United
States
Department
of
Agriculture
Forest
Service
eNumber
En gi n
rin g
Field Notes
Volume 13
4
April
1981
Engineering
Staff
Washington
LI
S
D.C.
Engineering Technical
Information
Field
System
Notes Articles Awards-1980
Foundation
Fork
Investigation
-North
Trinity River
Photogrammetric Measurements for
Land Surveys-Nicolet National
Forest Wisconsin
Ottawa National
Forest Michigan
Estimating Project Travel Cost
and Mileage
An
Empirical Evaluation of
the Proration Option of
Network Program
ENGINEERING IN
A FORESTRY ENVIRONMENT
M
I
N COST
United
States
Department
of
Agriculture
Service
Engineering Technical
Engineering
Staff
pp5i
St
April
Field Notes
Forest
Washington
Volume
Number
Engineering
D.C.
System
Information
R.K
UýS
PROFESSIONAL
DEVELOPMENT
DATA
MANAGEMENT
RETRIEVAL
contained
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developed
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FIELD
NOTES
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Because
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and
however
engineers.
REPORTS
13
4
1981
US
SEgyý
fOR15T
ENrOF
TO READERS OF
INVITATION
NOTES
FIELD
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FIELD
NOTES
AWARDS
ARTICLES
-
1980
for the Field Notes articles
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is
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AUTHORS
TITLE
RANK
Bath
1
Solar
2
Practical
Toilet
Solar
Facilities
Thomas
Smith
William
A.
Speer
James
Applications
-Wilderness
Boundaries
Describing
in
Some Comments on Methods
General Use One Land Surveyors
3
C.
C.
M.
Kocer
Doak
R-8
R-3
R-3
Viewpoint
Congratulations
the papers are
to
the winners
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will
be
forwarded
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soon
as
processed.
to the authors who
The thanks
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efforts are of
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rating sheets
value
to the field.
arti-cle
of the way
the year submit YOUR
are already one-third
through
for 1981.
Tell other engineers
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job or found abetter way of handling
and valuable
a particular
was interesting
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experience
to YOU.
We
Send
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to
- USDA
FOREST
SERVICE
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RP/E
1
SOME
OBSERVATIONS
RECENT
FIELD
on
NOTES
VOTING
non-A
rela-by
construc-A
or Stuffing
or
or
the
Ballot
Box
Shades of Old Tammany
The
Carpet-Baggers
Hall
Return
A WO protagonist
of proper presentation
of written
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to perform
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perusal of the
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peculiar possibility was posed
the preliminary
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the conclusions
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supported
iteration
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olfactory
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in the correspondents
tionships
that were
caligraphy
identified
in the
tion of the ordinal
indicators
of
selection.
a
pedan-on
Bevel-ed
to
wit
pervasive
and perhaps
pernicious
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singular similarities in ciphers
and
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utilized for
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seem-
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of preference
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tic position or pontificating
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oping
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tion of the actual
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response
obfusca-Presuming
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2
the ballots for
... Ergo
ing the most beneficial
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in the Field Notes in 1981 will
and dated by the
be signed
ers submitting
them.
---The
Editor
FOUNDATION
INVESTIGATION
NORTH
TRINITY
Alex
FORK
RIVER
Tary
Region
solution
most practical
to be
appeared
the use of a Caterpillar
966C front-end
loader with logloading
forks that was
available
for rental
from a logging
firm in the vicinity.
The 966C loader
when
adapted afforded an ideal working
platform for the drill rig furnished
by
Forest R-6.
the Umpqua National
5
Geologist
Shasta-Trinity
NF
of the North
The foundation
investigation
Fork of the Trinity River Weir entailed
the thickness
of
drilling to ascertain
the alluvium
in the channel
and the depth
of the bedrock
upon which the proposed
structure could be erected.
It should
be noted that bedrock
are
outcrops
of the stream
present on both banks
to adapt the loader
to the task
platform was built on the bottom forks
from 2- by 12- and 2- by 4-foot lumber
to provide the working
area for the drill
and the driller.
Two heavy-duty
garbage
cans or two 55-gallon
drums depending
on stream depth
were tied to the bottom
of the logloading
forks for stability.
Additionally this modification served
to slow or prevent
the bleed-down
of the
loader hydraulic system and the eventual
of the drilling platform.
sinking
Figure
1
is a photograph
of the 966C loader with
the small drilling rig mounted
on the
forks.
In order
a
One major impediment
existed Excessive
in an
turbidity could be introduced
active
fishery by the task of getting
the drill rig into the stream and moving
it from drill hole to drill hole.
After
consultation
with the California Department of Fish and Game and the California
Water
Quality Control
Board it was decided
that entry into the stream with
investigative
equipment
was
justified.
comment was expressed
about
An anonymous
the setup
It sure looks like Mickey
Mouse. Reply It worked -- and nicely
at that.
