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UBC Theses and Dissertations

Application of simulation technique in the study of sawmill productivity Aune, Jan Erik 1973

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THE APPLICATION OF SIMULATION TECHNIQUE IN THE STUDY OF SAWMILL PRODUCTIVITY by JAN ERIK AUNE Cand. a g r i c , A g r i c u l t u r a l University of Norway A thesis submitted i n p a r t i a l f u l f i l m e n t of the requirements f o r the degree of Master of Forestry i n the Department of Forestry We accept t h i s thesis as conforming to the required standard The University of British Columbia January, 1973 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or p u b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date - i -ABSTRACT A computer simulation program which, models the operation of a Brit i s h . Columbia coast dimension sawmill has been developed i n FORTRAN IV. The model represents the i n i t i a l log breakdown by a double cut, multi-pass band headrig, cant breakdown by a bulledger and the further processing on two resaws, pony edger and the double end trimsaw. Simulation of the headrig and bulledger operation i s event oriented, whereas the piece flow through the other processing units i s updated with 1-minute i n t e r v a l s . Flowcharts describe the routines b r i e f l y . The p r i n c i p a l types of data input are sawlog population c h a r a c t e r i s t i c s , machine c h a r a c t e r i s t i c s , buffer storage c a p a c i t i e s , and product output constraints. Information about the model operation i s c o l l e c t e d during the simulation runs, and the printed output includes p r o d u c t i v i t y i n Mbfm per 8-hour s h i f t , the time each saw was operating, i d l e , busy or blocked, the time the bulledger queue contained a given number of cants and histograms showing the queue length d i s t r i b u t i o n i n 10-piece classes f o r subsequent saws. V a l i d a t i o n of the model plays an important part i n system simulation. The approach has been to attempt a v e r i f i c a t i o n of the piece flow a r r i v i n g at trimmer, / / l and #2 resaw, ponyedger and greenchain. Although the p r o d u c t i v i t y figures obtained from simulation correspond to those experienced by the m i l l , the piece flow could not be v e r i f i e d . Irregular log shape, not r e f l e c t e d i n the sawlog population c h a r a c t e r i s t i c s and leading to more manufacturing of slabs i n the r e a l system, i s considered - i i -to be the p r i n c i p a l f a c t o r contributing to t h i s . Preferably, further modelling should lead to the development of one general assembly-system, which regards sawmills as a c o l l e c t i o n of interconnected components, with increased input and output f l e x i b i l i t y . - i i i -TABLE OF CONTENTS Page Abstract i List of Tables v List of Figures v i Acknowledgement v i i Introduction 1 Simulation — Objectives and Concepts with Particular Reference to Sawmilling 4 1. Basic Definitions 4 2. Planning a Sawmill Simulation Project 9 (a) Formulation of Problem 11 (b) Collection and Processing of Data 12 (c) Formulation of the Mathematical Model 14 (d) Estimation of Operating Parameters 16 (e) Evaluation of Model 17 Sawmill System Presentation 18 1. M i l l Description 18 2. Exogenous Factors Related to the System 21 3. Decision Making in Log and Cant Breakdown 23 The Sawmill Simulation Model 25 1. Gasp II Simulation Package 26 2. System State In i t i a l i z a t i o n 28 3. Sawing Decision Routines 32 (a) Headrig Decision Routine "HEAD" 33 (b) Bulledger Arrival Routine "AREDG" 41 (c) Bulledger Departure Routine "DPEDG" 41 - iv -Page (d) Cant Breakdown Decision Routines 46 4. Piece Flow Updating System 64 Verification and Validation of the Sawmill Model 75 1. Verification Strategy and Results 78 2. Considerations for Validation 83 Discussion 86 Conclusion 90 Bibliography 92 Appendix 94 - v -LIST OF TABLES Table Page i . Saw cutting regression equation estimates 39 i i . A r r i v a l d i s t r i b u t i o n i n pieces per minute f or 80 model and system f or saws and output to greenchain i i i . Mean values and standard deviations (SD) for 81 a r r i v a l d i s t r i b u t i o n s to saws and greenchain (pieces per minute) - vl -LIST OF FIGURES Figure Page 1. Outline of m i l l floor 19 2. Basic modes of GASP Control 27 3. General flowchart of Main Program 30 4. General flowchart of log arrival subroutine, HEARR 31 5. Detailed flowchart of headrig processing subroutine, HEAD 34 6. Detailed flowchart of depth of cut subroutine, CDEPT 40 7. Flowchart of bulledger arrival subroutine, AREDG 42 8. Flowchart of bulledger departure subroutine, DPEDG 44 9. Log geometry and variables for identification of cant 48 10. Flowchart of the process administrative subroutine, DCION 49 11. Flowchart of identification routine, IDENT 50 12. Bulledger saw blade positioning as related to cant characteristics at 10 feet from butt end 51 13. Flowchart of edger saw blade positioning subroutine, XSLAB 52 14. Cutting decision hierarchy for slabs and 2-inch, 3-inch and 4-inch cants 54 15. Flowchart of trimming/transfer subroutine, TRIM 57 16. Flowchart of 1-minute discrete interval updating subroutine, UPDTE 65 17. Flowchart of piece transfer subroutine, TRSFR 73 18. Comparison between the lumber yield from the Western Forest Products Laboratory recovery study, and the simulated yield for the m i l l under study. 82 19. Estimated relationship between sawmill productivity and average top diameter in log supply. Solid line i s hand drawn. 85 - v i i -ACKNOWLEDGEMENT I wish to acknowledge the assistance and guidance provided me by my Chairman of Committee, Dr. R.W. Wellwood, and by my thesis supervisor Dr. J. Dobie of the Western Forest Products Laboratory, Canadian Forestry Service. The constructive comments received from Mr. G.G. Young, Dr. A. Kozak and Mr. L. Valg, a l l of the Faculty of Forestry, are greatly appreciated. F i n a n c i a l assistance has been received from the Univ e r s i t y of B r i t i s h Columbia and through the Council of the Forest Industries of B r i t i s h Columbia Fellowship i n Wood Science, 1971-72. - 1 -INTRODUCTION The basis f o r an investment decision i s often the expected return to invested c a p i t a l . High returns from sawmill investments r e l y to a large extent upon a high p r o d u c t i v i t y of the m i l l . A correct estimate of t h i s f actor f o r investment analysis may be c r u c i a l . Today's sawmills frequently consist of between f i v e and ten processing u n i t s which i n t e r a c t to various .degrees. Often the p r o d u c t i v i t y of the m i l l depends on the p r o d u c t i v i t y of the main breakdown u n i t only; j u s t as often i n t e r a c t i o n s between machines are complex and estimation of p r o d u c t i v i t y requires more e f f o r t . The analysis i s further complicated by technical innovations, marginal improvement i n equipment and new methods, systems or p r i n c i p l e s which are believed to o f f e r d e c i s i v e advantages as compared to the o l d ones. With the v a r i e t y of types and models of equipment now a v a i l -able i t i s d i f f i c u l t to obtain a l l the data necessary for s e l e c t i n g an optimum combination, and a common r e s u l t i s that many newly constructed m i l l s operate lengthy time periods while c o s t l y debugging i s undertaken. Simulation of the production process, i f determined to be f e a s i b l e and r e l i a b l e , could prove a valuable t o o l i n reducing the r i s k of erroneous p r o d u c t i v i t y assessment by: a. simulating the e f f e c t of investment planned i n an already operating m i l l , or b . simulating several m i l l designs f o r d e t a i l e d comparison of pr o d u c t i v i t y i n case of new m i l l s to be erected. - 2 -This thesis attempts to show that p r i o r determination of p r o d u c t i v i t y through simulation i s f e a s i b l e although, as w i l l be discussed, extended e f f o r t s w i l l have to be made to ensure a better basis f o r v a l i d a t i o n of the simulated data output. One j u s t i f i c a t i o n for the use of the simulation technique i s c l e a r l y the cost savings expected when carrying out experiments on a f u l l scale system. Reduced r i s k i n the case of large investments i s another. Also, computer simulation allows f o r unlimited p o s s i b i l i t i e s i n changing parameters l i k e log supply and market constraint to show how such changes a f f e c t p r o d u c t i v i t y . The subject of simulation i n sawmilling merits i n i t i a l comments which are presented independently of the more intensive l i t e r a t u r e review. E a r l i e r approaches generally f e l l i nto one of the two following categories: 1. I t e r a t i v e c a l c u l a t i o n s performed on a log or cant i n order to show how various breakdown str a t e g i e s may r e s u l t i n d i f f e r e n t volume and value y i e l d s . One or more patterns would be claimed superior within given constraints. 2. Discrete event simulation of a sequence of operations or processes, i n order to predict the p r o d u c t i v i t y of the described system, as w e l l as to obtain a d e s c r i p t i o n of the behaviour of the system v a r i a b l e s . An a d d i t i o n a l dimension, time, has been added. - 3 -By far the largest amount of study that has been done to date falls into category 1 . Peter and Bamping (1962) presented a procedure whereby one shortleaf pine log could be sawn an unlimited number of ways to obtain data for evaluation of sawing methods and orientation of log defects to the sawing faces. They claim a better understanding of log quality and yield variations as influenced by sawing methods. Riikonen and Ryhanen (1965) applied digital computing to the problem of "maximization of the economic result in the processing of raw material". Their approach was to simulate different sawing alternatives on idealized logs and to select the most profitable. A more limited, but detailed effort was made by Woodzinski and Hahm (1966) who presented a computer program to determine the maximum utilization of a given board once the defects had been located and assigned coordinates. The U.S. Department of Agriculture, Forest Service, in their Forest Products Laboratory at Madison, Wisconsin, extended this, program to automatic location of defects by ultrasonics (McDonald et al. 1969) and, although presently limited to hardwoods, i t has resulted in a possible automatic grading system of boards (Hallock and Galiger 1971). Dunmire and Englerth (1967) did a yield study based on the same computer program. Other studies simulating the economy and recovery of sawing patterns were made by Juvonen (1967), Heiskanen (1968), Tsolakides (1969), McAdoo (1969), and Reynolds and Gatchell (1969). None comes forward with any new principles. One study dealing with analysis of the sawing process from the operational point of view shows the advantages of log sorting to increase productivity of the chipper headrig (Dobie 1970). By applying Monte Carlo analysis (see - 4 -p p . 