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RESEARCH REPORT SRR 73-3 AUGUST 1972

00 AN EQUILIBSRIUM FLOW MODEL OF THE NAVY'Sltdi ENLISTED PERSONNEL ROTATION PROCESS

Normnan i. borg~n r..-rry A, Seoo

Robert P. Thorpe

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Naval Personnel and Training Research Laboratory UNCLASSIFIEDSan Diego, California 92152 Sb GROuP

3 REPORT TITLE

An Equilibrium Flow Model of the Navy's Enlisted Personnel Rotation Process

4 CESCRIPTIVE NOTES (Type os report and Incluqive dales)

5 AU T.IORISI (Flirt name, middle Initial, last nate)

Norman I. BorgenJerry A. SegalRobert P. Thorpe

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August 1972 39 11@a CONTRACT OR GRIYNT NO 5.. ORIGINATOR'S REPORT NUMBERIS)

b. PROJECT NO SRR 73-3

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II SUPPLEMENTARY NOTES 42. SPONSORING MILITARY ACTIVITY

Chief of Naval Personnel (Pers-A3)Navy Department

,_ _ _Washington, D.C. 20370SI AiSTRACT

The periodic rotation of enlisted personnel between sea duty and shore dutyassignments is a firmly established Navy policy. The efficiency with which therotation process is managed, however, can have an effect on both the personnelreadiness of operating units and the morale of the indivliual Navy man. Thisreport describes a computerized model of the rotation p:ocess which will providerotation managers in the Bureau of Naval Personnel with a quantitative basis fordecisions, and the capabitity for the test and evaluntion of rotation policy.The model encompasses the basic variables and parameters governing the movementsof personnel between the broad categories of sea duty and shore duty. ,, The modelis based on an "equilibrium flow" concept (i.e., the movements of personnel shouldbe such that the relative proportions of personnel in the sea and shore compositeswill remain stable) and incorporates certain techniques of actuarial science toestimate the size of future "rotation eligible" populations. The model has beenused to test how changes to tour lengths and billet structures would contributeto more orderly and equitable rotation oi personnel. Examples of these and otherpotential application are given.

FORM (AE1DDI NOV "17 UNCLASSIFIED0102.014.6600 ,cunty classification

UNCLASSIFIEDSecurity Classification

14 LINK A LINK B LINK CKEY WOROS

ROLE WT ROLE WT ROLE WT

Manpower managementManpower modelsPersonnel rotationPolicy planningDecision makingActuarial scienceNaval personnel

(PAGE 2) SNOwity Cis-,sification

AN EQUILIBRIUM FLOW MODEL OF THENAVY'S ENLISTED PERSONNEL ROTATION PROCESS

by

Norman I. BorgenJerry A. Segal

Robert P. Thorpe

August 1972

PF39. 521.002.01.04

;1

Submitted by

M. F. Wlskoff, Ph.D., DirectorPersonnel Management Systems Research Department

Approved byEarl I. Jones, Ph.D., Technical Director

F. L. Nelson, Captain, USNCommanding Officer

Approved for public release; distribution unlimit~ed [

Naval Personnel and Training RPsearch LaboratorySan Diego, California 92152

A LABORATORY OF THE BUREAU OF NAVAL PERSONNEL

I•

PROJECT STAFF

Robert P. Thorpe, Program DirectorNorman I. Borgen, Project Director

PNCM J. A. Segal, USN, Project AssistantPN2 J. B. Hyndman, USN, Project Assistant

ACKNOWLEDGEMENT

To Dr. Raymond E. Willis of theUniversity of Minnesota for his

assistance in formulating thegeometrical representation of themodel described in this report.

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Report Title & No: An Equilibrium Flow Model of the Navy'sEnlisted Personnel Rotation Process (SRR 73-3)

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viii

F

CONTENTS

Page

I. INTRODUCTION ..... ...... . . . 1

Problem . . . . . . . . . . 0. . . . . . . .. . . .Background . . . . .. . ....... . .. o .Approach ... . . . . . . . . . . . . o

II. ENLISTED PERSONNEL ROTATION ......... .. 3

Objectives ...... . . . . . ........ . 3Rotation Process ................. 3Rotation Management Problem s ...... . . . . . 4

III. EQUILIBRIUM FLOW MODEL ............... 6

Concepts and Assumptions ......... .... 6Computational Elements .............. 13Applications . . . . . . . ..... 21

IV. SUMMARY AND CONCLUSIONS o o . . . . . . . . .. 27

References a o o o o o o 29A-(X

2l

I?

