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EXTENDED PLANNING IN THE NAVY AND THE
RESOURCE DYNAMICS PROJECT
Rolf Clark
Samuel B. Graves
Kathleen Sheehan
‘The George Washington University
ABSTRACT
The U.S. Navy's need for better long-range planning is
discussed in light of recent dynamic increases to force plans.
The difficulties embedded in the current planning and program-
ming process, and the problems they cause in developing valid
approaches are reviewed. ‘The ongoing "Navy Resource Dynamics"
project at The George Washington University is then presented
as a means of overcoming the difficulties, and providing a
timely planning model. The basis of the model is a lagged feed-
back analysis linking budget "flows" over time to weapon system
asset "stocks." The trade-off between naval force levels and
the cost of owning the forces is emphasized with force readiness
being a relevant measure.
Introduction
Naval long-range planning and its role in the planning,
programming, budgeting process (PPBS) will be discussed in three
sections. First, its relevance is explored; second, its diffi-~
culties and requirements are outlined. Third, an existing,
developing approach toward extended planning is discussed. A
summary of the views presented is that upcoming fiscal dynamics
make better planning essential, and that the inevitable difficul-
ties can be overcome to a large degree by the method proposed.
The military resource allocation process is inherently a complex
closed system--with feedbacks rife from initial fiscal formula-
tion right through the "end game" where final changes are made-~
but these feedbacks have been largely ignored because the PPBS
process has been treated as a simple open system without ade~
quate feedbacks. The approach discussed is a dynamic method
allowing for the feedback implications.
Is Extended Planning Necessary?
In a truly stable world, there is no overriding need for
long-range planning. Fiscal targets and resource allocations,
if either unchanging or changing in a "steady state” manner, can
be tracked and predicted using thumb rules easily understood and
implemented by the human-mind. Under stable growth, the Navy
budgets for aircraft spare parts, for example, may be safely
assumed to require some 25 percent of the new aircraft procure~
ment budget, which in turn is about 30 percent of total procure-
ment, which averages 40 percent of the total budget.
If such conditions remain the same year after year their
xesource allocation dynamics are relatively uneventful. There
are no severe lagged effects to imbalance the trends. But,
suppose that procurement lags (between budgeting for units and
their delivery) are four to six years, while for ownership--
maintenance, operating, manning--the lags are less than a year.
Then a major increase in force levels has lagged effects on
resource allocation trends. For ownership costs will not need
to rise until the four to six years when the newly procured units
join the active forces. As the fleet units do arrive, the lagged
but accelerated growth in requirements for ownership funds will
occur. That could coincide with efforts to reduce defense after
a long (four year) growth period--about the average time an
administration lasts. Reductions in overall defense spending
just as ownership needs accelerate will mean severe reductions
in procurements, for ownership funds are difficult to deny once
the systems and manpower are in place. A dynamic fiscal roller
coaster evolves.
Extended planning clearly takes on importance when fiscal
trends are dynamic...and actual defense spending plans call for
such dynamics. Consider Figure 1, The historical balance
between procurement and ownership is not to continue. The admin-
istration's planned real growth in defense budgets is unprece-
dented in recent peacetime planning, and dynamics are inevitable.
0.2 ACTUAL ESTIMATED
0.1
0.0
1968 ©1970 1975 1980 1985 1990
Figure 1. Funding Dynamics, U.S. Navy:
Procurement + Non-procurement
(3 Yr Moving Ave)
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It is hypothesized that the current PPBS process does not
provide a realistic projection of the long-range planning period.
For perspective, even when planned budget growth from 1972 to
1981 was relatively stable, procurement budgets projected one
year beyond the immediate budget year were revised downward by
about 15 percent when they became the actual budget one year
later. Ownership budgets, on. the other hand, were revised up-
ward about five percent. Clearly, the procurement versus owner-
ship planning process, even under stable budget growth, could
stand improvement.
But, even when total budgets remain constant and procure-
ments retain stable fractions of the total, policymakers may
want to consider major changes in force mix-~for example to an
all Vertical/short Take-off Landing (VSTOL) tactical air force,
or to smaller ships, or to a nuclear Navy, to a draft augmented
manpower force, etc. Or economic explorations may be necessary--
what if compensation growth must exceed inflation? what if GNP
growth is’ less than planned? What if the inflation norm exceeds
expectations? What if cost estimates are optimistic? What if
defense industries lose efficiency?
