This document describes a two-stage spatial forest planning system developed by Remsoft to help Champion International Corp. optimize harvest scheduling while complying with sustainability guidelines. Stage one uses linear programming to determine optimal harvest volumes over time. Stage two uses heuristics to allocate harvests to contiguous blocks that meet size, proximity, and green-up constraints, yielding near-optimal solutions within 15 minutes. The system provides satisfactory solutions for Champion's large, complex forests.

1. A system for solving spatial
forest planning problems
Karl R. Walters
Ugo Feunekes
Andrew Cogswell
Eric Cox

2. Introduction
• Ongoing relationship
– Remsoft
• small software developer specializing in
forest & fire management
– Champion International Corp.
• multinational integrated forest products
company
• Solution to a difficult
planning/scheduling problem

3. Historical perspective
• Champion controls more than 5
million acres in US
• traditional southern pine plantations
– large uniform plantations
– highly concentrated age classes
– basic PNV maximization LP models
– manual harvest blocking/scheduling

4. Historical perspective

5. Changing times
• 1995: AF&PA adopts Sustainable
Forestry Initiative (SFI)
– greatly reduced harvest block areas
– buffers separate concurrent blocks
– multi-year green-up intervals separate
adjacent blocks
• 1996: SFI compliance becomes a
condition of AF&PA membership

6. Changing times
• Sustainable Forestry guidelines
– no clear-cut harvest areas > 240 ac
– clear-cut harvest areas < 120 ac unless
absolutely necessary
– contemporary clear-cut harvest blocks
separated by buffers 120 - 300’
– no clear-cut harvesting adjacent to a
recent harvest until 4-5 years elapse

7. Southern pine plantations

8. Unit Restriction Model
Maximize i = index of planning units,
(1) Z = ΣiΣt αit xit t = index of time periods,
Subject to αit = benefit or revenue
associated with treating unit i
(2) Σt xit < 1 ∀i in period t
(3) Σi βit xit > Lt ∀t βit = volume contribution for
(4) Σi βit xit < Ut ∀t treating unit i in period t
(5) xit + xjt < 1 ∀i, t, j ∈ Ni Lt = lower bound on total volume
produced in period t
(6) xit = (0, 1) ∀i, t
Ut = upper bound on total volume
produced in period t
⎧1 if unit i is treated in period t
Ni = set of planning units adjacent
xit = ⎨
to unit i
⎩ 0 otherwise.

9. Area Restriction Model
Maximize A = maximum permissible
(7) Z = ΣiΣt αit xit contiguous area treated
Subject to vi = area of unit i
(2) - (4), (6)
(8) ƒit(vix) < A ∀ i, t ƒit(vix) = recursive function
summing all treated
⎧1 if unit i is treated in period t
neighboring units
xit = ⎨ associated with xit (if xit=1)
⎩ 0 otherwise.

10. Comparison
• URM • ARM
– as an MIP can be – unlikely to be
solved exactly solved exactly
– limited problem – heuristics do not
sizes solved yield optimal
– requires prior block solutions
delineation – block layout part of
– formulation may not solution
represent real – directly models
problem regulatory
constraints

11. Remsoft’s approach
• Develops commercial applications
• Most literature solutions unsatisfying
– specialized applications (research)
– limited to small problem instances
– clumsy/limited user interfaces
– poor data management features
– little or no documentation or technical
support available

12. Remsoft’s approach
• Simplify the problem
• Most of the management decisions
are made in strategic model
• Tactical decisions reduced to
minimizing deviations from strategic
• Only types scheduled during tactical
planning horizon are blocked

13. Remsoft’s approach
• 2-stage ARM (Jamnick & Walters)
– Use LP to determine an optimal
schedule of stand-types to cut
– Use heuristics to allocate harvest
treatment prescriptions to stands
• Contiguous stands assigned the same
treatment in the same period defines a block
• Harvest blocks must meet maximum size,
proximity and green-up restrictions

14. Stage One
• Stratify forest according to
developmental characteristics
• Assign each forest stand (map
polygon) to one stratum
• Generate and solve LP harvest
schedule using Woodstock
• Identify outputs to be used to
measure goal attainment in Stanley

15. Stage Two
• Set parameters (harvest block size,
proximity distance, green-up interval)
• Set acceptable flow variations from
LP targets
• Generate spatial harvest schedules
under different scenarios
• Retain best solution found

16. Stage Three
• Make adjustments to Stanley solution
to reflect operational realities
• Iteratively re-run Stanley until
acceptable solution results
• Generate mapped solutions
• Incorporate Stanley solution into
Woodstock LP model to test long-
term sustainability

17. Quality of Solutions
• Woodstock/Stanley approach
generates satisficing solutions only
• URM has optimal scheduling solution
but requires block layout a priori
• Stanley yields block layout as part of
solution but schedule is not optimal
• Use Stanley blocks in an MIP
formulation to determine quality

18. Case study
• Forest of pine plantations, cypress
ponds and bottomland hardwoods
• 87 000 acres, 13 000 map polygons
• 25 year strategic, 10 year tactical
planning horizons (1 year periods)
• Maximize PNV subject to non-
declining flow constraints on harvest
volume

19. Case study

20. Case study
• Champion S&S guidelines
– 10 ac minimum blocks
– 120 ac maximum blocks
– 300 ft proximity distance
– 5 year green-up delay
• Stanley parameters
– allow +/-5% deviation in periodic flow
– run time = 15 min (Pentium II-266)

21. Case study results
Program Execution time Solution
Woodstock 44 s, matrix generation
C-Whiz 20 s, LP solution 45 525 cunits/year
LP2WK conversion 3 s,
Stanley 900 s 34 266 cunits/year min
76.4% of LP optimal
MIP formulation 3893 s, stopped after 35 224 cunits/year min
(maxmin) 4 integer solutions 77.4% of LP optimal
Flow variation Stanley – 4.9% MIP – 0.3%

22. Champion’s experience
• Initially drawn to Woodstock due to its
flexible modeling structure
– Acquired two copies of Woodstock for
testing purposes in 1995
– Woodstock adopted company-wide in
1996 as strategic planning model
• Stanley acquired as tactical planning
model in 1996-97

23. Champion’s experience
• Nearing completion of a new unified
forest information system
– Woodstock/Stanley integral part of it
– yield models link directly to Woodstock
through dynamic link libraries
– standard procedures ensure integrity of
data across strategic & tactical levels
– minimal in-house proprietary software

24. Champion’s experience
• User satisfaction high
– system based on sound theory
– solutions that make intuitive sense
– software interface makes it easy for
planners to apply professional judgment
– holistic approach to data management
ensures integrity across planning levels
– quality software and technical support

25. Conclusions
• Remsoft developed general modeling
tools with flexibility in mind
– good use of available OR technology
• Champion sought software solution
adaptable to wide range of conditions
– same software can be used for very
different forestland/operations
– ongoing relationship with developers