Improving Lumber Cut-Up Manufacturing Efficiency Using Optimization Methods

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Title: Improving Lumber Cut-Up Manufacturing Efficiency Using Optimization Methods
Author: Zuo, Xiaoqiu
Advisors: Philip H. Mitchell, Committee Co-Chair
Urs Buehlmann, Committee Member
Myron W. Kelly, Committee Co-Chair
David A. Dickey, Committee Member
Abstract: Over the past decades lumber cut-up operations (rough mills), have changed from using extensive manual decision sawing systems to saws capable of automated decision making in an effort to save labor cost, increase yield, and reduce operational mistakes. Although a large amount of automatic and computerized equipment has been incorporated into rough mills, especially in the gang-rip first process, many of the process steps still rely on human decision making. Examples include choosing the appropriate grade of lumber for processing; designing the optimal arbor for the gang-rip saw; defining suitable part priority values for the chop saw. This research was conducted based on the hypothesis that these decisions can be improved through optimization strategies without extra capital investment. The first objective of this research was to develop a method to improve the arbor design on fixed-blade arbor gang ripsaws. The result was the development of software program - the Gang Ripsaw Optimizer (GRO) written using C++ language. GRO generates an optimized fixed-blade arbor design for a gang ripsaw that not only satisfies the cutting bill requirements but also produces a high yield in a balanced manner. The GRO program reiteratively searches and compares the optimal part combinations for each lumber width provided by the Romi-Rip simulator, the Forest Service rough mill rip-first process simulator. The program presents the optimal arbor blade spacing sequence and any part widths that are not included in the optimal arbor. More than one optimal arbor will be provided in cases where there are too many widths to be placed on one arbor. The validation results showed that the GRO program provides overall better solutions than the two other arbor design software programs, i.e., GRADS and GANGSOLV. The second objective was to provide a guideline for setting up static priority values of parts listed in a cutting bill. To develop a system that generates the most effective priority values (as defined by maximum yield), a study cutting bill with 20 part groups representing the average part sizes and quantities of actual rough mill cutting bills was created. A 20-factor face-center central composite design with 512 fractional factorial points, 40 axial points and three center points was applied to fit a second order polynomial model. In addition, a ridge analysis was applied to search for maximum yield as well as the correspondent critical values. These critical values were then used to generate the setup formula. Ten cutting bills typically found in industry were used to validate the new set up system. The results showed that the static value mode can result in a yield comparable to that given when the dynamic mode is used. On average, the yield generated from the static value mode was 0.57 percent lower than that achieved using the complex dynamic exponential (CDE) mode, 0.64 percent lower than the simple dynamic exponential (SDE) mode, and 0.39 percent lower than simple dynamic (SD) mode, respectively. The third objective of this research was to search for the optimal lumber grade combination that minimizes the raw material and total production cost of rough mills, a problem which is usually referred to as the least-cost lumber grade-mix problem. Previous research has used linear programming method without verifying the crucial assumption on simple linearity between yield and grade mix. This study proved that the simple linear relationship between yield and two-grade and three-grade lumber combinations does not hold for 90 percent of the industrial cutting bills. It is, however, impossible to predict the relationship between yield and grade mix since this relationship is correlated with the characteristics of both the cutting bill and the combination of lumber grades. In order to avoid violating the simple linearity assumption, a statistical optimization method, a five-factor mixture design, was employed to solve the least-cost lumber grade-mix problem. Five factors (lumber grades) are FAS, SELECTS, 1 Common, 2A Common, and 3A Common. Due to the problems of 3A Common lumber to obtain enough wider and longer parts, upper bounds as to the amount of 3A Common grade material were applied according to the difficulty levels of cutting bills. The model creates a lumber grade and cost response surface for all input solutions. By locating the lowest cost point of the surface, the corresponding lumber grade or grade mix is obtained. This optimal solution can consist of any number of different grades and allows the user to pre-specify the lumber grades and grade proportions available in a given situation.
Date: 2003-07-21
Degree: PhD
Discipline: Wood and Paper Science

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