Several
solutions were considered
to
minimize turbidity including
the construction
of a gravel berm to serve as
and
a drilling platform.
The cleanest
ý4
ý
bF
Figure
1.
966C
Loader
with
Drilling
Rig
3
meas-Land
PHOTOGRAMMETRIC
MEASUREMENTS
FOR LAND SURVEYS
NICOLET
NATIONAL
WISCONSIN
FOREST
OTTAWA NATIONAL
MICHIGAN
FOREST
Na.-ing
Victor
H.
Hedman
Region
9
Surveyor
In a discussion
of photogrammetric
urements for land surveys
there will be
a question
as to the attainable
degree
of accuracy
and the tolerance
error
allowable.
Is a positional
of
accuracy
1.5 feet or a relative accuracy
of
1 part
in 3000
and
supportable
ble for the rural land surveys
of
tional Forest boundaries
With the
advent
of electronic
distance
ments accuracies
than those
greater
made with photogrammetric
measurements
and this factor
are easily attainable
is reflected
in standards
of accuracy
quired in many of the States
however
it must be recognized
that these
ments are urban-oriented.
The need for
urban accuracies
is not evident
for
tional Forest lands
nor is there any
known
court
case that has challenged
photogrammetric
measurements
when proven
photogrammetric
techniques
have been
applied.
defensi-ated
measure-to
require-that
Na-changing
re-has
INTRODUCTION
In FY 1958
the line program was initifor locating
marking and maintainthe boundaries
of lands administered
and managed
Prior
by the Forest Service.
that time
little had been done to
maintain and perpetuate
the corners and
lines as established
by the public land
survey
system since then the emphasis
been on the recovery
restoration
and establishment
of corner positions
control the locations of National
Forest boundaries.
With the emphasis
to boundary
line locations
and
marking the use of photogrammetric
measurements
for locating the boundary
line between
corner positions
controlling
is one of the techniques
that is being
considered
and tested.
PHOTOGRAMMETRIC
MEASUREMENTS
the Forest Service
In 1958
Eastern
Region
used photogrammetric
measurements
as
a pilot
test project in the retracement and corner restoration
of a
survey
to
in Missouri.
The project
township
if photogrammetric
measurements
could
be applied
to land surveys
within
acceptable
limits of accuracy
was undertaken in cooperation
with the Washington
Office and Phelps County
Missouri.
The
work
included
the establishment
of section subdivisional
corners and the retracement
and recovery
of existing
corners.
The results were marginal
to techniques
and equipment
compared
now
available
for such projects.
and equipment have improved
Techniques
since 1958
and further improvement
can
be expected
however
increased
costs of
the limits of tolerance
narrowing
may not
be economically
justified
if present
limits serve
our needs.
The accuracy
of
photogrammetric
measurements
will improve
but it is not evident
that such
ments will match electronic
measurements.
is one of the tools of
Photogrammetry
measurement
that has a significant
place
in land surveying and related fields
and the results of tests and limitations
of photogrammetric
projects
on the
Nicolet
and Ottawa
Forests are pertinent.
measure-determine
con-metric
knowl-projects.
Several
before photogramyears elapsed
measurements
were started and
on the Chequamegon
and Ottawa
completed
National
Forests for smaller two-section
In recent years
larger 8and 16-section
projects were started and
completed
on the Superior National
Forest none of these was done with the
of locating and marking
the
boundary line and only corners were recovered
restored established and monumented.
Using aerotriangulation
coordinates
for these corner positions
the proven measurement
accuracies
on
projects ranged from less than
1
foot in horizontal
to a
position
of 3 feet in position
marginal tolerance
the majority of the tests for accuracy
of corner placement
were within
1.5 feet
position when
checked
by closed
ground
PHOTOGRAMMETRIC
TEST
PROJECTS
Error in photogrammetric
measurement
may
result from several sources
ground
trol accuracies
quality and scale of
aerial photographs
type of equipment
used and the level of skill and
edge of project personnel.
posi-purpose
The
aerial
is controlled
photograph
by
coordinate
targets of known
tions and it is further rectified
for
the tip and tilt and drift of the plane
as
each frame is exposed
in flight.
Bridging
techniques
by stereoplotter
are
used to tie photographs
The
together.
small discrepancies
in matching
ping photographs
to known
points common
to adjoining photographs
are known
as
residuals inherent errors that require
tolerance
if photogrammetric
acceptance
measurements
are to be used.
