Value recovery and production control in bucking, log sorting, and log breakdown.
This study investigates how value recovery and production control are affected by the measurement techniques used in bucking and log sorting. The study was approached using simulation techniques. A database of 48 well-described young softwood stems (Pinus sylvestris L.) served as the wood supply, and a sawmill simulator able to read and process the stems was used to predict the outcome of the sawing process. In the simulations, five bucking alternatives and three log-sorting alternatives were evaluated. In addition, combinations of production control were employed in bucking, log sorting, and log breakdown with the target set to produce a given volume share of four specific products. In total, 28 simulations were carried out. The results indicate that the bucking method has greater influence on value recovery than the method of log sorting has. Results also indicate that the more process stations involved in production control, the better the demand targets are met (the degree of apportionment), but the lower the value and volume recovery become. Production control in bucking, log sorting, and log breakdown had almost equal effect on the degree of apportionment.
The process of converting trees to lumber with grades and dimensions specified by the customer's need is a chain of closely linked operations. At an early stage of the process, the bucking operation occurs. In Scandinavia, bucking is typically done at the harvesting site, while in North America the bucking is often done at the sawmill. At this stage, where the stem is cut into sawlogs, the dimensions of a particular log (i.e., length and small-end diameter) place upper limits on the length, width, and thickness of the lumber that can be sawn from it. While shorter and smaller lumber dimensions can be sawn from the same log, production economy will suffer as the volume yield drops. This means that undersized logs, as well as oversized logs, are undesirable, and it emphasizes the importance of high measurement accuracy (Chiorescu and Gronlund 2000).
With the cut-to-length system, logs delivered to the sawmill do not carry information on their individual dimensions as recorded by the harvester. It is therefore necessary to measure the logs in order to assign an appropriate breakdown pattern to each log and optionally sort them into diameter classes representing different sawing patterns so that a batch of logs can be processed with the same sawing pattern. The measuring device used in log sorting measures the shadow of the log in one, two, or three directions, or the true outer shape with laser triangulation. Log sorting can be done before debarking, admitting the difficulties with varying bark thickness and missing bark on parts of the log, or it can be done on debarked logs for higher accuracy. With the tree-length system, the bucking and log sorting can be performed in one operation or in two separate operations using any of the these measuring devices.
The number of possible bucking patterns increases quickly with the length of the stem and the number of feasible log lengths. The number of possible bucking patterns can easily exceed 10,000. The optimization problem is usually addressed with dynamic programming (DP) (Dreyfus and Law 1977) maximizing the value of the logs cut from the stem (Pnevmaticos and Mann 1972). The challenging part of the problem is not the DP algorithm, but rather the pricing of logs. One way of pricing the logs is the use of a log price list with individual prices for different log dimensions. The log price list then controls the bucking, and as a consequence it acts as the interface through which the sawmill communicates its need for the supply of specific log dimensions. Another way of pricing the logs is by using a log breakdown simulator for estimating the value yield of a log. The integration of log breakdown into the bucking problem has been addressed in earlier research (Faaland and Briggs 1984, Reinders and Hendriks 1989, Maness and Adams 1991), where simplified log geometry models free from defects were used. A full 3D profile of a log with high accuracy opens up the possibility of simulating the outcome of products from a sawing operation with high precision. In such a simulation, it is possible to rotate the log, apply curve sawing and, finally, edge and trim the boards with respect to wane criteria. Different sawing patterns and positioning in the saws can be evaluated, and the set-up yielding the highest value can be chosen for each log.
In addition to 3D profiling of stems, their inner properties can be revealed using a computed-tomography-based (CT) scanning system, allowing for even more realistic simulation of the product's grades in production control. Due to high cost and low throughput, CT-based log scanners have not yet been deployed in bucking or log sorting, but they might well be in the future.
Further downstream, sideboards are processed by an edger in which the width is set and all boards are eventually trimmed to their final length. Both edging and trimming are based on optimizations that, preferably, are value based. Prices then can be used to control the operation in bucking, log sorting, and breakdown. Optimizing each process independently of the others may lead to solutions that are not globally optimal to the chain of operations converting trees to lumber (Nordmark and Chiorescu 2001). However, in order to reach a globally optimal solution for a sawmill's production, thorough knowledge of the entire wood supply for the targeted planning period is required. One alternative is to pass information about the ongoing production to all process stations to ensure that they all optimize on the same premises. Though still not globally optimal, it's a workable solution in real production.