Such questions have dynamic implications through the
resource allocation structure. shifting to a VSTOL fleet
causes increases in aircraft maintenance and fuel costs. These
increased maintenance and fuel costs detract, if budgets are
constrained, from procurement funds. Also, the smaller aircraft
carriers required mean more carriers could, over time, be
accumulated, but smaller ships are less fuel efficient and less
manpower efficient (on a per ton basis) so associated fuel and
manpower budgets need to rise accordingly. On the other hand,
the increased manpower intensity at sea means that savings in
manpower ashore can occur as more maintenance can be done under-
way. Such dynamics do not lend themselves well to "thumb rules."
Under conditions where overall force growth is anticipated
and force mix changes are to be explored, not only must the
dynamics be captured, but methods to rapidly alter the dynamics
are essential. ‘he current system cannot provide that capabil-
ity. A system that responds automatically in all necessary
dimensions is needed...one that is constructed to increase the
budgets for leasing commercial logistic ships, say, when the
ratio of Navy combatant to Navy support ships becomes too high,
and that automatically increases the mean skill levels of man-
power when units become more complex, and that alters mainte-
nance needs if fleet age changes due to altered procurement
amounts, etc, Such dynamics can either be reviewed in detail
when each policy alternative is considered, or they can be
built into a (computerized) model that can be used almost
instantaneously as the inputs are changed. The latter obviously
has practical appeal.
Some planning factors are more than simply complex. Polit-
ical factors, and simple human biases, can have major imbalancing
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6
impacts. For example, political determination that the economy
will improve faster than is reasonable can lead to underestima-
tion of inflation, which can cause the real funding available to
be far less than that planned. Or, the natural optimism of
project managers may result in underestimating the planned
costs (procurement or ownership) of their systems. On the
other hand, several years of. underestimation of costs and
inflation can cause cost estimators to bias their estimates
upward, sometimes to the point where they exceed logical
expectations.
Given such complexities, and such potentials for bias,
the answer to the question "is extended planning necessary?"
must be a strong affirmative.
Problems and Difficulties in Planning
The current PPBS entails, in essence, obtaining information
on hundreds of program elements and their associated costs, add-
ing them together, and then "adjusting" the sum to fit fiscal
limits. That, in itself, is a huge task, involving hundreds
of people from project offices, from resource sponsors, from
budget and analysis shops, from computer centers, etc. The
inputs to such a process are filtered through numerous briefings
and presentations in the management chain. The information has
been influenced by biases, by errors, and by political factors.
pata are misinterpreted through misunderstandings of, for
example, how inflation was used or was supposed to be used.
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Cost factors can be based on the wrong learning curves, or be
calculated in the wrong year's dollars. The hundreds of tele-
phone calls between the various echelons of the managerial chain,
from the secretariats, through the service chiefs' staffs, to the
material commands are not all consistent. The resulting costs,
the quantity projections, the escalation funding needed, can be
in error, or misunderstood, or both.
This data gathering process is not a one-time event even
for a given year. Changes to guidance and to programs occur
even before information requested on previous guidance is
received. Data, when received, may be based on different guid—
ance than that now assumed by the requestor.
Perhaps most significantly for present purposes, however,
is that as these myriad details come together in the PPBS pro-
cess, the budgets and plans they form run up against the annual
budget submission deadline. In a matter of a few days near the
end of the programming cycle, the resulting program must be made
to fit within fiscal limits, and also to satisfy, as much as
possible, the requirements of the sponsors who participate in
the final reviewing process. At this point (the “end game"),
large changes to cumulative appropriation categories and program
allocations may be made. Such changes impact the assumptions
underlying the detailed "gathering" process, which means the
costs and budgets provided lose validity. But there is scarcely
time to do another iteration of the hundreds of phone calls,
briefings, and compilations required to obtain valid inputs...
and far more than one iteration would be required. So, the
changes are made at an aggregate level, using intuitive logic,
and seat-of-the-pants policy. Subsequently, as budget and plans
become reality, the acquisition and support processes must adjust
to the unrealistic plans. Program cutbacks and stretch-outs
occur, and the mismanagement label is once again reinforced by
critics of defense.
The adjustments made to force the total budget authoriza-
tions to fit into fiscal constraints are impacted from another
direction--expenditures. Economic pressures to reduce or control
government spending are usually concentrated on the short term.
