Model Semantics

The model is the Daugherty (1991) case-study reproduced in ws3. This page records exactly what it computes and its known limitations.

The open-loop LP

A strata-based long-term timber harvest-scheduling LP. The forest is partitioned into development types (strata) by ecoclass, prescription, and age; the decision allocates stratum area to harvest over a 150-year horizon (15 x 10-year periods). The objective is maximization of present net value (PNV) at a 4% discount rate, with delivered-log prices escalating at 1%/yr for the first 50 years. A harvest-flow (even-flow) constraint ties each period’s harvest volume to within a tolerance of the reference period. Harvest regenerates the stand to age 0 (mature stands convert to the base managed prescription; managed stands regenerate to themselves).

This is a Model I formulation. Daugherty (1991) used Model II; the dynamic-inconsistency result is a property of the objective x flow-constraint x forest-structure interaction, not the variable-aggregation scheme (Gunn 2007, ch. 16 covers the Model I/II/III distinction). The ws3 Model II path is stubbed and is a deferred ws3 enhancement.

The case-study data

The thesis gives the case-study structure and anchor tables (Tables 5.1-5.5) but not the raw per-age yield curves, per-stratum areas, or detailed price/cost tables (those are in the archival USDA 1987 Umpqua EIS). The economics are reconstructed in fresh_daugherty.instance.reconstruct and calibrated to the Table 5.3/5.4 anchors; the yield-curve shapes are grounded in the Umpqua LRMP’s documented CMAI culmination ages (Table IV-3). This is a documented reconstruction with explicit assumptions (RECONSTRUCTION_ASSUMPTIONS), not a transcription.

Dynamic inconsistency

The open-loop LP is solved once over the full horizon (open-loop: the planner precommits future planners). The sequential-replanning simulator (fresh_daugherty.replan) re-solves from the realized state each period. The open-loop plan’s projected harvest diverges from the realized replanned trajectory: the plan is not followed, so it is not a credible basis for policy. This is the failure of Bellman’s principle of optimality, reproduced.

Known limitations

  • Reconstruction fidelity: the case-study economics are a documented reconstruction calibrated to the thesis anchors (PNV magnitudes match to ~1%; rotation ages are approximate, because the thesis’s irregular rotation pattern encodes the unavailable Umpqua yield tables).

  • Model form: Model I (not the thesis’s Model II); noted as a fidelity caveat, not a deviation of substance.

  • Simulator horizon: the default rolling fixed horizon avoids the terminal-period artifact of a shrinking horizon; both are available.

  • Regenerated-prescription choice: harvest regenerates to the base managed prescription; the full prescription-choice fan-out is a refinement.

  • Landbases 3-8 (area-control-harvest-derived) are documented as not yet constructed.