The bucking and sawing model described by Faaland and Briggs (1984) operates on a single stem at a time, while Maness and Adams (1991) focused on the log allocation problem where sawmill production was optimized on a weekly level. Maness and Adams (1991) also accounted for inelastic demand by controlling price/volume relationships. In this study, realistic log geometry and knot properties are considered to varying degrees in the bucking and sawing model, which accounts for inelastic demand by continuously controlling price/volume relationships.
The aim of this study was to investigate how value recovery and production control are affected by the measurement techniques used in bucking, log sorting, and log breakdown.
Material and methods
The study was approached using simulation techniques. A database of 48 well-described softwood stems served as the wood supply, and a sawmill simulator able to read and process the stems was used to predict the outcome of the sawing process. In the simulations, five bucking alternatives and three log sorting alternatives were evaluated. In addition, combinations of production control were employed in bucking, log sorting, and log breakdown with the target set to produce a given volume share of four specific products. In total, 28 simulations were carried out (Table 1). The results that were monitored were value and volume recovery and how well the targeted volume share of the four products was met. Results were further evaluated using partial least squares regression (PLS) (Geladi and Kowalski 1986).
Wood raw material
The wood raw material was a database consisting of 48 young Scots pine (Pinus sylvestris L.) stems with detailed descriptions in parametrical form collected from real trees. The diameter at breast height of the sampled stems ranged from 126 mm to 234 mm with an average of 161 mm and their heights ranged from 990 cm to 1603 cm with an average of 1328 cm. After felling, the trees were manually bucked and limbed. The sawlogs were transported to Lulea University of Technology where they were scanned in a CT scanner. Through image analysis of the obtained CT images, the outer shape and the internal knot structure of the logs were extracted. The format of the parametric descriptions is in concordance with the previously established Swedish Pine Stem Bank (Grundberg et al. 1995). During the whole process from the felling of the trees to the final database, great care was taken in order to allow for a correct reconstruction of the stems from the logs.
A validation of the parametric descriptions against real boards, sawn from three of the logs after CT scanning, showed that the number of knots and their positions were well described, as well as the log geometry, while the sizes of the knots had relatively large errors at positions close to the pith (Nordmark 2003). Although the descriptions deviate to some extent from the logs they were derived from, it was concluded that they could be used for simulating the yield of sawing.
The sawing simulator used (Nordmark 2002) is a Windows[TM]-based program developed in C++ with a graphical interface partly based on Open GL, allowing the user to view and interact with logs and boards in three dimensions. The software is capable of reading logs from the database and optionally assembling logs into stems for bucking into other lengths.
The sawmill modeled uses cant sawing, where the first sawing machine cuts the log into a block and side boards, while the second sawing machine cuts the block into two to four center boards and two to four side boards. Side boards are edged and trimmed, while trimming is the only operation on center boards. Both edging and trimming are value-optimizing operations based on lumber prices and grade. Grading is based on wane criteria and knot properties. The simulator also exposes a great deal of its functionality to a scripting module. Through scripts, simulations can be automated, and reports of the sawing process and properties of logs and boards can be tailored. The sawmill simulation software's ability to correctly predict wane and knot properties on boards from the database was validated in an earlier study (Nordmark 2003). In this study, logs were automatically rotated horns down (crook up), centered in both saws, and curve sawn. A minimum trimming of 50 mm at each board end was applied. The boards were graded A, B, or C following the Nordic Timber Grading Rules (Anon. 1994) where A is the highest grade. The grading rules define allowed wane, and the rules also state limits on knot diameter and sum of knot diameters on edges and faces for sound and dead knots, respectively. The boards were priced according to Table 2. A price penalty related to board length was introduced to account for production costs related to length. The relative value was set to 100 percent for length class 5400 mm and reduced in steps of 2 percent for each length decrement of 300 mm down to a relative value of 76 percent for length class 1800 mm. Without such price deduction, it is likely that most logs will be cut to minimum length due to log taper and volume yield relationship. No other costs were considered. By-products were given the price 200 SEK/[m.sup.3].