This means procurement accounts are impacted differently from
ownership accounts. Budget authorizations for ships and air-
craft, say, are expended only as systems are built. This means
authorized budgets for procurement are outlayed (expended) over
several years; less than five percent of the authorization for
a new aircraft carrier is actually spent in the budget year,
the rest over an eight-year period beyond. But the budget
authorizations for operating and maintenance are almost entirely
expended in the first and second years of the plan. The process
of reducing the planned authorizations of next year's budget,
when combined with the politically important goal of reducing
near term outlays (expenditures) therefore means the operating
and maintenance plans are the ones most likely to be cut. Plan-
ning imbalance will result unless such effects are anticipated.
The combined unlikelihood of 1) obtaining the correct
inputs in the gathering process, 2) obtaining those inputs
without the biases of the information providers and without
the biases of those providing the guidance, and 3) avoiding
end game changes that would alter the inputs if the necessary
feedback effects were reflected, lead to suggesting the PPBS
process be at least supplemented by another system.
An "analytic" planning approach is proposed. Vital
information embedded in the detailed planning inputs must be
translated into analytic models more easily used in conducting
the necessary explorations required by policy analysts. The
necessary compilation of data and statistical relationships,
and the production of useful output, must rely on efficient,
modern computing capabilities.
The System Dynamics Approach
Fortunately, system dynamics provides a well-established
framework which can be applied toward policy analyses in military
long-range planning.’ At The George Washington University a
system dynamics approach is applied to the U.S. Navy's resource
allocation problem, - The project is callea Navy Resource Dynamics
(NAVRESDYN) «
treferences [1] and [2] are descriptive for those
not familiar with system dynamics.
401
10
NAVRESDYN is a computer-based analytic model, which inter~
relates important variables through parametric relationships.
The model is truly dynamic, meaning that the feedbacks are such
that not only are the model parameters time dependent, but the
parameters change as the policy variables themselves change.
Thus, the maintenance parameters, for example, change as the
fleet age changes, and fleet’ age is affected by maintenance as
well.
In the current NAVRESDYN model, allocation must be made,
in the broadest sense, between acquisition and ownership. Owner-
ship involves operating and supporting the Navy's weapon assets.
Yet the cost of ownership of Navy systems cannot be treated
independently of the cost of acquisition, of naval readiness,
or of operating/maintenance/manning policies. All these aspects
must be included in the planning trade-offs.
The NAVRESDYN approach involves determining a historic
relationship between overall Navy ownership budgets (or fund
flows) and the stock of weapon assets in the inventory demanding
those flows. These historical relationships can help predict
future ownership needs, and this can be accomplished indepen-
dently of detailed project-by-project summation.
Any budget plan can be separated into two major catego-
ries--funds that are committed and those not committed. Broadly
defined, committed resources are those required to "own"
i
existing forces--personnel compensation, fleet maintenance,
fuel costs, are examples. To estimate the committed resources
in future budgets, one must understand the relationships
between the committed portions of the budget and the force
levels requiring the commitments. ‘his starting point can be
defined as "determining the cost of ownership," as it acknowl-
edges the need to operate and maintain existing systems at some
reasonable level of readiness. Determining and predicting such
ownership cost is not a trivial task. It requires developing
an understanding for the total Navy resource allocation process,
including the effects of changes in assets, support of those
assets and the resulting readiness, operating, maintenance, and
manpower policies and their impact on costs and readiness.
The basic premises for the Resource Dynamics approach are
1) that funding available over the planning horizon must be
allocated toward’ research and development (R&D), toward procure
ment, or toward ownership; 2) that accumulated assets determine
required ownership costs; 3) that required ownership costs can
be influenced through R&D funded designed improvements, (e.g.,
decreased failure rates, increased fuel efficiencies); 4) that
new acquisitions depend on the residual annual fundings remaining
after necessary ownership costs are funded; and 5) that force
readiness deteriorates if required ownership costs are not fully
funded.
Stated another way (and referring to Figure 2) quantity
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and quality of asset stocks determine ownership fund flow
requirements, Quantity depends largely on buys and on retire-
ments, while quality can be influenced by R&D expenditures.