-- I FIGURES

Page

1. Personnel Flow Rate (F) shown as a function of Numbersof Rotatable Personnel (N) and Length of Shore Tour inMonths (T). .. . ................... 7 7

2. Personmel Flow Rates (F) as a Function of the Number ofof Rotatables in Each Composite (N., N ) and the Pro-portional Tour Lengths of Each Composite (TI, T2 ) . . . 8

3. Cumulative Population Survivor Curve as Developed froma Length-of-Service Frequency Distribution. . . . . . . ii

4. Survivor Curve Envelope for Total Navy Population forYears 1966 through 1971 . . . . ...... . . . . . . 12

5. Billet Supply and Demand Rates as Determinants of theEquilibrium Tour Length as Applied to Personnel Rota-tion. . . . . . . . . . . . . . . . . . . . . . . .. . 15

6. The Personnel Rotation Model M¾•justed to ReflectEffects of Applying an Ob.!i:%. - Se-ivice Requirement toRotation Eligibility. . . . . . . . ........ 17

7. Personnel FRotation Moo.l incorporating Provision forObligated Service as a 1'otation Management Variable . . 18

8. The Biased rotation Management Model .......... . . . 20

,.x

AN EQUILIBRIUM FLOW MODEL OF THE NAVY'S ENLISTED ROTATION PROCESS*

I. INTRODUCTION

Problem

The planned periodic rotation of enlisted personnel between seaduty and shore duty assignments is a firmly established policy in theNavy. The magnitude of the task of managing these personnel movementsin an orderly and equitable manner is great, however. The numbers ofpersonnel involved, the complex relationships with other personneltransactions, and the necessity to respond quickly to actual or proposedchanges in the operational environment, often create rotation managementproblems difficult to isolate and resolve. The need exists, therefore,for the development of a broad range of new or improved management con-cepts, policies, and procedures based on a systems view of the rotationprocess. The effort described in this report is in response to this need.

Background

For some time this Laboratory has been developing computer basedtools and techniques for application in the Bureau of Naval Personnel(BUPERS) to help improve the management of the enlisted rotation system.This effort has resulted in a series of computerized models of the rota-tion process which have been used in BUPERS in various planning or policytesting applications. These models have successfully demonstrated notonly the feasibility of computerizing portions of the rotation dec'sionmaking process, but also the improvement in management that could resultfrom their use.

Approach

The primary emphasis throughout this effort has been on the develop-

ment of models of the sea/shore rotation process which would incorporatethe. major elements and characteristics of the process in such a way thattheir values aud relationships could be measured, manipulated, and ifpossible, predicted. It was intended that these models would provideBUPERS rotation managers with a quantitative basis for their decisionsand a capability to test and evaluate policy and procedural optionsrelated to the planning and control of personnel movements.

*A modified version of this report was presented as a paper (2) at the

Twenty-Ninth Military Operations Research Symposium, U. S. AIr ForceAcademy, Colorado Springs, Colorado, June 1972.

i i

This emphasis has required that a close relationship be maintainedwith the cognizant BUPERS managers. In effect, this relationship hasenabled a continuous analysis to be made of the rotation system. Overthe years the objectives for rotation have been redefined or given dif-ferent priority, new management problems have resulted, and new policiesand procedures have been implemented. It has been possible, however, toincorporate into the computer models being developed, many of thesechanges to the "real world" rotation system.

The general objective has been to try to ensure that the modelswould be acceptable representations of the actual sy, ham, with potentialapplication in helping to solve relevant rotation m,. agement problems.For example, after a series of tests, the SEAVEY Paiining Model (3,5)was operationally implemented in BUPERS for use in planning-the movementof personnel from sea duty to shore duty. More recently, a modificationof the Sea/Shore Rotation Model (4) was used by BUPERS managers to help deter-S~mine how changes to sea/shore billet structures and tour lengths mightincrease the opportunity for shore assignments for certain enlisted

ratings. Actual use of the models in these ways has not only helped tovalidate their conceptual framework but also provided some immediatebenefits to management.

This report describes ý_e "Equilibrium Flow Model" which has servedas the conceptual framework underlying these past model building efforts.This description is prefaced by a brief overview of the personnel rota-tion system and followed by an outline for the further development andapplication of the rotation model concept.

2

II. ENLISTED PERSONNEL ROTATION

The Navy enlisted personnel structure comprises approximately 70occupational skills referred to as "ratings." Each rating is subdividedinto "skill levels" which are reflected in pay grade designations ranging

from E-1 at the lowest entry level to E-9 which identifies the highestskill level of Master Chief Petty Officer. Additional occupational skills

are identified by a numerical coding system referred to as NECs (NavyEtlisted Classification Codes). Assignment of these codes typicallyfollows specialized training and may serve as a skill identifier subsumedeither under the broader rating designation or it might identify anentirely separate skill requirement. The Navy's "billet" structuregenerally parallels the personnel structure and consists of jobs or "tasks"to be performed on board ship or at shore based activities. These arereferred to as billets and serve to identify the skills required in sup-port of a variety of missions. It is within this personnel/billetstructure that the rotation of personnel takes place.

Objectives

The rotation of enlisted personnel between sea duty and shore dutyassignments is intended to achieve two basic objectives. One is todevelop in the career force a broad and expanding background of trainingand experience through a progression of varied duty assignments. Thesecond is to help compensate the Navy man for the hardships he experiencesduring long tours of sea duty away from his home and family, by providinghim shore assignments offering a more normal way of life. The process ofrotation is constrained, however, by the need to maintain a high level ofreadiness in the Navy's operating units. To this end, the transfer andreplacement of personnel must be accomplished with minimum effect on crewefficiency and individual productivity, but at the same time, with maximumconsideration feasible given to the needs and desires of the personnelinvolved. In summary, the efficient rotation of personnel can have asignificant effect on rhe overall personnel management system, on theoperational readiness of Naval Units, and on the morale and retentionprobability of the individual Navy man himself.

