Forest
Economics - Economic optimisation, risk and uncertainty
-
A possible mission in two sections!
- Optimal
forest economic planning in a world with stochastic events
By Peter Lohmander
www.Lohmander.com
Version 2002-03-15
Objectives:
When you have completed this mission,
you should:
- understand the foundations of optimal resource management in the presence of risk, sequential information and adaptive decisions.
- understand how to derive optimal objective function values and decision rules.
- understand how the time horizon, the rate of interest, the growth of the resource and other conditions affect the optimal objective function values and decision rules.
- understand how the properties of the stochastic events affect the optimal objective function values and decision rules.
- know the principles of stochastic dynamic programming
- know how to formulate and solve stochastic dynamic programming problems in finite time using VBScript and LINGO.
- know how to formulate and solve stochastic dynamic programming problems in infinite time using linear programming and standard software.
- know how to solve stochastic forest management problems in finite and infinite time using stochastic dynamic programming.
- know some typical optimal results
in forestry from your own region.
Locally relevant forest management parameters:
In this mission, you will notice that you need
some parameter values. Select locally relevant parameters! The principles
of the mission are not functions of the exact parameter values but the
results are much more interesting if you know that the parameters really
are relevant. It is also much easier to discover large errors if you know
something about what to expect.
Mission 1.
You own a forest stand. The next decision will be to harvest everything and replant a new generation. The volume per hectare and the growth per hectare and year are known functions. The price and harvest costs per cubic metre right now are known. The size per tree and the quality development of the stand are known functions of time. The stochastic properties of prices are known. The rate of interest in the capital market is known.
You can select to harvest the stand at any point in time. In order to simplify the problem, the last possible harvest year occurs 50 years from now.
You want to maximize the expected present value of everything which has to do with the management of this stand.
General questions:
Determine the optimal decision rules to be used in this problem!
Determine the optimal expected present values at different points in time (in case you have not already harvested the stand at that points in time).
Determine
the probability that it will be optimal to harvest the stand at the different
future points in time.
Detailed questions:
Which are the lowest prices (reservation prices) which motivate harvesting at different stand ages?
How sensitive are the expected present values and the reservation prices to the degree of risk in the probability functions (and/or probability density functions) of future prices?
How high are the probabilities that harvesting is optimal at different stand ages?
What is the meaning of flexibility in this stochastic dynamic optimization problem?
How are the optimal expected present values, reservation prices and harvest age probability distributions affected by:
a. Constraint 1: The lowest allowable harvest age
b. Constraint 2: The highest allowable harvest age
c. The properties of the volume function at high ages
Compare your results to the results in Chapter 12, The properties of the timber supply function in a risky world, in Johansson and Löfgren (1985). What are the main differences between your model and the models in J&L? Are there differences and/or similarities with respect to results?
Optimization approaches:
During Mission 1, you should use the following methods:
Stochastic dynamic programming in finite time with a continuous price dimension.
Stochastic
dynamic programming in finite time with discrete price states where price
transitions are described via a stochastic Markov chain.
Mission 2.
You own a forest stand. You use "continuous cover forestry" principles. This means that your forest consists of trees of different sizes. When you harvest, you cut some part of the stock and the remaining stock grows at least one more period. The growth is a known function of the stock level.
You want to optimize your decision rules. The stochastic properties of prices are known. The rate of interest in the capital market is known. You can select to harvest the stand at any point in time.
You want to maximize the expected present value of everything which has to do with the management of this stand. You have an infinite horizon.
General questions:
Determine the optimal decision rules to be used in this problem!
Determine the optimal expected present values for the possible states.
Determine the optimal harvest levels for the different possible price and state combinations.
Detailed questions:
How are the optimal decisions affected by the level of risk in the price process?
How are the optimal expected present values affected by the level of risk in the price process?
Compare
your results to the results in Chapter 12, The properties of the timber
supply function in a risky world, in Johansson and Löfgren (1985).
What are the main differences between your model and the models in J&L?
Are there differences and/or similarities with respect to results?
Optimization approaches:
During Mission 2, you should use the following method:
Stochastic
dynamic programming in infinite time with discrete price and volume states
where price transitions are described via a stochastic Markov chain.
Very important:
A reader with a good methodological education should be able to reproduce the presented results and conclusions. No necessary assumptions should be forgotten.
A reader
with a university exam should be able to read the text, understand the
purpose and the conclusions.
Deadlines:
According to later information
Links:
General adaptive forestry ideas:
( Slumpp1.htm )
Pulse harvesting
Continuous cover forestry
Some references on optimal sequential forestry decisions in the presence of risk