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Researchers have hypothesized that segmented processing of cutting orders may result in reduced yield compared to batch processing. This study simulated application of both the batch and segmented processing systems for a crosscut-first rough mill with manually operated saws. The processing of three cutting orders of increasing relative difficulty was simulated. Simulated yield results comparing segmented to batch processing systems showed significantly higher yields for the batch processing system for moderate and difficult cutting bills. Cutting bill difficulty reduced yield significantly more for the segmented compared to batch processing system. The batch processing system provided higher yields for the higher, more valuable lumber grades. No significant difference in the number of cutting operations between batch and segmented processing was detected. [PUBLICATION ABSTRACT]
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Abstract
Researchers have hypothesized that segmented processing of cutting orders may result in reduced yield compared to batch processing. This study simulated application of both the batch and segmented processing systems for a crosscut-first rough mill with manually operated saws. The processing of three cutting orders of increasing relative difficulty was simulated. Simulated yield results comparing segmented to batch processing systems showed significantly higher yields for the batch processing system for moderate and difficult cutting bills. Cutting bill difficulty reduced yield significantly more for the segmented compared to batch processing system. The batch processing system provided higher yields for the higher, more valuable lumber grades. No significant difference in the number of cutting operations between batch and segmented processing was detected.
The expense and complexity of actual rough mill studies have led researchers to develop rough mill computer simulations to model the rough mill lumber cut-up process. These simulations allow control of the variables that influence yield that are not possible to control in an actual rough mill production situation (Wiedenbeck et al. 1994). Researchers and managers have used the simulations to manipulate the important variables to determine their influence on yield and productivity.
Nearly all furniture production rough mills cut interior and exterior dimension parts to order rather than to stock. The parts typically are components of various sizes required for a single product or a related group of products. For this reason, only limited numbers of each part size are required and the needed quantities of each part size differ.
Rough mill managers assign parts to be cut by individual machines to fulfill the requirements of each cutting order. In a crosscut-first rough mill, in which both crosscut saws and straight-line ripsaws are manually operated, only a limited number of parts are assigned to each machine (Wylie 1954).
The limitation on the number of parts cut at each machine is imposed by the physical requirements of the machines and the limitations on the decision-making capacity of the operators. For example, no more than five part lengths are usually assigned to be cut simultaneously on a manually operated crosscut saw. Operators must attempt to determine the best combination of part lengths to most effectively utilize the available lumber length or to utilize the distance between defects. If the number of part lengths is larger than five, this task can become difficult and impossibly complex for an operator (Wylie 1954, Steele et al. 1998). Limiting the number of parts cut at a machine may result in a yield decrease (Wylie 1954) but no research has been performed to test this hypothesis.
Numerous rough mill computer simulations have been developed to simulate the crosscut-first rough mill lumber cut-up process (Thomas 1962, 1996, 1998; Wodzinski and Hahm 1966; Brunner et al. 1987; Harding and Steele 1997). Thomas (1962) developed software to investigate the relationship between yield and part sizes by lumber grade. In his study, a computer algorithm mapped board defects and computed lumber yields. Due to the insufficient computational capacity of computers at that time, Thomas first simplified the lumber cut-up algorithm by not subtracting kerf width from the cut parts. Program YIELD, developed by Wodzinski and Hahm (1966), is a crosscut-first rough mill simulation program designed to solve the inadequacies of no kerf loss and infeasible cut-up solutions from the previous computer algorithm developed by Thomas.
Table 1. - Volume, number of boards, average width, and average length of red oak lumber in the CUTSIM database.Table 2. - The easy cutting order in which values not contained in parentheses are the part numbers, values in parentheses are the individual crosscut saw followed by ripsaw identification numbers to which the part sizes were assigned to be cut. Total number of parts to fill the easy cutting order was 8,950; average part width was 2.1 inches; average part length was 21.5 inches; parts volume was 2,806 board feet.
Using program YIELD, Schumann and Englerth (1967) recalculated Thomas' part yields. They developed nomograms for 4/4 hard maple lumber, which estimated simulated parts yields for six lumber grades. Based on Schumann and Englerth's yield results, several computer programs were developed. OPTIGRAMI (Martens and Nevel, Jr. 1985, Martens et al. 1986), Optimal Furniture Cutting Program (Zielke et al. 1991), and Rough Mill Cost Cutter (Steele et al. 1990) estimate yield and apply production cost data by lumber grade to allow a linear programming solution to compute the least-cost mix of lumber grades to fill a cutting bill.
