frst 557 lecture 2a optimization & forest operations

FRST 557

Lecture 2a

Optimization & Forest Operations

In this module we will look at operational costs, production, quality, and the combination

of those objectives in planning.

It is not enough to plan to physically accomplish the objectives associated with forest

operations. You must also consider the economic viability of the operation, both now

and in years to come.

Optimum Road Spacing

1.0 Lesson Overview:

I. Forest Operations are a rather complex combination of phases (or functions) that

contribute to the management and harvest of the forest land base. Some of the

phases (e.g. yarding, loading, & hauling) clearly contribute to the harvest, and the

costs of these phases are obviously associated with the eventual sale of the

product and the profit or loss associated with the product. Other phases (e.g.

tending regeneration) may seem quite disassociated with the production of logs,

but are nevertheless a necessary part of the management cycle and therefore a

legitimate part of the cost that must be considered against any income.

There is always a strong temptation to minimize costs of each single operational phase.

The simplistic philosophy of such an approach is that, if every component has a

minimum cost, the total will be a minimum as well. While such an assumption may work

FRST 557 – Optimum Road Spacing

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cumulatively for some phases there are always phases that benefit from incremental

expenditures in other phases and therefore have an inverse cost relationship.

2.0 Lesson Objective:

In this lesson, you will take a scenario where an area being developed for a harvesting

operation will require two or more parallel roads. You will examine two operational

phases (road construction and yarding) that have cost trends that move in opposite

directions as one variable, the distance between roads, is increased or decreased. You

will become familiar with looking at the cost structure of each component and how to

find an optimum combination to minimize total costs. Although this is just a simple

example of the process of finding optimum combinations, you will be able to apply the

principles of this lesson to more complex situations.

3.0 Related Reading:

No extra reading is required for this module.

There are numerous publications on this topic that may be of interest to you for situations

that you need to evaluate in the future.

4.0 Lesson Preparation:

Consider a familiar situation where there are a number of (approximately) parallel roads.

You find these road networks in urban, rural, and forest areas. Ask yourself these

questions:

What is the purpose of the road system? (What does it access or develop?)

How far are the roads spaced apart?

What would happen if the road spacing was increased or decreased?

o To the roads and road costs per unit area

o To the resource (property etc.) developed or accessed by the roads?

5.0 Road Spacing and Yarding Distance

The variable for this lesson is the spacing or distance between roads in a parallel road

network. We will use “S” to represent this variable.


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ROAD

ROAD

ROAD

S

S

The spacing of the roads affects the maximum yarding distance to the road. We will

overlook variations influenced by topography and just assume that a boundary line will

be placed half way between the roads, and that the maximum yarding distance will be

“S/2”. The shaded area in the illustration represents a harvest unit that will have the logs

yarded by skidder or cable in a direction perpendicular to the roadside.

ROAD

ROAD

ROAD

S

S

S/2

S/2

Yarding Direction

Swing yarder decking logs at roadside.


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Assuming an even distribution of timber, the average yarding distance is one half of the

maximum yarding distance or “S/4”.

ROAD

ROAD

ROAD

S

S

S/2

S/2

S/4

S/4

6.0 Costs of Roads and Yarding

To evaluate the cost of any type of production, costs are usually divided by production

units to determine a per-unit cost. Since sales are based on volume in a forest operation,

the preferred unit of measurement is the cubic meter (m3).

6.1 Road Construction

Road costs tend to be examined on a per-kilometer or per-meter basis since the

primary unit of measurement is linear. The road however, does develop access to

an area, and that area supports a volume of timber. By determining the volume

developed by the road, or a segment of the road, a $/m3 cost can be calculated.

This may require a couple of steps, first entering the calculated area and then

entering an average volume per unit area. For example:

ham

kmha

km

m

ha

ha

km

kmmRoad

333

$$$

For this exercise, it is assumed that roads in a parallel configuration have

approximately the same cost, and that the cost will not change with changes to the

road spacing.

For convenience, let’s say that the harvest unit runs for one kilometer of road

length.


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ROADS/2

S/2

1 km = 1000 m

Let RV represent the road cost per unit volume (m3) that must be calculated.

RK is a predetermined (known) cost of building and maintaining the road per km.

V is the average recoverable volume of the timber in m3/ha.

S is the variable road spacing in meters.

Note that the calculation must keep all linear units the same (meters will be used).