6 ) i n d e s c r i b i n g t r i e h e a d r i g o p e r a t i o n , h e s h o w e d a p r o d u c t i v i t y i n c r e a s e o f " 1 1 p e r c e n t t o 1 5 3 p e r c e n t a s t h e a v e r a g e l e n g t h o f g a p b e t w e e n l o g s e l i m i n a t e d b y s o r t i n g , i n c r e a s e d f r o m 3 t o 3 0 f e e t " . T h i s t h e s i s i s e n t i r e l y d e v o t e d t o c a t e g o r y 2 . A B r i t i s h C o l u m b i a c o a s t d i m e n s i o n m i l l w a s s e l e c t e d f o r t h e s t u d y , a n d t h e m a c h i n e r y c o n s t i t u t i n g t h e b a n d h e a d r i g l i n e , i n v e s t i g a t e d w i t h r e s p e c t t o p r o c e s s i n g t i m e s a n d d e l a y " o c c u r r e n c e s . T h e s a w m i l l p r o c e s s e d m a i n l y w e s t e r n h e m l o c k (Tsuga Tieterophylla ( R a f . ) S a r g . ) a n d a m a b i l i s f i r (Abies amabilis ( D o u g l . ) F o r b . ) . T h e b r e a k d o w n d e c i s i o n s m a d e b y t h e m i l l s a w y e r s w e r e r e c o r d e d a n d s e r v e d a s a b a s i s f o r t h o s e f o r m u l a t e d i n t h e s i m u l a t i o n p r o g r a m . No a t t e m p t h a s b e e n m a d e t o o p t i m i z e t h e s e l e c t i o n o f c u t t i n g p a t t e r n s . R a t h e r , t h e i n t e n t i o n h a s b e e n t o p r e s e n t a g e n e r a l i z e d c o p y o f t h e r e c o r d e d p a t t e r n s a n d t o s t u d y t h e r e s u l t i n g p i e c e f l o w . S I M U L A T I O N - O B J E C T I V E S AND C O N C E P T S W I T H P A R T I C U L A R R E F E R E N C E TO S A W M I L L I N G D u r i n g t h e l a s t d e c a d e n u m e r o u s t e x t s d e a l i n g w i t h c o m p u t e r s i m u l a t i o n a n d s y s t e m s a n a l y s i s c o n c e p t s , t e c h n i q u e s , a n d a p p l i c a t i o n s h a v e a p p e a r e d . B e f o r e a t t a c k i n g t h e p r o b l e m o f s i m u l a t i n g a p a r t i c u l a r s a w m i l l , a s u r v e y o f s e l e c t e d r e f e r e n c e s w i l l b e m a d e i n o r d e r t o e s t a b l i s h g e n e r a l t e r m i n o l o g y a n d t o p u t t h e s p e c i f i c a p p r o a c h i n p r o p e r c o n t e x t . 1 . B a s i c D e f i n i t i o n s T h e h i s t o r i c a l d e v e l o p m e n t o f t h e s i m u l a t i o n t e c h n i q u e h a s i n c l u d e d t h e e s t a b l i s h m e n t o f a s p e c i f i c t e r m i n o l o g y . B a s e d o n N a y l o r et al. ( 1 9 6 6 ) , - 5 -Pritsker and Kiviat (1969) and Emshoff and Sisson (1970), a short glossary of terms is given below. SYSTEM MODEL ENTITY ACTIVITY EVENT ATTRIBUTE VARIABLE PARAMETER EXOGENOUS FACTOR ENDOGENOUS FACTOR STATUS VARIABLE FEEDBACK LOOP TABLE LOOK-UP A collection of interrelated objects necessary to make a realistic study of a problem under consideration. An abstraction of reality. A model can be physical, mathematical, graphical, logical or combinations of each. Object of a system; also, any distinguishable item, being, or processing unit within a system. A system function that usually takes time to accomplish. Point in time when the system changes its status. Characteristic of an event, entity or system. An attribute of the system that takes on different values within a simulation run. Characteristic of the system that has only one value within a simulation run. Parameter or variable has a value that affects, but is itself unaffected, by the system. Parameter or variable has a value determined by other variables in the system. Variable describes the state of a system or one of its components. A component takes its input from a portion of its own output from a previous period. A method of generating random variables with approximately the same probability as the real system does. - 6 -Naylor et al, (1966:3) formulated trie following definition of simulation: "A numerical technique for conducting experiments on a digital computer, which involves certain types of -mathematical and logical models that describe the behavior of a business or economic system (or some component thereof) over extended periods of real time". McMillan and Gonzalez (1965:13) called i t a representation of reality while citing another writer, Arthur (N.V.), as defining simulation to be "a dynamic representation achieved by building a model and moving i t through time". In order to avoid confusion one should distinguish clearly between Monte Carlo techniques and simulations, Monte Carlo analysis is used to solve a deterministic, analytic problem by converting i t to a probabilistic analog having the same mathematical formulation. A simulation model is constructed to best represent the observed behavior of a real system, rather than to provide an analog to an analytical model of the system (Emshoff and Sisson 1970:171). The application in this thesis is pure simulation and should not be connected to Monte Carlo analysis. A sawmill system may be defined as any combination of machines and conveyors dedicated to the breakdown of logs into green lumber. The system activity is lumber processing, but since the process usually is subdivided into several conversion steps, i t appears logical to refer to several activities as processing at unit 1, at unit 2, etc. Entities in this system are machines, transport conveyors, logs, cants and boards. The discrete event simulation of one machine, a top arbor edger, is described in the next paragraphs. - 7 -Considering only the top arbor edger, the system represents that of a single-channel queuing s i t u a t i o n . The events necessary to study t h i s simple system are a r r i v a l of a cant to the system, a completion of the processing of a cant by the edger, and the completion of the simulation at a s p e c i f i e d time or a f t e r the processing of a given number of cants. The l a t t e r can be regarded as a c o n t r o l type of event and w i l l not be discussed. A d e s c r i p t i o n of the event s e l e c t i o n l o g i c i s also excluded; i t i s s u f f i c i e n t to know that each event w i l l be scheduled to take place during the simulation i n the same order as i n the ac t u a l system. The edger status i s described by i t s queue length and busy, i d l e or delayed state. When operating i n l i n e with other machines, an a d d i t i o n a l s t a t e , blocked, w i l l occur when the subsequent saw's buffer storage has been f i l l e d to capacity. According to the status of the edger, d i f f e r e n t components of the event l o g i c are activated. For a complete d e s c r i p t i o n of the l o g i c , including the occurrence of blocking, i t i s assumed that sawn pieces, leaving the edger system, are transported to a following buffer storage. The a r r i v a l event l o g i c f i r s t tests the queue length v a r i a b l e against the buffer storage capacity. If the buffer storage i s f i l l e d , the a r r i v a l i s rescheduled to the time of completion of the on-going processing. With storage capacity a v a i l a b l e , the cant i s added to the queue. Should the edger be i d l e , the completion or departure event routine i s c a l l e d , and the departure i s scheduled. The a r r i v a l routine then generates the next a r r i v a l according to an i n t e r a r r i v a l time d i s t r i b u t i o n . - 8 -The departure routine performs as. follows; When i d l e , the c a l l has come from the a r r i v a l routine and the edger status changes: to busy. Feeding and sawing time f o r the new a r r i v a l are accumulated, and the departure of the cant scheduled. A t t r i b u t e s characterizing the departing pieces are generated according to the edger's cant breakdown l o g i c . The sequence of delay and interdelay times ( i d l e times excluded) i s reproduced as found through, timestudies. For each departure, the remaining interdelay time i s calculated and when turning negative, a delay time i s generated and added to sawing time. The departure, therefore, may or may not include a previous delay as characterized by the edger state being busy or delayed at departure time. When i n the delayed state, a new interdelay time i s generated before the state i s set to busy. The following buffer storage i s investigated to assure that space i s a v a i l a b l e f o r departing pieces. If f i l l e d , the edger i s set to blocked status, and the departure rescheduled to the time when space w i l l be a v a i l a b l e . Otherwise, the pieces leave the system, and the queue i s searched f o r a new cant to process. If empty, the saw i s set i d l e . With a cant waiting, the l o g i c i s s i m i l a r to that of the i d l e s t a t e . A blocked state indicates the end of the blocked period and status i s changed to busy, whereafter the pieces leave as explained above. The duration of each successive state i s recorded when a state change occurs, i . e . each time a piece i s either added or subtracted from the queue and when the saw becomes either i d l e , busy, delayed or blocked. - 9 -This description of the simulatipn of the arbor edger is, also valid for the other machine units in the sawmill system. Basically, therefore, the simulation program for the entire system w i l l schedule events which, according to the established operating logic, w i l l move logs, cants and boards through the different processes u n t i l the finished boards are transported out onto the greenchain. 2. Planning a Sawmill Simulation Project The flow chart below illustrates a common procedure that may be followed when a sawmill simulation i s desired CNaylor et al. 1966:24). It i s assumed that the justifications for the simulation approach have been stated. - 10 -a. Formulation of problem. b. C o l l e c t i o n and processing of data. c. Formulation of a mathematical model. d. Estimation of parameters. Accept Model • f. Formulation of computer program. g. V a l i d a t i o n . h. Design of experiments. i . Analysis of simulation data. The following subsections w i l l deal with d i f f e r e n t aspects of t h i s approach down to f ) : "Formulation of Computer Program". As the discussion of these points may be more i l l u s t r a t i v e when rela t e d to a p a r t i c u l a r case, the modelling and f i e l d work ca r r i e d out for this a p p l i c a t i o n w i l l be treated - 11 -along with the general concepts, Points -f) through i ) represent such c r u c i a l steps that they w i l l be handled i n separate sections. Ca) Formulation of Problem I n t u i t i v e l y , the problem of simulating the operation of a sawmill stands out as one of modelling a multistage queuing model. However, the system i s too complex for a pure mathematical a n a l y s i s , one d i f f i c u l t y being that, for some machines, the generated flow depends on the a t t r i b u t e s of the processed piece, i n addition to the exogenous v a r i a b l e s . These a t t r i b u t e s , i n p a r t i c u l a r the dimensions of the piece, are the r e s u l t of the breakdown decisions made at the previous saw and must be transferred together with the piece from one saw to the next. Some parts of a sawmill system are often a one stream/no buffer operation where the number of pieces flowing through at any time i s l i m i t e d . Other parts have buffer storages ahead of each saw which allows for the accumulation of several hundred pieces. The piece a t t r i b u t e s also become less important i n determining the processing time when reduced to boards or small cants. The i n i t i a l problem can therefore be divided into two: (1) A d i s c r e t e event simulation of the operation where processing time and material flow i s highly dependent upon the dimensions of the piece, and (2) a scanning and updating of the piece flow at constant time i n t e r v a l s for the processes where the influence of the piece a t t r i b u t e s i s i n s i g n i f i c a n t . In general, machinery processing logs and large cants belong to the f i r s t group, whereas resaws, trimmers and small edgers belong to the second. - 12 -(b) C o l l e c t i o n and Processing of Data No general pattern e x i s t s f o r data c o l l e c t i o n . Each, problem w i l l present i t s own requirements; consequently only those encountered i n sawmill modelling w i l l be discussed. Although the representativeness of c o l l e c t e d data versus the v a l i d i t y of the system behavior for model te s t i n g i s a s t a t i s t i c a l matter, the confrontation between them has indeed an impact on data c o l l e c t i o n and processing. For one thing, for how long a period should data be collected? In investment analysis the operating character-i s t i c s over the year are more important than the p a r t i c u l a r environment next week. I t i s well-known, however, that sawmills do not plan to meet yearly demand averages each week; neither do they receive log supply with yearly