The
uals cannot be reduced to zero by
sently known
and equipment.
techniques
ground
overlap-these
pre-traverse.
resid-of
5
Nicolet
National
vari-ance
Forest
are within
is
foot
1
2.1
of this section was done
photography
flying a single north-south
strip at
The
a photo
scale of 1 inch to 800 feet.
residuals and positional
differences
derived by the reading of eleven
common
photographs
are
points on overlapping
Note
that seven
of
shown in figure 3.
the eleven
differences
were
positional
between
0.6 to 0.9 foot which does not
for errors in field
allow much tolerance
measurements
if the positional
accuracy
by
requirement
is
2585.5
o
2586.2
N1/16
N
foot.
1
2573.6
2572.6
NW
rn
the maximum
The
In Forest County Wisconsin
a section
was subdivided
measby photogrammetric
urements using controlled
ground targets
near
were placed
figure 1.
Targets
lines that were to be lothe boundary
cated and marked
and the photogrammetric
measurements
from target to boundary line
the field control lowere compared with
cation
of the same lines figure 2.
The
variance
in photo
measurements
subject
residuals of photo
to the inherent
show that half the measurements
bridging
1
and
feet.
CN1/16
N N
1346.3
1346.4
2598.9
ý
o
2598.9
CE1/16
LO
N
lf
MM
2727.4
2728.7
CS1/16
S1/16
2764.9
2620.3
2620.5
SW
S1/16
2764.1
S1/4
104.0
103.8
S1/4
-ýE-ýc2620.5
-
2620.3
-
-
by
Figure
aerotriangulation
1.--Photogrammetric
Forest
6
IO
line targets
by field measurement
County
o9
coordinates
Measurements
Wisconsin.
of Section
20
T34N
R14E
4th
P.M.
Photo
Field
Line
N
N
CE
CS
1/16th-CN
1/16th
1/16th-North
1/16th-S
1/16th
1/16th
Figure
Residuals
17.0
16.2
1/16th-NW
SW-S
Control
Control
feet
16.3
West
0.50
0.63
0.80
-0.73
0.34
0.81
feet
Feet
0.7
1.2
3.6
1.7
1.9
39.7
89.8
40.8
1.1
91.0
1.2
75.1
73.0
2.1
20.3
21.1
28.8
30.0
0.8
1.2
27.3
27.3
0.0
7.1
7.2
0.1
35.3
35.9
0.6
38.3
38.6
0.3
7.0
6.4
0.6
Difference
East
in
15.0
2.--Comparison
of photogrammetric
field control locations.
Positional
Variance
Feet
measurements
with
photo-graphy
Using 1 inch to 500 feet
we attained
results comparable
to those
attained
by using 1 inch to 800
feet on the Nicolet
project.
racy.
test was made to determine
A second
whether
field control
could be held to
could we
the absolute minimum that is
obtain
results from offset
accurate
line by knowing
target to the boundary
only the distance between two
corner positions on the Y
ling targeted
axis or must we have known distances
corner positions
between
on
targeted
both the X and Y axes of the stereomodel
control--0.44
0.71
0.03
0.71
1.03
0.41
1.11
-0.46
0.91
-0.85
0.20
0.89
1.02
0.87
-0.21
0.91
-1.97
0.56
0.63
-0.28
0.47
-1.04
0.41
2.02
0.76
0.63
1.14
In a distance of 1 mile between
two
on the Y axis
targeted
corner positions
the error from six offset
targets to
the straight line between
corners ranged
As soon as we controlled
up to 5 feet.
the X axis the variance
dropped to 1.8
feet as the maximum difference.
viously there are no short cuts in
and procedures
to obtain
principles
liable results.
Ob-Testing
re-photography
Figure
Ottawa
We
3.--Residuals
National
and positional
differences.
Forest
can push limits and principles.
scale
needed
to determine
if larger
accuwould provide greater
7
CONCLUSIONS
land survey
Photogrammetric
projects have
standards
met FS Regional
for accuracy
1
part in 3000 1.5 foot positional
These accuracies
will not
accuracy.
meet some States
requirements
accuracy
however
the latter are urban-oriented
the conveyance
of lands in
--involving
urban areas.
We are not aware of any
court cases that challenge
photogrammetric measurements
for land survey.
The
Ottawa
test proved we could
not take
any short cuts in establishing
ground
control
for photogrammetric
measurements
from target to boundary
line.
8
The
Nicolet
test project
and other cited
projects prove that we can meet 1.5 foot
accuracies
for restoring or
positional
corner positions when
establishing
using
properly-spaced
ground control and proper
and equipment.
photogrammetric
techniques
there are limits on the use of
However
line
offset
a boundary
targets to locate
the FSM required
of 1 foot.
to
accuracy
The several
completed
projects indicate
would allow use
that a 2-foot tolerance
of photogrammetric
measurements and the
be relaxed if
FSM requirements
should
measurements
are to be
photogrammetric
used in locating the boundary
line.
ESTIMATING
PROJECT
COST AND MILEAGE
TRAVEL
John P. Haynes
Robert Harding
Civil Engineers
Region
AM
3
M
-
Mwc
head-INTRODUCTION
T
total travel
costs
the Ranger
Station
out
working
or other
of
quarters.
