Apresentação de Silvana Nobre, socio-fundadora da Atrium Forest Consulting durante o ciclo de seminários em Pesquisa Florestal Avançada na Universidade Politécnica de Madrid, em 20 de fevereiro de 2013.

1. The use of linear programming to
integrate forest operations
Silvana Nobre
Atrium Forest Consulting, Brasil
silvana@atriumforest.com

2. The use of linear programming to
integrate forest operations
1. Overview on Brazilian forest-based companies
2. First-sight Problem: Clonal seedlings allocation
3. Integration A: Plantation Activities Constraints
4. Integration B: Nursery Production process
5. Conclusions

3. 1 . Overview on
Brazilian forest-based
companies
Source: Bracelpa - 2010
179 units
from 400 to 237,000 ha
Total: 4,671,521 ha
Species: Eucalyptus,
Pinus, Teca,
Acácia, Paricá,
Araucária
Industries: Pulp & Paper
Solid & Panels
Steel Mills
Investments

4. 1 - Overview on Brazilian
forest-based companies

6. 2 - Clonal seedling allocation
Example….

7. 2 - Clonal seedling allocation
Tipical Pulp&Paper Forest Industry Unit
Industry Forest Unit
Productivity
Clear Cut
Annual Replanting Area
Spacing ( 2,5 x 3 )
Trees per area
Plantation eficciency
Seedling Need
95.254 ha
50 m3/ha.year
6 years old
15.876 ha
6 m2
1.667 trees/ha
95%
27.782.475 seedlings/year
Tipical Brazilian Stand
No Stands to plant in a year
Techinical Recomendation Units
Different Clones
20
794
4
6
TRU - 1
......
Fertilization x
---• Clone 1 – 300
• Clone 2 – 260
• Clone 3 – 220
Stand
1
3
5
3
4
3
794
......
Fertilization z
---• Clone 3 – 310
• Clone 1 – 250
• Clone 2 – 210
2
793
......
Fertilization y
---• Clone 2 – 320
• Clone 3 – 270
• Clone 1 – 230
2
4
TRU - 3
1
792
TRU - 2
1
2
ha
stands
Units
clones
TRU
4

8. 2 - Clonal seedling allocation
Maximizar Produção Potencial….
Max Z =
∑ P ij × X ij
•
Pij Probable Productivity of Stand i, if we plant clone j
•
Xij Area of Stand i, we will plant clone j
Exercise….
•
MS Excel ®
•
330 ha
•
5 stands
•
3 Technical Recommendation Units
•
3 Clones

9. Techinical
Recomendation
Unit
TRU1
TRU2
St1
Stands
Stand Area
St2
TRU3
St3
60
70
St4
80
St5
50
70
330
Clone
CL1
CL2
CL3
CL1
CL2
CL3
CL1
CL2
CL3
CL1
CL2
CL3
CL1
CL2
CL3
Productivity (m /
ha)
300
260
220
300
260
220
230
320
270
230
320
270
250
210
310
Sum: Stand-Clone
Area
60
0
0
70
0
0
0
80
0
0
20
30
0
0
70
3
Sum: Stand Area
60
70
80
50
70
330
Potential
Production (m 3 )
18,000
0
0
21,000
0
0
0 25,600
0
0
6,400
8,100
0
0
21,700
100,800
CL1
CL2
CL3
130
100
100
>=
>=
>=
100
100
100 ha
m3

10. 2 - Clonal seedling allocation
Max Z =
∑ P ij ×
X ij
•
Pij Probable Productivity of Stand i, if we plant clone j
•
Xij Area of Stand i, we will plant clone j
Subject to:
∑ X ij ≤ Ij, I =1, 2, 3, 4, 5 (stands)
∑ X ij ≥ Cj, j=1, 2, 3
(clones)
Where:
Ii, area of stand i that can be planted
Cj, at least this area must be planted with clone j

11. 3 - Plantation Activities Constraints
Exercise….
•
MS Excel ®
•
Pre-Planned Harvesting Process
•
Until 3 months after Harvesting
•
Planning Horizon: 12 months
•
Period: 1 month
•
1 team

