International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
3.1. CPM-PERT Cost and lime Analysis
PERT cost technique has two major aims. As first it provides
to make reasonable cost estimations to complete the project
with minimum cost in shortest time. As second, it helps to
maintain project planning and its control. Then, PERT cost
extraction technique, comparing the activities in the project
according to time and cost, completes them with minimum
cost in shortest time. The costs used in this method are direct
costs.
Activities and events are shown as those in Figure 4 for any
project (Biyik and Uzun, 1992). Lengths of the arrows are not
important, but their direction. They show progress of the
project.
E, Gy EF, Gi
Activity name Aj :
i Y: J
Activity time t;;
Tail event End event
Figure 4. Starting and finishing times of a project in CPM-
PERT method
Critical way is accepted as the way that needs longest time,
which is the time accumulated between starting and finishing
points.
In CPM technique, five types of time computations are done.
They are early starting, early finishing, late starting, late
finishing and free time computation processes.
Early starting time (Ep) is earliest starting time of an activity
and the activity waits until the finishing time of previous
activity.
Early finishing time (Ej) is computed adding activity time (t;)
to early starting time (Ey).
ERE (1)
Late starting time (Gy) is computed subtracting activity time
(t) from late finishing time.
G, 7 G,- tj (2)
Late finishing time (G,) is computed going backward from
finish point in PERT diagram. In some cases, it is possible to
go to the event point of the same activity by multipath
starting from end point of the diagram. Here, the shortest
computed times gives the late finishing time (Uzel, 1986).
Activities in a project can be divided in two groups as critical
and uncritical. Uncritical activities are the activities that do
not change total time of the project if they are finished in
loose time intervals fount out for them from CPM-PERT
diagram. Such activities are also called as activities of loose
time.
In CPM-PERT method, six essential procedures must be
followed in order for any project planning and its control.
They are as followings:
e Determination of project and project activities,
e Determining how the activities follow one another and
forming relations between them,
360
e Drawing a diagram shown the relations between the
activities,
° Time and cost estimation for every activities,
e Drawing the critical way on the diagram that has the
longest time,
e Carrying out planning, programming and controlling
procedures by means of the diagram.
3.2. Estimate Activity Times of PERT
A distinguishing feature of PERT is its ability to deal with
uncertainty in activity completion times. For each activity,
the model usually includes three time estimates
(Www.netMBA.com):
e Optimistic time (t,) : generally the shortest time in
which the activity can be completed. It is common
practice to specify optimistic times to be three
standard deviations from the mean so that there is
approximately a 1% chance that the activity will be
completed within the optimistic time.
e Most likely time ( t, ) : the completion time having
the highest probability. Note that this time is
different from the expected time.
e Pessimistic time ( ty ) : the longest time that an
activity might require. Three standard deviations
from the mean are commonly used for the
pessimistic time.
PERT assumes a beta probability distribution for the time
estimates. For a beta distribution, the expected time for each
activity can be approximated using the following weighted
average:
Expected time ( t, ) 2 (t, * 4t, * t,)/6 (3)
This expected time may be displayed on the network
diagram.
To calculate the variance for each activity completion time, if
three standard deviation times were selected for the
optimistic times, then three are six standard deviations
between them, so the variance is given by:
Oi 7 (tp—t, y6
Oe t) 6p (4)
ROPA y/g
Where;
Gze = standard deviation
Ou = variance
R= Standardized deviation
P, = programmed finishing time
As the variation t, of the activity rises, the possibility of
finishing reduces in estimated time. As the difference
between optimistic time and pessimistic time rises, the
differences between variation and standard deviation rises as
well.
4. PLANNING AND ANALYSING ACTIVITIES OF
SATELLITE IMAGE PROCESSING
Algorithm showing the evaluating and processing of raw
satellite image which was recorded in GIS is shown in
Figure 5 ( www.gis.tagem.gov.tr).
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