Giese and Danielson (1983) developed the CROMAX crosscut-first software with an incorporated database of digitally described lumber that allowed determination of maximum yields from user described cutting bills. CROMAX employed no simplifying algorithms but rather performed an exhaustive search for the best parts cut-up solution. Numbers of parts of each size could not be specified, however, so that the algorithm did not match modern rough mill practice.
A digital database that allows parts to be cut from lumber for each tested cutting order removes the limitations presented by the previous nomograms derived from program YIELD (Hoff 2000). This technique enables researchers to simulate the precise part sizes and quality classes required to produce the given cutting orders (Harding and Steele 1997).
The CORY program was developed to simulate both the crosscut-first and rip-first methods of lumber cut-up in the rough mill. CORY was designed to calculate cutting yields and optimal sawing solutions for parts of fixed dimension based on cutting orders where part numbers are specified. CORY requires users to access their own digital database of lumber to utilize the simulation software.
RIP-X (Harding and Steele 1997) is a computer program designed to provide linear programming least-cost grade mix solutions such as are produced by OPTIGRAMI, the Optimal Furniture Cutting Program, and Rough Mill Cost Cutter. RIP-X, however, incorporates CORY as the rough mill simulation and is, therefore, able to obtain yield estimates for both crosscut-first and rip-first systems. RIP-X also incorporates a database of lumber developed for this specific application. This database contains six lumber grades totaling 13,262 board feet of red oak lumber. The database of lumber allows least-cost grade mix solutions for specific parts qualities, whereas previous software was limited to the part quality classes specified by the nomograms developed by Schuman and Englerth (1967).
ROMI-CROSS (Thomas 1998) is a crosscut-first rough mill simulation that also employs a digital database of red oak lumber. It has improved capabilities compared to CORY in that the order of parts size production can be prioritized by algorithms that differ from CORY's traditional algorithm favoring length.
Gatchell and Thomas (1997) applied rough mill simulation to compare processing rates and costs between 1C and 2AC lumber grades. Steele et al. (1998) also employed computer simulation to compare processing rates by lumber grade in crosscut-first rough mills. Both groups of researchers measured processing rate as the number of cutting operations performed by operators at each machine type in the rough mill. Cutting operations were defined as the number of cuts (crosscut, rip, and salvage) performed by each simulated operator.
All of the computer simulations just cited have modeled the parts production process by a method termed batch processing, by which all parts are produced by one saw of each type. For certain rough mills, this will result in an accurate rough mill simulation. For example, a rip-first rough mill in which a single gang ripsaw is followed by a single optimizing crosscut saw is a situation in which batch processing of parts is an accurate assumption for both machines. Multiple gang ripsaws followed by multiple optimizing crosscut saws, if the same parts sizes are cut on each machine, would also be accurately modeled by the assumed batch processing of parts.
Table 3. - The moderate cutting order in which values not contained in parentheses are the part numbers, values in parentheses are the individual crosscut saw followed by ripsaw identification numbers to which the part sizes were assigned to be cut. For the moderate cutting order, the total number of parts was 5,421; average part width was 2.8 inches; average part length was 38.3 inches; approximate parts volume was 4,037 board feet.Table 4. - The difficult cutting order in which values not contained in parentheses are the part numbers, values in parentheses are the individual crosscut saw followed by ripsaw identification numbers to which the part sizes were assigned to be cut. Total number of parts was 4,650; average part width was 3.0 inches; average part length was 39.1 inches; approximate parts volume was 3,788 board feet.
However, for rough mills where multiple manually operated crosscut or straight-line ripsaws are employed, the batch processing assumption docs not provide an accurate simulation. In this case, the total cutting order is segmented into smaller cutting orders that are assigned to the multiple machines. This segmenting of the cutting order will be termed segmented processing.
