1^0
DEWEY
HD28
.M41A
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Development Projects Cost Dynamics
Ali N.
Mashayekhi
WP#3919
June 1996
System Dynamics Group
Alfred P. Sloan School of
Management
Massachusetts Institute of Technology
50 Memorial Drive
Cambridge,
MA 02139
MASSACHUSETTS INSTITUTE
OF TF'^wMOLOGY
SEP 16
1996
LIBRARIES
D-4634
Development Projects Cost Dynamics
DEVELOPMENT PROJECTS COST DYNAMICS
By: Ali N. Mashayekhi
MIT
E60- 357, System Dynamics Group,
30 Memorial
Dr.,
Camb. MA, 02139
June 1996
Abstract
Cost and time overruns have been a
in
many
common characteristic
of development projects
countries. This paper presents a theory of cost and time overruns based
cost structure.
The
on project
cost of a development project consists of base cost and progress cost.
Base cost keeps a project ready
for physical progress. Progress cost creates real physical
progress in the project. This cost structure has an important inherent dynamic characteristic
An
with implications for the efficiency and effectiveness of project management.
between annual budget and ongoing projects
ineffectiveness unrelated to the quality of
results in an increasing inefficiencies
management
in individual projects.
conditions, the policy governing the starting rate of the
important.
The
theoretical
framework presented
causes of time and cost overruns
in
imbalance
in this
new
projects
paper can explain
Under such
becomes very
at least part
of the
terms of imbalance between development projects and
development budget. The paper also suggests some policy recommendations for
new
and
starting
projects.
Key words:
Project
management, development
projects, time overruns, cost overruns
Introduction
In the evolution of
economic growth theory, gross national investment has
remained an important determinant of the growth of national production capacity
However,
the efficiency
and effectiveness of
not been discussed in the literature.
The
the investment processes at a
macro
1.2,3.4,5
level has
efficiency and effectiveness of such a process
is
very important to the real contribution of investment to the growth of production capacity.
Low
efficiency in the investment process
unit of gross investment
made.
Low
would
result in less
production capacity for each
effectiveness of the investment process results in a
long construction period and increases the capital cost of investment projects. The
efficiency and effectiveness of the investment process
becomes very important
growth of national production capacity when governmental investment
projects constitutes a major part of national investment, as
countries.
is
the case in
in
to the
development
many developing
Development Projects Cost Dynamics
Development projects
are investment projects, undertaken
by the governments of
developing countries to construct infrastructure and production capacities to enhance and
facilitate the
development processes.
cost and time overrun in their
costs
Many
developing countries have been experiencing
development
projects^.
For example,
and construction time of development projects are usually much larger than
planned. Figure
1
shows
which projects are completed according
to the
and long construction time region of the
(1,1) indicates a position in
planned cost and time. All of the
development projects completed during 1989 and 1990
in project
in Iran are located in the
scatter, indicating
low efficiency and effectiveness
underestimation and inflation can contribute to the cost overrun. But not
of the cost overrun shown in Figure
sale price index in Iran rose
from 100
1
can be attributed
in 1980, to
390
to these
in 1989,
However, government projects usually enjoyed
2.
for their foreign procurements.
two
factors.
and 530
average price index for a uniform capital expenditure from 1980
in
The whole
1990 \ The
1990 was around a
to
a fixed official
exchange
rate
For the domestic purchase of goods and services,
development projects usually had access
at
high cost
management.
Initial cost
factor of
initially
the ratio of actual cost and construction time to planned values for
development projects completed during 1989 and 1990. Point
all
completion
in Iran,
to
goods
at prices set officially
by the government
a level lower than market prices. Therefore, inflation for the development project
was
lower than what the general price index shows, and certainly inflation alone can not explain
the
whole cost overrun. Because different prices
difficult to
determine
how much
consultants. There are
is
exist to
usually done based on
two reasons
some
some
extent,
depend on the
unrealistic.
is
want
to
total cost
second, the credibility of the consultant would be under question
be
is
not a major factor
detailed feasibility studies by
that the consultant should not
cost of the project. First, the consulting fees
to
it
of the cost overrun was due to intlation.
The underestimation of cost, which might
because cost estimation
that existed simultaneously in Iran,
if
underestimate the
of the project and
the estimate turned out
Development Projects Cost Dynamics
S
H
Q
tn
z
z
<
-1
a.
z
o
S
a:
Z
O
H
UJ
S
>
O
Z)
0^
q;
[U
LiJ
<
D
H
U
<
u.