average d i s t r i b u t e d c h a r a c t e r i s t i c s . For investment analysis purposes i t appears important to account f o r v a r i a t i o n s i n the exogenous var i a b l e s during the year as w e l l . In t h i s p a r t i c u l a r example, a less time-consuming, but f a r more inaccurate approach has been used. The recorded v a r i a b l e s are assumed to be representative for the year and extreme environmental conditions are furnished by manipulation of the exogenous variables i n s p e c i a l l y designed experiments. Further, the machine f a i l u r e d i s t r i b u t i o n s are assumed to be stationary, and processing rate of trim, resaw, and edger sawyers are considered to be independent of queue length. The actual system, on the other hand, i s exposed to c y c l i c a l phenomena. Examples are d i f f e r e n t log supply during the winter months, since logging operations take place at lower a l t i t u d e C a t l e a s t i n the B.C. coastal region); c e r t a i n periods (spring?) may have a higher labour turnover rate, and demand may be c y c l i c according to the a c t i v i t i e s of the construction industry. In order to provide a sound base for investment decision the data - 13 -should convey this type of variation to the model in order to carry out the testing in a representative environment. Processing rate for a l l units except the headrig and the top arbor edger were found in this application by piece counts. Observation periods were clustered to ten consecutive, 1-minute periods, each cluster assigned to a different saw and attended to in random order during the day. Processing rates were found to be normally distributed when analysed as histograms. However, the data will be heavily exposed to autocorrelation; that is, i f the sawyer is working at a high rate in a particular minute he will most probably be working hard in the next 1-minute period as well, and the production from two periods will be positively correlated. On the other hand, since process capacity in the model is selected at random from a frequency distribution, this autocorrelation which is present in the real system will be absent in the model. The random selection of 10-minute periods may, however, reduce the bias of the average value. Each saw has been studied with respect to delay and interdelay times for 200 minutes. Total observation time is the sum of smaller periods, 20-30 minutes long, sampled at random over 4 days. The data could not be fitted to any theoretical distribution and were reproduced by the model through the table look-up method*. The delay times include mechanical and electrical failures as well as operational delays. * See Emshoff and Sisson, pp. 181, for a description. - 14 -The raw material characteristics had been studied for one year by the sawmill company. Log length (feet) and top diameter Cinches) for each log were recorded ahead of bucking. From a separate sample of 400 hemlock logs, taken by the Western Forest Products Laboratory, the taper (inches/foot) was distributed in five classes from 0.05 inches/foot to 0.25 inches/foot. As the mill could only handle logs up to 42 feet, the log supply was scanned and those longer than 42 feet bucked according to mill specifications. The taper was generated by the table look-up method, and a top diameter calculated for the butt log where bucking took place. Log lengths, as appearing after scanning and bucking, were distributed in 2-foot classes for each top diameter. The other constraint, market demand, is far more complicated and has been dealt with much more summarily. The mill output is distributed on a number of product types, grades, and sizes with final classification being done by the sorting on the greenchain. In this study only product sizes are considered. The entire expected output for the mill for 1972 has been distributed on board width classes and one special product, 12-inch by 12-inch, for the Japanese market. Volume generated by the program logic will therefore be added to the same classes and sawing operations carried out in a way that satisfies this width distribution. (c) Formulation of the Mathematical Model Again, model building is highly related to the actual problem under study. Furthermore, i t is an art not easily mastered. According to Naylor et al. (1966:32-33), two basic designs have emerged from formulating mathematical models for use in computer simulation: - 15 -1. Generalized designs represent an attempt to des.cri.be the behaviour of an entire system; examples being the business from or the economy of a nation; and, 2. Modular or building block, designs which indicate formulation of a general model based on a set of models describing the major components of the system, a block recursive model. This approach proves particularly convenient for complex systems whose components operate in a sequence. Emshoff and Sisson (1970:54) divide methods of identifying and modelling of subsystems into three groups: 1. The flow approach is used for systems having dynamic properties determined by the flow of physical or information entities through the system. A subsystem is identified by examining points that produce a physical or information change in the flowing entity. 2. The functional approach is used when no observable flowing elements exist in the system, but when there is a reasonably clear sequence of functions to be performed. 3. The state change approach is applicable to systems that have a large number of independent relationships for which no specific subgrouping can be observed. The method of analysis requires examination of the state of the system at points of time. - 16 -The sawmill production process, possesses dynamic properties as well as physical entities. Unfortunately, the number of entities rapidly becomes large, making i t inefficient to deal with each entity, individually a l l the way through the mill. At the same time, the sawmill system is clearly functional with well defined sequences of operations. The building of this sawmill model involves primarily approaches 1. and 3. The flow approach is represented by the discrete event simulation of log and cant processing. The flow of boards and small cants is updated with 1-minute intervals following the state change approach. Cd) Estimation of Operating Parameters Econometricians have had to worry themselves over parameter estimation for years. Goldberger (1964) and Johnston (1963) provided discussion of techniques for compensating for problematic phenomena occurring in data. The most common data process is the one already outlined for this model, that is, to collect the values of a variable over time and to compute a frequency distribution from which such values are assumed to derive. Pro-cedures for this basic statistical process can be found in most statistics texts. High expenses will be incurred in observing, recording, and collecting data which may be incomplete or inaccurate. Frequently, variables are found to have cyclical or growth trends or other dynamic properties, and data must be represented as time series. If data are subject to interaction of several variables that are exogenous to the model but related in the outside environment, these variables may vary together and cause multicollinearity. - 17 -The basis for investigations of these complications is far too limited in this crude application. But, certainly, before going to the large investment of developing a general and universal sawmilling investment model, these factors should have been considered in detail. (e) Evaluation of Model Initial testing of a model involves primarily testing of assumptions that have been made at an earlier stage, Later the output generated by the model will be tested for validity. Naylor et al. (1966:36-37) present a li s t of possible statistical tests which are designed to give answers to the following questions: 1. Has any nonsignificant variable been included which contributes very l i t t l e to the ability to predict the behaviour of the endogenous variables? 2. Has any significant exogenous variable been excluded that is likely to affect the behaviour of the system's endogenous variables? 3. Has any relationship between the system's endogenous and exogenous variables been formulated inaccurately? 4. Have a l l parameters of operating characteristics been properly estimated? 5. Are the estimates statistically significant? - 18 -Evaluation of the proposed model of the sawmill requires that some of these questions, No. 3 i n p a r t i c u l a r , be overlooked f o r reasons noted i n the section on Estimation of Operating Parameters. In f a c t , one can only suspect inaccurate formulations, there being no way of p r e d i c t i n g the e f f e c t upon the endogenous variables u n t i l the system s e n s i b i l i t y has been tested. SAWMILL SYSTEM PRESENTATION For the purpose of simulating a p a r t i c u l a r sawmill, no d e t a i l e d t e c h n i c a l d e s c r i p t i o n of the equipment i s warranted. An ou t l i n e of the flow paths, and a statement of those variables i n f l u e n c i n g the sawing and flow decisions, w i l l s u f f i c e and w i l l be presented i n the next sections. On the other hand, when the objective i s to compare m i l l systems, other factors such as make, model, p r i c e , p h y s i c a l capacity and feedspeed range, sawing capacity, space requirement, and in/out feed arrangements of i n d i v i d u a l units become more important. Proper i d e n t i f i c a t i o n of the system on a l l counts i s then necessary. 1. M i l l Description An o u t l i n e of the m i l l i s shown i n Figure 1. The simulated part i s shaded grey. Because of i t s s i m p l i c i t y , the framesaw l i n e w i l l not contribute anything towards res o l v i n g the d i f f i c u l t i e s i n programming the breakdown l o g i c and i s therefore excluded. The headrig i s a double cut bandsaw; the edger or bulledger i s a top arbor edger with f i v e independently positioned c i r c u l a r saw blades. Together, these two saws constitute a common f i r s t breakdown combination i n B.C. #2 GREENCHAIN A PONYEDGER //I RESAW # 2 DEBARKER T FRAMESAW,OR GANGSAW CIRCULAR EDGER #2 RESAW I A A #1 DEBARKER TOP ARBOR EDGER, OR BULLEDGER DOUBLE TRIM 3 AW TRIMMER OR TRIMSAW A A A HEADRIG TIMBER OUTFEED 1_J 1—1 o LU • s o o < LU X CUT-OFF SAW # I GREENCHAIN A I Figure 1. Outline of m i l l f l o o r . The shaded area includes the simulated operations. - 20 -Coast m i l l s . Although, the edger has the capacity to process t h i n cants on top of each, other, or narrow: cants side by side, t h i s i s not often done. When i t happens, board foot volume i s l o s t because of d i f f i c u l t i e s i n p o s i t i o n i n g the saw. There i s no reason to include the occurrence of these cases i n the model, and edger as w e l l as other saws are assumed to process cants one by one on a f i r s t come, f i r s t served basis. The trimsaw has 21 c i r c u l a r saw blades preprogrammed to the most common trim operation, but t h i s can be overridden manually as the piece c h a r a c t e r i s t i c s require. The two resaws are handsaws and the ponyedger i s a small arbor edger with two independently positioned c i r c u l a r saws. The double trimsaw i s simply two manually manoeuvered c i r c u l a r cut-off saws. If the only remaining processing to be c a r r i e d out on the piece a f t e r the bulledger i s resawing, the piece w i l l be diverted to #2 resaw. If ri p p i n g or further trimming a f t e r resawing i s required, the piece w i l l be directed to J l resaw. At times, when eit h e r of the two resaws breaks down, and i t s storage area becomes f i l l e d , the piece flow i s directed to the other. As #2 resaw cannot d i v e r t pieces back to the ponyedger for r i p p i n g , such boards are c o l l e c t e d on the greenchain, together with other misjudged pieces, and transported by forktruck back onto the #1 resaw feed board through a s p e c i a l pocket. In case of a major resaw breakdown causing congestion at the other resaw as w e l l , the head sawyer i s instructed to produce more 2-inch boards to r e l i e v e pressure on the system. Regardless of the p h y s i c a l a t t r i b u t e s of a cant, the product on the - 21 -greenchain w i l l at most have passed through the bulledger, trimmer, one resaw, ponyedger, and double trimsaw. Because of wrong decisions, i t frequently happens that a board c i r c u l a t e s twice through the resaws and/or ponyedger. Although i t poses an i n t e r e s t i n g problem, no attempt has been made to study the flow i n such d e t a i l as to discover t h i s kind of malpractice. Consequently, the model assumes "correct" decisions at a l l stages. From t h i s i t follows that no board reaches the greenchain i n an unfinished condition and the model w i l l not r e f l e c t the actual feedback of half-processed boards to the f i r s t resaw. About 15 percent of the production consists of 12-inch by 12-inch and 14-inch by 14-inch timbers destined f o r Japan and A u s t r a l i a . These timbers, as they come through the bulledger, are delayed on the conveyor b e l t u n t i l a d d i t i o n a l material from the same cant has been diverted to the trimmer. They are then pushed onto a s p e c i a l conveyor f o r grading and cut to exact length. Pieces trimmed off i n t h i s process and blocks not meeting the grading standards, are fed back onto the bulledger feed conveyor during headrig delays, or the headrig i s stopped i n order to allow these pieces to be fed to the edger. When the headrig i t s e l f processes t h i s product, the block i s transferred to the s p e c i a l conveyor d i r e c t l y without having to pass through the bulledger. 