2011 3rd Conference on Data Mining and Optimization (DMO) 28-29 June 2011, Selangor, Malaysia

978-1-61284-212-7/11/$26.00 ©2011 IEEE

Optimisation Model of Selective Cutting for Timber Harvest Planning in Peninsular Malaysia

Munaisyah Abdullah, Salwani Abdullah, Abdul

Razak Hamdan

Faculty of Information Science and Technology University Kebangsaan Malaysia

43600 Bangi, Selangor Darul Ehsan {Munaisyah,salwani,arh}@ftsm.ukm.my

Roslan Ismail Malaysia Institute of Information Technology

University Kuala Lumpur 50250 Kuala Lumpur

drroslan@miit.unikl.edu.my

Abstract— Timber Harvest Planning (THP) model is used to determine which forest areas to be harvested in different time periods with objective to maximize profit subject to harvesting regulations. Various THP models have been developed in the Western countries based on optimisation approach to generate an optimal or feasible harvest plan. However similar studies have gained less attention in Tropical countries. Thus, this study proposes an optimisation model of THP that reflects selective cutting in Peninsular Malaysia. The model was tested on seven blocks that consists a total of 636 trees with different size and species. We found that, optimisation approach generates selectively timber harvest plan with higher volume and less damage.

Keywords-Timber harvest planning, optimisation model, selective cutting

I. INTRODUCTION Doyle [1] defined planning as a problem solving

technique. An efficient problem solving strategy plays a fundamental role for developing an effective solution technique in decision making process. Timber Harvest Planning (THP) problem is related on deciding which forest areas to be harvested in different time periods [2]. The decision process not only deals with selection of numerous harvest blocks, but also evaluation of conflict in management objectives. These objectives are to maximize the profit and simultaneously fulfill the environmental issues to protect non-timber values of a forest. This problem known as a difficult combinatorial optimisation problem that is to find an optimal arrangement, grouping, or selection of discrete objectives usually finite in number [2].

Many countries impose harvest regulations to achieve the non-timber objectives such as biodiversity conservation, wildlife habitat protection, water quality preservation, and erosion reduction. For examples, a set of Sustainable Forestry Initiative (SFI), developed by the American Forest and Paper Association (AE & PA) is used as a guideline for most industrial forest land owners in the United State, and a Selective Management System (SMS), developed by the International Tropical Timber Organization (ITTO) is used as

a guideline for selectively fell a tree in tropical countries. One of the initiatives in SFI is to prevent clear cutting until adjacency areas have reached a minimum height in a particular planning period. This restriction is aimed to avoid negative impacts on various forest values, such as erosion, habitat disruption, or water quality deflation due to a large opening area in a forest land [3].

Many optimization models for THP that comply to this restriction have been developed in the US. The models are used to form a harvest area with an objective function to maximize the harvest volume subject to the harvest regulations and implement clear cutting technique. Basically, a forest area will be divided into numerous harvest blocks with difference sizes which are then grouped together to form a harvest area. The size of a harvest area is restricted to the maximum allowable clear cut area. (McDill et al. [4]; Goycoolea et al. [6]). The disadvantage of this approach is that it may affect the harvest volume by limiting the available blocks for harvesting [ 8 ].

McDill et al. [4] presented a MILP model that allows neighboring blocks to be harvested as long as their combined areas were less than the maximum allowable harvest area. Goycoolea et al. [6] developed an extended area restriction model (EARM) to maximize the net benefit over specified time horizon subject to maximum area constraints. The advantage of the proposed solution is that it could generate an optimal harvest plan, but the solution quality is very sensitive to the problem size [4]. However, Constantino et al. [7] had presented an improvement MILP model formulation, area restriction with stand-clear-cut variables (ARMSC) to improve the efficiency of the solution to the THP problem with maximum clear-cut size constraints. The model was tested with both real and hypothetical forests ranging from 45 to 1,363 polygons and obtained slightly above 1% of the optimal solution in a reasonable computation time.

Besides that, many published research works have also proposed meta-heuristic techniques to cater for a bigger problem size. However, these techniques do not guarantee for optimality [9]. Baskent and Jordan [5] developed a model to maximize total harvested over time and maintain harvest

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openings within a minimum of 40 ha and a maximum of 100 ha using SA approach. The model was tested on a 987 stands using hypothetical forest landscape. They found that the objective accomplishment was varied from 72% for even flow harvest to 99.9% for adjacency delay.