O
o
<
Development Projects Cost Dynamics
provide a better understanding and management of the overall dynamics of a single projects
•2. 13
and the impact of client-contractor relationship on project delay and cost
Although the quality of project management
factor causing long construction times
is
very important,
and high completion
costs.
^'^.
not the only
is
it
There are factors outside
of project managers' control that contribute to such low performance.
One such
factor
is
a
lack of balance between the development budget and financial resources required for
development projects. In developing countries, the need
available resources are low. There
sectoral officials to start
is
always pressure from
new development
projects.
for
development
is
high and
citizens, regional officials
These pressures lead
and
an imbalance
to
between available resources and the number of projects consuming those resources.
In Iran, for
example, according
Budget Organization
in 1991, the
to the information
budget allocated
obtained from the Plan and
was
to the construction of a hospital
about 30 percent of what was required to complete the ongoing projects on time with a four
years construction period.
was about 22
In 1987, the allocated budget to water projects
percent of the budget required to complete those projects within an average construction
time of five years
'5.
This paper shows that this kind of imbalance between available and required
resources has a profound impact on the performance of development projects.
cost
model
is
developed and presented
perfect project
in the next section.
management and without any
development projects are affected by
management
project
requires a sound
number of projects and
Model
1:
this
The model shows
inflation, the cost
imbalance.
project
even with
and completion time of
Any improvement
macro management of
that
A
in
the balance
development
between
total
available resources in the development budget.
The Basic Dynamics of Project Cost Structure
The annual
and progress
cost.
cost of each project can be divided into two cost categories: base cost
Base cost consists of
all
cost elements that should be paid to keep a
project ready for physical progress. Base cost includes such items as the salary and
overhead costs of the project manager and his
staff, the
cost of keeping contractors
and
consultants related to the project, and the cost of having construction machinery,
equipment, and construction materials on
that,
when
site.
Progress co^r consists of those cost elements
paid in addition to the base cost, can create real physical progress. Progress cost
includes such items as construction materials, construction labor, and the operating cost of
construction equipment. Each project can be finished
cost has been spent to complete
all
when
a certain
amount of progress
the necessary activities in the project.
Base cost has
Development Projects Cost Dynamics
priority over progress cost, because base cost should be paid to create a condition in
which
progress cost can be effective.
Figure 2 shows a causal loop diagram of a basic dynamic cost structure model. The
model consists of a
another
as
shown by an arrow connecting
is
commonly used
is
'^^ '^.
positive or reinforcing loop
in
the
System Dynamics
'6- ^^- '^- ^^:
and
or
^-^>'
variable on
two variables with the following convention
— =>—^>-0 -T->~0 when x^O
dx
— -^0 when x>Q
<0
X —^^y =>
^
X
The dependency of one
dt
or
dy
The
dt
variables of the basic
P=
Number
model
are:
of ongoing development projects
Unit project
is
at different stage
and measured
in
terms of unit project.
defined as a project that requires a certain amount of progress cost, called
u,
to be
completed within normal construction time.
S =
new
Starting rate of
projects in each year
number of ongoing development
C=
Completion
rate of
measured
in unit
projects per year that increases the
projects.
development projects
each year measured
in
in unit
projects per year that
decreases the number of ongoing development projects.
BB =
Required annual base budget to pay base cost of development projects measured
PB =
Progress budget available to pay for progress cost
D=
Total development budget
U =
Progress cost required to complete a unit project
b =
Annual base cost of a
in
A causal
The equations
'''
m-^^
in at a
normal construction time $/project.
unit project in $/project/year.
^P-
--C
Drr*PB^
2:
in $/year.