With the high cost of fuel and mileage
to have torn
targets it was a mistake
down those remote work
centers.
This
statement
was overheard
recently and may
or may not have been valid.
The work
centers in question were in poor repair
and were
the required
deemed
not worth
under the pollution
abateexpenditures
ment program.
The proper question
is
and
Considering energy conservation
personnel
ceilings where are work
centers justified
Something more than
intuition is needed
this
to answer
d-2t
T
c
rt2
C
total travel
costs
of a work
center.
2rt1
J
2m
AT
re-lating
t3W
d
d
question.
work
center needs the
help determine
following expressions were derived
hours work
project work travel
schedules labor costs per diem rate
and vehicle
costs.
The total costs are
the sum of personnel
costs for travel
time the vehicle costs and the per diem
costs.
These
formulas can be used to
travel
time miles
compare personnel
and costs for various work center alternatives or various work hour schedules.
out
working
W-2t1-2Wt3
11
1
C
ANALYSIS
ml2
2
T
3
W
WS
d1
d
-
Twc
To
P
total travel
time in person-hours
out of the Ranger Station
working
or other headquarters.
2Jt
total
travel
time in person-hours
out of the work
center.
2Jt1
AP
P
-
Project
work
r
Average
labor
W
Length
field
d
1
t3
working
W-2t
t
J
t2
2
d-2t2
Pwc
Where
1
P
t3W/d
-2Wt
d
3
person-hours
$/hour
costs
of workweek
or stay
Length
of work
day
hours
Travel
time
HQ
to WC
Travel
time
HQ
to
project
hours
Travel
time
WC
to
project
hours
miles
hours
in
hours
11
Distance
HQ
to WC
12
Distance
HQ
to project
miles
13
Distance
WC
to
miles
C
Crew
m
Vehicle
S
Subsistence
wc
Size
persons
project
in one
mileage
vehicle
cost
$/mile
person-Mwc
M
Total
miles
Total
miles
Travel
w/o
W.C.
in
2J12
Cd-2t2
Travel
2J11
w/W.C.
in
13W/d1/t
J
$/day
Project
Work
is the number
of
hours of work
needed or planned on
Travel time is not included.
site.
CW-2t1-2Wt3
d
9
r
labor costs
is the total
Average
charge for salaries
for
appropriation
the crew per hour divided
by the number
of people on the crew.
This must be
for work
schedules
that require
overtime payments.
ad-justed
cost of using
weigh against
work
center.
the work
center should
not
the justification
of the
Hewlett-work
cal-worked
Instructions
Program
The
or stay in field
length of workweek
describes how long the crew would
while at a work
center before returning to the headquarters.
If the crew
a regular 40-hour
week while
at
the work
center before returning
to the
headquarters W would equal 40.
If they
worked
ten 8-hour days with 4 days off
W would equal
80.
W
d
The length of work
would be 8 for
day
a normal
8-hour day.
Where work
schedules call for two different work
days
such as eight 9-hour days and one 8-hour
would be the average
day
or 8.89
d
hours
HP-97
These
calculations
can be easily done on
desk top calculators
such as the
Packard
HP-97.
The following program
was designed
for the HP-97 and will
culate
Pwc AP
Mwc AM
Twc
cards
the
and AT.
Magnetic
containing
from the authors
program are available
Region
3 Engineering staff unit.
P
M
T
The accompanying
Work Center Travel Cost
and Mileage
Summary Sheet is used to
summarize the estimated costs when more
than one project
is involved.
Load the
Then
enter
program into the calculator.
the values
for variables P through
S
into storage registers
0
C.
through
Press the button A to activate
the
The estimated travel
time miles
and costs will be printed.
pro-gram.
possi-used
sched-on
C
The crew size
refers to the average
number of people riding in a vehicle.
Where
the crew rides in one vehicle
C
the number of people on the
would equal
crew.
Where
more than one vehicle
is
C would equal
the number of people
the crew divided by the number of
vehicles
m
The vehicle
mileage
cost
is the total
cost including F.O.R.
or other monthly
costs plus the mileage
The
charge.
monthly
charge must be prorated
to
the
miles driven.
Where
estimated monthly
more than one vehicle
is used
will
cost per mile.
equal the average vehicle
m
When
justifying the construction
of or
the retention of a work
center
compare
the annual cost of the work
center with
the total travel
cost savings
when using
Do not add in the
the work center.
results for projects which will not save
If the work
money using the work center.
center is used for these projects
it
be to save miles.
The additional
Before
the calculations
for an
accepting
individual
project explore other
ble project
variables such as work
ules and crew sizes.