The bucking patterns of the stems were value optimized using dynamic programming, with the exception of one manual alternative where the crosscuts were arbitrarily chosen. The discretation was 100 mm, meaning that crosscut positions were evaluated every 100 mm along the stems. Five bucking alternatives were evaluated:
Manual. -- This is how the original logs were cut in reality when they were sampled from the forests. Logs were cut with lengths between 3100 mm and 5500 mm with a 300-mm length module. No optimizing calculations were done.
2D. -- This is a value-optimizing bucking where the value is given by a log price list with individual prices for different combinations of log small-end diameter and log length. Diameters of the stems were derived from the stems' cross-section areas with the interval 10 mm lengthwise. The diameter profile of each stem was then filtered so that no increases in diameter were allowed in the direction from the butt end towards the top. The stem feature array passed to the bucking algorithm was the diameter profile along the length of the stem without any information on out of roundness or crooks, hence 2D.
2D8. -- This alternative follows the method of 2D, but with an error added to the diameter profile in order to simulate the accuracy of a harvester-based bucking system (Moller and Sondell 2000). Each stem was given a random error on the diameter with a normal distribution of N(0, [[sigma].sup.2]) with the standard deviation set to 8 mm.
3D. -- The full 3-D profile of the stems was used. Prospective logs as segments of the stem were passed to the sawmill simulator, which simulated the breakdown and outcome of products. The returned estimated value was used to price the logs; i.e., no log price list was used. As no knot parameters were passed, the optimization approaches maximization of volume recovery.
CT. -- Like 3D, but in addition to the full 3-D-profile, the interior knot structure of the stem is known. Thus, the bucking is truly value optimized.
The log price list used in the 2D and 2D8 bucking cases (Table 3) was compiled from the results of an optimized bucking and log sorting, i.e., the CT bucking/CT log sorting case.
In this study, the meaning of log sorting is restricted to determination of the appropriate breakdown pattern for individual logs. Three alternatives in log sorting were evaluated:
Diameter. -- Based on the log's small-end diameter, the breakdown pattern is given by a look-up table (Table 4).
3D. -- The full 3-D profile of the logs was used for simulated sawing. Two or three sawing patterns were evaluated for each log: the normal pattern given by the look-up table and the patterns with diameter intervals above and below. For the smallest logs, only the pattern with a diameter interval above was added. The pattern giving the highest value in the simulated sawing was chosen. No knot parameters were passed to the simulated breakdown, so the optimization approaches maximization of volume recovery.
CT. -- As 3D, but in addition to the full 3-D profile, the interior knot structure of the logs is known. Thus the log sorting is truly value optimized.
Production control was implemented by an algorithm continuously adjusting the prices of the controlled boards and, in the case of 2D bucking, the price of corresponding log dimensions (Eq. ). When the desired share of a particular product is lower than the target share, and the share is decreasing, the product price is raised. If the target share is higher than desired, and the share is increasing, the price is lowered. Whenever the share is moving towards the target, the price remains.
Equation : Production control algorithm:
d[s.sub.n] = S[p.sub.n,i] - S[p.sub.n,i-1] 
d[t.sub.n] = S[o.sub.n] - S[p.sub.n,i]
[DELTA][c.sub.n] = u * [lambda] * Dm * ([d[t.sub.n]]/[S[o.sub.n]]) [lambda]Dm[greater than or equal to][DELTA]c[greater than or equal to]-[lambda]Dm
[C.sub.n,i+1] = [C.sub.n,i] + [DELTA][c.sub.n]1 + Dm[greater than or equal to]C[greater than or equal to]1 - Dm
P[c.sub.n] = P * [C.sub.n]
ds = change of share ([per thousand])
i = stem being processed
n = product under control
dt = deviation from target ([per thousand])
Sp = share produced ([per thousand])
So = share ordered ([per thousand])
[DELTA]c = change of coefficient
Dm = allowed deviation of price coefficient (%)
[lambda] = step control parameter
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
C = price coefficient
Pc = control price
P = selling price
In this study, maximum price deviation (Dm) was set to 50 percent, and the step control parameter ([lambda]) was set to 0.1. Price coefficients (C) were initialized to 100 percent and volume share produced was initialized to 0. Recovered volumes and coefficients were updated after each processed stem. The list of controlled products is given in Table 5. Log dimensions corresponding to the controlled center boards are shown in Table 6. The dynamic prices of boards and logs (Pc) were only used for controlling the production. In the summation of values presented, all boards were priced according to Table 2.