12. One more Dimension: Time
>>>> Schedule problem
Techinical Recomendation Unit
TRU1
Stands
TRU2
Stand Area (ha)
St1
St2
St3
60
Clone
CL1
Productivity (m3 / ha)
CL2
CL3
CL1
300
260
220
Sum: Stand-Clone Area (ha)
60
0
0
60
TRU3
St4
70
CL2
CL3
St5
80
CL1
CL2
CL3
50
CL1
CL2
CL3
70
330
CL1
CL2
CL3
300
260
220
230
320
270
230
320
270
250
210
310
70
0
0
70
0
50
30
80
0
50
0
50
0
0
70
70
330
Potential Production (m3)
18,000
0
0
21,000
0
0
0
16,000
8,100
0
16,000
0
0
0
21,700
100,800
Months
1
2
3
4
5
6
7
8
9
10
11
12
30
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
30
30
0
0
0
0
0
0
0
0
0
0
0
0
0
Plantation per Period (Decision Variables)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
0
0
0
0
0
0
20
10
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
10
30
0
0
0
0
0
0
0

13. Stands Available to be planted
(Harvest constraint)
From short term Harvest scheduling model
Techinical Recomendation Unit
TRU1
Stands
TRU2
Stand Area (ha)
St1
St2
St3
60
1
2
3
4
5
6
7
8
9
10
11
12
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
70
0
0
0
0
0
0
0
0
1
1
1
1
TRU3
0
0
0
0
0
0
0
0
1
1
1
1
St4
St5
80
Stands Available to be planted (Harvest constraint)
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
50
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
70
330
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0

14. Operational constraint: Plantation Team Capacity
Techinical Recomendation Unit
TRU1
TRU2
Stands Stand Area (ha)
St1
60
St2
TRU3
St3
70
St4
80
St5
50
70
330
Plantation per Period (Results)
1
2
3
4
5
6
7
8
9
10
11
12
30
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
30
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
30
0
0
0
0
0
0
0
0
20
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
20
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
10
30
0
0
0
0
0
0
0
Monthly
Plt (ha)
30
30
30
30
30
30
30
30
30
30
30
0
330
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
=
Monthly Plt
Constraint
30
30
30
30
30
30
30
30
30
30
30
30
330

15. 3 - Plantation Activities Constraints
Max Z = ∑ P ij × X ijk
•
Pij Probable Productivity of Stand i, if we plant clone j
•
Xijk Area of Stand i, we will plant clone j, in period k
Subject to:
∑ X ij ≤ Ij, I =1, 2, 3, 4, 5 (stands)
- Area Constraints
∑ X ijk ≥ Cj, j=1,2, 3
(clones)
- Biological Constraints
∑ X ijk ≤ Tk, k= 1 to 12
(periods)
- Plantation Team Capacity
∑ X ijk = 0 , for some stands i in some periods k - Harvest Constraints
Where:
Ii, area of stand i that can be planted
Cj, at least this area must be planted with clone j
Tj, maximum productivity of a team plantation in each period k

16. 4 - Nursery production process
1st Step :
Clonal Garden
2nd Step : Collect mini-cuttings
from mini-stumps
3rd Step : cuttings production

17. 4 - Nursery production process
4th Step : Green House
5th Step : Open Space Growth

18. 4 - Nursery production process
6th Step : Seedlings Deliver Space
•
MS Excel ®
•
Constraints:
 Cutting production team
 Green House Occupation
 Clonal Garden Capacity

19. Seedlings requirements per clone per period
TRU1
TRU2
TRU3
Stands
St1
Replant Eficiency (%)
3%
Spacing (trees/ha)
1667
Stand Area (ha)
60
Clones
CL1
CL2
CL3
CL1
Months
16,250
15,234
22,544
6,043
0
0
0
0
0
0
0
0
13,835
0
0
0
0
0
0
0
0
0
0
0
21,425
7,689
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
23,843
16,250
16,250
39,000
St2
St3
3%
1667
70
CL2
CL3
St4
3%
1111
80
CL1
CL2
CL3
St5
3%
1111
50
CL1
Seedling requirements per Period Per Clone
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 16,935
0
0
0
0
0 25,445
0
0
0
0
0 21,843
0
0
0
0
0
0
0
0
0
0
0 26,152
1,172
0
0
0
0
0
0
0
0
0
0
0
0
0
12,337
0
0
0
0
0
0 12,510
0
0
0
0
CL2
0
0
0
0
0
0
8,271
7,006
9,345
16,323
0
0
CL3
0
0
0
0
0
0
0
0
9,094
7,177
0
0
3%
1515
70
CL1
0
0
0
0
0
0
14,801
0
0
0
0
0
CL2
330 ha
CL3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
26,325
18,228
12,116
17,028
20,733
0
0
0
0
0
Seedling Requirements per clone
CL1
CL2
CL3
16,250
13,835
21,425
15,234
0
7,689
22,544
0
26,325
6,043
16,935
18,228
0
25,445
12,116
0
21,843
17,028
14,801
8,271
20,733
0
33,158
1,172
23,843
9,345
9,094
16,250
16,323
7,177
16,250
12,337
0
39,000
0
12,510
It determines mini-cuttings requirements ….