Segmented processing is also practiced when multiple gang ripsaws do not process the same cutting bill or when a gang ripsaw changes blade-spacing combinations while processing a single cutting order. Likewise, when optimizing crosscut saws operate in a rough mill, each must process the same cutting bill for a batch processing assumption to result in an accurate simulation. If the optimizers process different part sizes, the total cutting order is produced by the segmented processing method.
As a replacement and extension of CORY, the CUTSIM software was designed to allow simulation of crosscut-first rough mills employing either batch or segmented processing methods (LaGarde 1996, Steele et al. 1998). For a segmented processing system, a variable number of saws can be assigned a limited number of parts sizes from the total cutting bill. Depending on the cutting bill, 3 crosscut saws and as many as 10 straight-line ripsaws can be assigned to cut the required parts. The simulation employs the same red oak database incorporated in RIP-X (Harding and Steele 1997) as shown in Table 1.
The objective of this study was to determine the influence on yield and number of cutting operations of segmented versus batch processing of parts production in a crosscut-first rough mill.
Procedures
The CUTSIM crosscut-first software was used to simulate both the batch and segmented processing systems for a crosscut-first rough mill. Production of parts for three cutting bills with an increasing level of difficulty for each were simulated for both the batch and segmented processing systems. The three cutting bills were adapted from Gatchell and Thomas (1997) and have been previously designated as easy, moderate, and difficult, respectively, by Steele et al. (1998). These easy, moderate, and difficult cutting bills are given in Tables 2, 3, and 4, respectively. Part quality specified for the simulation was clear two face and yield was obtained. For each of the three cutting bills we simulated the cut-up of lumber from each of five individual lumber grades. Ten replications were performed for each cutting bill and lumber grade combination.
The level of cutting bill difficulty is indicated by the increasing width and length of parts required when progressing from the easy to moderate and moderate to difficult cutting bills. The easy cutting bill required shorter and narrower parts than the moderate and difficult cutting bills, with an average part width of 2.1 inches and an average part length of 21.5 inches. For the moderate cutting bill, the average part width was 2.8 inches with an average part length of 38.3 inches. For the difficult cutting bill, average part width was 3.0 inches and average part length was 39.1 inches.
For each cutting bill, the procedures employed by Steele et al. (1998) were followed. By these procedures three crosscut saws were assigned part lengths to produce by both the segmented and batch processing methods. For the segmented processing method, the number of lengths assigned to each crosscut saw depended on the total number of lengths required. Likewise, subsequent ripping of parts to width by the segmented processing method required that a variable number of straight-line ripsaws be assigned to each cutting bill depending on the total number of part widths and the part numbers required. The crosscut and straight-line ripsaws to which each part were assigned are indicated in parentheses to the right of the part quantity designations in Tables 2, 3, and 4.
Experimental design
Comparison-of-means tests were performed by the least significant difference (LSD) method after determining significance of treatments in the ANOVA as recommended by Fisher's Protected LSD procedure (Steel and Torrie 1980). All tests of model, treatment, and means comparisons were conducted at the 0.05 level of significance.
Results
Total lumber yield
The results of the Model 1 ANOVA indicated statistically significant interaction between the cutting bill term and the terms representing both lumber grade and processing system. The presence of interaction prevented examination of the influence of the main effect variables. Therefore, Model 1R(a) with the cutting bill term eliminated was applied to the yield data for each cutting bill.
The ANOVA results using Model 1R (a) showed that the term representing interaction between lumber grade and processing system was significant for the moderate and difficult cutting bills. This same interaction term was not significant for the easy cutting bill. The fact that there was significant interaction between lumber grade and processing system for the easy cutting bill, and not for the moderate and difficult cutting bills, indicated that the differences between processing systems varied depending on the lumber grade processed. This interaction was eliminated by applying reduced Model 1R(b) to the yield data for each individual lumber grade and cutting bill. The ANOVA results for Model 1R(b) showed that the model and the term representing processing system were significant for the moderate and difficult cutting bills. However, for the easy cutting bill, the processing system term was not significant, indicating no statistical difference in yield between batch and segmented processing. For the moderate and difficult cutting bills, the model and main effects were significant as required by Fisher's Protected LSD prior to proceeding to the comparison-of-means tests.