A measure of how well the target shares of the controlled products were met is given by Equation . The measure is further referred to as the apportionment degree. The interpretation is that the better the orders are met the closer to 1000[per thousand] will the apportionment degree be. Any deviation from the target will give a lower value.
Equation : Definition of apportionment degree:
Apportionment degree = 1 - [N.summation over (n=1)]|S[o.sub.n] - S[p.sub.n]| 
N = number of controlled products
In order to allow for the production control parameters to stabilize, the set of 48 stems was run in two consecutive runs without resetting the parameters in between in all simulations.
Partial least squares
Partial Least Squares (PLS) regression was chosen because it is based on the assumptions that the x-variables are correlated, that there is noise in the data, and that there can be structures in the residuals (Lindgren 1994). Because of this, PLS regression was well suited to this investigation, and the PLS analysis was carried out using the software SIMCA-10.0 (Anon. 2002). Coefficient of determination ([r.sup.2]) and a [Q.sup.2] value based on cross validation (Martens and Naes 1989a) were calculated. [Q.sup.2] represents the proportion of variance of y-values in the test set that is explained by the model. Hence [Q.sup.2] is a measure of the model's ability to predict future observations, i.e., observations that were not included when building the model. A model that explains random variations in the training set will fail when tested on new observations; hence [Q.sup.2] will be low for such a model (Martens and Naes 1989b). In the analysis, dummy variables were used to indicate the treatments engaged in each simulation. A dummy variable was given the value 1 if the treatment was used in a simulation and given the value 0 if it was not.
[FIGURE 1 OMITTED]
Value recovery and volume recovery resulting from the simulations without any production control are shown in Table 7 and Table 8, respectively. Manual, 2D, and 2D8 bucking had low value recovery compared to 3D bucking. The highest values were achieved with CT bucking. Value recovery is also influenced by the method of log sorting used. The results rank Diameter log sorting as giving the lowest values and CT log sorting as giving the highest values. Furthermore, the bucking method is shown to have greater influence on value recovery than does log sorting. Volume recoveries follow the same pattern in general, but with a few exceptions. The relative differences between treatments are smaller, and Manual bucking gave higher volume recovery than 2D8, although value recovery was lower.
Results of the simulations with production control employed are shown in Table 9. The apportionment degree was on average 981[+ or -]11[per thousand] with production control compared to 949[+ or -]18[per thousand] in the simulations without production control. The highest degrees of apportionment were achieved with 2D and 2D8 bucking. The degree of apportionment varied less with the type of log sorting applied. Value recovery and volume recovery rank the combinations of bucking and log sorting in the same order with production control employed as with no production control.
The PLS model was calibrated with two principal components and with [r.sup.2] = 0.76 and [Q.sup.2] = 0.59. A plot of the weights used to combine x-variables and y-variables (w*c) in the two components is shown in Figure 1. Value and volume recovery are strongly correlated to each other, and the type of bucking applied has a large influence, while the type of log sorting has a somewhat smaller influence on value and volume recovery. Whenever production control is employed, indicated by the variable ProdCtrl, volume and value are decreased. The more process stations involved in production control (variables BuCtrl, LsCtrl, and BdCtrl), the lower the value and volume recovery, but the apportionment degree increases. The type of log sorting has low influence, while the type of bucking has a moderate influence on the apportionment degree.
First, it must be emphasized that this study was based on a wood supply of a limited origin both geographically and biologically, and the results are discussed within this context. Furthermore, if production costs had been included, other results might have been achieved. However, the results may serve as indicators of relationships in a broader sense.
Simulating the process of converting trees to lumber made it possible to compare alternative ways of bucking and log sorting while eliminating differences in the raw material input between runs. Simulating reality is a cost-efficient way of screening for relationships, but the relationships found should be verified in reality before they are considered true. However, no indications within the results arrived at in this study lead towards the conclusion that the relationships found are inconsistent with real-world practice.
The bucking method had the greatest influence on value and volume recovery. In order to extract maximum value from the wood raw material, bucking of stems and sorting of logs into sawing patterns must be based on knowledge of the stem's outer shape and a precise description of its knots. CT scanning of stems is a future possibility to provide such information. It was included in this study to provide a benchmark of the value potential of the wood raw material. At the other end of the spectrum is Manual bucking, which is rare in practice due to the mechanization of forest operations. 2D8 bucking with a log price list resembles a harvester operating in the cut-to-length system where diameters under bark are predicted from measurements over bark. This is the dominant practice in Scandinavia. 2D bucking, i.e., correct measurement of diameters under bark, was included to make it possible to compare the method of 2D bucking with other methods without the effect of measurement accuracy. 3D bucking without errors was superior to 2D bucking without errors in this study.
