An exercise in the use of harvest scheduling tools to explore various aspects of a resource capability model with multiple objectives

1. Harvest Scheduling & Policy Analysis
Karl R. Walters,
Forest Planning Manager, Forest Technology Group
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2. In this section…
We will review terminology
Outcomes
Conditions
Activities
Linear programming (LP)
Develop a base LP model for the Daniel Pickett forest
Stratification
Yields
Actions & Transitions
Make changes to the base model to evaluate different policies
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3. Terminology Review
Outcomes
More traditional outputs of economic goods & services
Timber harvest volume, recreational visitor days, forage in AUM’s, etc.
Conditions
Current & future spatial and element structure of forest ecosystem
Area by stand or habitat type, # of snags/ac, road densities, etc.
Activities
Human related disturbances occurring on the forest
Harvest acres, prescriptions used, miles of road built, etc.
Any of these can be viewed as positive or negative depending on goals
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4. Terminology Review
Linear programming
Constrained optimization problems
Without constraints, there is no LP problem
Allocation or scheduling of scarce resources
Key assumptions
Linearity: relationships are strictly linear
If you double the acres harvested, the volume harvested also doubles
Divisibility: any fractional quantity is allowed
Any fractional acre can be harvested; otherwise is mixed-integer
programming (MIP)
Deterministic: all coefficients are known with certainty
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5. Daniel Pickett Forest*
Could be anywhere
Specifics of site quality, location & species not identified
2500 acres
1000 ac = good site, well stocked, healthy, 100 yrs (old growth)
500 ac = poor site, cutover, diseased, 100 yrs (old growth)
1000 ac = poor site, well stocked, healthy, 10 yrs (young growth)
* Based on material from Davis et al., Forest Management, 4th ed. 2001. Chapters 3 & 12.
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6. Daniel Pickett Forest
3 Watersheds
Dogwood Creek
Trout Creek
Whitewater Creek
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7. Daniel Pickett Forest
Streamside Management Zones
100 ft buffers
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8. Daniel Pickett Forest
2 Site Classes
Good (red)
Poor (green)
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9. Daniel Pickett Forest
Stand Condition
Healthy, well stocked (green)
Diseased, cutover (red)
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10. Daniel Pickett Forest
Existing Forest Characteristics
Mixed forest type*
Watershed
Management emphasis (timber
production vs SMZ)
Site quality*
Stand Condition*
Harvest Units
* drivers of growth & yield
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11. DP Resource Capability Model
Known Management Objectives/Constraints
Maximize net present value of forest using 4% discount rate
Harvest volume not to vary by more than 20% period-to-period
At least 200 ac must be set aside in park-reserve status
At least 100 contiguous acres of existing healthy old growth must
be set aside as uncut park to protect the habitat of endangered owl
No more than 700 ac can be harvested in each of the first 3
periods to give a good distribution of area by ages
Even-aged prescriptions should not exceed 40% of total forest
Clearcut prescriptions = no more than 20% of forest area and no
more than 30% of each watershed
Desired future conditions based on WHR system
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12. DP Resource Capability Model
Outcomes & Activities (Outputs) Model codes
PNV (4%) OFpnv4
Harvest volume OQvol
Acres in park-reserve status OAreserve
Acres in owl habitat status OAowl
Acres harvested OAharv
Acres clearcut harvested OAcc
Acres in evenaged Rx’s OAeven
Acres clearcut in each OAccdc, OAcctc OAccwwc
watershed (spatial constraint)
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13. DP Resource Capability Model
Desired future conditions Outcomes
Based on Wildlife Habitat Acres within each desired
Relationship classification WHR class
Species (1 class – mixed species) OAm1m, OAm1d (250 ac @8)
Size class (6 diameter classes) OAm2m, OAm2d (250 ac @8)
Stand density (2 classes) OAm3m, OAm3d (500 ac @8)
OAm4m, OAm4d (750 ac @8)
OAm5m, OAm5d (250 ac @8)
OAm6m, OAm6d (500 ac @8)
DFC in period 8
No more than 20% change
period-to-period thereafter
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14. DP Resource Capability Model
Four Management Prescriptions (Activities)
Rx1=even-age, 30 yr rotation, plant & regeneration harvest in 30 yr
All stand types are eligible for this prescription
Rx2=even-age, 40 yr rotation, naturally regenerate with supplemental
planting if need, commercial thin at age 20, regeneration harvest at age 40
Only good sites are eligible for this prescription
