A system for solving spatial forest planning problems

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Implementation of Woodstock and Stanley at Champion International

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A system for solving spatial forest planning problems

  1. 1. A system for solving spatial forest planning problems Karl R. Walters Ugo Feunekes Andrew Cogswell Eric Cox
  2. 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. 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. 4. Historical perspective
  5. 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. 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. 7. Southern pine plantations
  8. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 19. Case study
  20. 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. 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. 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. 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. 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. 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

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