20. Mini-cuttings requirements
Subject to:
Cutting production team constraint
mCt
Team
mini-Cuttings Requirements per clone mCt Need
CL1
25,000
23,437
34,683
9,297
0
0
22,771
0
36,682
25,000
25,000
60,000
CL2
19,764
0
0
24,193
36,350
31,204
11,816
47,369
13,350
23,318
17,625
0
CL3
10,679
36,563
25,317
16,827
23,650
28,796
1,627
12,631
9,968
0
17,375
0
55,443
60,000
60,000
50,317
60,000
60,000
36,215
60,000
60,000
48,318
60,000
60,000
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
60,000
It determines mini-stumps requirements ….

21. Mini-stumps requirements
Subject to:
Mini-Stumps that already exists in the Nursery
mini-Stumps Requeriments per clone
CL1
5,000
4,687
6,937
1,859
0
0
4,554
0
7,336
5,000
5,000
12,000
CL2
3,294
0
0
4,032
6,058
5,201
1,969
7,895
2,225
3,886
2,937
0
CL3
1,780
6,094
4,220
2,805
3,942
4,799
271
2,105
1,661
0
2,896
0
mini-Stumps in Clone Garden per clone
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
<=
CL1
16,000
16,000
16,000
16,000
16,000
16,000
16,000
16,000
16,000
16,000
16,000
16,000
CL2
8,000
8,000
8,000
8,000
8,000
8,000
8,000
8,000
8,000
8,000
8,000
8,000
CL3
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000
10,000

22. Max Z = ∑ P ij × X ijk
• Pij Probable Productivity of Stand i, if we plant clone j
• Xijk Area of Stand i, we will plant clone j, in period k
Subject to:
Area Constraints (stands)
∑ X ij ≤ Ij,
I =1, 2, 3, 4, 5
Biological Constraints (clones)
∑ X ijk ≥ Cj,
j =1, 2, 3
Plantation Team Capacity
∑ X ijk ≤ Tk, k = 1 to 12
Harvest Constraints
∑ X ijk = 0 , for some stands i in some periods k
Cutting Product.Team Capacity
∑ d j X ijk ≤ D k
Greenhouse Max Space
∑ g j X ijk
Mini-Stumps in the Nursery
∑ s j X ijk ≤ S jk , for j =1,2, 3 and k= 1 to 12
+
k= 1 to 12
g j X ijk-1 ≤ G k , for k = 1 to 12

23. Where:
I i,
area of stand i that can be planted
Cj, at least this area must be planted with clone j
Tj, maximum productivity of a team plantation in each period k
dj, nursery efficiency of clone j
Dk cuttings team capacity, in period k
gj, green house occupation factor of clone j
Gk green house maximum occupation in period k
s j,
mini-stumps need factor of clone j
Sjk mini-stumps in the Nursery in production of clone j, in period k

24. 5 - Conclusions
In one year, on 10% of the area you could have
planted the 1st clone, but you planted the 2nd one
10% area
>>>
10% diff produc >>>
Production difference >>>
Minimum Wood value >>>
Prouction Diff Value
Prouction Diff Value
•
>>>
MS Excel ® simplified exercise
•
•
>>>
5% of potential production
10% productivity from first to second clone
1,588 ha
3
30 m /ha
3
47,627 m
50 R$/m3
2,381,355 R$
850,484
€

25. silvana@atriumforest.com
www.atriumforest.com