Figures 1 and 2 show the results of the comparison-of-means tests for yields between processing systems by lumber grade for the moderate and difficult cutting bills. For all lumber grades, the batch processing system had a significantly higher yield than the segmented processing system for both the moderate and difficult cutting bills. For the moderate cutting bill (Fig. 1), the batch processing system mean yields were 61.5, 48.48, 38.77, 22.02, and 9.34 percent for lumber grades FAS, F1F, 1C, 2AC, and 3AC, respectively. By contrast, the mean yields for the moderate cutting bill for the segmented processing system were 57.96, 44.66, 35.3, 19.38, and 8.71 for lumber grades FAS, F1F, 1C, 2AC and 3AC, respectively. The mean yield loss associated with application of segmented rather than batch processing for all grades combined was 2.8 percent for the moderate cutting bill.
Figure 1. - Mean percentage lumber yields for batch and segmented processing systems for the moderate cutting bill. Means with the same letter did not differ significantly.Figure 2. - Mean yield differences between batch and segmented processing systems for the difficult cutting bill by lumber grade. Means with the same letter did not differ significantly.
For the difficult cutting bill (Fig. 2), the batch processing system mean yields were 61.64, 45.22, 33.02, 12.48, and 5.12 for lumber grades FAS, F1F, 1C, 2AC, and 3AC, respectively. The mean yields for the difficult cutting bill for the segmented processing system were 55.75, 39.66, 29.12, 9.76, and 3.46 for lumber grades FAS, F1F, 1C, 2AC, and 3AC, respectively. For the difficult cutting bill, the mean yield loss associated with application of segmented rather than batch processing was 3.9 percent. These results indicate that the batch processing system obtains significantly higher yields than the segmented processing system. In addition, the amount by which batch was superior to segmented processing increased from 2.8 percent for the moderate cutting bill to 3.9 percent for the difficult cutting bill. Therefore, it appears that the superiority of the batch system increased as cutting bill difficulty increased.
Mean yield differences
To test the statistical significance of the relationship between cutting order difficulty and processing system yields, Model 2 was applied. The dependent variable was the yield difference obtained by subtracting segmented processing yields from batch processing yields. Therefore, a positive value indicated superiority in yield for the batch processing system. The Model 2 ANOVA showed that a statistically significant interaction was present between cutting bill and lumber grade main effects. In the presence of this interaction, assessment of the influence of the main effects was prevented. For this reason, the term representing lumber grade was removed and a reduced model, Model 2R, was applied to the data for each lumber grade.
The Model 2R ANOVA results showed Model 2R and the term representing cutting bill to be significant, satisfying the requirements of Fisher's Protected LSD procedure and allowing comparison-of-means tests to be performed. The comparison-of-means tests compared the mean yield differences between processing systems for each cutting bill by lumber grade. As shown in Figure 3, the easy, moderate, and difficult cutting bills differed significantly for each lumber grade with the single exception of the 2AC lumber grade for which there was no significant difference between the moderate and difficult cutting bills. For the easy cutting bill, the mean yield increase for batch above segmented processing was 0.46, 0.47, 0.52, 0.33, and 0.31 percent for the FAS, F1F, 1C, 2AC, and 3AC lumber grades, respectively. The mean yield increase for batch above segmented processing for the moderate cutting bill was 3.54, 3.82, 3.47, 2.64 and 0.63 percent for the FAS, F1F, 1C, 2AC, and 3AC lumber grades, respectively. For the difficult cutting bill the mean respective yield increase for batch above segmented processing was 5.89, 5.56, 3.9, 2.72, and 1.66 percent for the FAS, F1F, 1C, 2AC, and 3AC lumber grades. Yield differences for batch compared to segmented processing for all grades averaged 0.4 percent for the easy cutting bill and, as previously noted, 2.8 percent for the moderate and 3.9 percent for the difficult cutting bills.
Figure 3. - Mean yield differences between batch and segmented processing systems for the easy, moderate, and difficult cutting bills by lumber grade. For each lumber grade, means with the same capital letter did not differ significantly.Figure 4. - Mean yield differences between batch and segmented processing systems for the easy, moderate, and difficult cutting bills by lumber grade.