However, the similar studies, to the best of our knowledge, have gained less attention in tropical countries despite numerous news related on environmental destruction due to timber harvesting had been reported [10,11]. We believe a proper planning strategy leads to effective monitoring and control of harvesting operations. Therefore, the aim of this study was to introduce an optimisation model of timber harvest planning that reflects the selective cutting in Peninsular Malaysia. This approach has allowed us to compare the impacts of generating a timber harvest plan that incorporate optimisation process in term of improving harvest volume and reducing damage to the residual trees.

This paper is organized as follows; section II describes the materials and methods employed in this study, section III discuss the results gained, and conclusion and future research directions are presented in section IV.

II. MATERIALS AND METHODS

A. Data Data for this study were based on tree making data

derived from reserve forest Bintang Hijau Kuala Kangsar with estimated total area of 80ha. These data related on detail information of trees with diameter at least 30cm dbh (diameter at breast height). The information included plot number, tag marking tree, tree species, and estimated logs in each tree, tree diameter, felling direction, and tree status. Stem height was manually calculated based on tree diameter-stem height timetable grouped by tree species. Each plot consists of an average of 5 potential trees to cut and 3 trees to retain including fruit trees such as Durian and Petai. In this study, 2-4 plots were combined to form a block. Table I shows examples of data used in this study.

TABLE I. TREE MARKING DATA

Bk# Tree Information TreeID Species Diameter CutDeg Status

1 L2T31 M.TEMBAGA 45 135 3 1 L3T61 M.SERAYA 23 0 1 1 L7T95 SESENDOK 34 0 2 2 L10T155 DURIAN 25 0 2 2 L1T165 KEDONDONG 30 0 2 2 L1T171 NYATUH 71 90 3

Table II shows the trees distribution in each harvest block. Total tree (TT) in each harvest block is an accumulative of three category of tree status: (1) Common tree (CT), a group of trees with diameter less than 30cm dbh; (2) protected tree (PT), a group of trees with diameter greater or equal with 30cm dbh but less than 45 cm dbh; (3) Potential tree to cut

(PT2C), a group of trees with diameter greater than 45cm dbh.

TABLE II. TREE DISTRIBUTION

Bk# TT PT2C PT CT 1 81 15 10 56 2 92 24 13 55 3 89 36 17 36 4 93 28 23 42 5 92 13 33 46 6 91 22 17 52 7 98 27 26 45

B. Model Formulation We developed two modelling approaches: (1) a Selective

Harvest Planning Model (SHPM), a harvest planning model which is used to form harvest area without optimisation approach, and (2) a Selective Harvest Planning Optimisation Model (SPOM), a harvest planning model which is used to form harvest area based on optimisation approach. SHPM was used for a baseline comparison. SPOM was used for comparing the impacts of applying optimisation techniques in improving harvest volume and reducing damage to the residual trees.

Four decision variables were used as constraints: Required tree diameter (RTD), a minimum diameter requirement for a tree to be felled; Required future stock (RFS), a minimum estimated trees to be felled in next planning rotation in each block; Economic harvesting (EcoH), a minimum number of trees to be felled in each block; and Maximum harvesting (MxH) or Allowable harvesting (AH). MxH represents a maximum harvest volume in each block for SHPM while AH represents a maximum harvest volume in each planning period for SPOM.

Model formulation for SHPM is shown as follows:

TD ≥ RTD (1)

n

∑ FSi ≥ RFS

i=1

(2)

n

∑ T2Ci ≥ EcoH

i=1

(3)

n

∑ T2Ci ≤ MxH

i=1

(4)

Where: i=harvest block; TD=Tree Diameter; FS=Future Stock; and T2C=Tree to Cut. The decision to form a harvest area in SHPM is based on four constraints: (1) indicates that TD must be greater or equal with RTD, (2) indicates that total FS in each harvest block is greater or equal with RFS, (3) indicates that total T2C in each harvest block is greater or equal with minimum tree to cut in each block for economic harvesting, and (4) indicates that total T2C is less or equal

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with MxH. In this model formulation, no optimization was required.

SPOM is an optimisation model that reflect the selective cutting technique in Peninsular Malaysia with an objective function to maximize the harvest volume subject to constraint (5) – constraint (8) as shown in the model formulation below:

Maximise Objective Function (Q):

n

Q = ∑ Hvi X

i

i=1

subject to: TD ≥ RTD (5)

n

∑ FSi ≥ RFS

i=1

(6)

n

∑T2Ci ≥ EcoH

(7)

i=1

∑ Hv ≤ AH

i=1

(8)

Xi = { 0, 1 }

Where: Hv = Harvest Volume; and X = decision variables

(1 if block is harvested, 0 otherwise) . The objective function (Q) is to maximize the harvest volume in each planning period subject to four constraints as following: (5) indicates that TD must be greater or equal with RTD, (6) indicates that total FS in each harvest block must be greater or equal with RFS, (7) indicates total T2C in each harvest block must be greater or equal with EcoH, and (8) indicates that total Hv in one planning period must be less or equal with AH.