Pyear.
u
Figure
in $/year.
for the
S
BB-e^b
loop diagram of basic dynamic cost structure model.
model presented
(1)
(2,
in Figure
2 are the following:
Development Projects Cost Dynamics
PB{t)=D{t)-BB{t)
(3^
BB{t)=bP{t)
Equations
to
1
(4)
4 lead
to the following tlrst order differential equation:
"
"
(5)
is 20;
solution to Equation 5
The general
-(
/
h
r
-('-r)
Uit)
= P{0)*e" +\e"
P(t)
—)dT
(5(0
(6)
In a simple case
when
the Starting Rate,
constants, then the general solution
+ uS
PiO)b
/'(0=—
-^
reduced
is
-D
+—b
b
From
equations
—
P(0) b
=S
C{t)
and
2, 3, 4,
7, the
S-D
+u
to:
D-uS
I—
-r
^"
7
and Development Budget, D, are
5,
(7)
completion
rate, C,
becomes:
->
e"
(8)
As Equation 7 shows,
D-uS
.^
e
r,
Startmg
Rate
•
,.
if the
the
•
is
number of projects has an unstable equilibrium value of
D-P(0)b
Sc =
b
J
Under
,,
.
^.
this unstable
equilibrium, the
u
Completion Rate
that the
C becomes equal
Base Budget
to the Starting Rate
BB=P.b and
Progress Budget
S and the number of project
PB = Cu=
Su
add up
is
such
to total
Development Budget D.
b
If
S becomes larger than
equilibrium value such the coefficient of ^"
its
Equation 7 becomes positive,
>-
,
then
Number
of Projects
in
P increases
b
to infinity
and the Completion Rate
C decreases to
and then, mathematically, to negative
values. This characteristic of the solution indicates that the completion cost of projects
could go to infinity and the efficiency of investment goes to zero. Under such conditions,
capital investment
would not lead
to
any increase
in
production capacity. If S
becomes
b
smaller than
its
negative, then
equilibrium value such that the coefficient of ^"
Number
of Projects
P
in
Equation 7 becomes
declines exponentially and the Completion Rate
Development Projects Cost Dynamics
increases to infinity. This unrealistic behavior, as will be discussed and corrected later,
is
the result of a simplistic assumption of constant progress cost for a unit project.
Figures 3a and 3b
when
starting rate
by one
is
unit at year
results
from the behavior of the model
increased or decreased by a step function from equilibrium value of 5
1.
P(0}=20, b=.l, D=7,
show some numerical
The parameter values
S=5
at equilibrium.
for the behavior
shown
in
Figure 3 are: u=l,
Development Projects Cost Dynamics
project
assumed
is
to
be constant as
budget per unit of project
When
u.
rises, the
u remains constant, as the annual progress
completion time shortens and could approach zero
while the progress cost of a unit project does not change. This assumption will be relaxed
in the next section in order to
Model
2:
modify the equation
Variable Progress Cost for Unit Project
when
In reality,
the completion time shortens to values less than a
completion time, then coordination of different
become more
to get the
for the completion rate.
activities
and also overtime and
costly and the progress cost of each unit projects should rise.
completion time close
to zero, the unit cost
4. In the
the exponential decay behavior.
shown
new model, two
The new
shift
works
At the extreme,
should approach infinity. In order to
capture this characteristic of the progress cost, the basic model
2 as sketched in Figure
normal
is
modified to create Model
negative loops are added that will control
variables and connections relative to Figure 2 are
in bold.
np
—
— ».PBR
*»-u
Figure 4: Model 2 with a variable unit project progress cost.
In the
new model,
the following
two equa.lons
are
added
of the unit cost:
uit)
= f{PBR{t)) = a + (5iPBR{t)) A
PBR=£mm
np
(9)
(10)
In which:
PBR =
Progress Budget Ratio (Dimensionless)
np = Normal Annual
(X,
P, and
X
Progress Budget per Project (SA'ear/Project)
are constants
to capture the vT-jnhjiify
Development Projects Cost Dynamics
Equations 9 and 10 indicate that when progress budget per project
value, then
PBR=I
larger than normal,
and " ~
PB/P
>~
^ However, when
PBR >
then
1,
complete a unit project becomes more than
PB
> o=
=>
PBR —>
°o
progress budget per project
.
np and
and «
—> oo
its
which means
is at its
u> a+fi
that
normal
becomes
means progress cost
to
normal value. At the extreme when
it is
impossible to complete a project in
zero time.
The new model, consisting of Equations
nonlinear
first
order differential equation.
It
1
may be
to
4 and Equations 9 and 10,
model
values set for Figure
3:
|3=.l,
is
.25,
complete a unit project
is
Figure 5 shows
is
1
and the normal annual progress budget
imply a third assumption, which
assumed
to be
parameter
X=3, np=.25. The two assumptions that the
necessary progress cost to complete a project
for a project, np,
21.
for the following parameter values in addition to those
a=.9,
a
solved for specific parameter values
with computer simulation using a simulation software such as Vensim
the behavior of the
is
4 years.
is
that the
normal time
to
Development Projects Cost Dynamics
progress cost of a unit project rises and does not allow the completion rate to rise to
infinity.