2. Exogenous Factors Related to the System As the actual system consists of two p a r a l l e l production l i n e s , with #1 resaw and ponyedger s e r v i c i n g the framesaw l i n e as w e l l , the i n t e r a c t i o n between the two needs to be c l a r i f i e d . - 22 -The log supply recorded is. that of the total mjp.1. Clearly, the logs taken out to feed the framesaw- will change the diameter and length distribution of the remainder. No records exist describing the framesaw logs. The decision as to where a particular log is going, is taken by the debarker operator, and is based on maximum diameter, form, and length. Knowing the saw's approximate yearly production capacity, an estimate as to the diameter and length distribution of the framesaw log supply can be made and deducted from the total supply. Since the model's production is constrained by its product mix, the total mix for the mill must be corrected for the yield contributed by the framesaw line. Yield from logs diverted to this saw is not recorded separately in the mill. Neither was the framesaw production studied by Western Forest Products Laboratory during the processing of their 400 logs. Only very rough estimates can be made as to this product distribution, and the best available is that provided by the simulation model when processing log sizes similar to those present in the framesaw log supply. These may, therefore, be used to correct the total mix. Finally, the arrivals from the framesaw line will constitute a part of the queue at the #1 resaw and the ponyedger. The arrival rate of these pieces has been recorded and is found to be approximately 9 percent of total on the resaw and 20 percent on the ponyedger. In order to cope with this, the arrivals to #1 resaw and ponyedger from the framesaw will be generated once a minute from the actual arrival distribution, the pieces added to the queue and processed. It is assumed that thereafter the pieces go out on the greenchain. - 23 -3. Decision Making in Log and Cant Breakdown The decision as to what to cut, where to cut, and when to cut the possible cant and board sizes in a typical dimension mill, is far from a set of clear cut rules. There are general guidelines, such as those given out by the Council of the Forest Industries of British Columbia in their Sawmill Manufacturing and Lumber Recovery Seminar Booklet, but these are frequently overridden by local requirements, as well as being ignored by malpractice. Because of the premium price paid for clear material, the i n i t i a l log breakdown is geared towards maximum recovery of this grade; something that makes sense economically, but which results in a large variation of log breakdown patterns even within one-inch diameter class. It is, as understood from above, rather difficult to establish a decision rule for headrig cutting based on exterior log characteristics alone. Log quality, and quality of last sawn face, are even more important in deciding when an additional cut is to be made, the thickness of that cut, or whether the log should be turned a quarter turn or a half turn. The logic used in this model is a stochastic replica of the decisions actually made in sawing the 400 hemlock logs, with butt diameters varying from 11 inches to 36 inches, The bulledger decisions are somewhat easier to perceive as they are mostly guided by special widths in immediate demand, and maximum volume recovery. For cants less than 6 inches thick, the sawyer would select widths in a way that satisfies both the demand and recovery requirements. For cants 6 inches or larger, he will cut to the final board-thickness C2-inch nominal) or a multiple of this. Only in special cases, e.g. for a 12-inch cant, - 24 -will he look for a special product like 12-inch by 12-inch timber. When the physical attributes of the cant are known, the decision making is reduced to a maximization of volume within existing product constraints. In general, trimming takes place on boards longer than 26 feet. Depending on the width and length, either 14, 16, or 20 feet are trimmed off the best end. This may change with special requirements for product length, but does not represent any problem for theoretical decision making. Actually, the problem is more severe in practice, as boards may contain irregularities in dimensions as well as defects which would have to be trimmed off. Special decision rules exist for resaws and ponyedger, mainly to assure sufficient consideration of the recovery of high grades and maximum volume. These may be studied in the above mentioned guidelines, but will not be reflected explicitly in the decision making of the model, which will act only on the necessity of keeping a maximum board volume within the physical limits set by the log. As will be seen in the next chapter, many of the considerations mentioned here, the importance of grade in particular, will have to be overlooked at this stage. The decisions expressed by the computer program will not be an exact copy of those actually taking place. They are hoped to be, however, sufficiently similar to generate a piece flow through the entire mill which, to a certain degree, will correspond to that of the real system. - 25 -THE SAWMILL SIMULATION MODEL The model to be described in this section represents the shaded area in Figure 1. It has been simulated under various conditions with the objective of describing the queue formation at each individual saw, as well as volume output on #1 greenchain for given time periods. To do so, two interrelated structures have been formed and put to work: 1. A technical logic that purports to reflect the log breakdown and decision patterns in the observed mill system; and, 2. A structural logic that controls the model operation in simulated time and does the record keeping usually associated with any simulation programs. The first structure has been developed by the writer while the second has been provided by the GASP II simulation package (Pritsker and Kiviat 1969), slightly modified to better f i t the IBM 360/67 computer and the Fortran G compiler, GASP II is suitable for discrete event simulation, and is applied here in two ways: To simulate defined physical events actually taking place in the system, mainly those associated with the headrig/bulledger combination, and to simulate an event at fixed time intervals to update the queue and record the final output at trimmer, #1 and Ml resaws, double trimsaw, and ponyedger. - 26 -The model in its. present state. i,s. only applicable to the obseryed system, but could be generalized to include other mills of similar layout. For easier perception of the concept established in the routines, flow charts representing the logic of these are presented along with their description. 1. GASP II Simulation Package The following explanation of GASP II is based on the book "Simulation with GASP II" (Pritsker and Kiviat 1969). The functional capabilities of GASP necessary for every simulation are: a. System state initialization. b. Event control. c. Information storage and retrieval. d. System performance data collection. e. Program monitoring and error reporting. f. Statistical computations and report generation. Of these a), b), e), and f) are basic control modes whereas c) and d) provide a data processing capability activated by the technical logic. The basic modes of GASP Control are shown in Figure 2. A l l the above-mentioned capabilities are connected via the GASP Executive subroutine which itself is called only by the programmer-written Main Program. GASP Executive assures that a l l segments of the simulation happen in the correct order; as such i t calls for initialization of variables and establishes files, obtains the first (and the next) event through the programmer written event routines (scheduling), updates the current time, monitors the - 27 -^ Start ""^ GASP executive System state initialization L Event control Event 1 I E Z V 5 Event 2 I Event n I Program monitoring and error reporting Program trace Error report JL Statistical computations and report generation J Figure 2. Basic modes of GASP Control (From Pritsker aiid Kiviat, 1969) - 28 -events as, they happen and determines, when simulation w i l l stop, whereafter f i n a l reports- on endogenous, exogenous and status v a r i a b l e s are printed. 2. System State I n i t i a l i z a t i o n The numerous GASP var i a b l e s and constants necessary to permit s t a r t i n g of the simulation w i l l not be discussed. In general, the i n i t i a l system state may be any state acceptable within the physi c a l l i m i t s of the system; for sawmills, however, the various events are interlocked i n a way that leaves only one of two p r a c t i c a l options open: a. The m i l l i s cleared, a l l queues are empty, a l l machines are i d l e and s t a t i s t i c a l storage arrays are i n i t i a l i z e d to zero; or, b. The i n i t i a l state i s the f i n a l state of the previous run. In both cases the model performance w i l l move towards a steady state within the set constraints; the steady state being characterized by stationary d i s t r i b u t i o n s of the endogenous random v a r i a b l e s . The time necessary to reach the steady state i s of importance when designing the simulation experiments, and i f the changes i n the exogenous va r i a b l e s between two consecutive runs are small, option b) above w i l l l i k e l y reach the steady state f a s t e r than i f the experiment should be repeated from state a). The t r i a l s c a r r i e d out with t h i s model w i l l u t i l i z e option a). While GASP var i a b l e s are i n i t i a t e d within the GASP package, the variables necessary to simulate t h i s p a r t i c u l a r sawmill system are i n i t i a t e d i n the Main Program. Among these, only the ones representing the constraints on the m i l l ' s operation w i l l be further discussed. - 29 -The log population is characterized by a percentage distribution of the number of logs in 1-inch top diameter classes, a percentage distribution of the number of logs in 2^foot length classes within each top diameter and an overall percentage distribution in 5 taper classes, from 0.05 inch to 0.25 inch in 0.05 inch intervals. The taper represents the decrease in diameter per linear foot, moving from butt end