Given fiscal constraints, ownership costs (plus research and
development) when deducted from the fiscal level provided,
determine the procurement residuals that can augment the asset
stocks. Procurements, as they accumulate, lead to asset levels
which determine ownership requirements, which in turn lead to
future procurements, given future fiscal constraints. This
circularity can be broken in one of two ways: 1) more funding
is provided so that both acquisition and support can increase,
or 2) support can be under~funded so that acquisition can
accelerate--but this latter leads to reduced readiness of the
required forces, to larger force levels, and, therefore,
greater ownership requirements downstream. The circularity is
illustrated in the diagram.
Counterintuitive results often occur when such feedbacks
are properly modeled. Attempts to increase the fleet size by
allocating more procurement funds toward buying smaller units
can backfire. The reduced efficiencies and shorter life spans
of smaller units can lead to more rapid turnover and large
delayed needs for fuel and manpower. Consequently, Policy- +
makers benefit in two ways when the entire feedback structure
is developed. First, they are forced to make explicit the
assumptions made. Second, they can see the impacts of changes
to those assumptions.
13
INACTIVATION >) MTBF...
VE
ASSETS
(STOCK)
OWNERSHIP FUNDS
REQUIRED
—____ cumuarive
MAINT/UNIT
OVHL/UNIT
CHARACTERISTICS
MPR/TON
——— cum
#
z
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ss Ben / 3
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38 gf Fe!
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MAINTAINING
POLICIES:
MANNING, OPERATING
SHORTFALL
READINESS
CAPABILITY Cc
Simplified Resource Dynamics Structure
Figure 2.
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14
The "stocks-flows" logic embedded in Figure 2 is funda-
mental to the study of systems, and the Navy's resource alloca-
tion system is no exception. The figure shows one (annual)
iteration.which can be described through a system of (differ-
ence) equations wherein the system states, controls, and out-
puts at one point in time (t), are dependent only on 1) its
states one time period earlier (t-1), 2) the controls (budgets)
applied between the two time points, 3) the parameters (or
constraints) of the system. In the figure the "states" of the
system are the asset stock and the cumulated ownership shortfall;
the "controls" are the inactivation rate and the budget flows
(which evolve from the operating/maintenance/manning policies) ;
the "parameters" are the force characteristics plus all the
constants used in the relationships between variables (for each
arrow in the figure can represent several relationships which
must be derived statistically). The "force characteristics”
are determined by numerous ownership costs, such as maintenance
costs per unit, manpower requirements per ton, fuel use per ton
per hour, overhaul costs per unit, etc., most of which can be
affected through proper design improvements, meaning increased
R&D expenditures. Finally, the "outputs" shown are the number
of ships, and the readiness decay measure, though any variable
can be printed as an “output"--certainly budgets flows are all
candidates.
The model is, in essence, the set of difference equations
representing a single time period, and the computer then iterates
15
the model through as many time periods as required, calculating
the value of all states, controls, parameters and outputs at
the first time point, then the second, etc., until the entire
time horizon is "simulated."
Of course, Figure 2 gives an oversimplified look at the
model. For example, "Assets" are, even in’ the simplest form
of NAVRESDYN, split into ships and aircraft assets, and each of
those is disaggregated by age category--30-year old ships, 29-
year old, etc, The "ownership" flow shown is made up of ship
maintenance, ship operations, ship manpower, and ten or so
miscellaneous accounts--similarly for aircraft.
A note on the "readiness" direction of the research is
appropriate. Readiness measures are considered in the form of
readiness "indicators"--overhaul backlogs, spare parts short-
falls, manpower skill and quantity factors, steaming hours per
ship etc. Policymakers involved in budget allocations can
influence success in combat basically through control of
resources affecting such indicators. A task group commander
must ultimately ensure his forces are "ready" in the more
traditional sense of operation or unit readiness, but he will
have an easier time if policy level resource sponsors have :
provided adequate levels of spares, training time, manpower,
maintenance, etc., to the task group in the first place. The
hypothesis is that the fleet will have higher material readiness,
personnel readiness, mission readiness, operational readiness,
16
and less casualties, if resource allocators have monitored the
“readiness indicators," and allocated intelligently toward those
areas they can affect. Of course such allocations detract from
procurement funds, and numerous trade-offs between force levels,
and force readiness, can be explored by policymakers if the
proper planning tools exist.