The log price list was compiled from the results of an optimal processing in bucking and log sorting. In practice, the construction of log price lists is more complicated and it is likely that the log price list used in this study was more correct than one would expect a log price list used in reality to be. The desired shares of the controlled products were directly translated to shares of log dimensions for production control in 2D/2D8 bucking. However, the volume yield of boards varies with log dimension, and in order to make a correct apportionment of logs to fit the targeted products, this log/yield relationship should preferably be accounted for.
The method of log sorting also influences value and volume recovery in the way that the more information about the logs that is processed, the better the performance. The spread in value recovery was lower in terms of the method of log sorting used than it was in terms of the bucking method. This reflects the situation that dimensions and knot properties of a log to a large extent also determine the dimensions and grades of the boards sawn from it. Thus, the alternatives for processing the logs originating from a stem are fewer compared to the alternatives available when the stem is being bucked.
The purpose of including production control was not to evaluate the algorithm, but rather to investigate how different treatments in bucking, log sorting, and log breakdown affect the degree of apportionment. There may be better, more efficient algorithms applicable, and the applied algorithm could have been better tuned. The obtained PLS model showed that in order to achieve a high apportionment degree it is almost equally important to employ production control in the process stages of bucking, log sorting, and log breakdown. Furthermore, the model shows that all process stages should be employed. At the start of production, where the volume produced is low, the volume share of a controlled product takes a large leap whenever such a product is produced. As a consequence, the volume share and the control price coefficient will oscillate around the target until a large total volume has been produced. The limited number of stems processed when evaluating production control in the simulations may have been insufficient for avoiding that type of randomness in the apportionment degree. 2D and 2D8 bucking had a positive effect on the apportionment degree compared to 3D and CT bucking. One reason may be the randomness just mentioned. Another likely reason is that the value of a log given by a breakdown simulation is the sum of the value of the products extracted from it. A board with specified dimensions and grade is only part of the summed value. From this it follows that the value of logs will be less sensitive to changes of the controlled products price coefficients when predicted from a breakdown simulation, compared to the case where the log's price coefficient is changed directly, as in the case of 2D bucking with a log price list.
Using 3D optical scanners in combination with a log breakdown simulator in bucking and log sorting makes it possible to extract high value from the wood raw material. With the concept, log price lists become obsolete, easing communication between different processing stages. Until industrial CT scanning is available, there are other possibilities for implementing the inclusion of lumber quality in bucking and sorting decisions. The detailed model of the log mantel obtained from 3D scanning can be used for predicting the quality of the sawn goods (Lundgren 2000). The two-way x-ray log scanner is also applicable for predicting board quality with high accuracy alone (Grundberg and Gronlund 1997) or in combination with an optical 3-D scanner (Oja et al. 2003). Further studies should focus on including quality predictions in bucking and log sorting decisions and on validating the results presented here on a larger and more heterogeneous raw material.
