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Road Network Design Problems with Spatial Harvest Scheduling

Evelyn W. RichardsForest Engineering Faculty of Forestry and Environmental ManagementUniversity of New Brunswick

______________________________________________________________Evelyn Richards, Forest Engineering, UNB 2

Road Network Design Problems with Spatial Harvest Scheduling

Adjacency ConstraintsWhat is the real definition?

Modelled adjacency conditions: a mis-match

Results from a Stand-Centred Model

Road Network PlanningImportance

Integer models that can work

Integrating Access and Harvest Planning

Spatial Datasets: where are they?

Summary


Adjacency

What is the real definition?

How have we modeled it? A mis-match?

Does this matter?

‘Exact’ Solutions

Stand Centred Model

Examples and Results


Adjacency Definition

Given an existing clearcut and a definition of the maximum clearcut size M = 50.

1)Adjacent areas not to be harvested until area is regenerated

2)If harvesting in an adjacent area would increase the size of the clearcut beyond M, then it is forbidden.

1) or 2) ?

20

3040

30

35

20


There is a significant difference

20

30 40

30

35

2020

30 40

30

35

2020

30 40

30

35

20

a

a

Harvest now

Harvest during green-up period


What has been modeled?

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30 40

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35

20

20

30 40

30

35

20

1 Pre-blocked prior to modeling.

2 Not pre-blocked: the model groups stands dynamically.

3 Not pre-blocked: openings can ‘grow’ to maximum size over several periods.

We developed a Stand Centred Model that gets near-optimal solutions

Closer to regu

lation

Trickier

tom

odel


Does Adjacency Matter?

Forest 1 period 2 period 3 period

Eldorado 0.31% 3.25% 7.00%

nbcl9_01 3.40% 5.12% 7.83%

nbcl9_01b 0.77% 3.12% 6.60%

nbcl9_01c 0.88% 3.08% 6.99%

nbcl9_01d 1.14% 3.73% 7.68%

Percentage Reduction in Objective Function: NPR

This is the percentage reduction in AAC when there are greenupconstraints.


Harvest & Road ChoicesGiven a set of stands or blocks, and a potential network of road segments that access all stands:Choose the best set of harvest and road construction projects


Harvest and Road PlanningIntegrated Model

Maximize Net Revenue - Road Construction Costs -Transportation Costs

Subject to:1. Average ending age >= 752. Non-Declining Yield (Maximum increment 10%)3. Adjacency Constraints4. All timber transported to exit node5. Road Network Connectivity


Linked Models1. Maximize Net RevenueSubject to

Average ending age >= 75Non-Declining Yield (Maximum increment 10%)Adjacency Constraints

2. Minimize Road Costs + Transportation Costs

Subject to• Harvest Solution Found in 1.


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200

400

600

800

1,000

1,200

5x5 10x10

Roa

d C

onst

ruct

ion

Cos

t (D

isco

unte

d $'

000)

Linked Models Integrated

Results: Benefits of Integrated Model

19.38%

8.36%


Comparing Solutions

Linked Process Integrated Model


Impact of Greenup on RoadsMinimize NPV (Transport + Build)Subject to: Volume >= Minimum

6x6

-

100,000

200,000300,000

400,000

500,000

0 1 2 3

# Greenup Periods

Minimize NPV (Transport + Build)Subject to: Volume >= Minimum

10x10

-

500,000

1,000,000

1,500,000

2,000,000

2,500,000

0 1 2 3

# Greenup Periods

Clearly, longer green-up increases road costs when volume is fixed


Impact of Greenup on RoadsRoad Construction Cost

-20,00040,00060,00080,000

100,000120,000140,000

1 2 3 4 5 6

Planning Period

0 1 2 3

Road costs increase and roads are built earlier


Spatial Datasets: Do we have any?

Crown License 5, NB

131029 polygonsMean area: 0.4699Maximum: 133.6287Minimum: 0.0000


Spatial Datasets

•Photo Interpretation

•Tile Matching

•Slivers and Fragments from buffering

•...


The Result?

This "stand" has 29 adjacent stands!

... no polite way to express it


Aggregation heuristics

Match important featuresMerge sliversSearch for wild shapes (shape index). . .

5881 Polygons Meanarea = 10.27

131029 polygonsMean area = 0.4699


ifmlab.for.unb.ca/fmos

1. Existing "real" forests

2. Research Forests

3. Forest Generator

4. Forest Generator with roads


nb crown licence 5


Forest Landscape Generator


Forests and RoadsSimulates stands and potential road networks.Users enter parameters for distributionsCreates data structures necessary for optimization models.


Summary

Spatial acess and production modelsInteger programming optimization brings clarity yield interesting insightsare tractablerequire better datasets


Thanks!


Hierarchical FM Re-visited

What outputs from higher levels need to be enforced at lower levels?Strategic Tactical

AAC?Spatial AAC?Exact Aspatial Schedule?

Strategic

Tactical

Tactical/Operational

Annual

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