towards the top end of the log. The input log population differs from the actual population only in that butt diameter is calculated on the basis of logs being represented by truncated cones. The headrig cutting pattern is selected according to the butt diameter. As these patterns not only vary with the physical measurements of the log, but with surface quality, rot, and sweep as well, each 1-inch butt diameter class is assigned one of three patterns, selected according to its relative occurrence as found in the Western Forest Products Laboratory's log study. The i n i t i a l basic input factors (not GASP variables) are presented in Appendix 1. These will vary from one mill to another and will only be discussed in connection with changes in the exogenous variables for different experiments. In order to start the simulation, the main program calls subroutine GASP, which in turn calls routine DATAN where GASP variables and i n i t i a l events are read in and initiated. The principal tasks of the main program are given in Figure 3. The i n i t i a l event to occur is the selection of the first log; thereafter the sawing event routines generate the necessary events themselves. The first updating is initiated as well, at time 1 minute from start. The log arrival routine HEARR Cflow chart in Fig. 4), apart from the - 30 -^ Start ^ 1 Set card reader and p r i n t e r code I I n i t i a l i z e random number generators. I Read diameter, length, taper, interdelay time, delay time and headrig c u t t i n g pattern di s t r i b u t i o n s T Create table look-ups for these d i s t r i b u t i o n s VRead trinilengths, production c o n s t r a i n t s , board and cant dimensions, saw kerf and maximum buffer storage for saws Read headconveyor distances and conveyor v e l o c i t i e s I I n i t i a l i z e v a r i a b l e s for queue lengths, processing v a r i a b l e s and temporary storage arrays JL C a l l GASP ^ End • ^ Figure 3. General flowchart of Main Program. - 31 -^ ' Start ^ I n i t i a l i z e v a r i a b l e s for headrig processing Generate top diameter, length and taper for next log Calculate butt diameter Find cant v a r i a b l e s for next log C a l l CDEPT (Fig.6) I Schedule headrig departure for f i r s t slab from log ^ Return ^ Figure 4. General flowchart of log a r r i v a l subroutine, HEARR. - 32 -initialization, is scheduled b,y- the cant departure routine HEAD (Fig. 5) only when the last cut in the log has Been made and the two cants f a l l onto the conveyor leading to the bulledger. HEARR generates uniformly distributed random numbers between 1 and 100 which correspond to the column subscripts for the top diameter, length, and log taper arrays. It calculates the butt diameter as if the log was a truncated cone and looks up the pattern to be applied. Before returning to GASP Executive, the time necessary to load the log onto the carriage, approach the saw blade, and saw the first slab is accumulated and added to present time, TNOW. The departure of the slab from the carriage is scheduled by filing time of departure and event code in an attribute array NSET. Through a particular routine SET, a l l removals and entries in NSET are immediately followed by an updating of the arrays pointer system. Several possibilities exist as to the decisive logic giving the next event. Here, as cants and boards in a sawmill mostly flow from saw to saw in an orderly sequence, a first come, first serve logic is applied. Thus, at any time, the event with the lowest scheduled time will be the next to occur. 3. Sawing Decision Routines Only long training and a quick mind can provide the kind of creative reflexes which result in constant proper treatment of logs, cants, and boards under changing constraints. It would, therefore, be presumptuous to claim that a set of rigid and simple decision rules would be able to copy the proper sawing decisions in exact detail. Rather, the described routines aim at a quantitative approximation to the result of the actual - 33 -decisionsj that i s , as, close as considered necessary- to generate the number of pieces that form the queues in the buffer storage at each saw, at any point in time. Ca) Headrig Decision Routine "HEAD" Although the sawing patterns are selected according to their approximate relative occurrence within the diameter class, the conditionally derived set of operating rules represents a deterministic sequence of subevents. These are executed one by one unti l the entire log has been converted. The log arrival routine HEARR CFig- 4) selects the sequence and executes the f i r s t step, whereafter the cant departure routine HEAD (Fig. 5) takes over. An example of the one dimensional subevent vector is shown below and explained for a log with butt diameter 25 inches. 271 002 088 271 002 088 271 002 088 271 003 066 007 1 2 3 4 5 6 7 8 9 10 11 12 13 Each subevent or action is coded in three digits. The f i r s t action always represents the cut of a slab, and slab thickness at butt end scaled up by 100 is given. When the departure of this slab i s due, HEAD is called. HEAD investigates the slab to determine whether i t w i l l yield a board, and i f so transfers i t to the bulledger queue and moves on to investigate the next action (No. 2 in array above). If the next code is less than 66, the code represents a subscript in the cant thickness array CTIK. Thus, 002 above indicates a cant to be cut, i t s actual thickness is found in CTIK (2) and the processing time for the cut is calculated. The departure time for this cant is scheduled, i t s physical attributes are determined and control Figure 5. Detailed flowchart of headrig processing subroutine, HEAD. - 35 -Scale down ac t i o n code by 100 1 < f Set distance to top surface Set top surface v a r i a b l e s to zero f C a l l CDEPT (Fig. 6) I Set distance to closest surface of cant I C a l l CDEPT (Fi g . 6) T Calculate sawing time I Schedule next cant departure and update log v a r i a b l e s / ~ A 1 Return J Figure 5. Detailed flowchart of headrig processing subroutine, HEAD, continued. - 36 -Determine action Add traveltime to accumulating v a r i a b l e Increment action array subscript <5 Add 1/4 turn time to accumulating v a r i a b l e I Increment face i n d i c a t o r by 1 Increment action array subscript Turn on slab i n d i c a t o r Turn o f f l a s t cut i n d i c a t o r Schedule a r r i v a l of a new log ^ Return ^ C o l l e c t log data i f l og to be sampled Reset log v a r i a b l e s to zero I E s t a b l i s h cant c h a r a c t e r i s t i c s of l a s t cant JL Turn on l a s t cut i n d i c a t o r Add 1/2 turn time to accumulating v a r i a b l e Increment face i n d i c a t o r by 2 Increment a c t i o n array subscript Turn on slab Indicator ~ 3 T C o l l e c t busy s t a t i s t i c s f o r headrig Set headrig to blocked status ^ Return ^ Figure 5. Detailed flowchart, of headrig processing subroutine, HEAD, concluded. - 37 -returned to GASP. At departure time HEAD is again called, and the cant is transferred to the bulledger queue. Upon investigation of the next action, 088 is found. This code represents a 90° turn of the log and the necessary time consumption to carry out this action is accumulated. Since a turn of the log means that a new face of the log is to be opened, the next action will necessarily yield a slab. The face indicator is incremented by one and an indicator assuring that the next cant is treated as a slab is turned on. Events for the above log proceed until the code 066 is found. This code tells that the previous cut was the last cut. Every last cut contributes two pieces, so that the next action, which is the last action, provides the thickness of the final cant. The characteristics of this cant are determined and, as the last cant always departs together with the previous one, no further scheduling of cant departure from this log is required. At this point a new log arrival is scheduled, the lag time depending on the position of the carriage at time of last departure. It is assumed that the log supply always keeps up with production. The two codes not present in the above example are 099, which indicates a 180° turn of the log resulting in face indicator being incremented by two, and 077 which specifies that the carriage will travel to its previous position without making a cut. For each action the processing time is found. Loading of carriage, movements of carriage apart from the actual sawing, and turns of the log - 38 -are represented by constants which, are accumulated according to the processing logic. These factors will have the same average value no matter what the applied pattern. The actual sawing time, on the other hand, depends on the location of the cut in the log. A previous study by Row et at. (1965) showed that depth of a cut was the most significant factor in determining cutting velocity on handsaws; also a conclusion in this investigation. Saw cuts on the headrig were timed to 1/100 minute and depth of cut estimated at 10 feet from the butt end. Apart from depth of cut, thickness of cant, log length and top and butt diameter were tried as independent variables in several regression equations. The dependent variable was the calculated feedspeed in feet per minute in a l l the runs. For the bulledger the independent variables were thickness of cant, cant length, and number of saw blades actively involved in the sawing. Results of the regression analyses for both saws are shown in Table 1. For the headrig the significant variables were depth of cut and thickness of the cant; for the bulledger, the thickness of cant and its length. Given the purpose of providing an average estimate of the sawing time according to the selected cutting pattern, the equations are judged to estimate the time with sufficient accuracy. As the program proceeds through the action array, a routine CDEPT (Fig. 6) calculates the depth of cut on the four quadrants, and stores a negative value for the component left of center line and a positive value for the component right of center line. In this way, every cant leaving the headrig is assigned sufficient attributes to identify i t when being further processed. The only necessary conditions are that the log shall TABLE i Saw Cutting Regression Equation Estimates 1. Headrig Regression analysis, the dependent variable is feedspeed (feet per minute) Variable Name X ^ = Depth of Cut X2 = Cant Thickness Intercept Standard Error of Estimate Residual Variance Multiple Correlation Coefficient R Squared Variance Ratio (F) Independent Variable Regression Coefficient Standard Error 0.264833D 04 0.572158D 02 1) 0.182408E 03 0.249519E 02 2) 1/X1 1/X2 = 0.133756E 03 = 0.512440E 02 = 0.262595E 04 = 0.71751 = 0.51482 148.555 With 2 and 280 Degrees of Freedom Variance Ratio (F) 210.793 5.258 2. Bulledger Regression analysis, the dependent variable is feedspeed (feet per minute) Variable Name X^  = Cant Thickness X2 = Cant Length Intercept Standard Error of Estimate Residual Variance Multiple Correlation Coefficient R Squared Variance Ratio (F) Independent Variable ln(Xj Regression Coefficient -0.873351D 02 0.382948D 02 Standard Error 0.677077E 01 0.175165E 02 = 0.357834E 03 = 0.402718E 02 = 0.162182E 04 = 0.79045 = 0.62481 86.597 With 2 and 104 Degrees of Freedom Variance Ratio (F) 166.380 4.780 1 ) 0 . 2 6 4 8 3 3 D 0 4 = 0 . 