Although Model 2 improved the basic model
behavior
as
not
is
shown
Figure
in
completion
rate to
In the real
As
when
still realistic
to face a
the starting rate increases
drop
by a step function. Such a
rise,
causes the number of projects to go to infinity and the
5, unrealistically
drop exponentially.
world the starting
rate
is
not disconnected
from the
state
of the system.
the starting rate responds to the condition of the development projects in the system,
neither the
number of projects nor completion time
Model 2
modified to consider such forces acting on the starting
Model
is
3:
The
will
go
to infinity. In the next section,
rate.
Endogenous Starting Rate
starting rate of
who manage
a
new
projects
is
the
most important
development budget. On one hand, decision makers are usually under
Due
foster sectoral or regional development.
low standard of
the
hand,
when budget
become
rate
be decided by those
rate to
pressure from different national or regional organizations to start
As
in the starting rate, its
to
new
projects in order to
population growth and a desire to improve
living, these pressures are high in
developing countries.
availability for existing projects drops
On
the other
and completion time of projects
too long, social, political, and economic pressures build up to decrease the starting
of new projects so that existing projects can be completed before
will be discussed later,
it
new ones
are started.
turns out that the policy that governs the starting rate decision
has a profound impact on the performance of development projects regardless of the quality
of management
system and
at the project level.
The
starting rate that influences the
performance of the
being influenced by that performance, becomes an important endogenous
is
variable in the model.
Model
the feedback
3,
sketched in Figure
from the
state
6, is
developed
to capture the starting rate
of the system on the starting
rate. In
Model
3,
process and
two new negative
feedback loops are added to Model 2 that control the exponential growth of the number of
projects and completion time.
Figure 4 are
in bold.
starting rate
is
availability
The
The new
variables and connections in Figure 6 relative to
starting rate in Figure 6
based on a policy under which the
influenced by an exogenous desired starting rate as well as by budget
and completion time. The starting
such a policy. This policy
exercised, as
is
was the case
is
rate decision
does not have to be
made under
one possible alternative which might be more broadly
in Iran according to
10
my
observation and experience, and will be
—
Development Projects Cost Dynamics
examined
here. After the
consequences of such a policy
is
discussed, then an alternative
policy formulation will be examined.
np
^^u
-PBR
^
Figure
6:
Model
3 with
Equations of the new model consist of
endogenous
equations
1
ES
starting rate.
to 4, 9,
10,
and the following
equations:
S{t)^ ES{t)-EB(t)- ET(t)
EB(t) =
MPRit))
d{PR{t))
"
/
/, (•)
(11)
>
(>,/,(0)
=
fr
=
0;/,"'^(l)
=
I
(12)
= {PBR{t)-PR{t))/T,
d^
(13)
ET{t) = f,{PT{t))
/,(•) <0;/,(.v <
^
d{PT{t))
1)
=
fr
- l;/2(-) = /a™" =
(^4)
= {CT{t)-PT{t))/r,
dt
CTit) =
P{t)IC(t)
(16)
In which:
CT = Completion Time Ratio,
ET = Effect of Completion Time on Starting Rate,
Tn = Normal Completion Time,
Pi?
=
Perceived Budget Ratio,
11
Development Projects Cost Dynamics
PT =
Perceived Completion
r
Time
Ratio,
T
and
'
The
-
are time constants
starting rate of
new
projects in Equation
1
is
1
equal to the exogenous starting
ES, multiplied by the effect of budget availability, EB, and the effect of completion
rate,
time, ET.
The
effect of
budget availability, EB,
is set
as an increasing function of the
Perceived Budget Ration, PR, in Equation 12. The effect of budget availability
be bounded between zero and one.
to
make
one,
When
the starting rate zero.
EB
reaches
its
maximum
effect of completion time
at
When
the Perceived
to
on the starting
rate,
rate.
When
makes
ET will
Budget Ratio, PBR,
ET,
is set
Equation
in
be bounded between zero and one.
less than one,
zero,
is
is
EB
will be zero to
one or larger than
one and does not have any impact on the starting
Perceived Completion Time Ratio, PT,
assumed
budget availability
assumed
is
When
rate.