Simply enter the
variables into the appropriate
changed
and press button
AQ
storage registers
Enter on the work sheet
the results for
the project plan most likely to be used.
for each project
the procedure
Repeat
the results on the work
summarizing
sheet.
step-by-step
assist the estimator
an illustrative
example is shown along with the
of using the program.
procedure
To
stor-wil
10
Steps
1.
according
2.
age
Load program into calculator
to H-P instructions.
Key
project variables into
one project
at a time.
registers
Variable
Sto
Project
Reg
Project
1
1000
800
r
1
7
7
7
$/hr.
W
2
40
80
40
hrs.
d
3
8
10
10
hrs.
tl
4
.7
.7
.7
hrs.
t2
5
1.00
1.00
1.50
hrs.
t3
6
.
.2
.5
hrs.
11
7
15
15
15
miles
8
20
20
30
miles
13
9
10
5
10
miles
C
A
3
3
3
m
B
.5
.5
.5
$/mile
S
C
16
16
16
$/mile
HAPPY
Headquarters
Center
CREEK
Work
ýtzaTECT
oSEGT
Values
Time
rave
M
AP
WC
erson/hrs
erson/hrs
miles
mi
R.-ARDW6
by
Date
VJC..
personP/hrs
Projects
people/vehicles
Done
BUFFALO ZuN
Location
Center
600
2TD
Travel
3.
p-hrs.
0
Example
2.
3
J
12
Work
Project
2
I\
Miles
c
es
.efi $p
Travel Costs
ý
dollars
miles
2
250
74
176
I
667
41RZ
1174
583
3
257
qi
161
174
638
1D77
2 657
1130
2251
52110
w
dollears
AT
dollars
24181
I
oZ
556
2101
6.
7.
8.
TOTALS
of
Cost
Projects Worked
Work Center.
Effective
Out of
567
COMMENTS
Fozz-Ec-F
IIUoRK1/JG
BUM1\IATEO
AND W
ILL
FROM
BE
337
170
Our GO
I
Coný6rl
JJo2KED
Ta
OF
2i.iJTE2
12K-
FREkrQUART
CENTER
EFEECýRuF-
COST-
Cosr3AVINCxs
THUS
OF
I-r
\Ab9K
WAS
ý-p-m1TeR_
I
I7zosEC
2
oýýcx
3
WC
TRAVEL
S8
4.582
5
týzasEC.r
uQ
WORK
.o
Ts
TIETOTAL.T1AF-AILEA1EiANI
R1
OUT-
W0
3381
COST
MILEAGE
SUMMARY
SHEET
11
Exanrple
Q
Optional
3.
Press
RRG
PRINT
and accuracy
of varithe storage registers.
to check
contents
ables keyed
into
1
Project
- Storage
Value
Register
Sto
4.
print
Printout
Actual
600.00
W_
7.00
40.00
8.00
d
tl
t2
t3
11
2
13
C
M
PROGRAM
Program
Ste
267.
0
T
-63
00
003
RCLO
36
004
RCL5
36
21
x
RCL3
36
007
2
1
2
M
3
0.75
4
1.00
5
0.50
15.00
20.00
6
10.00
9
3.00
A
0.50
16.00
B
0.00
D
0.00
0.00
E
RCL5
36
-
011
2756.
8
-759.
Twc
AT
C
I
5.
033
034
-45
-
STOE
35
035
068
Repeat
steps
2-4
for each
103
RCL2
36
104
RCL3
36
00
CHS
-22
071
RCL8
36
08
105
05
038
RCLD
36
12
106
-35
107
03
039
040
072
073
RCLB
-35
041
16-11
074
075
RCLA
02
RCLD
RCL5
36
14
076
RCLI
36
01
110
36
05
077
078
RCL5
36
05
111
042
36
14
-55
PRIX
SPC
-14
05
043
-45
044
-24
045
STOD
35
-14
046
RCL8
36
-24
14
36
02
048
015
RCL3
36
03
049
-24
050
PRTX
06
051
STOI
-14
35 46
-35
052
RCL2
36
053
RCL3
36
RCL4
36
04
-55
021
RCLO
022
x
023
RCL2
024
36
36
2
RCL4
36
RCL9
056
057
x
-24
058
059
04
060
-45
028
RCL2
36
02
062
029
RCL6
36
06
063
-35
36
061
RCL7
RCLO
36
36
36
RCLA
36
RCLD
36
-35
112
-55
113
RCLI
36
RCLO
14
114
x
-35
115
RCLE
-14
116
35
46
117
PRTX
36
02
118
CHS
085
086
RCLC
36
13
119
RCLI
-35
120
087
RCL3
09
089
36
2
x
090
01
36
-55
00
-35
RCL2
088
04
-35
STOI
03
36
x
084
x
06
-55
083
02
x
RCL4
109
PRTX
36
15
-24
-14
-22
36
46
-55
03
121
PRTX
02
122
SPC
16-11
-14
-35
123
124
SPC
SPC
16-11
-24
SPC
16-11
16-11
091
RCL2
36
02
125
-55
092
RCL9
36
09
126
00
093
094
-35
STOD
03
127
128
STOE
35
15
-24
129
STOI
35
46
07
130
DSF2
07
15
096
11
097
098
03
065
PRIX
-14
-24
066
CHS
-22
x
RCL3
36
095
-24
-24
064
x
108
03
-35
082
-35
x
RCLE
11
-24
36
x
11
-35
36
36
RCL6
081
-24
055
02
36
08
079
080
x
02
-24
-35
-24
00
-
x
RCLA
054
027
RCL3
x
-35
02
025
-14
-24
-55
102
16-11
RCL2
020
101
PRTX
SPC
014
x
46
-55
069
070
047
36
36
-24
-14
14
RCL6
RCLI
PRTX
35
016
067
15
PRTX
030
dollars
3514.