2 6 4 8 3 3 - 1 0 2) 0.182408E 03 = 0.182408-10" - 40 -^ Start ^ Calculate radius of log 10 feet from butt Calculate depth of cut at given distance from center as i f only one face has been opened < Yes Right vectors h a l f depth Le f t vector=-half depth Depth of cut= depth Yes Le f t vector=-distance to previously cut face Right vector=half depth Depth of cut=right-left Return 3 Right vector=distance to face 1 No L e f t vector=-half depth Right vector=half depth Depth of cut=depth Yes 1 L e f t vector=distance to face 3 i ^ Return • ^ Figure 6. Detailed flowchart of depth of cut subroutine, CDEPT. - 41 -have to be turned i n one d i r e c t i o n only, and that no cant except the very l a s t can contain the center of the log. Each saw cut i s half taper or p a r a l l e l to the center l i n e through the log. At time of cant departure, therefore, the cant i s e i t h e r added to the bulledger queue or, i f there are only a few pieces i n that queue, an a r r i v a l to the edger i s scheduled to account for the time the cant w i l l have to t r a v e l across the conveyor. If by any chance the edger queue should be f i l l e d to capacity, the headrig receives an imposed delay u n t i l the edger takes on a new cant. Whereas the trimsaw and subsequent saw queues are assigned an estimated number of pieces as maximum, the bulledger queue i s measured i n inches as cant sizes vary considerably. (b) Bulledger A r r i v a l Routine "AREDG" This routine serves i n only one capacity; namely, adding the cants to the edger queue. If the queue i s empty i t c a l l s the edger processing routine as w e l l . By d i v i d i n g cants into two groups, those waiting to be served and those i n movement on the conveyor, a more r e a l i s t i c p i c t u r e of the queuing s i t u a t i o n as i t a f f e c t s the processing i s obtained. In short, i t means that when a l l the cants on the conveyor move, the queue length i s considered to be zero. A flow chart of the routine i s shown i n Figure 7. (c) Bulledger Departure Routine "DPEDG" The piece c h a r a c t e r i s t i c s are important i n determining what path the piece - 42 -^ Start ^ Take bulledger queue length s t a t i s t i c s \t_ Remove f i r s t piece i n t r a n s i t Y Add one piece to bulledger queue Yes Take status s t a t i s t i c s for bulledger Set bulledger busy Turn on no-transfer i n d i c a t o r I ' C a l l bulledger departure routine' DPEDG (Fig.8) ^ Return ^ Figure 7. Flowchart of bulledger a r r i v a l subroutine, AREDG. - 43 -w i l l follow through the m i l l . The bulledger departure routine, DPEDG (Fig. 8) determines i n d e t a i l the y i e l d from each cant, and assigns a set of codes which guides the further processing and queuing. Each f i n a l board occupies a l i n e i n the two dimensional storage array STOGE. At each scheduled cant departure, these w i l l be transferred to the three dimensional routing array IROUT which l a t e r i s handled by the updating l o g i c . A f t e r the transfer of pieces i n storage, or d i r e c t l y i f the bulledger was previously i d l e , the queue i s searched for a new cant. If the queue i s empty, the edger i s set to i d l e . If not, the cant processing time i s found from the regression equation. Before the departure of the sawn cant i s scheduled, the remaining interdelay time i s checked. If a delay i s scheduled to occur before the cant has been e n t i r e l y processed by the edger, the delay period i s generated and recorded before processing, and the departure i s delayed accordingly. Because of the combined d i s c r e t e event simulation of the headrig/bulledger combination, and the one minute d i s c r e t e i n t e r v a l updating a f t e r the bulledger, the i n t e r f a c e between the two becomes d i s t o r t e d . The trimsaw production i s transferred at the end of each updating and w i l l lag 1 minute behind the bulledger operation. It i s necessary, therefore, to apply two v a r i a b l e s f or the trimsaw queuelength. One records the length according to the actual transfers to and from the queue. The other takes - 44 -Transfer boards i n storage to 1R0UT f i l e 1 Update trimsaw queue length r Reset storage f i l e length to zero 0 Yes Reschedule board departure according to delay Take blocked period s t a t i s t i c s ^ . Return ^ Figure 8. Flowchart of bulledger departure subroutine, DPEDG. - 45 -I Yes .Take bulledger queue length s t a t i s t i c s T Remove one cant from queue I C a l l c u t t i n g (decision complex} (Fig.10) ] Take bulledger status s t a t i s t i c s r Set bulledger i d l e ^ Return ^ J. Reset board width access switches occurs^ Yes next I Accumulate s t a t i s t i c s on busy time Set bulledger delayed Generate delay period Accumulate s t a t i s t i c s on delay time Generate new interdelay time Accumulate s t a t i s t i c s on headrig blocked time Set headrig busy ^ Return Schedule s t a r t : of headrig Figure 8. Flowchart of bulledger departure subroutine, DPEDG, concluded. - 46 -on the value of the first after each updating and accumulates only the half of the actual arrivals providing an estimate of the average queuelength during the 1-minute period. If the trimsaw is delayed or blocked and its average queuelength reaches the maximum level, the bulledger will be blocked as well. As the time of trimsaw restart is known, the piece being processed in the bulledger will have its departure rescheduled to that moment. (d) Cant Breakdown Decision Routines In deciding how to break down the cants into end products some rigid decision rules become necessary. In this application the principle of maximum volume of square edged lumber within 1 percent of the set product distribution constraints is followed. Any width class contributing more to the total volume than permitted by the constraint will not be produced until its relative volume again drops below the limit. From this i t follows that the decisions will not be optimal for any given period of time. On the other hand, additional but somewhat arbitrarily applied rules that ensure that the widest cants will yield the largest widths will serve to decrease the probability that, e.g. only 3-inch, 4-inch, and 6-inch widths are available for the processing of a 30-inch wide cant. The set of decision routines identifies the cant or part of the cant, selects the proper sawing decision routine and, if warranted, trims the boards while continuously accumulating produced volume within width classes, filing processed boards in the interim storage STOGE, or filing - 47 -pieces to be reconsidered or further processed in the buffer storage XNTRM. The log and cant variables necessary for proper identification of pieces later in the process are illustrated in Figure 9. Figures 10 and 11 represent the flow chart for the decision routine DCION which, in fact, has only an administrative function, and the identification routine IDENT. When studying IDENT, Figure 9 should be consulted for explanation of the variable names. In total, four different routines for determination of the location of saw blades at the bulledger are necessary, depending upon the thickness of the cant and whether or not the positioning of the saw blade should be symmetrical around the center line of the cant. The different ways of positioning the saw blades are illustrated in Figure 12 with reference to the appropriate routine for saw blade location, which in turn is represented by a flow chart of XSLAB in Figure 13. Cants with thicknesses greater than 4 inches will have their boards filed in the STOGE array directly. Only the unedged side sections will be put into XNTRM as slabs for further consideration. Cants with thickness 4 inches or less, and slabs will enter XNTRM before being investigated as to trimming and further processing. Figure 14 illustrates the decision heirarchy for slabs and 2-inch, 3-inch and 4-inch cants. Boards from 2-inch and 3-inch cants are investigated as to trim only. BORX TORI Corresponds to B TOLE Corresponds to C DDIST Corresponds to A Variables used i n the subroutines CDEPT, KEARR, HEAD and IDENT(Fig.11) at 10 feet from butt end: A=XDIST(IFAS), distance from centerplane to cut surface on face IFAS B=RIGHT(IFAS), distance from centerline(projected on face IFAS) to r i g h t sidecut C-=XLEFT(IFAS), as above, but to l e f t sidecut B+C=depth of cut, DEPTH C E N T E R L I N E FOR SLABS' TORI = TOLE=0 Figure 9. Log geometry and variables for identification of cant. - 49 -Figure 10. Flowchart of trim administrative subroutine, DCION. - 50 -No Yes Take piece c h a r a c t e r i s t i c s out of XNTRM Cant c h a r a c t e r i s t i c s are o r i g i n a l a t t r i b u t e s Figure 11. Flowchart of i d e n t i f i c a t i o n routine, IDENT. - 51 -1. Cant thickness < 4 inches Sidecuts < board thickness Resaw cut to be considered i f thickness > 1 x board thickness. Distances between bulledger saw blades correspond to board widths or n x board v;idths(n les s or equal to 3). Positioning i s symmetrical around center l i n e . 2. Cant thickness < 4 inches One sidecut > board thickness Resaw cut to be considered i f thickness > 1 x board thickness. Distances between bulledger saw blades correspond to board widths or n x board widths(n less or equal to 3). Pos i t i o n i n g i s l a t e r a l s t a r t i n g from sidecut closest to center l i n e . 3. Cant thickness > 4 inches' Sidecut < cant thickness Distance between bulledger saw blades equals n x board thickness(here n equals 2 ) . P o s i t i o n i n g i s symmetrical around center l i n e . Dotted l i n e s represent l a t e r resaw cuts. 4. Cant thickness > 4 inches One sidecut > c a n t thickness SIDE-CUT Distance between bulledger saw blades equals n x board thickness (here n equals 2 ) . P o s i t i o n i n g i s l a t e r a l s t a r t i n g from sidecut c l o s e s t to center. Dotted l i n e s represent l a t e r resaw cuts. Figure 12. Bulledger saw blade positioning as related to cant characteristics at 10 feet from butt end. - 52 -f Board variables are those stored i n f i r s t l i n e i n XNTRM Yes 1 Board v a r i a b l e s are those from o r i g i n a l l og E Kerf equals ponyedger kerf Kerf equals bulledger kerf t F i l e the sidecuts d i r e c t l y into IROUT coded for chipper 1 Start search f o r saw blade positioning y i e l d i n g maximum volume s t a r t i n g with l a r g e s t width Calculate number of pieces that f i t across surface No Number^s. Yes equals z'ero^ No Calculate length and volume of each board and store i n d i v i d u a l l y . Accumulate volume ure 13. Flowchart of edger saw blade positioning subroutine, XSLAB. Accumulate volume for product widths V Accumulate volume for log Transfer each board width and length into columns 3-8 in XNTRM ^ Return Figure 13. Flowchart of edger subroutine, XSLAB, saw blade p o s i t i o n i n g concluded. Bulledger Sawblode Positioning 1st resaw cut a f t e r edging and trimming. Bulledger cut based onconsideration of I and IV only. Length of board di c t a t e s trimming point. I I : 2nd resaw cut y i e l d s a board which i s directed through ponyedger. I l l : Remaining slab does not y i e l d a board and i s chipped. IV: Trimmed of f piece y i e l d s one board and i s directed through resaw once. Order i n trimsaw queue : I,II,III,IV - II with trim i n d i c a t o r and a l l with the same queue number. Order i n resaw queue I,II - with the same queue number. IV - with the following queue number. Figure 14. Cutting decision hierarchy for slabs and 2-inch, 3-inch and 4-inch cants. - 55 -Slabs and 4-inch cants are treated in a more elaborate way. The bulledger decision routine assumes first that an imaginary cut is to be made by the resaw, separating a 2-inch cant from the slab or the 4-inch cant. A limited number of board combinations are located on the top surface of the 2- inch cant, the one yielding maximum volume (within the product distribution constraints) determining the location of the bulledger blades. This constitutes the bulledger decision and will, since the saw blades run through the entire cant, impose physical limitations on the decisions that may be taken f or the upper separated part. An illustration of the XNTRM (I,J) array will facilitate perception of the logic (I represents the boardnumber within the cant, starting with one; J points to the storage location for the board characteristics explained below). \ j 1 2 3 4 5 6 7 8 9 10 11 12 13 l \ 1 5.86 -5.89 0 0 0 0 0 0 6.24 16 18 30 0 2 5.89 -5.86 0 0 0 0 0 0 6.24 16 18 • 30 0 Two pieces have been filed in XNTRM. Both are side slabs from a 12-inch cant with headsaw cut on face 1 and 3 only. Column 13 indicates the type of piece the data describe. A zero refers to a slab, one to