Figure 4 repeats the analysis of Figure 3 in line graph rather than histogram form. This presentation allows a better visual appreciation of the fact that there is also a lumber grade influence on the degree of yield superiority of the batch above the segmented processing system. The presence of significant interaction, as previously described, prevented a statistical analysis of this relationship. It is visually clear from Figure 4 that, as lumber grade decreased, the superiority in yield of the batch processing system also decreased. The degree of decrease was influenced by the degree of difficulty of the cutting order with a very slight decline in yield as lumber grade decreased for the easy cutting bill. For the moderate cutting bill, a higher rate of decrease in the processing system yield differences was demonstrated as lumber grade decreased. The by-lumber-grade rate of decrease is greater still for the difficult cutting bill. One exception to the consistent decrease in yield with decreasing lumber grade was found for the moderate cutting bill for the F1F lumber grade, where the yield difference was 3.82 percent compared to 3.54 percent for the FAS lumber grade. The yield increased slightly for this single case. These results indicate that the yield superiority of the batch versus segmented processing system is influenced by lumber grade. The superiority of the batch processing system is greatest for the higher lumber grades and decreases as lumber quality decreases.
Cutting operations
The Model 3 ANOVA was applied to determine the significance of the number of cutting operations. There was significant interaction between the lumber grade term and cutting bill term and between the cutting bill term and processing system term. Therefore, Model 3R with the cutting bill term eliminated was applied to the yield data for each cutting bill. The Model 3R ANOVA was significant, as was the lumber grade term for each of the three cutting bills. However, the processing system term was not significant. This indicated that, for these cutting bills, there was no difference between the batch and segmented processing systems in number of cutting operations.
Similar tests were performed to evaluate the differences in processing systems for each individual crosscut and straight-line ripsawing station. The results indicated that no statistically significant difference in the number of cutting operations performed existed between processing systems at each sawing station.
Summary
A comparison of simulated yield results between batch and segmented processing systems showed that significantly higher yields were achieved with batch processing for the moderate and difficult cutting bills. Mean yield increase for batch above segmented processing for all lumber grades was 2.8 percent for the moderate cutting bill and 3.9 percent for the difficult cutting bill. Statistical comparison of the yield decrease as cutting bill difficulty became greater indicated that the segmented processing system yields are significantly and negatively influenced by an increase in cutting bill difficulty.
Graphical analysis of the differences in by-lumber-grade yield results for each cutting order showed that the segmented processing system yields were also sensitive to lumber grade. This sensitivity was related to cutting bill difficulty. The yield differences for the easy cutting bill decreased only slightly as lumber grade decreased. The rate of yield decrease with decreasing lumber grade increased for the moderate cutting bill and the rate increased further still for the difficult cutting order. This indicates that the batch processing system will provide better relative yields than will the segmented processing system for the more valuable lumber grades. In addition, the superiority of the batch processing system for the higher lumber grades is highest for the more difficult cutting bills.
No significant difference in the bctween-processing-system number of cutting operations required to fill the cutting bills were detected. This indicates that, while lumber yields are sensitive to batch versus segmented processing, labor costs should not be influenced.
Conclusions
The results of this study indicate that the rough mill batch processing system provides significantly higher yields than does the segmented processing system. The improvement in yields becomes higher as cutting order difficulty increases. The yield improvement of batch versus segmented processing is more important for the higher, more expensive, lumber grades.
The yield superiority of the batch over segmented processing will vary with parts sizes produced and machine assignments of the parts. However, the evidence from this current study indicates that when choosing rough mill systems, managers should consider the superiority of batch versus segmented processing. Rough mill designs that assign parts to be cut at the fewest number of machines should have the highest yield, all else equal. Batch processing is especially important for those operations processing difficult cutting bills and high-grade lumber. Most rough mill simulations model only the batch processing system. Yields estimated for these systems will probably be artificially inflated unless the system modeled is truly a batch system. Estimates will be particularly inaccurate for difficult cutting bills and when high-grade lumber is processed.
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Philip H. Steele*
Jonathan E. Aguirre
The authors are, respectively, Professor and Graduate Research Assistant, Forest Products Lab., Mississippi State Univ., Mississippi State, MS 39762-9820. This study was partially funded by the USDA Wood Education and Resource Center, Princeton, WV. This paper was received for publication in August 2002. Article No. 9537.
* Forest Products Society Member.
©Forest Products Society 2004.
Forest Prod. J. 54(1):40-46.
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