The
as an decreasing function of the
14. Effect
of completion time
is
Time Ratio
is
Perceived Completion
be one to indicate that completion time does not affect the starting
completion time ratio approaches
infinity,
EB
reaches
its
minimum
zero and
at
the starting rate equal to zero.
Equations 13 and 15 represent an exponential adaptive process
to
update the
perceived information about budget availability and completion time ratio of the projects.
T
T
and - are time constants for the two exponential averaging processes. Equation 16
1
calculates the completion time ratio, CT.
current completion time by dividing the
denominator of Equation 16
The
is
overall performance of the system
The Completion Time
is
to
Ratio, CT,
when
cost, the
is
to T^.
by completion time
completion
measured by
to the
denominator of the equation,
Equation
that is
is
completion cost
The numerator
unit progress cost, given in
by
the
completion
the ratios of
calculated in Equation 16.
progress budget availability,
normal and equal
projects
rate.
The
completion time
normal or standard completion time and completion
to calculate the ratio of the
Normal completion
project
number of
the
Normal Completion Time.
and completion cost of projects
added
The numerator of Equation 16 estimates
PBA,
is
9, plus
is
cost.
The following equation
is
normal completion cost, CR.
is
the completion cost of a unit
one and completion time of the project
the actual completion cost,
which
is
equal to
annual base cost for a unit project multiplied
approximated by dividing the number of projects
rate.
uj^jr^b^iPitmrn
a + (5 + bT„
12
to the
Development Projects Cost Dynamics
,..
The new model
to the
is
a set of third order non-linear differential equations. In addition
parameter values presented for Model
2, the
following numerical values for the
parameters were assumed to solve the model through simulation:
T,
=
2, Tt
=
2,r„
=
4,
all in
Graph Lookup
years.
The two
functional relationship as
shown below:
new
Development Projects Cost Dynamics
equilibrium, pressures from low budget availability and long completion time force the
system
to
lower the starting
settles in a
new
rate to
become equal
equilibrium. But the
new
to the
equilibrium achieved under such pressures
characterized by low efficiency and low effectiveness.
30
6
25
ProjecLs
Projecis/Year
Projecis
completion rate and the system
is
Development Projects Cost Dynamics
25
6
Projects
12
S/Year
15
ProjecLs
Projects/Yeiir
ProjectsA'ear
4
$/Year
1
Development Projects Cost Dynamics
calculate the completion time ratio as a performance index. According to the
desired
number of projects, DP,
development budget,
in
D(t),
is
policy, a
calculated by Equation 18 based on the available annual
and the required annual budget
for a unit project to
normal completion time with the required progress budget available, or
be completed
PBR=
1
Then
.
in
equal to the completion rate plus an adjustment term to
Equation
17, the starting rate is set
adjust the
number of projects toward
of
new
the desired
number of projects by an adjustment time
Tj.
DP{t)S{t)=C(t)+-
Pit)
^'
(17)
D(t)'
DP{t)=
^
*.(«-%
^«
(18)
In which:
DP(t) = Desired
^3
= Time
The new model
model can be reduced
which p =
Number of Projects
to
Desired
Number
following simple differential equation:
-I^-^^^-pP+^DlO
1
and
(Years)
main equations of the
a first order differential equation. Six
is
17
=
,.g.
T
1
The
.
Tj
r,
Pit)
of Projects (Projects)
t^Tnb + a+p
Tj
In
Adjust
to
to the
P(f)=-— P(r)+—
Number
= PiO)-e-" +1^-""-^'
T^-b +
a+p
general solution to equation 19
is:
DiT)dT
(20)
Suppose the system
starts
from an equilibrium
in
which P(0) =
time
-. If at
'•
the
P
development budget drops by a step function from
then the solution for
P(f)
As Equation
P
after
t^
its initial
equilibrium, Dq
,
to
D^- n,
will be:
= 2LA_iZ_iL(l_g-p('-'.))
P
P
21 shows, based on the
new
forr>/,
policy, as
(21)
f
—>
<»,
P(/)
=
-i
2
which
is
P
equal to the desired number of projects for the
new
new
level of
development budget. At the
equilibrium level, budget will be available to finish the projects
normal
cost.
number of
During the transition from
project
is
initial
equilibrium to the
at a
normal time with a
new equilibrium when
the
not yet adjusted to the desired level, the completion time and
16
.