Rotation Process

As already defined, personnel rotation refers to ehe planned reagsign-ment of personnel between sea duty and shore duty. The process throughwhich these movements are made is quite simple in theory. With a fewexceptions, each Navy ship, aircraft squadron, and shore station is

categorized for rotation purposes as either sea duty or shore d,.}. Menare assigned to these activities for a tour of duty of prescribed 1!rngth.Normally, when a man completes a prescribed tour of sea duty, he wi]l

3

be rotated and reassigned to a shore duty activity. Similarly, a mancompleting a tour of shore duty will receive a sea duty assignment (6).

It should be noted, however, that the rotation process merely

"triggers" those personnel movements. The actual reassignment of these

personnel to new duty stations is carried out through the distributionand assignment process. The distribution function is intended to ensurethat each Navy activity receives its "fair share" of the available per-sonnel. The assignment function, in turn, is intended to match asaccurately as possible the requirements of specific "billets" with thequalifications and desires of the particular individuals available forassignient. Both the rotation and assignment functions, however, areconstrained by distribution policies and procedures. In the simplestsense, the rotation process determines when personnel are to be moved;the distribution and assignment process determines to which areas orbillets they should be reassigned.

Rotation Management Problems

Rotation management is primarily concerned with achieving orderlyand equitable rotation of personnel between the sea duty and shore dutycomposites. Orderly rotation refers to the goal of maintaining more orless equal flows of personnel between sea and shore. Ideally, a manrotating from either sea duty or shore duty would be replaced by a manrotating from the opposite composite at about the same time. In thisS~ideal case, there would be neither an undesirable overlap of assignments

with both men occupying one of the billets nor an undesirable gap betweenassignments with one or both billets remaining vacant for a time. A majorproblem for rotation management is to determine the combination of sea/shore tour lengths that would result in personnel flows at least approach-

ing the order of this ideal state.

The lengths of sea and shore tours are also factors in achievingthe management goal of equitable personnel rotation. In this sense,"equitable" refers to the state where there would be equal sea toursand shore tours for all personnel in all ratings. At present, this isnot the case. The inequitability existing among ratings results, forthe most part, from the differences in their ratios of sea billets toshore billets. In some ratings where there are many more sea billetsthan shore billets, personnel are required to spend proportionallylonger time at sea than on shore. Where the ratio is more nearly equal,the time spent at sea and on shore is also more equal.* The problem forrotation management, in this regard, is to increase, whenever possible,the opportunity for shore assignment for the appropriate ratings.

*There are some ratings that have more shore billets than seabillets, and longer shore tours than sea tours. In general, however, over allratings, there are approximately twice as many sea billets as shore billets.

4

__ -- e•=li__ - , I I1

This is not an easy task however. The number of billets for a rating is,in effect, a statement cf where and to what extent the skills of therating are required. Thus, if a particular skill cannot be utilized inan activity, no billet requirements will be specified. Those ratingsrepresenting "shipboard" skills are most often the ones with low shoreduty opportunity. How to utilize these ratings ashore in a manner thatis both financially practical and productively feasible is the essenceof the problem.

Rotation management has traditionally dealt with personnel at the"rating-pay grade-NEC" level because this is the level at which dutyassignments are made. This represents the management level necessaryto appropriately allocate the personnel resources throughout the Navy.Considering the amount of detail, the inherent complexity, and the mag-nitude of the management task, this level could be referred to as the"microlevel" of rotation management. Higher level managers and policymakers have little need for the detail required at the microlevel,utilizing instead generalized data representing selected aggregates ofpersonnel. The present personnel/billet structure lends itself readilyto several possible intermediate management levels such as aggregates ofpersonnel by total rating, rating groups (i.e., a collection of relatedoccupational specialties), or by pay grade across ratings. The highestpractical management level would consider total Navy sea and shoreaggregates for purposes of rotation management. This top level couldbe referred to as the "macrolevel", existing at the opposite extremefrom the microlevel.

The "Equilibrium Flow Model" described in the next section haspotential application at each of these levels of rotation management.

5

III. EQUILIBRIUM FLOW MODEL

The "Equilibrium Flow Model" represents the framework underlying thevarious models of the sea/shore rotation process which have been developedas part of this research effort. This section includes aescriptions of(1) the concepts and assumptions upon which the model is based, (2) itscomputational elements, and (3) some policy testing applications. Al-though the model is computerized, portions of the following descriptionsare presented in geometric terms to help the reader visualize the rela-tionships among the elements along with the dynamics resulting fromvarying selected parameters.

Concepts and Assumptions

The models of the sea/shore rotation process are based on threemajor concepts whicn, in turn, are based on several assumptions about therotation system, the relationship between certain variables, and the char-acteristics of the sea/shore populations of personnel. These concepts andassumptions are described below.

1. The Dynamic Equilibrium Concept

It is assumed that, ideally, the rotation system should be inequilibrium in the sense that the relative proportions of personnel ineach composite should remain stable. As already noted, one of the majorconstraints operating in rotation management is the number of billetswithin the sea/shore composites. In many ratings, however, the total num-ber of personnel available is insufficient to "man" all of these billets.In such cases, "manning levels" are established to indicate the propor-tions of billets in each composite that will be manned. The rotation ofpersonnel must, therefore, be carried out In a manner that will maintainthe composite manning in an equilibrium condition.