T
STOD
026
743.
7
012
019
miles
1035.
QMwc
013
018
1778.
M
036
037
11
-24
008
017
111.
Code
DSPO
010
hours
155.
Key
Function
LBLA
009
1
LISTING
002
006
Project
will
project.
001
005
12
of Example
AP
S
032
Printout
Pwc
r
calculator
P
Re
J
031
Press button
out costs.
099
100
RCL7
36
-55
RCLB
36
x
RCLA
36
131
0
R
00
35
-63
14
02
-31
12
132
RTN
24
-35
133
R/S
51
11
CONCLUSIONS
Since developing
these formulas it
became
evident
that a major use of the
program will be for project planning.
Whether
or not a work
center exists
travel
time miles and costs can be
estimated for alternatives
such as different work
schedules
and crew sizes
or for using the work
center or not
using the work
center
Personnel
and mileage
ceilings
constraints are becoming
more important
considerations
and may justify using an
center or building
a new
existing work
favor-able.
one
even where
are not
economics
This program allows quick
analysis
so that the trade-offs
can be considered
This program was designed
to
cost of working
out of a work
the cost of working
out of a
such as the Ranger Station.
where crews are stationed
at
the
compare
center with
headquarters
However
the work
costs can be compared
for using
different
work centers by considering
one work
center as the headquarters
and
the other
as the work
center.
Travel
time from HQ to WC
and distance
from HQ to WC
would then be entered
centers
as
0.
11
t1
13
AN EMPIRICAL
EVALUATION
OF THE PRORATION
OPTION OF MINCOST NETWORK PROGRAM
mainte-Management
Peter
Sciences
U.S.
Variable
cost
nance cost.
Wong
Forest
Berkeley
Staff
cost
hauling
Equation
Service
Step
Calif.
Iteration
2.
Iteration
1
1
is greater
than 10 go to
variable cost on each
Recompute
to the
link for each sale according
formula
following
If
mainte-more
construc-as
INTRODUCTION
iteration
step
The
MINCOST Program has been used frein recent years by transportation
quently
for network
in place
of
analysts
analyses
sophisticated
computer models such
the Timber Transport Model Transand the Integrated
shipment Model
Model.
Resource
MINCOST appeals
Planning
to users mainly because
of simplicity
in
data input and insignificant
computer run
costs.
When
the problem is to obtain the
best network
and where best is usually
defined in terms of minimum total cost
the proration option
is most often
chosen.
5.
1
Variable
cost
hauling cost
nance cost
Equation
reconstruction
tion cost
cost/traffic
flow
traffic volume
on
the link from last
iteration if it is
than 0
greater
or
current
timber sale
volume otherwise
vari-the
where
traffic
The
purpose of this paper is twofold.
the heuristic
algorithm used by
proration
since
option is documented
few users
if any are familiar with the
algorithm.
the characteristics
Second
of the algorithm are studied
a
through
series of small hypothetical
examples.
Generate a minimum path
for each
Step 3.
timber sale on the basis of the new
able cost for the links.
First
PRORATION
Step
1.
Step 4.
Is the traffic volume
from all
timber sales on each link of the network
for the current
iteration
to that
equal
iteration
If yes
of the previous
go to
ALGORITHM
The heuristic
algorithm of
option is described
below.
Iteration
5.
If
Step
5.
Terminate
step
2.
algorithm.
Legend
1
100
100
the
Sale
1
22
to
small numerical example below
how the algorithm works.
The
schematic
network
is shown in Figure
1.
For simplicity all links are 1 mile in
and with hauling
cost of $10/mi/
length
timber unit.
The construction
costs for
links
1
3
and
2
3
are $1000
and $10000 respectively.
h10
2
go
The
For each timber sale generate
a minimum
cost path to a market through
a mill on
the basis of the following variable cost
for each of the network
links.
