Simulation Model
Gross margin templates were developed for a number of livestock and forestry enterprises. A Monte Carlo simulation approach was used to select values from statistical distributions of animal production, stock mortality, plantation forestry yield and prices which were then used to calculate possible gross margin values. Correlation between variables were maintained using Spearman's rank correlation coefficients.
Linear Programming Model
The linear programming sub-model selects enterprise combinations in order to maximise expected net revenue (Z) subject to constraints on available land classes, seasonal pasture growth, seasonal feed deficit, target income and an acceptable mean negative deviation of revenue from a target income. The linear programming model may be stated as (Parton and Cumming 1990):
Maximise Z = R X
subject to: AX<B; R*X+d->T; Pd- <D; X, d->0
Where
R* = is a series of m, 1 x n simulated net revenues for each enterprise option derived
from the simulation model described above;
R = 1 x n vector, the mean of R*.
X = 1 x n vector of activity (enterprise) levels;
B = 1 x k vector of resource constraints;
A = k x n matrix of resource requirements (mainly seasonal pasture dry matter required by
each class of livestock stock, area required to grow forest trees);
T = m x 1 vector of equal target income (fixed financial obligation);
d- = 1 x m vector of negative deviations from target;
P = 1 x m vector of probabilities (each equal l/km);
D = a scalar, parameterised from 0 to large value (desired expected negative deviation
from T);
n = number of activities (1 sheep class, S beef cattle classes, 2 forestry enterprises);
m = Number of observations (50);
k = number of resource constraints (7 land classes, available seasonal pasture dry matter
growth on each land class, maximum winter feed deficit).
The model maximises the expected net farm income subject to constraints shown above and for specific levels of downside risk. Results for different levels of risk aversion are achieved by solving the model successively for parameterised values of D, from 0 to a large number. The solution for D equal to zero corresponds to a (safety first) no risk decision rule, while the solution for very large D is equivalent to the solution from a deterministic linear program.
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