Optimal selective logging regime and log landing location models: a case study in the Amazon forest

SILVA, Paulo Henrique da; GOMIDE, Lucas Rezende; FIGUEIREDO, Evandro Orfanó; CARVALHO, Luis Marcelo Tavares de; FERRAZ-FILHO, Antônio Carlos

doi:10.1590/1809-4392201603113

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Agronomy and Forestry • Acta Amaz. 48 (1) • Jan-Mar 2018 • https://doi.org/10.1590/1809-4392201603113 copy

Optimal selective logging regime and log landing location models: a case study in the Amazon forest

Regime de corte seletivo ótimo em modelos de locação de pátios de estocagem de madeira: um estudo de caso na floresta amazônica

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

Reduced-impact logging is a well known practice applied in most sustainable forest management plans in the Amazon. Nevertheless, there are still ways to improve the operational planning process. Therefore, the aim of this study was to create an integer linear programming (ILP) to fill in the knowledge gaps in the decision support system of reduced impact logging explorations. The minimization of harvest tree distance to wood log landing was assessed. Forest structure aspects, income and wood production were set in the model, as well as the adjacency constraints. Data are from a dense ombrophylous forest in the western Brazilian Amazon. We applied the phytosociological analysis and BDq method to define the selective logging criteria. Then, ILP models were formulated to allow the application of the constraints. Finally, 32 scenarios (unbalanced forest, UF, and balanced forest, BF) were generated and compared with real executed plans (RE). Robust results were achieved and the expected finding of each scenario was met. The feasibility to integrate ILP models in uneven-aged forest management projects was endorsed. Consequently, the UF and BF scenarios tested were efficient and concise, introducing new advances for forest management plans in the Amazon. The proposed models have a high potential to improve the selective logging activities in the Amazon forest.

KEYWORDS:
forest planning; reduced-impact logging; integer linear programming; sustainable forest management; Liocourt quocient

Notation	Description
Z	Vector resulting from the sum of log skidding distance i to log landings j.
c_ij	Log skidding costs (Euclidean distance) between tree i = {1, 2, ..., 1.699} and log landing j ={1, 2, ..., 366}.
x_ij	Binary decision variable {0, 1} used to skid tree i to log landing j.
v_ij	Tree commercial volume (m³) i designed to log landing j.
N	Total number of inventoried trees.
P	Total number of log landings.
VPMIN_j	Minimum timber volume capacity of log landing j.
y_j	Binary decision variable {0, 1} to activate log landing j.
VPMAX_j	Maximum timber volume capacity of the log landing (350 m³).
k	Number of diameter classes k = {1, 2, ..., 18}.
l	Number of species l = {1, 2, ..., 23}.
D_j ^kl	Maximum number of trees, identified as species l and diameter class k, able to be harvested based on the DBq method and dragged to log landing j.
VG_g	Maximum timber volume allowed to be explored in grid g (200 m³).
NA_g	Total number of trees to be explored per grid g.
w_g	Total number of trees in grid g.
g_g	Binary decision variable {0, 1} able to activate or not the harvest in grid g.
M	Total number of grids.
b_gk	Coefficient derived from the adjacency binary matrix {0, 1}.
e	Grid index of each adjacency matrix row.
D_máx	Maximum log skidding distance (400 m).
r_ij	Timber selling price of tree i (U$ 25.71 m^-3).
R_mín	Minimum income to be obtained at the end of the project (U$142,857.14).

Models	Equations
Models	2	3	4	5	6	7*	8	9	10	11	12	13	14
1	x	x	x	x	x	x						x	x
2	x	x	x	x	x	x					x	x	x
3	x	x	x	x	x	x			x	x	x	x	x
4	x	x	x	x	x	x			x	x		x	x
5	x	x	x	x	x	x		x			x	x	x
6	x	x	x	x	x	x		x				x	x
7	x	x	x	x	x	x	x				x	x	x
8	x	x	x	x	x	x	x					x	x
9	x	x	x		x	x						x	x
10	x	x	x		x	x					x	x	x
11	x	x	x		x	x			x	x	x	x	x
12	x	x	x		x	x			x	x		x	x
13	x	x	x		x	x		x			x	x	x
14	x	x	x		x	x		x				x	x
15	x	x	x		x	x	x				x	x	x
16	x	x	x		x	x	x					x	x

Scenarios	Models	Shannon index	Pielou	N_h	BA_h	Volume	Income
Scenarios	Models	Shannon index	Pielou	N_h	(m² )	(m³ )	(US$)
1	1	3.30	0.8896	931	527.16	6,791.92	174,649.4
2	2	3.30	0.8896	931	527.31	6,793.85	174,698.9
3	3	infeaseble solution
4	4	infeaseble solution
5	5	no solution before exceed run time limit
6	6	no solution before exceed run time limit
7	7	3.30	0.8896	931	527.61	6,789.88	174,596.9
8	8	3.30	0.8896	931	527.62	6,797.96	174,804.9
9	9	3.30	0.8896	931	527.21	6,792.95	174,676.0
10	10	3.30	0.8896	931	527.37	6,793.22	174,682.9
11	11	infeaseble solution
12	12	infeaseble solution
13	13	no solution before exceed run time limit
14	14	no solution before exceed run time limit
15	15	3.30	0.8896	931	527.32	6,793.90	174.700,3
16	16	3.30	0.8896	931	527.24	6,791.29	174,633.1
17	1	3.23	0.8718	563	423.47	5,555.60	142,857.1
18	2	3.23	0.8719	563	423.61	5,555.56	142,857.1
19	3	3.20	0.8637	340	218.40	2,819.60	72,503.7A
20	4	no solution before exceed run time limit
21	5	3.23	0.8704	530	422.15	5,555.57	142,857.1
22	6	3.23	0.8705	530	422.31	5,555.57	142,857.1
23	7	3.23	0.8719	563	423.61	5,555.56	142,857.1
24	8	3.23	0.8719	563	423.61	5,555.56	142,857.1
25	9	3.23	0.8719	563	423.61	5,555.56	142,857.1
26	10	3.23	0.8719	563	423.61	5,555.56	142,857.1
27	11	infeaseble solution
28	12	infeaseble solution
29	13	3.22	0.8697	524	422.18	5,555.58	142,857.1
30	14	3.23	0.8699	527	422.46	5,555.56	142,857.1
31	15	3.23	0.8719	563	423.61	5,555.56	142,857.1
32	16	3.23	0.8719	563	423.61	5,555.56	142,857.1

Instituto Nacional de Pesquisas da Amazônia Av. André Araujo, 2936 Aleixo, 69060-001 Manaus AM Brasil, Tel.: +55 92 3643-3030, Fax: +55 92 643-3223 - Manaus - AM - Brazil
E-mail: acta@inpa.gov.br

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[1] * Corresponding author: lucasgomide@dcf.ufla.br