Table 1. -- Study set-up: combinations of bucking, log sorting, and production control. Production control Simulation Bucking Log sorting Bucking Log sorting Breakdown 1 Manual 3D No No No 2 Manual 3D No Yes Yes 3 Manual CT No No No 4 Manual CT No Yes Yes 5 Manual Diameter No No No 6 Manual Diameter No Yes Yes 7 2D 3D No No No 8 2D 3D Yes Yes Yes 9 2D CT Yes Yes Yes 10 2D CT No No No 11 2D Diameter Yes No No 12 2D Diameter Yes No Yes 13 2D Diameter No No No 14 2D8 3D Yes Yes Yes 15 2D8 3D No No No 16 2D8 CT Yes Yes Yes 17 2D8 CT No No No 18 2D8 Diameter Yes No No 19 2D8 Diameter Yes No Yes 20 2D8 Diameter No No No 21 3D 3D No No No 22 3D 3D Yes Yes Yes 23 3D CT No No No 24 3D Diameter No No No 25 CT 3D No No No 26 CT CT No No No 27 CT CT Yes Yes Yes 28 CT Diameter No No No Table 2. -- Timber price list used. Price by board type Grade Side boards Center boards (SEK/[m.sup.3]) (a) A 3000 1850 B 1400 1600 C 1100 1000 (a) SEK = Swedish krona. Table 3. -- Log price list used in 2D bucking. Log small-end diameter Length 100 mm 130 mm 150 mm 170 mm 185 mm 195 mm 210 mm 220 mm (mm) (SEK/volume by top measurement) 2200 630 699 736 768 791 804 824 836 2500 682 756 796 831 856 870 891 904 2800 734 813 856 894 920 936 959 973 3100 775 859 905 945 972 989 1013 1028 3400 827 916 965 1008 1037 1055 1080 1096 3700 858 951 1001 1045 1076 1094 1121 1137 4000 889 985 1038 1083 1115 1134 1161 1179 4300 930 1031 1086 1134 1167 1187 1215 1233 4600 951 1054 1110 1159 1193 1213 1242 1261 4900 982 1088 1146 1197 1232 1253 1283 1302 5200 1013 1123 1182 1234 1271 1292 1323 1343 5500 1034 1146 1207 1260 1297 1319 1351 1371 Log small-end diameter Length 230 mm 250 mm (mm) (SEK/volume by top measurement) 2200 847 869 2500 917 940 2800 986 1011 3100 1042 1068 3400 1112 1140 3700 1153 1182 4000 1195 1225 4300 1251 1282 4600 1278 1311 4900 1320 1353 5200 1362 1396 5500 1390 1425 Table 4. -- Sawing patterns and related log small-end diameter intervals. Log small-end diameter interval Sawing pattern Minimum Maximum First saw Second saw (mm) 100 129 19,75,19 19,38,38,19 130 149 19,100,19 19,38,38,19 150 169 19,100,19 19,50,50,19 170 184 19,125,19 25,50,50,25 185 194 19,125,19 19,63,63,19 195 209 19,19,150,19,19 19,25,50,50,25,19 210 219 19,19,150,19,19 19,25,63,63,25,19 220 229 19,19,175,19,19 19,25,50,50,25,19 Table 5. -- Order specification used in the production control studies. Thickness Width Length Grades Desired share of board volume (mm) ([per thousand]) 19 75 2400 B, C 20 38 75 3000 A 20 38 100 3900 A, B 20 50 100 3300 B 20 Table 6. -- Log tally specification used in the production control studies. Log specification Board dimension Small-end diameter Length Desired share of log volume (mm) ([per thousand]) 19 by 75 by 2400 -- -- -- 38 by 75 by 3000 100 to 129 3100 20 38 by 100 by 3900 130 to 149 4000 20 50 by 100 by 3300 150 to 169 3400 20 Table 7. -- Value recovery, no production control. Bucking Log sorting Manual 2D8 2D 3D CT All (SEK) Diameter 7931 7963 7986 8398 8771 8210 3D 8081 8116 8184 8496 8782 8332 CT 8167 8234 8299 8556 9088 8469 All 8060 8104 8157 8484 8880 8337 Table 8. -- Volume recovery, no production control. Bucking Log sorting Manual 2D8 2D 3D CT All (%) Diameter 41.9 41.4 42.2 43.4 44.0 42.6 3D 42.2 42.0 42.4 44.0 43.5 42.8 CT 42.2 42.2 42.6 43.4 45.3 43.1 All 42.1 41.8 42.4 43.6 44.2 42.8 Table 9. -- Simulation results with production control employed. Production control Log Log Vol. Simulation Bucking sorting Bucking sorting Breakdown yield Value (%) (SEK) 2 Manual 3D No Yes Yes 41.8 7986 4 Manual CT No Yes Yes 42.0 8193 6 2D Diameter No Yes Yes 41.4 7836 8 2D 3D Yes Yes Yes 41.8 8084 9 2D CT Yes Yes Yes 42.2 8235 11 2D Diameter Yes No No 42.0 7946 12 2D Diameter Yes No Yes 41.7 7901 14 2D8 3D Yes Yes Yes 41.3 8030 16 2D8 CT Yes Yes Yes 41.6 8195 18 2D8 Diameter Yes No No 40.8 7828 19 2D8 Diameter Yes No Yes 41.3 7879 22 3D 3D Yes Yes Yes 44.0 8487 27 CT CT Yes Yes Yes 44.9 9039 App. Simulation degree ([per thousand]) 2 985 4 973 6 965 8 988 9 990 11 975 12 996 14 990 16 997 18 964 19 983 22 969 27 977
Anonymous. 1994. Nordic Timber Grading Rules. ISBN 91-7322-175-9. Arbor Publishing, Stockholm, Sweden. 64 pp. (in Swedish.)
