Based on my other question, here is a simpler hypothetical exercise that isolates that time constraint issue all together:
- A farmer has 1000 ha forest that is already at a mature age assumed to be 40
- currently 200 ha are of wood type A and the rest are of wood type B
Wood types A and B have the following m3 per ha
Age yield_A yield_B
25 10 10
30 20 20
35 31 49
40 40 63
45 50 70
Wood types regenerate at the following rate (m3/ha):
Age regen_a regen_b
5 3 4
10 11 19
15 24 35
20 35 48
25 50 69
30 75 86
35 101 121
wood type A sells for \$100/ha while type B sells for \$75/ha. Prices will increase 3% per period
Optimization:
Maximize the revenue of the farm over a 40 year period as well as period over period assuming 5 year periods and at that after 40 years , 70% of the forest is still planted.
Attempted solution:
Optimization functions:
max_revenue_period_n = ($_a * vol_a + $_b * vol_b) for period n
max_revenue_overall = ($_a * vol_a + $_b * vol_b)
Constraints:
at age 40: vol_a_40 + vol_b_40 >= 0.6 (vol_a_0 + vol_a_40)
Question:
How can I incorporate the time aspect of yields, regeneration, and optimizing over multiple periods into the problem?