There are, however, a number of forces constantly acting to dis-rupt any achieved equilibrium. Sea/shore billet requirements, personnelinventory levels, personnel management policies, and operational commit-ments are in a continual state of flux. More accurately then, rotationmanagement could be considered as the process of trying to maintair. a"dynamic equilibrium" (7) within a turbulent environment.

2. Personnel Flow Concept

Management actions associated with personnel rotation involvethe transfer of personnel upon completion of predetermined tour lengths.When personnel are moved for rotation purposes, a vacancy is created thatmust also be dealt with. Ideally, as part of the rotation concept, therewill be someone waiting for assignment to the billet being vacated uponsimultaneously completing his own assigned tour. This creates anothervacancy to be filled by yet another move, so that there is in effect achain reaction of reassignments and vacancies throughout the system.

66

The mechanics of rotation, then, may be viewed as a set of billet vacanciesoccuring regularly over time with a concurrent movement of individualsbetween the two broad ccmposites of sea and shore populations.

The "Personnel Flow Concept" refers to this movement of personneland the interaction between numbers of personnel and tour lengths ()generate somewhat predictable flow rates. In effect, it is assumed that thenumber of personnel moving from a composite each month is a function of thenumber of people in the composite and the prescribed tour length in months.This relationship can be expressed as:

(1) F

where: N = number of rotatable personnel

T = tour length in months

F = personnel flow rate per month

A geometric representation of these basic rotation elements indetermining a "shore vacancy rate" is shown in Figure 1.

N

4 T

Figure 1. Personnel Flow Rate (F) shown as a Function of Numbers ofRotatable Personnel (N) and Length of Shore Tour in Months (T).

7

In Figure 1 the personnel flow rate (F) is the portion of thetotal number of personnel (N) that has moved during the basic time unit ofone month. As additional time passes, the supply of vacated billets ac-cumulates until the complete tour length has elapsed at which point theentire original population will be completely displaced by a new population.With billet supply being set equal to the demand for vacated billets amongthe sea population, the personnel flow rates will be the same for bothcomposites. This relationship between the "shore vacancy rate" and the"sea replacement rate" is shown in Figure 2, where the slope of the hypo-tenuse represents the identical flow rate between the two populations.

N2

N1

F

ST2T-

Figure 2. Personnel Flow Rates (F) as a Function of the Number ofRotatables in Each Composite (N1 , N2 ) and the ProportionalTour Lengths of Each Composite 1T1 , T2 ).

8

The relationship shown in Figure 2 can also be expressed as:

(2) N1 = F1 =F 2 N2T1 -- 2-

where: NI, N2 = Number of rotatable personnel in the shore

and sea composites, respectively

Ti, T2 = Tour length in months for shore and sea

F = Shore vacancy rate per month

F2 - Sea replacement rate per month

From the relationships shown in Figures 1 and 2, and expressedin equations (1) and (2), the values of one or more variables can bechanged to determine the resulting effect on the others. For example,one could determine the appropriate sea tour for a given sea/shore billetratio and prescribed shore tour, or how many additional billets would beneeded for equal sea/shore tours holding the size of the sea populationconstant.

In actuality, of-course, the rotation system is seldom exactlyin equilibrium and the flows of personnel between sea and shore areseldom exactly equal. The Dynamic Equilibrium Concept and the PersonnelFlow Concepts are important, however, because they enable the variablesaffecting the rotation process to be mathematically related. By sodoing, they can represent the :ideal against which to measure thepresent rotation process and to test existing or proposed rotationpolicies.

3. Rotatable Population Concept

An analysis of the rotation process has shown that not all

personnel serving at sea or on shore at a particular time will necessarilybe eligible for rotation at a future time. Some personnel will be in

special programs or in billets which are managed outside of normal rota-tion procedures. Before completing a prescribed tour of duty, some per-sonnel may leave the service while others may be promoted to another paygrade or transferred to another rating where a different tour lengthSpolicy might apply. Some others may complete a tour but be ineligible torotate because of insufficient obligated service or because of operationalcommitments. Therefore, in order to effectively plan the movement ofpersonnel, some assumptions must be made about the nature and size of the"rotatable population" which can be expected to be eligible for rotationat some future time.

F9

Predicting the size of future populations has historically beenviewed as a problem of predicting future numbers from analysis and inter-pretation of Navy "reenlistment rates." Close examination of the reenlist-ment rate concept, however, indicates that it has certain limitations thatreduce its effectiveness for purposes of rotation management. A moresuitable rate for the purpose mentioned may be developed by analysis ofthe number of personnel who remain in service as measured by the prcportiorsof personnel at each year of service that continue into the following year.These rates are referred to as "continuance" rates and are developedindependently of considerations relating to enlistment contracts (9). Onemajor advantage of a continuance rate over a reenlistment rate Is that itmaintains a specific relationship to the time dimension that may rangefrom one day to the maximum 30 year service career.