C. Solution Approach The solution approach was divided into two phases: (1)

pre-processing phase used for identifying potential tree to cut based on tree diameter, estimating damage to residual trees based on cutting degree, tree location and stem height, and estimating future stock from residual trees, and (2) decision making process used for forming harvest area. Fig. 1 shows the flow chart of describing the procedures involved.

Figure 1. Flow chart describing Pre-processing Phase

C1 indicates constraint (1) in SHPM and constraint (5) in SPOM. Potential trees to harvest refers to a group of trees with diameter at least 45cm dbh. For each of the potential tree to harvest, damage analysis is performed to estimate damage to the residual trees. The damage could be due to stem or crown. In this study, we consider damage due to stem as a major damage while damage due to crown as a minor damage. Damage to residual trees is calculated based only on major damage. Future stock refers to residual trees with diameter at least 30cm dbh. Total future stock in each block is calculated after damage analysis was completed. Both models were run using the same pre-processing phase before implemented the harvest area formation phase.

In SHPM, a harvest area is formed by selecting any block that meets all the constraints as shown in Fig. 2: C2 refers to constraint (2), C3 refers to constraint (3), and C4 refers to constraint (4). Harvesting would not be allowed in any block that violated constraints C2 and C3. However, if C4 is violated, harvesting is permitted but the total tree to cut must be less or equal with the value that has been assigned to MxH.

Figure 2. Flow chart describing Decision Phase in SHPM

The decision making process in SPOM is shown in Fig. 3. C6 refers to constraint (6), C7 refers to constraint (7) and C8 refers to constraint (8). The decision to form the harvest area involves saving trees from harvesting if C6 is violated. However, harvesting would not be allowed if no more tree can be saved to fulfill C6. Harvesting is also not allowed to any block that violated C7. A harvest area is formed by selecting the most promising blocks to achieve the desired harvest volume with minimal damage to the residual trees and provide enough stock for future crop.

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Figure 3. Flow chart describing Decision Phase in SPOM

D. Test Cases Five test cases were created; T1, T2, T3, T4 and T5. In

this study, RTD was assigned to 45cm diameter at breast high (dbh) regardless of tree species for simplicity in all test cases. RFS value was gradually increased to observe the impacts of future stock towards harvest volume and damage to the residual trees. In T1, RFS was assigned with value 3 to represent the smallest number of tree for future stock in each harvest block. In the subsequence test cases, the value will be increased by 5, thus the value of RFS in the last test case would be 23.

EcoH was assigned with value 7 in all test cases to represent the economic harvesting. While the value of MxH in SHPM (1) or AH in SPOM (2) depends on the problem size to control the inconsistency of total harvest volume for both models. For example, base on our data distribution as shown in Table II, each block in (1), we assigned MxH at most 20 trees to be felled, thus total harvest volume of seven blocks would be 140. But, we choose total harvest volume as 100 instead of 140 because we consider some of the blocks consist of less than 20 PT2C. Hence, AH in (2) was assigned to 100. Table III shows the first three test cases.

TABLE III. TEST CASES

Decision Variables

T1 T2 T3 (1) (2) (1) (2) (1) (2)

RTD 45 45 45 45 45 45 RFS(+5) 3 3 8 8 15 15 EcoH 7 7 7 7 7 7 MxH 20 - 20 - 20 -

AH - 100 - 100 - 100

III. RESULT AND DISCUSSION

Table IV shows the performance of SPOM as compared to SHPM. Two parameters were used as a performance measurement: harvest volume (HV), a total number of tree to be felled and damage to residual trees (Dmg), a total number of damaged trees due to stem. As can be seen in T1, with a minimum value of RFS, only a slight difference of HV that is 7% was observed in SPOM. However, when we increased the RFS value in T5, we can see the difference significantly. None of the blocks in SHPM is available for harvesting which lead to zero value of harvest volume. Thus the performance of SPOM is 100% better than SHPM. Fig. 4 shows the effect of increasing the FS value towards harvest volume.

