MARV 15 Mathematical methods for forest planning

1
MARV 15Mathematical methods for forest planning

• Juha Lappi

2
Forest planning at stand and forest level

• starting point of planning
• we can predict how trees grow
• we can do treatments whose effects can be
  predicted
• harvests getting timber
• silviculture getting costs
• we can compare costs and benefits
• uncertainty expected value/variance

3
Economic planning

• measure costs and benefits in euros
• predict price development
• price of money interest
• saving interest/interest for loans
• in forestry long time horizon how to compare
  euros in different time points

4
stand/forest

• planning can be made at stand level, if it holds
  for income and costs
• euro_t(stand1stand2) euro_t(stand1)euroja_t(sta
  nd2)
• holds if labor and machines have unlimited
  availability at fixed price and price of timber
  does not depend on the amount
• utility(euro_t1 euro_t2) utility(euro_t1)hyöty
  (euro_t2)

5
Present value

• How to compare money flows from present to
  infinity?
• Perfect capital market
• unlimited loans
• unlimited savings
• saving interest loan interest
• gtfor all time preferences one can maximize net
  present value

6

• present value
• i interest
• r 1i
• Rt net income at year t

7
Rotation

• Repeat the same cycle, starting from bare land
  with value L

8
Rotation/value growth

• Fix regeneration and thinnings presnet value P
• Value of final cutting V(t), G(t)V(t1)-V(t)

9
Stand level optimization

• decision variables species, regeneration method,
  fertilization, timing, intensity and methods of
  thinning
• optimization methods
• direct search
• random search
• dynamic programming
• nonlinear programming

10
decision tree
P periods each has t nt alternatives Nn1
.np timing of treatments beginning, middle or
end of period
11
Decision tree/J

• can be used for
• stand level optimization
• to generate schedules for forest level analyses
• generate a tree
• node z at period t
• function next() daughter node
• function branch() sister node

12
Planning at forest level

• needed, when
• limited availability of labor or machines
• Non perfect capital market
• amount of timber has influence on price
• can be used to analyze the space of alternative
  cutting profiles