a 2-inch or 3- inch cant and two to a 4-inch cant. Column 1 gives the distance from centerplane to the right wane or edge on the cant surface closest to the center, column 2 the distance to the left. These distances correspond to those earlier noted under the section, headrig decision routine "HEAD", routine CDEPT discussion; their difference corresponds to depth of cut at the headsaw. Columns 3-8 are the storages for board widths and lengths to be made from the slab, but which have not yet been fully considered as to trim and resawing. Column 9 gives the distance from the center line to - 56 -the cant surface, and columns 10-12 store the top diameter, butt diameter, and length of the log. The routine DCION checks that no boards have been filed by testing column 3, then calls the identification routine for a decision as to what maximization routine should be applied, In this case the cant will be considered to be symmetrical around the centerline, since the previously mentioned imaginary resaw cut will not yield square edges at 10 feet from the butt. The routine SSLAB is called which tries to f i t one or more boards as described earlier. Details about each board are not obtained but, assuming that in this case a 6-inch board yields maximum volume, its length is 30 feet. XNTRM now will show: \ J 1 2 3 4 5 6 7 8 9 10 11 12 13 1 5.86 -5.89 3 30 0 0 0 0 8.19 16 18 30 0 2 5.89 -5.86 0 0 0 0 0 0 6.24 16 18 30 0 Columns 3 and 4 have now been filled respectively with the width code and length of a board, so that when DCION again checks first line in XNTRM, this is registered and the routine TRIM (Fig. 15) is called. TRIM checks first the length of the board. If longer than 26 feet, a trim indicator is turned on and the distance from the butt end to the trimsaw cut is determined according to the width and length of the piece; for this board i t is 16 feet. As the trim will cut off the entire slab, the upper 22 feet is considered a separate piece, and the values in line 1 in XNTRM are changed to represent that upper part. The 16-foot board is now ready processed, and filed in STOGE, while the upper layer of the slab is - 57 -Has "S. Yes ^ a n t been through^ bulledger Set kerf and l e t log variables be those for cant V Set kerf and take log variables from XNTRM )<_ Transfer board lengths and f i n d the longest i Determine trim length based on longest board i n piece V Recalculate butt diameter and length for remaining piece which now occupies f i r s t l i n e i n XNTRM V Turn on trim indicator Check the piece c h a r a c t e r i s t i c i n d i c a t o r f o r appropriate address Figure 15. Flowchart of trimming/transfer subroutine, TRIM. - 58 -Increment trimsaw queue number by 1 \_ ? / ' 1 : — j Add 1 to resaw i n d i c a t o r of l a s t piece i n array STOGE Schedule piece for double trimsaw No / C a n \ Yes more resaw cuts be made ? Turn o f f resaw indicator -H 666 H* Turn on resaw i n d i c a t o r L*— Figure 15. Flowchart of trimming/transfer subroutine, TRIM, continued. - 59 -Piece i s a 2-inch or 3-inch cant and w i l l not be resawn 1 Yes Schedule piece to double trimsaw — J ^ r < — V Piece has thickness > 4 Inches and w i l l be resawn Figure 15. Flowchart of trimming/transfer subroutine, TRIM, continued. - 60 -Condition for no edging of next l e v e l piece i s length within 4 feet of length of base l e v e l piece Figure 15. Flowchart of trimming/transfer subroutine, TRIM, continued. - 61 -Schedule piece to Ol resaw £ •Turn i n d i c a t o r on Yes 'Turn i n d i c a t o r o f f I Schedule piece to ponyedger and double trimsaw Yes Schedule piece to ponyedger Yes Move storage XNTRM 1 l i n e up since piece has been processed F i l e trim i n d i c a t o r i n l a s t l i n e of array STOGE Yes Turn trim i n d i c a t o r o f f Move storage X1ITRM 1 l i n e back, to accomodate next l e v e l to be resawn Return > Figure 15. Flowchart of trimming/transfer subroutine, TRIM, concluded. - 62 -rechecked to see if i t yields another piece. This 16-foot slab will not yield additional boards, but if i t would have, the XNTRM would have been backspaced one line to accommodate the top layer in the first line. As i t is, XNTRM will show only two lines: \ ^ J 1 2 3 4 5 6 7 8 9 10 11 12 13 1 5.86 -5.89 0 0 0 0 0 0 6.24 16 16.93 14 0 2 5.89 -5.86 0 0 0 0 0 0 6.24 16 18 30 0 Note that the distance from center line to closest surface of the cant is set back to the original in the first line; that is, i t will be considered as an entirely new slab. The log data have been updated to account for the trimming. After the next evaluation the first line will have been processed completely, XNTRM will be updated one line, and the process will start over again with the second slab. Four-inch cants are treated very much the same way, only with a few shortcuts due to the fact that the number of resaw cuts that can theoretically be made is one, whereafter the boards can be transferred to STOGE two at a time. Also, similar trim considerations are made in the maximization routines for thick cants. If the maximum volume of the cant's output is made up by a number of pieces larger than can be produced by the bulledger saw blades, the boards are aggregated to a maximum of three, side by side. Hence, the columns 3-8 for board storage in XNTRM. Trim is decided on the length of the - 63 -longest board i n t h i s case and, unless, the trimmed-off part i s reconsidered completely, side boards i n the aggregation may be erroneously trimmed. As w i l l be described i n the next section, which treats the piece flow updating system, the columns i n the STOGE and IROUT arrays contain saw number codes f o r further routing of the pieces a f t e r the trimsaw. Because of the perfect form of the t h e o r e t i c a l logs i t i s r e l a t i v e l y easy to decide on the path each board w i l l have to take through the m i l l . Two-inch cants y i e l d i n g s i n g l e boards have t h e i r output directed through the trimsaw and onto the greenchain. If boards are aggregated side by side they w i l l f i r s t be s p l i t on the ponyedger, and the longest board which was end trimmed by the trimmer, leaves f o r the greenchain. The remaining one or two boards i n the aggregate w i l l have to be end trimmed by the double cut-off saw, unless a l l were of f u l l length i n i t i a l l y . Two-inch boards aggregated v e r t i c a l l y , as found i n 4-inch cants, are transferred to #2 resaw only i f both boards i n the piece are within 4 feet of the established length. Otherwise they are directed to the #1 resaw. Afte r being resawn, the 2-inch boards are considered as explained f o r the 2-inch cant. Slabs always go to the #1 resaw, since they w i l l next be edged on the ponyedger which cannot be reached from the //2 resaw. Each piece at each saw w i l l be assigned a queue number through the elaborate i n t e r a c t i o n between DCION, TRIM, and the saw blade p o s i t i o n i n g routines, SSLAB, XSLAB, SSCAN, and XSCAN. (The flow chart of XSLAB i s the only one presented as they are a l l based on the same p r i n c i p l e ) . If the piece contains more than - 64 -one board, each line in STOGE and IROUT representing boards from the same piece will have the same queue number. 4. Piece Flow Updating System The subroutine UPDTE (Fig. 16) investigates the projected interdelay and delay times for the coming minute. Each saw is ranked as to the end of its present state and UPDTE follows this ranking through the minute while summing up delayed and working periods. The advantage in so doing can be found in the detailed accounting of the interaction between saws. If, for example, the ponyedger has a breakdown period and its queue reaches maximum, a delay is imposed on the other saws as well, since the conveyor streams can no longer move. An imposed delay is recorded for the other saws that are working for this period. The ranking is readjusted to let the end of the delay for the blocking saw become the next state change. Blocking is at that time turned off and the other saws reassume their previous activity. According to the processing rate and the time the saw actually operates, the number of processed pieces is found. UPDTE is rescheduled to one minute later. Average queue length and number of arrivals are recorded for each 1-minute period. As both processing rates, delay and interdelay time distributions have been recorded at the mill, the arrival rate distribution becomes important for the verification of the model, since i t is the breakdown logic that will generate the arrival flow. The three-dimensional array IROUT (I,K,J) contains the codes of boards and cants ahead of trimmer, #1 resaw, ponyedger, double trimsaw and #2 resaw. - 65 -^ Start JL Generate next updating Generate production rates for next period I Calculate feedrates from headconveyor to d i f f e r e n t saws f o r next minute J Determine f i r s t ranked saw Yes i> 4000 Find status of that s a w ' I V Saw i s working Update flow since l a s t changeN of status C a l l WORK Accumulate busy time s t a t i s t i c s Generate delay time Set saw to delay status 6 Figure 16. Flowchart of 1-minute d i s c r e t e i n t e r v a l updating subroutine, UPDTE. - 66 -Saw i s i d l e No change i n status before end of minute. Saw i s updated 1 Yes / 1 Accumulate i d l e time s t a t i s t i c s Set saw to busy state •ml Saw ranked according to next change of status C a l l RANK No Inter • 'aelay time Yes 1000 to Next change of status set to time now plus remaining i n t e r delay period I time now 1 s^. \ No change i n status before end of minute. Saw i s updated r Interdelay time set to zero Interdelay time reduced for period up to end of minute I Saw ranked according to next change of status C a l l RANK , 1000 Figure 16. Flowchart of 1-minute discrete interval updating subroutine, UPDTE, continued. - 67 -Set time of next change of status Saw ranked according to next change of status C a l l RANK X Jioooj Saw ranked according to next change of status C a l l RANK T IioooI Figure 16. Flowchart of 1-minute d i s c r e t e i n t e r v a l updating subroutine, UPDTE, continued. - 68 -1 — — — < saw t Calculate and accumulate a r r i v a l s for past period V Update queue I Accumulate s t a t i s t i c s on delay Generate interdelay time Set saw to busy state 9 Accumulate status time s t a t i s t i c s Generate i n t e r d e l a y time Set status to blocked I Saw ranked according to next change of status C a l l RANK I 1000 Figure 16. Flowchart of 1-minute discrete interval updating subroutine, UPDTE, continued. - 69 -Yes Set next change of status to end of delay Reduce delay time by remaining part of minute Turn o f f blocking i n d i c a t o r Saw Is ready updated Yes Saw ranked according ^to next change of statusy C a l l RANK Calculate flow for previous period 1000 Set next change of status Determine time u n t i l maximum reached. Update flow to that point. Turn on blocking in d i c a t o r for this saw 3> Saw ranked according to next change of status} C a l l RANK Figure 16. Flowchart of 1-minute discrete interval updating subroutine, UPDTE, continued. - 70 -Update a l l saws to end of delay f o r blocking saw or to end of minute Yes Find status of saw *©• Accumulate s t a t i s t i c s Accur.ulate s t a t i s t i c s on i d l e time on busy time f Add amputated working time to interdelay tine f Update flow to saw for previous period Set status to blocked Update flow to saw for previous period-I Adjust delay time f o r interrupted delay time Set next change of status to end of delay for blocking saw ± 3000 Saw ranked according to next change of status C a l l RANK Figure 16. Flowchart of 1-minute d i s c r e t e i n t e r v a l updating subroutine, UPDTE, continued. - 71 -Yes 1000 Record a r r i v a l s to each saw Record average queue length f o r the 1-minute period V  Transfer production f o r each saw C a l l TRSFR(Fig . l7 ) ( ) Figure 16. Flowchart of 1-minute discrete interval updating subroutine, UPDTE, concluded - 72 -J stands for the column number where