Sale No.
no
step
illus-trates
the proration
1
100
flow
No.
units of timber
network
node
at
enter
2.
1
2
h10
c10000
h10
c1000
h
Mill
Figure
1.
Market
Schematic
c
hauling cost
construction
$/mi/timber
cost in $
in
unit.
Network
15
h10
2
Minimum paths
for the two
Iteration
1.
sales are generated
using hauling
cost
shown in Figure 1.
The solution
is shown
in Figure
2.
\100
1/
h10
h10
O
Legend
100
means
100
timber is
the link.
Figure
1.
$10
of
this
$1000/1
iteration
1
2
101
$1010.
is
Iteration
of
hauled along
h10
cost on each
Iteration
2.
The hauling
link is recomputed using equation
1
3
will have the
For example link
new hauling
cost.
following
cost
Hauling
The solution
in Figure 3.
2.
units
h1010
h110
shown
-
3
Figure
However
3.
Since there was no timber
Iteration
-o-3
and the
hauling
over link
timber sales volumes are different
for
the two sales the hauling
cost used here
would not be the same for both
sales.
For sale No.
the hauling
cost for
1
is
3
1
as
cost
Hauling
a
$1000/1
$10
Sale No.
-ý--
b
O
2
is
Iteration
h1010
1
$20
mini-mum
Sale
No.
c
2
h10
100
O
100
h109
4a
Traffic
b.
Flow
4.
Iteration
h20
Pattern
3
O
1
-ý
2
100
f
100
f
O
O
3
16
3
for the sales are
paths
and
The
flow pattern
a traffic
paths
generate
shown in Figure 4c.
O
Figure
1
$1000/100
1
h109
2
for
cost
$10
The minimum
cost
shown in Figure
$1010
1
the hauling
No.
cost
Hauling
follows
h10
2
for sale
3.
h10
o
Iteration
4.
We again recompute
the
costs on the links using equahauling
tion
and then generate
minimum
cost
The result of this iteration
is
paths.
shown in Figure 5.
o
100
1
101
h10010
h20
3
Figure
5.
Iteration
4
algo-are
Iteration
5.
As in iteration
3 the
cost used here for link
2
3
hauling
would depend on the sale under study.
The minimum
cost paths
for this iteration
shown in Figure
and
The
6a
a
Sale No.
4
b.
b
1
traffic flow pattern
is shown
resulting
in Figure
6c. Since the traffic on
each link for this iteration
is the same
in iteration
as
the heuristic
rithm terminates.
Sale No.
h10
c
2
Flow
Pattern
h10
100
100
100/
l
h10010
Traffic
h19.9
h110
O
O
Figure
101
h19.9
6.
Iteration
3
5
17
Omile
EMPIRICAL
EVALUATION
10
of the proration heuristic
studied
algorithm
by means of a series
of small hypothetical
problems.
The
behavior
10.
is
Problem 1.
The triangular network
shown
All links are 1
in Figure 7 is used.
in length.
O
of the solution
is
The traffic pattern
shown in Figure 7.
The solution
value
is $220.
The optimal
solution
is for
timber sales to use paths
1
2
3
and
2
3
The optimal
solution
value
is $180.
In this case the MINCOST
value is 40/180
x 100
22% higher
than the optimum.
10
h1
thesoluIn trying to force
select the path
1
2
3
in
1 we increased the construction
problem
cost on each link by 10 times.
However
the solution traffic pattern
remained
1.
The deviation
the same as in problem
of this solution
from the optimum is
2.
x
100
h1
Problem
7.
1
10
to
$2020-$1530/$1530
c100
3
Figure
tion
p
10
c100
solu-tion
Problem
h1
c50
10
c500
O
h1
2
32%.
that
A review
of the algorithm indicates
the solution is insensitive
to the construction
cost assigned
to link
The MINCOST solution
for a case where
no
construction
cost is assigned to link
is shown in Figure
8.
The
shown in Figure 8 is
x 100
96% higher than
the optimum.
D2
Q-2
solu-tion
$2020-$1030/$1030
10
10
c1000
c1000
h1
h1
3
Figure
Problem
8.
2
10
Problem 3.
The triangular network
is
used again but with construction
costs
in such a wa
that would make
assigned
the path
1
2
3
more attractive
1.
The solution of this
than in problem
is shown in Figure
9.
This soluproblem
tion is $1520-$1030/$1030
x 100
than the optimum.
48% higher
10
c500
O
c1000
h1
10
10
c500
h1
h1
O
Figure
18
9.
Problem
3
$4060-$3100/$3100
from
4.
A network
constructed
is used
to detertwo triangles
stacking
of
mine if the solution
traffic pattern
in a more comearlier problems
persists
The network
and the MINCOST
plex network.
solution
are shown in Figure 10.