There exists a close mathematical relationship between continuancerates and length-of-service distributions for any given population. Suchdistributions do not require any assumptions of linearity with respect torate of change or "normality" of frequency distributions in their appli-cation. In addition, the continuing product of continuance rates willgenerate an equivalent "life survivor curve" for the given population, aprofile more suited to rotation management models. The development of asimilar curve is illustrated in Figure 3, where an actual populatioafrequency distribution is converted to a "survivor curve" by subtractingfrom the total population beginning at TIME0 the frequencies for each suc-0cessive point in time. The curve thus generated is cumulative in the sensethat each of the values on the curve represents numbers of personnel at orbeo the corresponding points in time.

The general applicability of an actuarial theory concept to rota-tion management procedures rests on an analogy drawn among those elementsof birth, life, and death in actuarial science QIy and the organizationalequivalents of entry into active service, active service, and release fromactive service. The organizational equivalent of "life expectancy" isreferred to as "length-of-service expectancy" or "time-in-grade expect.ency"depending upon the nature of the aggregate population under consideration.Development of the concept in the following paragraphs translate otheractuarial elements into equivalent organizational elements.

A simple survivor model may be developed by observing a relativelylarge number of personnel who have entered the organization and n¶oting theeffects occurring over time as the number is diminished by those leavingthe population (8, I0). This model of a single population may be extendedin concept by observing a succession of groups entering the

10

100- 99.9

* 93.3

78.375- .. SURVIVOR CURVE

I-lz 66.3IiiU

wa.% 0 50.70 50-

_-

LENGTH -OF -SERVICEFREQUENCY DISTRIBUTION

25-2.20.8

0 V

0 12 24 36 48 60 72 84 96 108

MONTHS

Figure 3. Cumulative Population Survivor Curve as Developed from aLength-of-Service Frequency Distiibution.

Ii

organization at evenly spaced time intervals such as years. As timepasses, each year group will move from one "length-of-service" timeinterval to the next. When the maximum length-of-service time span haselapsed, an equivalent to the life span of a population, the first groupwill have been diminished to zero. Once this point has been passed, therewill remain within the total population, a stabilized distribution ofpersonnel by length-of-service categories for, as some personnel are lost

from the population they are replaced by others moving in from the nextshorter length-of-service group. The values determined for each sealctedpoint in time may be plotted graphically to form a "survivor curve" forthe population. Figure 4, illustrates a survivor curve envelope for actualdata representing total Navy population for the years 1966 through 1971showing the relative stability of the population in terms of a cumulativelength-of-service frequency distribution. Only the highest and lowestvalues for this period have been plotted.

100

75

Ift-

M 505 f

H 73l

196thog 1971.

a. 252

S" +0 -- ----- --- -• •05 10 15 20 25 30

• LENGTH-OF-SERVICE" YEARS

S~Figure 4. Survivor Curve Envelope for Total Navy Population for Years ,\,• ~1966 through 1971. i

i4

This model of a stationary population approximates very closelythe structure of an existing population where losses at each point in timeare used to generate requirements for replacements. This is generallycrue in the Navy's determination of promotion requirements. This con-cept already exists in Navy planning where the stationary population isreferred to as the "force structure." That application is to total Navypopulation where the numbers are large, but the concept has equal applica-tion to subpopulations represented by various aggregates subject to avariety of management actions such as rotation. The data can be expectedto exhibit somewhat less stability as population size decreases, but longi-tudinal data samples can aid the manager in determining posaible trendsor other fluctuations that must be a•:ticipated. Advance knowledge ofpending policies relating to early discharges, reenlistments, delayed oraccelerated promotions, etc., can be uf considerable aid to the managerin anticipating shifts in foree structure that will affect the shape ofthe "survivor" curve. Similarly, improved personnel retention willproduce an age shift in the population that has important consequencesfor the rotation manager.

Computational Elements

The preceding sections have identified and described the essentialelements of rotation management. These are: (1) the number of "rotationidentified" sea and shore billets, (2) the time dimension represented bytour lengths, (3) the personnel flow rate, (4) the obligated servicerequired for rota;:ion eligibility, and (5) the "survivor curve" for thepopulation being managed. These elements can now be combined in computa-tional reiation-'hips somewhat analagous to an economic model of supplyand demand. The description of the computational elements of the basicrotation model will be followed by a description of a version of the modelwhich permits additional management inputs.

Since rotation occurs between the two gross composites of sea andshore, the model structure will be more readily understandable by fol-lowing the traditional practice of establishing certain fixed parametersfor one composite and absorbing necessary adjustments in the secondcomposite. The more stable element in rotation has long been the shoreassignment, usually accompanied by assurances of a prescribed minimumtour. This practice will be continued for purposes of model description.'Also, for descriptive convenience, billets will be assumed to be manned

at the 100 percent level so that numbers of billets and personnel maybe used interchangeably.

1. The Basic Rotation Model

The personnel flow rate from sea to shore has been established

as identical to the shore vacancy rate resulting from tour completions.Ideally, sea replacements will also be at their tour completions whenrotated. The rate of personnel flow may be regulated by the rotationmanager through adjustments to the tour lengths. Shore tours are pre-

13

scribed by' policy and serve to maintain a fairly high degree of stabilityIi within the shore composite, but sea tours must be determined in relationto the shore vacancy rate, the ratio of sea to shore billets, manninglevel pulicies, and size of the "rotatable" sea population.

