What's It All Mean?
Well, this is a way of portraying a sample solution from the following paper
that John Rust and I have written, entitled
In a nutshell, we divided up a particular forest district into hectares,
squares that are one hundred metres by one hundred metres. On each, we
estimated harvesting and transportation costs and, for each, we know an
equation of motion that determines the volume of harvestable timber. We
solved thousands of stochastic dynamic programming problems and then aggregated
the solutions. The movie has three parts: On the left is a map of the
geographic area, the Fraser Timber Supply Area (TSA). The black is land that
cannot be used for growing trees. The remainder of the squares change colour
as the trees grow: Seedlings are white; mature trees are dark green.
The top panel on the right is a time-series graph of a mean-reverting
AR(1) stochastic process of lumber prices. In the panel below is graphed
the total volume of timber available for harvest, obtained by aggregating
the individual harvesting decisions of over 200,000 virtual harvesters. We
have simulated this TSA for five hundred years.