sij
C
*ý P- 0 pm 0 -0s
cc 00 00 cc 00, 00 00 a- op- 0c
0- ON ONi 00 0- e-P-"1 0 '-0
'NO& -oO 0.1 040 -40N 00 NO " PW ro on.*
mN - -44Ne t*A)N W).-
2109
APPMHDIX 7
0 %
N
000000000 CDNO-*'O04)%O
et so 0 00000 6 C
*0Vr0F-rVIO*0 .- 00000QO-000 JO4U. LLB
I.-
WU 9000000000 0~f 00000001000
000 0000 00 000 00 cc0
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i- u
;0000 ý-00 00000
U.10.i. I( 0P 0~ 0- Q-coo-
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T fnw~no.-*I0 lQt@I0I TN
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.-
C40 N -000 Wc MNI NO4 N*- Ny- tn
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woo. cm 00 Q"C4 -
NO * '010 NN ON *W) V00 7 ma m
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
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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
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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.