Alan L Patz.

Manpower flow problems and goal programming solutions online

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LIBRARY

OF THE

MASSACHUSETTS INSTITUTE
OF TECHNOLOGY



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WORKING PAPER
ALFRED P. SLOAN SCHOOL OF MANAGEMENT



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MANPOWER FLOW PROBLEMS
AND GOAL PROGRAMMING SOLUTIONS



Alan L. Patz



MASS. !NST. T£Cli,
FEB 3 1969

DLWEY LIEi!ARY



MASSACHUSETTS

INSTITUTE OF TECHNOLOGY

50 MEMORIAL DRIVE

MDGE. MASSACHUSETTi



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MANPOWER FLOW PROBLEMS
AND GOAL PROGRAMMING SOLUTIONS



Alan L. Patz



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1969


i DuVVl'j


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366-69
Not to be reproduced in whole or in part without author's permission,






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MANPOWER FLOV/ PROBLEMS AND GOAL PROGRAMMING SOLUTIONS



2
Introduction and Purpose



General

A thoroughly familiar homily is that human resources are the most
valuable and most difficult to manage assets of any organization. The
implication is usually that the v7ords "resources" and "assets" tend to
camouflage the moral, ethical and political issues which impinge upon
manpower and personnel problems and that any manager who ignores these
issues can expect extremely hazardous consequences. Therefore, any attempt
to manage human resources must be based upon a sound understanding of the
structural, policy and behavioral variables of the organization being
considered .

Structural variables . — Human resources are managed, or reacted to,
within some sort of formal organizational structure, and this structure is

important because it represents the boundary conditions or limits within

4
which this management or reaction occurs. Examples of boundary conditions



1. The model presented in this paper is the result of a manpovjer
planning study conducted in the Personnel Studies Division, Directorate of
Personnel Studies and Research, Office of the Deputy Chief of Staff for
Personnel, Department of the Army. The officers, enlisted men and civilians
who, in one way or another, contributed to this paper are gratefully
acknowledged.

2. ttoson llaire discusses many of the issues related to personnel
flow problems in his article "Approach to an Integrated Personnel Policy,"
Industrial Relations , VII (February, 1968), 107-117.

3. See Marcus Alexis and Charles Z. Wilson, Organizational Decision
Making (Englewood Cliffs, N. J.: Prentice-Hall, 1967), pp. 3-13.

4. This statement may at first appear to be tautological. However,
it is simply a statement of the typical interactive types of phenomena that
one encounters when studying human behavior. In other words, managers
affect structure as well as being affected by it.



fi»y8821



are the total number of people in the or[»anizat:Lon, the classifications

applicable to this total, number, and the constraints applicable to each

classification. Structural constraints are often the result of experience,

intuition and judcuicnt, but often the lad; of such constraints may be

the most difficult management problem. Suppose, for example, that a

manager's experience and jud;;ment indicate that he should have M types of

people and that the size of each group should be IL through N respectively,

One of his problems then is to attain N, through K, individuals for each

1 M

of the types; but, more than this, he must also maintain this structure
over time.

Policy variables . - Tlie maintenance of a structure over time,
however, requires that some attention be paid to procuring, training,
selecting, promoting, retiring and, in total, sustaining the people who
comprise this structure. Pay, fringe benefits and incentive problems
become significant and, in general, the manager is faced x^;ith personnel
policy problems. That the manager is faced with policy problems is simply
another way of saying tliat he is faced with the problem of setting
organizational goals or objectives. ile must someliow come to grips with
problems like how many people to procure from each of several sources;
when to protiiote people; hov; many people are to be promoted; what sort of
variances from his "ideal" structure can be tolerated; and how many
people must he retain in each of his personnel categories in order to
maintain a relatively smooth flov; of people into, through and out of his
organization. Purtherraore, he must solve the structural and policy
problems in a fashion that induces the required behavior from the



1. See Pvichard W. Cyert and Janes G. March, A Behavioral Th.eory
of the Fir..i (Englevrood Cliffs, N. J.: Prentice-Hall, 1963), pp. 27-36



participants in his organization, if ii'iis sor^ of solution is not
possible, the manager v;ould at least like to know what sort of behavior
is required. The required behaviors then become management goals also,
i.e., conditions that must be attained and maintained if anything
resembling a smooth flow of people is to be achieved.

Behavioral variables . - Two of the problems mentioned in the
preceding paragraph - procurement and retention - are easily classified as
behavioral variables. In order to survive, an organization must be able
to induce the initial and continued participation of potential and current
organizational members. This requires "joining" and "staying" behavior
on the part of the participants, and such behavior is obviously influenced
by structural and policy variables. Any organization ttiat fails to
provide the necessary inducement - because of structural and policy
problems — will, at best, experience high turnover rates and general
personnel flow turbulence. This, in turn, leads to serious cost and
effectiveness problems. Cost and effectiveness may not be as easily
measured as turnover and turbulence at any point (or interval) in time,
but the longer run effects will be all too obvious.