The
value
is $4060 which
is
MINCOST solution
Problem
x
100
31%
higher than the optimum.
The traffic
remained the same when the timber
pattern
sale volumes at nodes 5 and 6 were
to 5 units.
We can see that the
changed
traffic pattern
here follows those of
1
problems
through
3.
10
10
c500
W
5
6
10
c1000
W
10
10
/
c1000
h1
c500
h1
2
10
c1000
h1
c1000
//
30ý
0
h1
3
Figure
10.
Problem
4
19
100
1
Problem 5.
A network
similar to the one
1
is used
here except
used in problem
that flow between
nodes 1 and 2 is perThe solumitted in either direction.
is shown in Figure
tion for this problem
11.
The MINCOST solution
value
of $2020
solution.
coincides with the optimal
h10
c0
_ý
lO
2
10
h10
h10
c10000
c1000
3
Figure
The timber sales volumes of
Problem 6.
the
5
are revised
to investigate
problem
to timber volumes.
of MINCOST
sensitivity
The MINCOST solution
and the network
used
MINCOST obtained
are shown in Figure
12.
solution
value
of $110020.
the optimal
Problem
11.
5
0000
1
h10
c0
2
10001
ý
h10
c10000
h10
c1000
3
Figure
The network
shown in Figure
Problem 7.
would
13 is used
to test whether MINCOST
of paths
to permit
select a combination
link by both
sharing of a construction
The MINCOST
solution of
timber sales.
to the optimal
$10000
corresponds
solution.
12.
Problem
6
100
100
O
h10
c2000
h10
c2000
2
h10
c2000
h10
c10000
h10
c10000
200
O
Figure
20
13.
Problem
7
Problem
8.
The network
shown in the
1 MINCOST
Users Guide is employed
Region
of MINCOST on a
to check the performance
The
slightly more realistic network.
network
characteristics
are summarized in
Table 1 below
CONCLUSIONS
con-3
the
the
preceding
examples we can see
MINCOST solution
may be the
It is not
optimum or very far from it.
obvious
for what network
characteristics
or a bad
we can expect
a good solution
one.
More empirical evaluation
of
MINCOST using larger and more realistic
is
Forest Service
network
problems
A theoretical
way.
analysis of the
heuristic
algorithm and
proration
of MINCOST with other available
parison
will be
network
analysis procedures
ducted in the near future.
From
that
under-which
com-solution
The
MINCOST solution
is shown in Figure
value
is $511872.
The
Its solution
solution
is shown in Figure
optimal
15
has a solution
value
of $506944.
Therefore for this problem the MINCOST
is within
1% of the optimum.
for replacing
link
Note that
except
D-Lo-7
4
in the optimal
soluby
tion the remaining networks are the same
for the two solutions.
14.
It is clear
from the examples that
until more is known
about the quality of
the
the solution
produced
by MINCOST
solution
should
not be accepted
blindly.
---1
---2
---3
---4
---5
---7
---8
---9
---10
Table
Link ID
Node
Node
Length
Mile
1.--Network
$
Characteristics
Haul
Forward
1
2
4.7
38200
---
1
4
8.2
68400
1.31
5
3.8
61300
0.91
3
4.2
27800
---
4
3.6
50000
0.91
4
4.1
32500
0.91
7
4.9
72700
0.71
5
5.0
50000
0.91
0.51
2
6
6.2
---
6
2.0
32500
0.71
8
6.2
---
0.51
6
7
2.5
50000
0.91
6
8
7.1
28000
0.51
8
8.2
---
0.41
10
11.7
---
0.51
8.7
---
0.31
10
28.2
---
0.41
11
16.7
---
0.31
11
0.0
---
0.0
4
9
8
Cost
Construction
Cost
Per Mile
Backward
$
1.31
1.31
0.91
0.51
---21
10200
10200
4800
6200
6200
sale
sale
sale
2
sale
4800
sale
2
--ý-C
sale
3
O
O
Ný
.
1
0
N
3
O
C
T
/
6
Ný
-
4
102 00
5
CO
Ch
r
i
4
5
C1
ý
ci
7
6
16400
i
CO
-1
7
6
8
8
.QO
00
ý
ar
mill
0
10
qpp
9
mill
milli
Network
Not
22
to
mil
1
market
21200
Schematic
9
11
market
14.
03
ý0
11
Figure
10
Layout of Big Creek
Solution
and MINCOST
21200
Figure
Schematic
15.
Scale
U.
S.
Network
Layout of Big Creek
and Optimal Solution
Not
Scale
to
GOVERNMENT
PRINTING
OFFICE
1981
340-938/314
REST
SERvq
U
S
ENTOrA61ET.
TECH
INFORMATION
J6.TEM
Volume
13
Number 4
April 1981
Engineering
Field
Notes