Figure 5 is a geometric representation of the model where thehorizontal time scale is graduated in months to serve as the units of timecommon to both sea and shore composites. Supply is equivalent to thenumber of shore billets being vacated in the base composite due to expiringtour lengths, and demand is represented by the number of personnel atsea that are seeking shore billets upon completion of sea tours. In aleft to right time orientation, the rising shore vacancy slope and thedescending survivor curve commence at time "zero months" and intersectat a point determined by the combined rate of convergence. The separaterates are not necessarily identical, typically they will be different,the demand curve exhibiting relatively slow rates of decline ior seniorcareer personnel and rapid rates of decline for lower skill level per-sonnel. A perpendicular dropped from the intersection of the two converg-ing curves will locate an "equilibrium point" representing the length oftime that must elapse before the sixpply of vacated shore billets willequal the demand for shore billets among the sea population. The equalsupply and demand numbers may be derived from the vertical scale at apoint horizontally to the left of the curve intersection. Since bothslopes are cumulative, the measure.• reflect the number of personnel in

each composite that will equal or exceed the tour lengths in terms oflength-of-service. They thus comprise the two rotatable populationssubject to rotation management.

The foregoing illustration assumed a zero service obligatiorn forrotation eligibility which is 6nly applicable to career personnel w•i.hten or more years of active service. For personnel with less than tenyears of service a minimum of 14 months obligation is typically requiredto insure at least 12 months on an assigned duty station. Those rateswith relatively high retention characteristics might be reqaired toobligate themselves for an entire shore tour in order to bf. eligiblefor rotation. This obligated service requirement provides the managerwith an extra device to manage his population to better wr'et rotationrequirements. The applicable generalization relating tn obligatedservice is that the greater the obligated service requirement that i6imposed, the fewer personnel will be available for rctation.

Whatever obligated service factor is sele4;ted by a manager, therotation model can be appropriately adjusted to estimate the resultingequilibrium point. With reference to Figure 5, on,, can ULhuitivelysense the effect of lengthened service requirements by noting the rate

at which the population continues to diminish as time is evrtended beyondthe limits of the sea tour. If eligibility criteria are modified to re-quire longer service, fewer personnel will be available for rotation with

14

-- ' I. .. - .~"° °

DEMAND

ESTIMATEDSUPPLY SEA NON.

75 ROTATABLES

6.3

EQUILIBRIUM POINT

U 52 --- --

LL ~50.70

z'U IMIw ESTIMATED

S 27 SEA------- ROTATABLES

25- ZEROOBLIGATION

0 12 24 36 48 60 72 84 96 108 120MONTHS

PRESCRIBED ISSHORE TOUR

30 MONTHS

INITIAL SEA TOUR•" ~~ESTIMATE "•

58 MONTHS

Figure 5. Billet Supply and Demand Rates as Determinants of the

Equilibrium Tour Length as Applied to Personnel Rotation.

11

!.5

resultant shorter tours. Conversely, if service obligations are short-ened, greater numbers of personnel will be available with resultant longertours.

For the purpose of illustration, assume that the oblieated servicerequirement is set to the length of the shore tour of 30 months. Byviewing the completion of a sea tour followed by a shore tour as a ro-tation cycle, it becomes convenient to consider rotation as a sequence oftours with alternate periods divided between the two composites. By fol-lowing the survivor curve beyond the initial 58 month sea tour for anadditional 30 months, the population can be observed to decrease from 52percent of the start population completing the sea tour to 30 percentcompleting a rotation cycle of 88 months. This procedure, however,fails to establish the equilibrium point for rotation. An adjustment tothe location of the survivor curve is necessary in order to incorporatethe effects of an extended service obligation. In order to get thesurvivor curve to appropriately intersect the shore vacancy slope it isnecessary to "retard" the survivor curve an amount equal to the obligationimposed. This is illustrated in Figure 6 where a set of points on eachside of the shore vacancy slope are transferred "backwards in time" toreflect the effects upon the population of a 30 month extension of time.The new equilibrium point is now seen to occur at 43 months, reducing the' rotation cycle from 88 months to 73 months, some 14 months shorter thanbefore the obligation was applied.

Since the equilibrium point may occur anywhere along the twocurves, the entire survivor curve is "retarded" in the model by movingthe 100 percent point in a negative direction away from the zero pointof the sea tour so that a time measure equal to the entire rotationcycle is bridgcd by the survivor curve. The equilibrium point will nowoccur at a point above the terminal point of the sea tour as shown inFigure 7.

A schematic-conceptual difficulty c'curs here in representingthis effect geometrically. Personnel serving in the rotation cycleusually start out in the seg Lour followed by a shore tour. With timebeing represented directionally from left to right, the obligation mightappear to precede the sea tour. Interpretation requires that the managerrecognize that the sea tour occurs first in this Instance and the neg-ative months shown for obligated service indicate the time that wouldremain for an individual upon reaching the rotation point at the end ofhis s a tour if he were to have rotati.ia eligibility. Once this ar-rangement is accepted, it becomes a simple matter to input whateverobligated service requtrement is desired to determine tht appropriaterotation equilibrii"m point.