______. 2002. User guide, SIMCA-P and SIMCA-P+10. Umetrics AB, Umea, Sweden.
Chiorescu, S. and A. Gronlund. 2001. Assessing the role of the harvester within the forestry wood chain. Forest Prod. J. 51(2):77-84.
Dreyfus, S.E. and A.M. Law. 1977. The Art and Theory of Dynamic Programming. Mathematics in Science and Engineering. Vol. 130. ISBN 0-12-221860-4. Academic Press, New York. 284 pp.
Faaland, B. and D. Briggs. 1984. Log bucking and lumber manufacturing using dynamic programming. Management Sci. 30:245-257.
Geladi, P. and B.R. Kowalski. 1986. Partial least-squares regression: A tutorial. Anlytica Chimica Acta 185:1-17.
Grundberg, S. and A. Gronlund. 1997. Simulated grading of logs with an X-ray Log-Scanner. Grading accuracy compared with manual grading. Scand. J. Forest Res. 12:70-76.
______, ______, and U. Gronlund. 1995. The Swedish Stem Bank: A data base for different silvicultural and wood properties. Res. Rept. TULEA 1995:31. ISSN 0347-0881. Lulea Univ. of Tech., Lulea, Sweden.
Lindgren, F. 1994. Third generation PLS: Some elements and applications. Dissertation. ISBN 91-7174-911-X. Umea Univ., Umea, Sweden. pp. 17-41.
Lundgren, C. 2000. Predicting log type and knot size category using external log shape data from a 3D log scanner. Scand. J. Forest Res. 15:119-126.
Maness, T. and D. Adams. 1991. The combined optimization of log bucking and sawing strategies. Wood and Fiber Sci. 23(2):296-314.
Martens, H. and T. Naes. 1989a. Multivariate Calibration. ISBN 0-471-93047-4. John Wiley and Sons, New York. pp. 254-258
______ and ______. 1989b. Multivariate Calibration. ISBN 0-471-93047-4. John Wiley and Sons, New York. pp. 237-250.
Moller, J. and J. Sondell. 2000. Customer-driven assortments call for better diameter measuring: Improvements possible in the forests. ISSN 1103-4173. Result 15, SkogForsk, The Forest Research Inst. of Sweden, Uppsala, Sweden. 4 pp. (in Swedish with English summary.)
Nordmark, U. 2002. Integrating the bucking operation with production control in sawmilling. Licentiate Thesis. 2002:58. ISSN 1402-1757. Lulea Univ. of Tech., Lulea, Sweden.
______. 2003. Models of knots and log geometry of young Pinus sylvestris sawlogs extracted from computed tomographic images. Scand. J. For. Res. 18:168-175.
______ and S. Chiorescu. 2001. Satisfying consumer demand--A comprehensive view on the sawmill economy using simulation techniques. In: Proc. of the 7th Inter. Conf. on Sawing Technology. R. Szymani, ed. Wood Machining Inst., Berkeley, CA. pp. 2-10
Oja, J., S. Grundberg, J. Fredriksson, and P. Berg. 2004. Automatic grading of saw logs--A comparison between X-ray scanning, optical 3D scanning and combination of both methods. Scand. J. Forest Res. 19:89-95.
Pnevmaticos, S.M. and S.H. Mann. 1972. Dynamic programming in tree bucking. Forest Prod. J. 22(2):26-30.
Reinders, M.P. and H. Hendricks. 1989. Lumber production optimization. Eur. J. Opl. Res. 42:243-253.
The author is a Research Scientist, Lulea Univ. of Technology, Dept. of Wood Technology and Sveaskog AB, SE-941 86 Pitea, Sweden. This study was done within the SkeWood program, and funds were provided by The Swedish Agency for Innovation Systems (VINNOVA) and Sveaskog AB. This paper was received for publication in March 2004. Article No. 9852.
*Forest Products Society Member.
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|Publication:||Forest Products Journal|
|Date:||Jun 1, 2005|
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