Table 1. Silvicultural actions proposed for the two products.
TIMBER SCENARIO
Age Operation Intensity
10 years pre-commercial thinning 350 trees/ha, with a density of 500 trees/ha
after this treatment
20 years pruning mainly in the lowest branches
40 years commercial thinning low thinning, with a density of 225 trees/ha
after this treatment
Rotation age (80–150 years) clearcuts leaving 10 seed trees by ha
CONE/PINE NUT SCENARIO
Age Operation Intensity
10 years pre-commercial thinning 350 trees/ha, with a density of 500 trees/ha
after this treatment
15 years pruning lowest branches up to 40–60% of the height
45 years commercial thinning low thinning, with a final density of 100 trees/ha
after this treatment
Rotation age (80–150 years) clearcuts leaving 10 seed trees by ha
Table 2. Costs associated with each scenario.
TIMBER SCENARIO
Year Operation Cost
following final cutting fenced to restrict grazing 1126.16€/ha
10 years pre-commercial thinning 285 €/ha
20 years pruning and removal of fence 552.62 €/ha
40 years commercial thinning 598 €/ha
CONE/PINE NUT SCENARIO
Year Operation Cost
following final cutting fenced to restrict grazing 1126.16€/ha
10 years pre-commercial thinning 285 €/ha
15 years pruning 440 €/ha
20 years removal of fence 112.62€/ha
45 years commercial thinning 870 €/ha
1

Fig. 1. Flow chart of PINEA2 model.

Table 3. Pay-off matrix. View in new window/tab.
Table 4. Forest area oriented towards each silviculture in the mixed scenario.
  NPVT NPVPN NPV TH YPN Volume control Regulation Ending forest inventory
Area orientated to timber silviculture 918.9 0.0 366.0 579.5 0.0 965.9 1093.6 777.3
Area orientated to pine nut silviculture 477.6 1396.5 1030.5 817.1 1396.5 430.6 302.9 619.2
Table 5. Solutions obtained using the goal programming method.
  TIMBER SCENARIO CONE/PINE NUT SCENARIO MIXED SCENARIO
λ = 1 λ = 0 λ = 1 λ = 0 λ = 1 λ = 0
NPV 782 070.8 701 682.8 823 957.6 823 896.9 872 732.3 841 638.9
TH 225 767.7 216 817.7 232 353.5 232 304.2 230 030.1 255 831.4
YPN 15 364 450.0 16 167 820.0 22 078 710.0 22 076 390.0 21 934 640.0 19 512 580.0
Volume control 0.0 1225.1 2293.3 2293.1 0.0 838.8
Regulation 123.6 318.8 141.8 141.8 164.7 198.8
Ending forest inventory 4629.9 13 079.5 47 022.9 46 999.3 35 780.8 48 135.1
NPV: total net present value of timber harvests and pine nuts yield
TH: timber harvests
YPN: yield of pine nuts
Volume control: sum of deviations of the volume control criteria in all the periods
Regulation: sum of deviations of the regulation criteria in all the periods
Ending forest inventory: sum of deviations of the ending forest inventory criteria in all the periods
Table 6. Area associated with each silviculture varying the parameter λ.
  λ = 1 λ = 0,8 λ = 0,6 λ = 0,4 λ = 0,2 λ = 0
Area orientated to timber silviculture 157.1 157.0 171.9 202.7 291.5 341.0
Area orientated to cone/pine nut silviculture 1239.5 1239.6 1224.7 1193.8 1105.0 1055.5
Table 7. Pay-off matrix in timber scenario when the initial constraint of minimum yield of pine nuts has been removed. View in new window/tab.