From the above illustration, 1 km of road will develop both sides of the road for a

combined distance of S = S/2 + S/2

The area developed by 1 km of road will be 1000S m2, which is converted to

hectares (1 ha = 10,000 m2) or S/10 ha

The total volume developed by 1 km of road will be the area times the per hectare

volume or V*(S/10) = VS/10

The road cost per unit volume will take the cost of a kilometer of road and divide

it by the volume developed by that kilometer.

RV = RK/(VS/10)

VS

RR K

V

10

Example: The following chart is an example of the trend in road costs per cubic meter developed

(RV) as the spacing increases.

Road cost (RK) is $85,000 per km and the volume is 850 m3/ha.


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6.2 Yarding

Yarding production is measured directly in cubic meters, which makes the unit

cost calculation fairly straightforward. At the end of a working day, both a cost

and a production can be determined to calculate yarding $/m3.

Once the crew and machinery is on site, yarding production cost is a combination

of variable and (relatively) fixed times and costs. In this case, where we want to

consider the effect of yarding distance on the cost, we will focus on variable costs,

which are a function of yarding distance.

Fixed time and cost:

Hooking and unhooking logs average per turn (e.g. minutes per cycle)

Delays and breakdowns average per turn

Variable time and cost:

Outhaul time average per turn

Inhaul time average per turn

0

2

4

6

8

10

12

14

16

18

60

80

10

0

12

0

14

0

16

0

18

0

20

0

22

0

24

0

26

0

28

0

30

0

32

0

34

0

36

0

38

0

40

0

42

0

44

0

46

0

48

0

50

0

52

0

54

0

56

0

58

0

60

0

Ro

ad

Co

st

($/m

3)

Road Spacing (S) in meters

Road Cost versus Road Spacing


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INHAUL

OUTHAUL

SKIDDING CYCLE: VARIABLE WITH DIST?

1. OUTHAUL YES

2. HOOK-UP NO (USUALLY)

3. INHAUL YES

4. UNHOOK NO

5. DELAYS NO (USUALLY)

For the purpose of this lesson, we will not consider impacts of capital spending

versus current operational costs or any other economic effects of time or

utilization. We will work on the basis of costs and production occurring within a

finite time.

This example also assumes that nothing will happen in the yarding phase that will

change the cost dramatically at some yarding distance due to a loss of defection or

a similar problem.

We will use the following equation for this:

4

SCY

Where:

Y = average yarding cost for the variable average yarding distance ($/m3)

C = the cost to yard 1 m3 of logs one linear meter

S/4 = Average yarding Distance (from Section 5.0)

To determine C it is necessary to combine the operating cost of the yarder with a

yarding rate. Operating cost can usually be determined for a machine from

accounting records and will likely be expressed in $/hour. It is critical that a

constant time units be selected for final calculations!

The yarding rate most likely needs to be determined from some form of

production analysis and may involve some work sampling time studies. Whether

cable or ground yarding, each turn will include an inhaul and outhaul. The inhaul

includes the turn of logs and can be expected to be slower than the outhaul.

Although a speed will normally be reported as distance units per time unit, the

inverse is needed for the calculation of C.


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Example: A Madill 122 swing yarder has had the following data recorded and averaged for

the outhaul and inhaul cycles. Any fixed time (again averaged) associated with

the cycle, such as tensioning the lines, is not included. :

Outhaul average: 6.69 m/second = (1/6.69) =

0.1494 sec/m = (0.1494/60) =

0.00249 minutes/m

Inhaul average: 5.02 m/second =

0.1992 sec/m =

0.00332 minutes/m

TOTAL: 0.00581 minutes/m System cost at this location: $267/hour = $4.45/minute

Average turn volume: 1.20 m3

The incremental yarding cost is:

mmm

mC //0215.0$

20.1

min

$45.4

min00581.0

3

3

That is, it costs an incremental $0.0215 per cubic meter to yard each additional

linear meter yarding distance.

As demonstrated in 5.0, each additional meter in road spacing will result in ½

meter increase in maximum yarding distance and ¼ meter in the average yarding

distance.

The following chart illustrates the relationship of road spacing to the variable

yarding cost.