16

100-

ESTIMATEDSEA NON.

75- 30 ROTATABLES4-MONTHS

I-

w

-J- Z

0- SHR TOU 30

w,• 52 . . . . ... //o N

" " ESTIMATED0. SEA

5 ROROATATABLES

OBLIGATI•;N

SII

S0 12 24 36 48 60 72 96 108 120

S~43 8

i • ~SHORE TOUR,•3

30 MONTHS e--MONTHS"I

INITIAL SEA TOUR

YESTIMATE58 MONTHS

INITIALS~~ROTA7'ION-"'

CYCLE ,,r88 MONTHS

Figure 6. The Personnel Rotation Model Adjusted to Reflect Effects ofApplying an Obligated Service Requirement to RotationEligibility.

17

100-

75-

Lu

w7

LL 50-

0:4 a.

SEAROTATABLES

00- _ ___ __

-30 -24 .12 0 12 24 36 48 60 72 84 96

SHORE TOUR PRESCRIBED 4o*SERVICE OBLIG.00- SHORE TOUR .•

30 MONTHS 30 MONTHS

ESTIMATEDSEA TOUR43 MONTHS1. - EQUILIBRIUM ROTATION

"�I; CYCLE 73 MONTHS

Figure 7. Personnel Rotation Model Incorporating Provision for ObligatedService as a Rotation Management Variable.

N1II

2. The Biased Rotation Management Model

Rotation management has been presented as a problem of identify-ing the quantifying relevant rotation variables and bringing them togetherin a model that simulates the dynamics of personnel rotation movementsover time. Two duty composites are postulated and billet supply and de-mand rates are derived so as to intersect at a point that representsthe equilibrium condition for the variables specified. The actualongoing condition ic extremely dynamic and the model output may or maynot fit the realities of the situation for very long periods of time.

To aid the manager in dealing with the uncertainties he willencounter, a deliberate bias may be introduced into the model so as toinfluence the direction that certain characteristics of the managedpopulation might take. Careful monitoring of the effects of decisionsbased on this model will serve to inform the manager whether or not thesituation is developing as intended.

Figure 8 illustrates the manner in which the rotation model maybe structured so as to conform to predetermined and desired character-istics of rotation. One set of supply and demand curves are carefullyderived to represent the best estimate of actual conditions. Assumethe average shore tour is set at 30 months and a 30 month serviceobligation applies for rotation eligibility. The equilibrium sea tourfor that population according to Figure 8 is 40 months. The managerdesires to reduce sea tours for this population and decides to do thisby increasing shore vacancy rates by means of shorter shore tours. Heselects 24 months as the optimal shore tour and will require 24 monthsobligated service for rotation eligibility. Now he must study theforce structure of the population and seek a survivor curve for expectedconditions. He is aware that the population has been experiencing lowreenlistment rates and rapid promotion rates, and he foresees littlechange in the next three to four years. Consequently, he expects thefuture survivor curve to drop from five percentage points at earlierand later years of the service and up to ten perce:.tage points belowthe current curve at the four and six year reenlistment points. An ad-justed survivor curve is drawn through the series of lower pointspr:oviding an estimate of the future populatioi. dcpletion rate. Thet-lective of the 24 month shore tour with 24 months obligation will besupported by an equilibrium sea tour of 33 months.

Recognizing this as an estimate and long range goal, the managermay decide to "hedge" a bit and select an intermediate tour for assigningto personnel rotating back to sea. It would be more desirable froma stability point of view to bring about the change in tours gradually.This would give the system a chance to adapt to the implemented changesand permit the manager to evaluate whatever occurs to determine whetheror not the system is moving in the direction he intended.

19

19

Tt is important to note that for many rates 'elatively long timeperiods must elapse before evaluation is possible. These time periodswill more than likely even exceed the rotation manager's own tour sothat, in effect, he escapes the consequences of his decisions. Thisprovides an important justification for employing a model for rotationmanagement as a means of providing a management continuity essential tolong term control of the rotation process.

us

V10

7u

.4

U '

C:F 12 241/ 36 40] 6A 2 84 96 108I

0

0 12 24 36 a 60 72 84 96 too

024 MONTH 0 12 24 36 4 0 7 4 9OBLIGATION -| 4 40 0 7 4 9 0

[•..30 MONTH •"r BLIGATION•

Figure 8. The Biased Rotation Mlanagement Mtodel.

20

Applications

In the preceding section some of the possible applications of the

Equilibrium Flow Model were mentioned. This section provides additionalillustrative examples of how the model might be applied to problems en-countered in rotation management. Each application is presented as a '"problem" with the information needed for its solution also given. Thesolution is illustrated in geometric terms in an accompanying figure. Asalready noted, the Equilibrium Flow Model is computerized and these

applications could be performed by the computer with relative ease. Thegeometric representations of the problems as given here, are intended tofacilitate understanding of the conceptual relationships between thevariables as well as the computations that would be performed by thecomputer.