Procurement and retention are only a small subset of the relevant
beliavioral variables. Aspirations and expectations, for example,

are significantly affected by structural and policy considerations, and

2
they, in turn, affect participation and performance. Interpersonal



1. James G. I'larch and Herbert A. Gimon, Organizations (New York:
Wiley, 195C), pp. G3-111.

2. Mathematical formulation of aspiration level theory can be
found in the author's Ph.D. dissertation "Aspirations, External Goals and
Performance" (unpublished Ph.D. dissertation. Graduate School of Industrial
Administration, Carnegie Institute of Technology, 1S67), pp.6-42, and in
Andrew C. Stedry's book Dudgct Control and Cost Dehavior (Englewood Cliffs,
N. J.: Prentice-Hall, 13G0), op. 17-42.



relationships cannot be ignored, and the list could be extended indefinitely,
But, the list need not be so extended in order to note that structural,
policy and behavioral variables are intimately related and that the problems
associated v\7ith personnel flows are in many v^ays no different frora any
other organizational problem. The study of human behavior in organizations
simply has many paths covered with the same concepts, relationships and
pitfalls .
Purpose

The purpose of this paper, then, is twofold. First, a method of
solving for the conditions necessary to attain and maintain a steady state
personnel flovj through an admittedly highly structured but not highly
unusual organization v;ill be presented. This method will be shown to
have the desirable characteristic of being able to simultaneously consider
a large number of management goals and some of the structural, policy
and behavioral variables related to these goals. And, second, it will
be shovjn that analyses of the type to be presented are extremely useful
in that:

1. They focus attention on critical organizational problems.

2. They are constructively self-destructive in that they highlight
their ovm shortcomings and point the \;ay to more satisfactory solutions.

3. Tliey provide a means for integrating personnel policy problems.



1. Uaire, loc. cit.



Basic Structural Considerations

Initial assumptions and considerations

Suppose that a decision has been made to have M levels (grades,

ranks or types) or individuals in a given organization and that the

normal or expected carrer of each individual is Y periods. (A period

may be a year, six-months, a quarter or any other similar definition.)

Denote the levels as K, through IC, respectively and provide an ordering

such that K, is a lower level than K„ , K„ is a lovjer level than K and

so on until K^ ■> is a lo\



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where 0.0 < p. . , < 1.0, is associated with each cell in Figure 2 that
is indicated to be a promotion point. At this point, however, the next
obvious step is to consider ways of associating a specific promotion
rate with each promotion point. One might, for example, conceive of
flovj tiiodels that maximize proraotion rates subject to various flow
conditions and structural constraints or models that limit promotion
rates to different ranges for different levels in the organization
subject to a similar set of constraints^ But one of the striking
observations that can be made in many organizations is that personnel
managers have fairly definite ideas about promotion points and promotion
rates and feel that these two problems should be considered as policy
matters and not as flow optimization dimensions. The arguments raised
in support of this position can be very convincing and tend to force
one to the conclusion that promotion points and promotion rates should
be one of the most flexible aspects of a personnel flow model. In this
w.iy, various promotion point and proiaotion rate policies can be tested
for their effects on the flovj of people into, through and out of a
particular structure. The manager can then decide v^hich policy set to
choose based upon some compromise between flow consequences and his
experience and judgment concerning the effects that promotion rates have



1^ The term "personnel managers" is used here in the general
sense and refers to individuals responsible for formulating and/or
executing various implicit and explicit personnel policies.



14



on turnover and procurement problems. Uigli proiiotion rates, for example

niay tend to Iceep people in an orj^anization and solve various recr'jiting

problems; low promotion rates may have the opposite efTect. But the

choice of a mechanism for determining promotion point and promotion rate

policies must ultimately be determined on tlie basis of how these policies

interact with various structural and behavioral variables.

Tlie selection of appropriate promotion rates becomes even more

difficult because of the f^roup splitting at promotioa points. Referring

again to Figure 2, it is noted that only one group is present at each of

the level one promotion points but that tvjo groups are present at each

of the level two promotion points. Tliree groups Xi7ill be present at each

of the level three promotion points, and this progression will be

amplified depending upon the number of levels and the number of promotion

points per level. Thus, a qualitative question arises which focuses on

the "liow to promote" problem as 'vjell as the "how many to promote" or the

promotion rate problem. Should the groups who reach the promotion points

vjith fevjer career periods have higher promotion rates than the groups

vjith more career periods at the same promotion point? In Figure 2, for

example, should the promotion rate applied to group X^ „ be higher

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than the one for group X^ j. „? If this were the case and if it is

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assumed that the "best" people are alvviays promoted first, the effect of

such a promotion policy V70uld be to advance the best people faster than
anyone else. And, indeed, an implied policy to advance the best people
faster than anyone else would seem to embody one of the standard values
shared among most personnel managers.

An additional variable and an example . - Suppose that at some



15



higher organizational level, say k, that there are eleven groups of
people, group A through group K. The eleven groups have resulted
from earlier group splitting and group forming at the promotion points
\;ith the result that some groups have been promoted to level k much
earlier in their careers than other groups. Furthermore, suppose that
there are three promotion points at level k for promotion to level k+1 .
This situation is diagrammed in Figure 3. The career periods have been
arbitrarily designated to by y, through y.,,> and the level periods
have been simply listed as 1, 2, 3 and 4. Level period 2 would be the
early promotion point, level period 3 the normal, and level period
4 the late promotion point « Finally, suppose that the middle group,
group F, is the "normal group." A normal group is one composed of some
individuals who have alu-ays received normal promotions and others who
have received some coiiibination of early, normal and late promotions
such that the end result is equivalent to that of all normal promotions,

Nov;, at the end of level period 1, group F is of size F^ .
At the end of level period 2 - and prior to the promotions to level
k+1 — this group is of size F„ . Similarly, at the end of the subsequent
periods and prior to the promotions in these periods, the group is of
sizes F., and F. . One fairly reasonable assumption is that F >F^F„>F^^
and that the losses from one period to the next can be separated into
tvjo categories:

1. Losses due to people voluntarily leaving the organization
for other organizations - retention losses.



1. The change in notation has been used in this example only for
purposes of simplicity.



16



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Online LibraryAlan L PatzManpower flow problems and goal programming solutions → online text (page 1 of 3)