|
 Printer Friendly |
Arbitrary model choices
One interesting, and sometimes perplexing, consequence of using linear programming (LP) for forest planning is that decision variables - the choice of how much area of a certain forest class to treat with a certain action in a certain planning period - may assume values in a seemingly random or arbitrary fashion. Arbitrary activities can in turn produce arbitrary forest outputs such as wood inventory levels and age class distributions, so it is important to be aware of arbitrary choices in your forest planning/harvest scheduling analyses.
In a forest planning/harvest scheduling context, a decision variable represents the amount of area of a forest class to treat with a management action in a planning period. Decision variables can assume any value, but are typically bounded by the total area in the class and zero (non-negativity being one of the assumptions of LP). The value assigned to a decision variable is usually determined by the objective function or limited by a constraint; however, if the variable does not contribute to the objective function and it is not included in a constraint row, then any value it assumes is essentially arbitrary.
Consider the following example. Assume that we have a Woodstock model with two management actions, clearcut harvest and planting. After regeneration harvest, forest types naturally regenerate, but may be converted to plantations immediately following harvest. The objective is to maximize the total volume harvested over 20 planning periods subject to an even-flow harvest volume. We are interested in how much area is being planted and, primarily, whether or not the planting decisions are arbitrary.
The model chose to plant, on average, approximately 15,330 hectares - almost 70% of the area harvested - per period. If we exclude planting entirely from the model and re-optimize, the total volume harvested is unchanged clearly indicating that planting does not increase the harvest volume - we won't get into the reasons why - and, more importantly, that the planting activities produced in the first run are completely arbitrary.
Rather than excluding planting - after all it likely makes sense in some situations - we can have the model make judicious planting choices by incorporating planting decision variables in the objective function.
For example, we can change the objective function to maximize the difference between the total volume harvested and the area planted, meaning that planting will lower the objective function value, i.e., is undesirable, unless offset by a larger increase in the total volume harvested.
In other words, the model will choose to plant only if it increases the harvest volume. By doing this, we eliminate arbitrary planting choices. We could also weight area planted in the objective function to better reflect the area/volume relationship, which as stated is one-to-one.
The example presented here represents an extreme case of arbitrary choices. Generally speaking, models that maximize present net value, i.e., that have costs associated with management actions, are impervious to arbitrary choices. Models that maximize volume may be more susceptible to arbitrary choices, but are typically tightly constrained, which favor judicious decision-making. The upshot is that a little scrutiny is justified when analyzing the management schedule produced from an LP. Abnormally high or low activity levels may indicate that the decisions were made arbitrarily.
An interesting aside, in an arbitrary decision environment, different LP solvers will produce different management schedules. For example, the planting schedule described above was produced using an interior point solver. I solved the model using a simplex solver and it chose to plant, on average, just under 7,700 hectares per period, about half as much as the other solver, and 12 periods had no planting at all. The differences can be chalked up to the different algorithms used to solve the matrix and the fact that planting decisions are of no consequence to the model.
|
|
Stora Enso Predicts a 2.5% Savings
“We asked, ‘If we had made the decision and optimized the problems, how much money would we have saved?’” The answer was approximately 2.5 percent.”
- Continue reading...
- View all case studies...
|
 |
|
|
|