Five problems have been selected to demonstrate the procedures andversatility of the model. The first problem demonstrates its basic usein determining the equilibrium sea tour for a prescribed shore tour,while the others deal with variations of the basic problem. The prob-lems can be stated as follows:

1. Estimate the length of sea tour necessary toachieve rotation equilibrium for a prescribed shoretour.

2. Estimate the additional number of shore billetsneeded to support a sea tour after it has been reducedfrom 72 to 60 months.

3. Estimate the length of reduced shore tour nec-essary to support a 60 month sea tour after it hasbeen reduced from 72 months.

4. Estimate the length of shore tour necessary tosupport an equilibrium sea tour that is less than apolicy-prescribed minimum 36 months after such seatour has been increased to the prescribed minimum.

5. Estimate the change to the number of shore billetsnecessary to provide equal 36 month sea and shore toursin place of actual 30 month shore and 39 months seatours.

21

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SUMMARY AND CONCLUSIONS

The Equilibrium Flow Model described in this report has been developedfor use by managers of Navy enlisted personnel rotation systems. It isapplicable at all management levels by suitable aggregation of the datafor population being managed. Management levels closest to the functionallevel of personnel assignment can utilize the model to derive equilibriumtour lengths for prescribed conditions existing for the population theycontrol. They may also use the model to test the probable results ofproposed policies such as changes to tour lengths and obligated servicerequirements. It may be used to resolve rotation problems such as esti-mating the changes required to the billet structure to improve rotationfor selected communities.. The model may also serve as a heuristic learn-ing device for training new rotation managers and it may be used tobuttress communications efforts to higher levels regarding rotation problemareas.

Higher levels of management concerned primarily with very broad policydeterminations may utilize the model to pretest a variety of policies aimedat improving the rotation system over a longer time frame than rotationmanagers usually consider. Since rotation management usually operates inan open system environment, top managers must evaluate the effects of out-side influences such as are reflected in the service cut-backs on manpower,conversion to an All Volunteer Force, effects of a zero draft, large scaleship decommissionings and base closures, and marked changes in retentionthat may be expected to result from various proposed and implementedpolicies.

The Equilibrium Flow Model could also be useful as a basis for thedevelopment of a family of computer models of the career enlisted personnelrotation system. These models could be used to support the decision-makingfunctions involved in the management of the rotation process. Somespecific applications might include (1) testing rotation policy and datainputs; (2) planning personnel movements within existing policy and pro-cedural constraints; (3) monitoring those distribution and assignmentactions which are triggered by rotation movements; and (4) evaluating theoverbll operation of the rotation system in terms of specified managementobjectives (e.g., equitable rotation opportunity, unit stability, "fairshare" distribution, career development).

As components of an improved career enlisted rotation system, thesemodels would enable BUPERS rating managers to plan and control the movement,placement, and utilization of enlisted personnel more efficiently and ef-fectively than is now possible under the present system and procedures.In the broad sense, the use of the components of such a system could beexpected to lead to more orderly and equitable personnel movements, moreeffective utilization of skills, greater personnel stability at the unitlevel, and the capability for more personal and meaningful considerations

for the needs, desires, and expectations of the individual enlisted manand woman.

27

REFERENCES

1. Berkson, J., "Life Expectancy", Encyclopedia Britannica, 1969, XIII.

2. Borgen, N. I., Segal, J. A., and Thorpe, R. P., "An Equilibrium FlowModel of the Navy's Enlisted Rotation System", paper presented atthe Twenty-Ninth Military Operations Research Symposium, U. S. AirForce Academy, Colorado Springs, Colorado, June 1972.

3. Borgen, N. I., --I Thorpe, R. P., Further Development and Implementa-tion of the SEAVEY Planning Model, San Diego: U.S. Naval PersonnelResearch Activity, September 1967 (SRR 68-4).

4. Borgen, N. I., and Thorpe, R. P., A Computerized Model of the Sea/Shore Rotation System for Navy Enlisted Personnel, San Diego: NavalPersonnel and Training Research Laboratory, February 1970 (SRR 70-20).

5. Conner, R. D., Thompson, B. E., and May, R. V. Jr., Development ofthe SEAVEY Planning Model, San Diego: U.S. Naval Personnel ResearchActivity, June 1966 (SRR 66-24).

6. Enlisted Transfer Manual (NAVPERS 15909B) Chapters III and VII.

7. Kast, F. E., and Rosenzweig, J. E., Organization and Management: ASystems Approach, New York: McGraw - Hill Book Company, 1970,pp. 125 - 127.

8. Kaufmann, A., Methods and Models of Operations Research, EnglewoodCliffs: P_-entice Hall, Inc., 1963, pp. 204 - 208.

9. Report of the Secretary of the Navy's Task Force on Navy/Marine CorpsPersonnel Retention, Department of the Navy, Washington, D. C., 25January 1966, Volume V (FOR OFFICIAL USE ONLY).

10. Sasieni, M., Operations Research - Methods and Problems, New York:John Wiley and Sons, 1959, pp. 112 -117.

11. Sorenson, R. C., Logical Model Repre -ina Personnel Flow in theU.S. Army: Considerations Relative Lu Reduction of Turbulence,Washington, D. C.: U.S. Army Personnel Research Office, July 1965(Technical Note 156).

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