Having a model incorporating such considerations, one can
execute a program using base case assumptions. Figure 3 pro~
vides a comparison of two modes: a fiscally constrained mode
as has been described, and a “force level" mode wherein the
types of ships and aircraft to be acquired are specified without
fiscal constraints. The fiscal case determines how many ships
and aircraft can be procured within prescribed budgets after
first paying the ownership costs, while the force level case
determines how much it will cost to buy and own the units
planned.
Given a base case, one can conduct various "what if"
exercises. These come in various categories, for example,
budget changes, price inflation changes, changes to ship and
aircraft characteristics, changes to production efficiencies,
changes in the force mix.
By way of demonstration, Figure 4 provides a hypothetical
fiscally constrained case in graphical form. The base case
shows ship, aircraft, fleet value (ships and aircraft valued
405
a
BIL 83$ Ee
150
100
50 po
1984 85 86 87 88 89 90 91 92 93 94 95 96 97 YEAR
‘MODE YEAR BUDGET SHIPS ACF MANPOWER
FORCE LEVEL 1984 $698 548 6070 551 (THOU)
1989 110 560 7100 586
1993 143 550 7700 620
1998 171 580 7850 719
FISCAL CONSTRAINT 1984 73 548 6070 551
1989 96 568 4600 530
1993 100 548 5400 580
1998 105 537 5500 616
Figure 3. Force Level vs. Fiscal Constraint Modes
‘MPR(000's)
300 + “s- ACET (X10)
200 re: Value (BIL $)
100 F
7990 2000 2010 2020 © YEAR
Figure 4, Ships, Aircraft, Manpower, and Asset Value,
Base Case
18
at cost) and required manpower projections, under a fiscally
constrained case. In this run, future ship and aircraft unit
costs have been assumed to grow at historic rates (five to seven
percent) and the Navy budget grows, in constant dollars, by
seven percent per year for five years, then by one percent for
the remainder of the planning horizon. Several factors are
noteworthy. First, both ship and aircraft unit levels lag the
budget growth. This is consistent with the lag in deliveries
of aircraft (two-three years) and ships (three-eight years)
beyond the budget year. Second, with ship and aircraft procure-
ment costs growing at five percent to seven percent and budgets
eventually growing only 1.0 percent, units must eventually
decline. Note, however, that value continues to rise, as each
unit is far more "valuable" than the unit being replaced and
real budgets do grow. Third, aircraft units, lasting only 15
years or so, decline sooner than ships, which last 30 years.
Fourth, the lag between budget growth decline and unit count
decline is longer than the normal budget-to-delivery lag. This
is because within the model, attempts to avoid fleet decline
in- numbers feeds back as a policy to retain units beyond their
normal service life..,but that ages the fleet and eventually
leads to higher maintenance costs and accelerated declines
later. Fifth, note that manpower continues to increase beyond
the decline in fleet units, because fleet value continues to
grow. Finally, the eventual manpower decline occurs because
of manpower efficiencies associated with the more costly, but
more automated units, and also because the increasing value of
19
the fleet causes more of the budget to go toward ownership
accounts, so fleet asset growth is slowed.
With this base case for reference, other excursions can
be explored. Figure 5 asks "what if budgets grow one percent
less, each year, than planned."
1990 2000 2010 20200 YEAR
Figure 5. Ship Reductions Associated with Budgets
1% Less than Planned
Figure 6 shows the "what if the force mix is changed"
example, where a total shift to a VSTOL (Vertical/Short Take
Off Landing) tactical aircraft force is programmed. This case
is interesting, for the VSTOL force allows smaller aircraft
carriers, presumed to save money and therefore increase fleet
406
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numbers. A counterintuitive decline in numbers occurs, however,
for several reasons. First, VSTOL aircraft cost more per unit
for equivalent capability, have higher attrition rates, and
shorter service life. Second, their maintenance costs (compare
the “aircraft maintenance" budgets) are considerably higher.
Third, the smaller ships are less manpower and fuel efficient
on a per ton basis, consequently proportionately more money is
required for ownership. Further, VSTOL capable ships other
than aircraft carriers are more expensive than their non-VSTOL
capable predecessors. These types of results, natural in feed-
back models, are unlikely to be incorporated in a static (open
system) approach to planning.