4

SCY


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7.0 Minimum Total Cost

The objective of this exercise is to determine the road spacing that will minimize the total

cost. Road costs per cubic meter developed (RV) decrease as spacing increases; however,

the variable yarding cost per cubic meter (Y) increases. Combining the charts in section

6 produces the following where

Total Cost = Road Cost + Yarding Cost

T = RV + Y

or

4

10 CS

SV

RT K

0

0.5

1

1.5

2

2.5

3

3.5

60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600

Vari

ab

le Y

ard

ing

Co

st

($/m

3)

Road Spacing (meters)

Variable Yarding Cost vs. Road Spacing


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The minimum total cost occurs where the slope of the “Total” Curve is equal to zero.

The following chart is an expansion of the critical portion of the preceding chart.

0

2

4

6

8

10

12

14

16

18

60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600

Co

st

($/m

3)


TOTAL COSTS

Roads

Yarding

TOTAL

0

1

2

3

4

5

6

300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600

Co

st

($/m

3)


TOTAL COSTS

Roads

Yarding

TOTAL


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To determine the minimum point, take the first derivative of the equation for the total,

and set it to the slope zero:

CV

RS

C

VS

R

C

VS

R

dS

dT

CS

SV

RT

K

K

K

K

40

4

10

04

10

4

10

2

2

2

CV

RS K40

If road costs (RK) increase, spacing (S) increases.

If yarding costs (C) increase, spacing (S) decreases.

If stand volumes (V) increase, spacing (S) decreases.

Example: Using the numerical data from the previous examples:

RK = $85,000 / km

V = 850 m3/ha

C = $0.0215 /m3/m

metersCV

RS K 431

8500215.0

850004040

Optimum spacing between parallel roads is 431 meters (S).

Maximum yarding distance is 216 meters (S/2).

Average yarding distance is 108 meters (S/4)

T

DT = 0


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8.0 Variations

The model and example used in this lesson assumed a parallel road design and yarding

with skidders or cable systems in a direction perpendicular to the road. This model can be

expanded for more complex designs that repeat the pattern. Examples are shown in the

following illustrations.

l = LATERAL YARDING DIST

S = ROAD SPACING

ROAD

SKYLINE CORRID0R OR SKID TRAIL

ROAD

Skyline Corridors or Skid Trails

W

S

MAIN ROAD

TRAIL

MAIN ROAD

BR

AN

CH

SPURs

l

Main Road, Branch Road, Spur Road, & Trails

9.0 Modifications to the Road Spacing Problem

How can we deal with the fact that roads and skid trails are not always straight lines?

What if there are landings with a fan-yarding pattern? Do we have to use volume as the

costing denominator?

Decision making and planning for forest operations is extremely complex because of the

number of factors that enter the process. Often a simple (but wise) modification to a

simple analysis will provide an adequate answer.


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In irregular terrain, it is not possible to design for parallel roads.

9.1 Winding Factors

The use of a “winding factor” is an easy adjustment to the basic spacing analysis

to deal with roads and skid trails (or yarding roads) that are neither straight nor

perfectly parallel.

There is a need to provide for road junctions, curves, switchbacks…

There is a need to provide for realistic skidding paths.

ROCKWATERWAYS

TERRAIN

GRADES SOILS

OBSTACLES

ROAD

By examining actual plans, measurements can be measured or estimated to

indicate a percentage increment over a parallel and straight pattern.


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Let WR equal the winding factor for roads

o E.g. 1.15 is a 15% increase over the base road system

Let WY equal the winding factor for yarding

o E.g. 1.10 in a 10% increase in yarding distance above the pattern

that is perpendicular to the road.

The equation from Section 7.0 can be adjusted as follows:

Y

RK

CVW

WRS

40

Using the data from the previous example with the example factor from above:

metersS 44110.18500215.0

15.18500040

9.2 Using Area Rather than Volume

Sometimes it is easier to express costs relative to area developed instead of

volume. In this case, all costs will be expressed in $/ha rather than $/m3.

The objective is still to minimize the total cost:

Total Cost = Road Cost + Yarding Cost

TA = RA + YA

Road Road cost per hectare is developed as in Section 6.1 but without the need to adjust

for volume.

kmha

km

ha

km

kmhaRoad

$$$


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ROADS/2

S/2

1 km = 1000 m

The area developed by 1 km of road will be 1000S m2, which is converted to

hectares (1 ha = 10,000 m2) or S/10 ha

The road cost per ha will take the cost of a kilometer of road and divide it by the

area developed by that kilometer.

RA = RK/(S/10)

S

RR K

A

10

Note the absence of V in the denominator.

