Sawmilling process

The sawmill's production flow began with the debarking process (Figure 1), which is intended to protect the cutting tools in the later sawing. Each log was then processed on two bandsaws with carriage. To do this, the log was positioned and fixed on the carriage’s moving squares, and the carriage advanced facing the bandsaw where cuts were sequentially made according to the diameter and quality of the log (primary cuts). The pieces in process, resulting from the primary cuts, were transported and processed in two double horizontal resaw bandsaws (bandsaw 1 and bandsaw 2), obtaining sawnwood pieces with a defined thickness. The pieces requiring an additional process were sent to a single horizontal resaw bandsaw (bandsaw 3). The next step was to eliminate the edges present on the borders of each piece, which also involved dimensioning their width. The operation was performed by three circular edgers (edger 1, edger 2 and edger 3). Finally, the pieces were transported to a board separating machine, where they were sorted for separator placement and final packaging.

Figure 1 Diagram of the production flow in a custom-cutting sawmill that processes Pinus radiata wood. 

Logic of cutting decisions

The cutting plan is a logical sequence of successive cuts, defined by the operation of bandsaws with carriage. Figure 2 illustrates the three cutting decisions based on log diameter.

Figure 2 Cutting decisions applied to Pinus radiata logs according to their diameter. 

When making cuts on the bandsaw carriage, processing times varied according to log diameter and length, as well as the number of pieces delivered to the next machines. Thus, the routes taken by the pieces depend on the number of units queued in the transports of the following machines and the capacity of units queued in the transport between the machines involved. When the capacity is exceeded, the transports and machines are stopped or blocked, which can occur forward or backward from the production flow.

Development and validation of the simulation model

The sawmill has a series of transports and cutting machines that are operated in a synchronized manner by the equipment operators according to the type and quantity of pieces in process. The process presents failures in machines, variability in diameters and number of pieces that trigger high randomness. These attributes prevent its analysis with static models based on time studies. Therefore, in this research, a DES model was developed to analyze critical machines and evaluate opportunities for improvement.

The DES model was developed based on the logic of the cutting decisions for each log diameter. This logic was incorporated into the programming of the DES model through "virtual" labels that identified the entities (logs, pieces in process and finished pieces) advancing in the process. This identification allowed determining, for each entity, the cutting decision, the number of pieces to be obtained, and the direction of the production flow based on the processing capacity of the transports and machines in relation to time. The behavior of each machine in the system was examined and the flow of pieces was analyzed based on the cuts applied to the processed logs, under the different production scenarios. The DES requires that the characteristic times of the production process be treated with their variability; therefore, they must be transformed into probability distributions. The processing, failure and arrival times of entities (logs, pieces in process and finished pieces) at each workstation were recorded, and probability distributions were fitted for each of them. Based on historical information, two simulation models were developed for sawing P. radiata logs with lengths of 2.5 and 5.0 m, and diameters between 34 and 44 cm. This raw material was sawn to produce sawnwood at a single thickness of 5/4" with variable width. The number of logs processed per shift was considered as the model’s response variable. The logic of cutting decisions and the processing times of the equipment were programmed and entered into the Arena® 3.5 discrete event simulation software package (^{Arena, 2007}).

Critical machines and possible alternative flows were identified and their impact on the production flow was determined with a factorial experiment (k factors). The simulation model was validated by comparing the sawmill’s actual production indicators against those obtained by the simulation model. In particular, the number of logs processed per shift and the production per shift were compared, concluding that the DES model is a good representation of the actual system. Subsequently, the production flow study was initiated. For this, the simulation model was iterated and performance results of the machines and transports were obtained. The appropriate number of samples for analysis was obtained with a pilot test of five iterations of the model, with the purpose of obtaining the preliminary descriptive statistics of the process. The next step was to determine the number of model iterations according to a desired error and confidence level. Therefore, the number of replications or iterations to be performed, for each production flow study scenario in the model, was calculated using the formula suggested by ^{Montgomery, Runger, and Medal (1996)}:

n=ta/2n-1×Sxp × X-2

In this way, a number of 10 replicates was obtained for each production scenario (two log lengths) with an extension of 480 min for each run of the model, equivalent to one production shift of the sawmill. To determine the base production condition or pattern of the sawmill, the production results with 2.5 m and 5.0 m long logs were subjected to a descriptive statistical analysis and Tukey’s multiple comparison test (P = 0.1).

Identification of critical machines

The results of the five iterations of the simulation model were analyzed by determining the number of processed logs, units queued in transports between machines, machine usage factor, machine failure factor, factor without machine feeding, and blocking factor of each machine. Consequently, workstations with a usage factor close to 100 % and their number of queued units close to their design capacity were identified as critical machines.