Rx3=even-age, 90 yr rotation, plant & regeneration harvest in 90 yr
All stand types are eligible for this prescription
Rx4=uneven-age, small group selection, 2-ac or smaller openings, 60 yr
rotation (enter 1/6 of area assigned to Rx each decade, regeneration
harvest at age 60
Only good sites are eligible for this prescription
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15. DP Resource Capability Model
Stumpage Revenues Logging Costs
Healthy old growth= $4/cu ft Healthy old growth, on good
Diseased old growth= $2/cu ft sites = $1.00/cu ft
Young growth= $2.50/cu ft Diseased old growth, on poor
Site prep/Regen sites = $1.50/cu ft
Good sites= $500/ac Healthy young growth on good
sites = $0.75/cu ft
Good sites= $300/ac
Healthy young growth on poor
Management fees sites = $1.25/cu ft
Good sites= $30/ac/decade Discount rate
Poor sites= $20/ac/decade 4% discounted to middle of
planning period
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16. DP RCM – Base
Planning Horizon
_LENGTH = 12 decades
Objective
_MAX OFpnv4 _LENGTH
Constraints
None: pure profit maximization
Total forest acres = 2500 (LP constraint but always assumed)
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17. DP RCM – Base
Results
PNV = $10,852,028
Maximum volume change period-to-period = +∞,-100% (<20%)
100% of forest in evenaged Rx’s (<40%)
Maximum acres clearcut in 1st three periods = 443.92 (<700)
100% of Dogwood Crk assigned clearcut Rx (<30%)
100% of Whitewater Crk assigned clearcut Rx (<30%)
100% of Trout Crk assigned clearcut Rx (<30%)
0 ac assigned park-reserve status (>200)
0 ac assigned to uncut owl habitat preservation (>100)
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18. DP RCM – Policy 1 (original DP)
Original Daniel Pickett problem (Chapter 11)
Planning Horizon
_LENGTH = 12 decades
Objective
_MAX OFpnv4 _LENGTH
Constraints
OAreserve >= 200 1 ; at least 200 ac in park-reserve status
OAowl >= 100 1 ; at least 100 ac of existing good old growth uncut for owls
_SEQ(OQvol,0.2,0.2) 1.._LENGTH ; harvest volume to vary by < 20%
OIGvol >= 5000000 _LENGTH ; preharvest inventory[12] > 5000000
OAcc <= 700 1..3 ; no more than 700 ac clearcut harvested in 1st 3 periods
OArx2 >= 400 _LENGTH ; at least 400 ac of Rx 2 assigned
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19. DP RCM – Policy 1
Results
PNV = $8,279,139
Maximum volume change period-to-period = 20% (<20%)
Maximum acres clearcut in 1st three periods = 700 (<700)
200 ac assigned park-reserve status (>200)
100 ac assigned to uncut owl habitat preservation (>100)
Preharvest inventory in last period = 5,000,000 (>5,000,000)
92% of forest in evenaged Rx’s (<40%)
100% of Dogwood Crk assigned clearcut Rx (<30%)
93% of Whitewater Crk assigned clearcut Rx (<30%)
83% of Trout Crk assigned clearcut Rx (<30%)
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20. DP RCM – Policy 2
Constraints
OAreserve >= 200 1 ; at least 200 ac in park-reserve status
OAowl >= 100 1 ; at least 100 ac of existing good old growth uncut for owls
_SEQ(OQvol,0.2,0.2) 1.._LENGTH ; harvest volume to vary by < 20%
OIGvol >= 5000000 _LENGTH ; preharvest inventory[12] > 5000000
OAcc <= 700 1..3 ; no more than 700 ac clearcut harvested in 1st 3 periods
OArx2 >= 400 _LENGTH ; at least 400 ac of Rx 2 assigned
OAeven <= 1000 1.._LENGTH ; no more than 40% of forest in evenaged Rxs
OAcctc <= 0.3 * OAtc _LENGTH ; acres clearcut in Trout Crk < 30% of
watershed
OAccdc <= 0.3 * OAdc _LENGTH ; acres clearcut in Dogwood Crk < 30% of
watershed
OAccwwc <= 0.3 * OAwwc _LENGTH ; acres clearcut in Whitewater Crk <
30% of watershed
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21. DP RCM – Policy 2
Results
PNV = $4,006,265
Maximum volume change period-to-period = 20% (<20%)
Maximum acres clearcut in 1st three periods = 700 (<700)
200 ac assigned park-reserve status (>200)
100 ac assigned to uncut owl habitat preservation (>100)
Preharvest inventory in last period = 5,000,000 (>5,000,000)
30% of forest in evenaged Rx’s (<40%)
30% of Dogwood Crk assigned clearcut Rx (<30%)
30% of Whitewater Crk assigned clearcut Rx (<30%)
30% of Trout Crk assigned clearcut Rx (<30%)
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22. DP RCM – Policy 1
Desired Future Conditions
Acre proportions of period 8
Sequential change in proportions thereafter < 20%
OAm1m/OAm1d (250 ac @8)
OAm2m/OAm2d (250 ac @8)
OAm3m/OAm3d (500 ac @8)
OAm4m/OAm4d (750 ac @8)
OAm5m/OAm5d (250 ac @8)
OAm6m/OAm6d (500 ac @8)
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23. DP RCM – Policy 1
Habitat Composition
2500
2000
M6D
M6M
M5D
Acres of Habitat Type
M5M
1500
M4D
M4M
M3D
M3M
1000
M2D
M2M
M1D
M1M
500
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Planning Period
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24. DP RCM – Policy 2
Habitat Composition
2500
2000
M6D
M6M
M5D
Acres of Habitat Type
M5M
1500
M4D
M4M
M3D
M3M
1000
M2D
M2M
M1D
M1M
500
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Planning Period