Yarding Yarding cost per hectare is developed as in Section 6.2 but needs to adjust from

volume to area. The unit yarding cost “C” is expressed in units of $/m3/m, so the

volume per hectare (“V” from Section 6.2) is entered to convert to $/ha.

44

CSVVSCYA


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CV

RS

CV

S

R

CV

S

R

dS

dT

CSV

S

RT

YRT

K

K

K

KA

AAA

40

4

10

04

10

4

10

2

2

2

CV

RS K40

It should not be surprising that this equation is exactly the same as when costs

were given on a per-m3 basis.

10.0 A Final Word…

It is rare that the variables used to calculate optimum road spacing as in this lesson will

be as uniform as presented. The process can however be tried with several iterations with

a range of data to examine the effect on the optimum choice. Often the values of the

optimum do not change significantly, and the total cost difference, as seen on the “Total

Cost” charts do not vary significantly over a range of “S” values close to the optimum.

Caution must be exercised where costs change significantly at a certain point, or where

yarding becomes physically impossible. The chart below represents a situation where a

cable system loses lift at 200 meters total yarding distance (400 m spacing) and then

becomes physically impractical at 250 meters (500 m spacing). There may be compelling

reasons in other phases that make it desirable to extend the yarding to 250 meters, but

that would require the introduction of those phases into the analysis.

TA

DTA=0


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The deflection in this photo is adequate to lift the leading end of the log.

0

2

4

6

8

10

12

14

16

18

60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600

Co

st

($/m

3)


TOTAL COSTS

Roads

Yarding

TOTAL


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The tail block in this photo is at the extreme left. Note that there is no deflection beyond

the mid point of this yarding road. Inadequate deflection will adversely affect the

productivity and cost of the yarding phase.

Yarding costs can also be complicated by multiple methods on the same area. For

example, starting at the road, the first 20 meters may be “cherry picked”, the next 100

meters is “hoe-chucked”, and the rest is cable yarded. Each method will have a different

cost to distance relation that can be looked at first in isolation, but then as a combination.

Dispersal of activity over several years or even rotations can present a challenge to an

economic analysis. Costs need to be discounted to a common point in time for an

analysis to be valid.

Often a mathematical solution will be excessively difficult to set up and calculate, but

spreadsheets, charts, and a few iterations will provide some educated direction.

11.0 Try This

Given the following information, find the optimum road spacing.

RK = $40,000 / km

V = 400 m3/ha

All found cost of a skidder = $135.00 / hour

Average turn size = 1.73 m3

Average outhaul speed = 1.20 m/sec

Average inhaul speed = 0.65 m/sec

What is the total cost per m3 of roads and variable yarding at the optimum?

What would the cost impact be of an increase of 50 meters in road spacing?

What would the cost impact be of a decrease of 50 meters in road spacing?

What would be the impact on the optimum spacing if winding allowances of 10% were

added to both roads and skidding?


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Answer: RK = $40,000 / km

V = 400 m3/ha

All found cost of a skidder = $135.00 / hour = $2.25 / min

Average turn size = 1.73 m3

Average outhaul speed = 1.20 m/sec = 72 m/min = 0.0139 min/m

Average inhaul speed = 0.65 m/sec = 39 m/min = 0.0256 min/m

Average round trip speed = 0.0395 min/m

The incremental yarding (skidding) cost “C” is:

mmm

mC //0514.0$

73.1

min

$25.2

min0395.0

3

3

The optimum road spacing is:

metersCV

RS K 279

4000514.0

400004040

The total cost per m3 of roads and variable yarding at the optimum 279 meters:

3

279

/17.7$59.358.3

4

2790514.0

400279

4000010

4

10

m

CS

SV

RT K

If spacing is increased 50 meters to 329 meters:

3

329

/27.7$23.404.3

4

3290514.0

400329

4000010

m

T

From the optimum, the road cost decreases by $0.54/m3 but the yarding cost

increases by $0.64/m3 for a net increase of $0.10/m

3.


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If spacing is decreased 50 meters to 229 meters:

3

229

/31.7$94.237.4

4

2290514.0

400229

4000010

m

T

From the optimum, the road cost increases by $0.79/m3 but the yarding cost

decreases by $0.65/m3 for a net increase of $0.14/m

3.

The optimum road spacing (with winding factors) is:

metersCVW

WRS

Y

RK 27910.14000514.0

10.1400004040

In this case, the winding factors are the same and cancel out. Only different

factors would raise or lower the optimum spacing.

frst 557 lecture 2a optimization & forest operations

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