Optimal Rotation Length

Select the best supplied rotation by perpetual equal-cycle land expectation value with establishment and year-end annual holding cost; fixed real discount/price/productivity assumptions, not a continuous biological optimum.

Description

Land expectation value compares repeating rotation scenarios under fixed discount and cost assumptions.

Land expectation value compares repeating rotation scenarios under fixed discount and cost assumptions. Selecting the best supplied candidate differs from solving a continuous biological optimum.^[1]

When to use Optimal Rotation Length

Use this tool to select the best supplied rotation by perpetual equal-cycle land expectation value with establishment and year-end annual holding cost; fixed real discount/price/productivity assumptions, not a continuous biological optimum.

Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.

How to use Optimal Rotation Length and understand its results

Gather the tree inventory, plot measurements or model parameters. Check diameter, area, time and moisture conventions; keep paired observations aligned.
Enter candidateRotationYears, netHarvestRevenues, establishmentCost, annualHoldingCost, annualDiscountRate using the field table and calculation rules, then run the tool.
Read landExpectationValues, bestCandidateRotationYears, bestCandidateLandExpectationValue. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
candidateRotationYears	Candidate rotation years	list of number	Required
netHarvestRevenues	Net harvest revenues	list of number	Required
establishmentCost	Establishment cost	number	Required
annualHoldingCost	Annual holding cost	number	Required
annualDiscountRate	Annual discount rate	number	Required

Supply at least two increasing positive candidate years, aligned signed net harvest revenues, positive annual discount rate and nonnegative establishment/annual holding costs. Use stable log1p/expm1 discount factors. Return candidate values and the first candidate attaining the maximum.

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

LEV=[harvest revenue exp(−Tlog(1+r))−establishment cost]/[1−exp(−Tlog(1+r))]−annual holding cost/r

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
landExpectationValues	Land expectation values	list of number
bestCandidateRotationYears	Best candidate rotation years	number
bestCandidateLandExpectationValue	Best candidate land expectation value	number

json

{
  "input": {
    "candidateRotationYears": [
      1,
      2
    ],
    "netHarvestRevenues": [
      30,
      70
    ],
    "establishmentCost": 10,
    "annualHoldingCost": 1,
    "annualDiscountRate": 0.1
  },
  "output": {
    "landExpectationValues": [
      180,
      265.7142857142857
    ],
    "bestCandidateRotationYears": 2,
    "bestCandidateLandExpectationValue": 265.7142857142857
  }
}

Limitations and assumptions

Revenue, productivity and discount assumptions remain fixed across perpetual equal cycles. No market rates or continuous optimum are inferred.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Culmination Age MAI PAI: Audit sampled cumulative production through MAI and interval PAI, returning first age of sampled MAI maximum; distinct from existing one-interval increment formulas and no continuous unsampled peak inferred. For a complementary task, use Site Productivity Index: Compare accounted standing+removed+mortality production to a caller age/area-compatible reference; unlike standing-volume MAI, removals and mortality are included, with no universal yield class.

References

Optimal Rotation Length — tool.io

Similar or alternative tools

Culmination Age MAI PAI
Audit sampled cumulative production through MAI and interval PAI, returning first age of sampled MAI maximum; distinct from existing one-interval increment formulas and no continuous unsampled peak inferred.
Site Productivity Index
Compare accounted standing+removed+mortality production to a caller age/area-compatible reference; unlike standing-volume MAI, removals and mortality are included, with no universal yield class.