Application of the experimental design for the evaluation of the factors

A full 2k factorial experimental design was applied for the purpose of determining whether there is statistically significant evidence that the factors evaluated influenced the "production level" response variable. The factors identified and considered were:A) deliver from bandsaw carriage 1 to bandsaw 3; B) double debarker capacity; C) eliminate the failures of bandsaw 1 and 2; D) directly deliver the pieces from bandsaw 2 to edger 2 directly.

The effect of the factors was evaluated in the "applied" (+) and "not applied" (-) operational levels with respect to the reference condition, represented by the sawmill without making any type of change. Finally, the experimental design was evaluated with the Design Expert 6.0 statistical package (^{Design Expert, 2007}).

Identification of critical machines and proposals for improvement

The results at the production level for the base condition or pattern, represented by the current sawmill production flow, were: 1 489 logs per shift for 2.5 m long logs and 1 663 logs per shift for 5.0 m long ones (Table 1). Tukey's multiple comparison test showed statistically significant differences (P = 0.1) in production volume when processing different log lengths. This behavior is consistent with that recorded by authors such as ^{Steele (1984)} and ^{Cown, McConchie, and Treolar (1984)}, who reported an increase in production and yield by increasing the diameter and length of processed logs. On the other hand, these values coincided with the actual production data recorded in the sawmill, which fully validated the results obtained with the iterations of the DES model.

Like ^{Baesler et al. (2004)} and ^{Thoews et al. (2008)}, the results of the DES model were used to detect critical machines; although the detected machines differ, the same search method was applied focusing on machines that showed a high utilization rate. The results of the model with respect to the time use of the sawmill machines allowed identifying these machines and proposing modifications to the flow of semi-finished pieces. The modifications or factors evaluated are shown in Table 2.

Analysis of the proposed scenarios

The variety of factors to be studied can be very diverse; that is, from the increase in capacity of critical machines (^{Baesler et al., 2004}) and the storage location and size of products in process (^{Heshmat et al., 2013}), to changes in the distribution of the logs used in the sawmill (^{Grigolato et al., 2011}). However, this research focused on the first two factors, given that the sawmill is supplied with logs on the open market, which cannot be controlled.

The model generated 16 treatments from four evaluated factors. Table 3 shows the results of the effect of individual and combined factors on the response variable (logs per shift) in each production scenario (log length).

Analysis of the model for 2.5 m long logs

The analysis of variance (ANOVA) showed that the model was significant (F = 15.38; P < 0.001), with only a 0.1 % probability that it could be affected by some factor not included (Table 4). Similarly, when observing the F value of each factor individually, it was found that factor D had a greater effect on production, followed by factors A, C and B. As a whole, the factors were able to predict 84.83 % of the sawmill's production; therefore, the proposed model was able to adequately explain the production of 2.5 m long logs.

Table 4 Analysis of variance for the production of 2.5 m long Pinus radiata logs. 

Source of variation	Sum of squares	Degrees of freedom	Mean squares	F value	Prob>F
Model	82 876	5	16 576	15.38	<0.001*
A	16 256	1	16 256	12.80	0.004*
B	7482	1	7 482	5.89	0.034*
C	13 572	1	13 573	10.69	0.008*
D	40 804	1	40 804	32.13	<0.001*
Residual	13 971	11	1 270
Total corrected1	92 086	15
Standard deviation	30.35	R2	0.8483
Mean	1 588.63	Adjusted R2	0.7931
Coefficient of variation (%)	1.91	Predicted R2	0.6790
Sum of squared errors of prediction	29 558	Adequate accuracy2	13.364

*Significance level of 10 % by F test. ¹Represents the sum of A + B + C + D + residual. ²Measures the model's signal-to-noise ratio; generally, a value above four indicates a strong signal and, therefore, a reliable model.

The response surface of the model allows visualizing the conditions under which the highest sawmill production is obtained (Figure 3), which is possible to attain by setting factors B, C and D at their maximum level (+) and factor A at its minimum level (-). This allows production to be increased by 13 % with respect to the initial condition, that is, the production level increased from 251 to 298 m³·shift^-1 of finished product.

Figure 3 Response surface for production of the Pinus radiata sawmill with two log lengths (L): L = 2.5 m (left) and L = 5.0 m (right). Factors: A) delivery from bandsaw carriage 1 to bandsaw 3; C) failures eliminated from bandsaw1 and 2; D) pieces directly delivered from bandsaw2 to edger 2.