BASE CASE VSTOL CASE
SHIPS: 600 550
AIRCRAFT: 5900 5500
MANPOWER: 720,000 680,000
OWNERSHIP BUDGET: $ 36.78 $ 38.58
$ 4.08 $ 3.98
$ 4.1B $ 4.28
ACFT MAINTENANCE: $ 4.03 $ 5.73
VALUE OF SHIPS: $ 2448 $ 2438
VALUE OF ACFT: $ 65B $ 60.38
AGE OF AVE SHI 12.2 YRS 12.5 YRS
AGE OF AVE ACF" 9.2 YRS 9.5 YRS
AVE UNIT VALUE, SHIPS: $ 410M 450M
AVE UNIT VALUE, ACFT: $ 16.0M 15.8M
Figure 6. VSTOL Case
Statistical Analyses Supporting the Model
Model outputs are of course largely dependent on the
accuracy of model parameters and the functional forms relating
the variables. Of the numerous statistical explorations
407
al
conducted to date, only a handful of examples are mentioned
here. Typically, a crude statistical analysis is performed
to obtain model relationships, and, after testing the model to
the sensitivity of the relevant parameters, more detailed
statistical studies are conducted on the most sensitive para-
meters. This allows developing the model without delaying
until all detailed statistical analyses are performed, and also
makes the statistical analysis plan more efficient by stressing
the most sensitive parameters for exploration first.
In the area of fleet units and their characteristics,
analyses on trends in size, in cost per ton, on trends in asset
levels, on crew requirements per dollar of asset value, on
generating capacity per unit, on propulsion power, and in
carrying capacity per ton have been conducted. As examples,
over the past 20 years ships have grown about three percent
per year in size and 2.7 percent in cost per ton (constant
dollars). Aircraft unit costs have grown about seven percent
per year. Ship cost per ton has approximately matched the
growth in generating capacity per ton. Afloat manpower per
dollar: of asset value has declined some three percent per year
and, if one inspects budget trends, this has resulted in lower
fractions going toward military pay--from 23 percent in 1972
to only 14 percent in 1982--quite contrary to popular opinion
that military manpower costs are growing too fast.
22
An analysis of the last 1250 ships built shows some 25
percent of the units receive major conversions, and when con-
verted, some 50 percent of their initial value must be added
to accomplish the conversion, Such data is incorporated into
the model to allow adjusting fleet age (units are renovated
when converted) and also to allow changing manpower and com-
plexity factors.
The ownership costs associated with the fleet units have
been analyzed. Aircraft maintenance costs are about five per-
cent of aircraft asset value overall but must be disaggregated
into fixed wing, VSTOL, and rotary wing. Aircraft maintenance
varies only slightly with the age of the aircraft series,
largely because the aircraft modernization program keeps air-
craft fairly near their new condition. Aircraft operating
costs are determined as functions of aircraft weight and
thrust/weight ratios. Ship maintenance is determined to
require, overall, about four percent of ship value and, of
course, varies from type to type. Ship fuel costs are deter-
mined to rise with horsepower, tonnage, and generating capacity,
but a ten percent increase in each leads to only three percent,
two percent, and one percent increases in fuel. Aircraft fuel
use analysis required splitting aircraft into three categories.
Manpower costs ashore are inversely related to those at sea,
with, 20 percent elasticity--meaning each 1000-man reduction
at sea has been offset by a 200-man increase ashore, still a
saving, however.
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Conclusion
The statistical analyses, when combined with the logic
of stocks and flows in a feedback system model, provides one
means of at least partly overcoming the political realistics
and budget complexities of the PPBS process. A Resource
Dynamics approach, with historical knowledge built into a
computer model, allows making realistic projections of either
the costs of a desired fleet, or projections of a likely fleet,
given resource constraints. Rapid "what if" excursions around
the resulting base cases make realistic "policy analysis"
feasible, within available time frames and without involving
too many people--a fact which makes it politically possible to
explore even some sensitive options. Model disaggregation
allows more accuracy and the incorporation of readiness decay
as functions of shortfalls in manpower, maintenance, and
operations funding, allows making policy trade-off between
procurement and readiness. The modern computer, combined with
statistical facts and managerial knowledge, thus, has allowed
developing a naval policy tool within the System Dynamics
framework.
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SELECTED REFERENCES
[1] Forrester, J. W. (1964). Common foundation underlying
engineering and management, IEEE Spectrum 1,
No. 9, pp. 66-67.
12] Richardson, G. P., and A. L. Pugh, III (1981).
Introduction to System Dynamics Modeling with
Dynamo, MIT Press, Cambridge, MA.