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25. DP RCM – Policy 3
Constraints Constraints (cont’d)
*OBJECTIVE _SEQ(OIM6,0.2,0.2) 9.._LENGTH
_GOAL(g1,g2,g3,g4,g5,g6) ; minimize _SEQ(OIM5,0.2,0.2) 9.._LENGTH
deviations from WHR goals _SEQ(OIM4,0.2,0.2) 9.._LENGTH
*CONSTRAINTS _SEQ(OIM3,0.2,0.2) 9.._LENGTH
OAreserve >= 200 1 ; at least 200 ac _SEQ(OIM2,0.2,0.2) 9.._LENGTH
in park-reserve status
_SEQ(OIM1,0.2,0.2) 9.._LENGTH
OAowl >= 100 1 ; at least 100 ac of
existing good old growth uncut for
owls
OIM6 = 500 _GOAL(G6,1,1) 8
OIM5 = 250 _GOAL(G5,1,1) 8
OIM4 = 750 _GOAL(G4,1,1) 8
OIM3 = 500 _GOAL(G3,1,1) 8
OIM2 = 250 _GOAL(G2,1,1) 8
OIM1 = 250 _GOAL(G1,1,1) 8
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26. DP RCM – Policy 3
Results
PNV = $229,564
Maximum volume change period-to-period = -50%,+147% (<20%)
Maximum acres clearcut in 1st three periods = 302 (<700)
200 ac assigned park-reserve status (>200)
100 ac assigned to uncut owl habitat preservation (>100)
Preharvest inventory in last period = 5,002,078 (>5,000,000)
40% of forest in evenaged Rx’s (<40%)
50% of Dogwood Crk assigned clearcut Rx (<30%)
41% of Whitewater Crk assigned clearcut Rx (<30%)
28% of Trout Crk assigned clearcut Rx (<30%)
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27. DP RCM – Policy 3
Habitat Composition
2500
2000
M6D
M6M
M5D
Acres of Habitat Type
M5M
1500
M4D
M4M
M3D
M3M
1000
M2D
M2M
M1D
M1M
500
0
0 1 2 3 4 5 6 7 8 9 10 11 12
Planning Period
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28. DP RCM – Policy 3
Why can’t we meet DFC? What do we need to do?
None of the Rx’s will produce Develop new silvicultural Rx’s
M6M/M6D – only existing that can produce M6M/M6D
good old growth has it so it types
must be largely left
unharvested
Few Rx’s produce early WHR Possibly find better growth &
types yield models to predict WHR
Some constraints are too Explore additional scenarios
onerous Modify constraints
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29. DP Resource Capability Model
Features
Scheduled:
Clearcut final harvest, group selection, commercial thinning
Natural and artificial regeneration
Some variations of DP RCM not shown included fertilization
Tracked
Volume outputs, revenues, costs
Activity levels (acres treated)
Wildlife Habitat Relationship classification acres
Could easily track products, forage acres, etc.
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30. Forest Management Planning
What is required?
Computer hardware
Fast CPU, lots of memory, disk space (all much cheaper in recent years)
Computer software
Forest planning models
Commercial products: Woodstock, Ep(x), Habplan
Public Domain: Spectrum (FORPLAN), SARA
Growth & Yield models
Stand-level for volume/product outputs
Individual tree models for habitat/ecosystem variables
Geographic Information/Inventory
Sufficient and Complete
Expertise
Subject matter experts in economics, biometrics, forest management, GIS
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31. Visualization
Today
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32. Visualization – 20 years later
20-years into future
20-years into future
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33. Part 3 – Questions & Answers
In this section…
We will open up the discussion to questions from audience
What planning problems can I address using this technology?
How do I incorporate this facet of the problem into a forest planning
model?
How do I go from a strategic planning model to something I can
implement on the ground?
Discuss issues on technology and expertise
Should I do this stuff in-house, or should I contract it out?
Final take-away points
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34. Issues
Hardware is probably the cheapest aspect
Capacity continues to grow
Data availability is often more limiting
Access to growth & yield models
Plot data
Research and Development
In-house R&D, membership in cooperatives, public domain
Expertise
Requires a group of experts working together
Limited supply
Relatively few people available with the training/experience needed
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35. Final Thoughts – 7 Points
Know the long-term & short-term goals of the landowner/decision-
maker. Are these priorities documented?
Establish the time-frame for the analysis. Next year? Next 10 years? Next
20-50 years? All of these?
Do you need to consider county, state, federal laws or regulations? Do
outside interests need to be recognized in your plan?
Is spatially-explicit information needed for implementation?
Critically evaluate your available data. Is it sufficient and complete to
meet your planning needs?
How will your silvicultural prescriptions be generated? How will you
generate estimates of outcome arising from them?
Who are the people that will be doing this work for you? Are they in-
house specialists? Out-sourced specialists? Combinations?
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