Development Projects Cost Dynamics
completion cost will be more than normal. The completion time
ratio
and the completion
cost ratio can be calculated using Equations 2, 16, and 17.
The behavior of
the
model with
the
new
simulation for particular parameter values. Figure
when
starting rate policy
1 1
shows
can be examined by
the behavior of the
the
new
the
development budget. The parameter values for the behavior shown
same
starting rate policy
as those for the Figure 9
These parameter values make
10
$/Year
1.6
Ratio
7
$/Year
the initial equilibrium
is
disturbed by a step reduction in
and the value of adjustment time, ^3
P~
and ^ ~
^
^°
model with
^
is
in
set
Figure
1 1
are the
equal to 2 years.
Development Projects Cost Dynamics
Summary and
The
Conclusion
investment,
is
the important determinant of growth of production capacity. In a system of
development projects where limited resources support ongoing
new
effectiveness of the investment process to create
beyond
the level of project managers.
decision.
The
available
common
starting rate decision
The
projects, the efficiency
capacity
is
starting rate of the
influenced by decisions
new
project
one such
is
resources and has important dynamic implications for the efficiency and
investment projects as presented in
Investment project cost
is
The dynamic
arises
from the cost structure of the
this paper.
divided into two categories: progress cost and base cost.
cost consists of those cost elements that should be paid to keep the project ready
for real physical progress.
The progress cost consists of those
cost elements that should be
A
paid to create physical progress in the projects that are ready for such progress.
was defined
project
completed
and
is
at a
normal completion time. Each project can be measured
projects under construction
is
reduced by the rate of completion. The starting
management decision
The
cost
unit of
amount of progress cost
as a project that requires a certain
The number of
project.
and
changes the balance between the number of projects and
effectiveness of the investment process.
The base
amount of
efficiency and effectiveness of capital investment, in addition to the
in
terms of a unit
increased by starting
rate
be
to
new
on the new project
is
projects
the major
in the system.
model shows dynamic implications
projects
which are not related
showed
that
to the quality of
an imbalance between the
for the efficiency
management
common
at the project level.
resource and the
the system of projects into a trap of inefficiency
and effectiveness of
The paper
number of projects moves
and ineffectiveness
if
the starting rate
is
decided based on exogenous pressure and in reaction to budget availability and completion
time.
Under such
projects
would be more than normal and efficiency and effectiveness of
project declines.
to a
a decision rule, completion cost and completion time of
number
One
that
The paper shows
is
that
when
the starting rate adjusts the
development
the investment
number of projects
based on available budget, the inefficiency trap can be avoided.
management of development budgets
in
developing countries. Development budgets represent investments made by governments
in
different
area of application of this model
development projects
accelerate
is
the
to create infrastructure
economic growth and development. Due
and production capacity
to population
between the developed and underdeveloped world, there
pressure to foster development by starting
and regions. The pressure
to start
new
is
order to
growth and the large gap
usually a lot of socio-political
new development
projects in different sectors
projects creates an imbalance
18
in
between
the
Development Projects Cost Dynamics
development budget and the number of development
Such an imbalance decreases
projects.
the efficiency of limited investment resources available to the
countries.
To
government of those
increase the efficiency of their scarce investment resources, governments that
are responsible for
development budgets should make sure
that the
number of ongoing
projects are in balance with available budget.
The
application of the result
and the
projects,
common
resource
is
is
not Umited to the
not limited to the budget.
applicable to any situation in which an organization
development projects and a
common
management of development
resource
is
has base cost and. progress cost in terms of that
is
engaged
The
in a
results
of this paper are
number of simultaneous
required by the projects, and each project
common
resource.
The common resource
could be management time in managing different projects, programmers' time to create
different software, or researchers' time to pursue different research projects.
The
common
responsibility for creating balance
resources
is
above the level of a single project manager. In the case of a
development budget, the body
the responsibility of
between the number of projects and available
keeping
that prepares
and approves the
the
common
development budget has
this balance.
The model presented here can be expanded
stages of development.
total
to divide
Such disaggregation can be useful
ongoing projects into different
in discussing the allocation of
resource between different stages of projects during the transition from an
unbalanced and inefficient system
to a
balanced and efficient one.
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