A negative value of Dmg indicates the percentage of affected trees that can be reduced. In general, total affected trees depend on the number of trees to fill. In T3 and T4, less trees were filled in SHPM, thus less damage was recorded. Zero damage in SHPM was recorded in T5 because no tree was filled. However in T1 and T2, SPOM provide higher harvest volume with minimum damage to residual trees. The damage reduces up to 24% and 25% respectively. Fig. 5 shows the damage produced in both models. The findings are resulting from the planning strategy to form the harvest area for both models.

TABLE IV. SPOM PERFORMANCE AS COMPAREED TO SHPM

Test Model Parameters Performance* HV Dmg HV Dmg

T1 (1) 87 199 +7 -24 (2) 100 121

T2 (1) 67 158 +20 -25 (2) 100 94

T3 (1) 13 46 +76 +30 (2) 94 85

T4 (1) 13 46 +74 +47 (2) 86 129

T5 (1) 0 0 +100 +100 (2) 64 74

* = (( MI – SMS) / (MI+SMS)) *100)

0

20

40

60

80

100

120

T1 T2 T3 T4 T5

(1)

(2)

AH

RFS

Figure 4. Harvest Volume Comparison

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050

100150200

250

T1 T2 T3 T4 T5

(1)

(2)

Figure 5. Damage Comparison

Table V shows the harvest area formation in both models for T1 and T5 as a comparison. In SHPM, any block that violates RFS was prohibited from harvesting. For examples in T1 (Bk2 and Bk3), total tree to cut (T2C) was zero even though PT2C in both blocks was 24 and 36 respectively, while in T5, none of the blocks was permitted to be harvested. In SPOM, an approach to save PT2C from harvesting to fulfill RFS was proposed until no more PT2C was available to be saved. For example in T5 (Bk4 and Bk5), total T2C was 25 and 12 instead of 28 and 13 respectively. While in T5 (Bk1, Bk2, Bk3 and Bk6), total T2C was zero because all PT2C had been saved but total FS was still below the minimum requirement. The findings indicate that the planning strategy to save PT2C could provide more available blocks for harvesting even though less harvest volume would be produced.

Besides that, in SHPM, all available blocks that fulfill RFS and EcoH will be harvested, however the maximum allowable T2C must fulfill MxH requirement. For example in T1 (Bk4, Bk6 and Bk7), only a total of 20 T2C in each block was permitted to be felled instead of 28, 22 and 27 respectively. Thus in T1, a total of five blocks were available for harvesting which resulted a total of 87 trees to be felled. In SPOM, an optimisation technique to select the most promising blocks to achieve the target harvest volume was developed. For example in T1, to achieve our target of 100 trees, the combination of four blocks (Bk1, Bk2, Bk3 and Bk4) was selected which give a maximum harvest volume of 100 trees to be felled. Thus these findings demonstrate that the proposed algorithm could produce higher harvest volume with less blocks selected for harvesting thus reduce the number of damaged trees.

TABLE V. HARVEST AREA FORMATION

Model Bk# PT2C T1 T5 T2C B2H THV T2C B2H THV

(1) 1 15 14 14 0 x 0 2 24 0 x 14 0 x 0 3 36 0 x 14 0 x 0 4 28 20 34 0 x 0 5 13 13 47 0 x 0 6 22 20 67 0 x 0 7 27 20 87 0 x 0

(2) 1 15 14 14 0 x 0 2 24 23 37 0 x 0 3 36 35 72 0 x 0 4 28 28 100 25 25 5 13 13 x 100 12 37 6 22 22 x 100 0 x 37 7 27 27 x 100 27 64

IV. CONCLUSION

Overall, we can conclude that SPOM provides more available blocks to be harvested and selects the most promising blocks to achieve the desire objective with minimal damage to the residual trees. An optimisation approach therefore provides an intelligent alternative of problem solving technique to generate a near optimal plan that provides better monitoring and control of harvesting operations in Peninsular Malaysia. Our future work will focus on testing the performance of SPOM model using other meta-heuristic optimisation techniques. The experiments will be conducted using bigger problem size.

ACKNOWLEDGMENT

We would like to thank Jabatan Hutan Kuala Kangsar for their cooperation in providing the data.

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[10] W. S. A. Ghazalim, “Logging pelan threatens rhinoceros and tiger,” www.utusan.com.my/~Impak_Alam&pg=al_01.htm, 2009.

[11] Main article, “Logging lesion life,” www. kosmo.com.my/~Rencana_ _Utama&pg=ru_03.htm. 2009

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