the codes are stored, K for the row of the piece in the array and I for the saw number. For any defined I and K, IROUT (I,K,J), with J increasing from one to six, gives for each piece the queue number at the saw, trim action (for 1=1), the code I for the subsequent processing unit (J = 3,5) and codes for the number of times any board would have to pass through the #1 resaw (J = 6). At the end of UPDTE, the routine TRSFR (Fig. 17) is called. TRSFR scans through IROUT (I,K,J) and transfers the appropriate number of lines, as indicated by the production figure provided by UPDTE, onto the queue of the saw having the code number found in IROUT (I,K,3). The order of transfer as I is assigned the values from one to five is as given above. After each transfer IROUT is updated to again start from number one. whereas for the trimmer the number of pieces in IROUT represents the queue length, the subsequent saws have two measures for the queue. One, including the boards on the headconveyor (Fig. 1), corresponds to the present value of K. The other represents the number of boards already in the buffer storage immediately ahead of each saw. Pointers keep track of the total length of IROUT as well as the actual buffer storage queue length. The difference between the two represents the load on the headconveyor. Together with the distance from the trimsaw outfeed to the next saw's infeed and the average velocity of the headconveyor between the two points, these factors determine the arrival rate to each saw for the coming minute. - 73 -( s t - r t ) I n i t i a l i z e greenchain piece accumulator Set saw code f o r next saw transfer No 1 •^s. zero Remove f i r s t l i n e i n IROUT array Yes 3333 No Piece to be directed to' another saw Yes 1 F i l l i n piece a f t e r l a s t l i n e i n IROUT array corresponding to that saw r Check next l i n e i n IROUT array for t h i s saw •^777 Figure 17. Flowchart of piece t r a n s f e r subroutine, TRSFR. - 74 -Increase queue number by one for r e c e i v i n g queue Accumulate number of pieces flowing onto greenchain I Set previous piece code equal to present F i l l i n piece a f t e r l a s t l i n e i n IROUT array corresponding to r e c e i v i n g saw Set previous piece code equal to present Update queue where transfer has taken place 3333^>-Accumulate production s t a t i s t i c s Return Figure 17. Flowchart of piece transfer subroutine, TRSFR, concluded. - 75 -It has not been found necessary to assure that each piece maintain i t s absolute correct place i n each queue. Pieces coming from #1 resaw and direct e d to ponyedger w i l l be added to those coming from the trimsaw, although, i n the system, they w i l l mix a r b i t r a r i l y . VERIFICATION AND VALIDATION OF THE SAWMILL MODEL The two terms, v e r i f i c a t i o n and v a l i d a t i o n , are often used together and, indeed, at times may seem inseparable. They both constitute parts of a comprehensive evaluation of the simulation model and the data generated from i t . Their d e f i n i t i o n s may be stated as follows: V e r i f i c a t i o n . The process of est a b l i s h i n g the p r e c i s i o n with which the simulation program represents the system under study. V a l i d a t i o n . The process of es t a b l i s h i n g the accuracy with which the simulation program represents the system under study. As Fishman and K i v i a t (1967) understand i t , v e r i f i c a t i o n insures that a simulation model behaves as an experimenter intends, and v a l i d a t i o n tests the agreement between the behavior of the simulation model and a r e a l system. The above d e f i n i t i o n s point to the a p p l i c a t i o n of known s t a t i s t i c a l techniques i n order to reach a dec i s i o n as to " v e r i f i e d or not, validated or not". Considerable e f f o r t has been made by others to e s t a b l i s h a phi l o s o p h i c a l view on which the reasoning and actual t e s t i n g could be - 76 -based. Naylor and Finger (1967) discuss three methodological positions on the verification of theory; nationalism, empiricism and positive economics. By combining the three, they present the fourth, multistage verification, where each of the aforementioned tenets is regarded as necessary but not sufficient. The multistage, or stepwise, verification is concerned with: (a) Explicit formulation of postulates of hypotheses describing the behavior of the systems; (b) Verification of (a), subject to the limitation of existing statistical tests; and C c ) Testing the model's ability to predict the behavior of the system under study, i.e., validation. McClung 0-971) takes a more pragmatic approach. Through an evaluation of levels of environment in order of increasing complexity, he suggests an examination of the response given by the: (a) Basic system structure and algorithms; (b) System to changing conditions; (c) System to externally imposed constraints; (d) System to the real world. Before laying out a verifying strategy, i t is necessary to explicitly differentiate between the uses which may be made of the model. As stated above, the sawmill simulation model should inform about the planned system's productivity, and eventually separate between alternatives. Clearly a sawmilling model has a predictive function. Because the predictive result is dependent on the interaction between the saws, this - 77 -i n t e r a c t i o n should be described. Accordingly, the model w i l l f i l l an explanatory and d e s c r i p t i v e function as w e l l . From the discussion of the computer model, i t i s obvious that the model pretends to copy the actual system i n considerable d e t a i l . Points (a) and (b) above, formulated by Naylor and Finger (1967), and McClung's (1971) point (a), w i l l be s a t i s f a c t o r i l y answered i f , by concentrating on some key parameters and t e s t i n g them, the model can be said to copy the system i n s u f f i c i e n t d e t a i l to meet a set p r e c i s i o n requirement. On the other hand, i t i s d i f f i c u l t to set a precise requirement for a p r e d i c t i o n of the sawmill's output without knowing, for example, the r i s k an investor i s w i l l i n g to accept when basing h i s c a l c u l a t i o n s upon the predicted m i l l output. I t can also be argued that by applying a simulation model, the r e s u l t s are at l e a s t as precise as any c a l c u l a t i o n based on average values, and very l i k e l y better. The number of factors that can f e a s i b l y be measured i n a sawmilling process without disturbing the process i t s e l f i s l i m i t e d . The log supply can be continuously measured on the jackladder, and the present order f i l e governing the d e c i s i o n making i n sawing the log may be recorded without undue d i f f i c u l t y . However, continuous recording of the y i e l d from each log i s v i r t u a l l y impossible. Special studies of considerable depth are necessary to v e r i f y that the cutting decision l o g i c of the model indeed produces the same products from each log s t r a t a as do the sawyers i n the system. This may be c a l l e d a q u a l i t a t i v e v e r i f i c a t i o n and has been excluded because of l i m i t e d time and lack of resources. In i t s place a pure qu a n t i t a t i v e v e r i f i c a t i o n has been attempted, namely, the study of the - 78 -a r r i v a l stream to each saw measured i n number of pieces a r r i v i n g per minute. As only a piece count i s involved, the production process need not be disturbed. Also, a f t e r the i n i t i a l breakdown of the cant, when the d i r e c t r e l a t i o n s h i p between the breakdown l o g i c and the generated number of pieces becomes d i f f u s e , a r r i v a l s per time unit i s a more meaningful measure i n terms of queue length development at the various saws. Assuming an i d e n t i c a l set of constraints and operating conditions during data c o l l e c t i o n and model run, the model's operating l o g i c would be v e r i f i e d against the piece count done i n the m i l l . Since t h i s would be a s t a t i s t i c a l test of one set of d i s t r i b u t i o n s against another, the Kolmogorov-Smirnov two-sample goodness of f i t test appears appropriate. The next section describes the path of evaluation of the sawmilling model. 1. V e r i f i c a t i o n Strategy and Results Two i n i t i a l steps are necessary before the model can be said to y i e l d u s e f u l data. These include determination of: (a) M i l l operating time to reach steady state conditions; and (b) Operating period y i e l d i n g average values with an acceptable l e v e l of v a r i a t i o n . The model s t a r t s with a l l storage areas empty. As the d i f f e r e n t saws receive pieces they become operative. A f t e r some time an equilibrium i s reached. Measured over a s u f f i c i e n t l y long period the a r r i v a l d i s t r i b u t i o n s and queue length d i s t r i b u t i o n s become stationary. If the - 79 -model is stable, this period may be relatively short; if unstable, longer production runs are required to ensure a good precision in the collected data. The i n i t i a l run of this model corresponds to 24 hours of continuous operation of the system. Each two hours the collected distributions and their parameters were written out. After 8 hours of operation a l l distributions were found to be not significantly different to the one previously recorded, as were the subsequent ones. Although steady state was probably reached somewhat earlier, 8 hours was taken as the necessary system operating time before data collection and analysis could be made. Further, the length of operative time for experiments was studied. By running the model repeatedly with different random number seeds* for 24 or more hours, the recorded data would show very l i t t l e variation. However, computer cost would be high. After having tried successively longer time periods (after steady state was reached), a 5-hour system operating time was found to yield stationary distributions, although with a higher variation than for 8-hour runs. The coefficient of variation in volumetric output per 8-hour shift was found to be less than 6 percent with 6 repetitions. Five hours of operative time was therefore considered sufficient to adequately describe the system productivity. In order to verify the model, the hypothesis was: G That the arrival distributions obtained by running the model under the described average conditions as to log supply and product width A random number seed is a positive number which initializes a series of random numbers. - 80 -distribution, would not be significantly different at the 5 percent level from those recorded in the system. For more precise estimates the run was repeated 6 times with different random number seeds. Table 2, below, shows the comparison between model and system frequency distribution of arrival rates to each saw. Each class gives the range of pieces per minute. TABLE i i Arrival Distribution in Pieces per Minute for Model and System for  Saws and Output to Greenchain Arrival Rate Class (Pieces per minute) Saw 0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 Trimmer Model System #1 Resaw Model System Ponyedger Model System #2 Resaw Model System Greenchain Model System 25 13 40 24 88 53 42 24 16 22 30 18 29 49 11 35 40 36 24 10 28 19 18 21 1 6 14 23 25 20 15 21 9 6 0 4 3 13 18 17 2 20 3 0 0 2 1 3 10 17 0 3 1 0 0 1 5 10 2 2 0 0 0 0 - 8 1 -T h e s e d i s t r i b u t i o n s w e r e t e s t e d b y t h e K o l m o g o r o v - S m i r n o v t w o - s a m p l e g o o d n e s s o f f i t t e s t a n d , w i t h o u t e x c e p t i o n , t h e m o d e l d i s t r i b u t i o n w a s f o u n d t o b e s i g n i f i c a n t l y d i f f e r e n t f r o m t h a t o f t h e s y s t e m . T h e m o d e l m u s t , t h e r e f o r e , a t t h i s s t a g e , b e r e g a r d e d a s n o t v e r i f i e d . A b e t t e r p e r c e p t i o n o f t h e d e v i a t i o n s f r o m t h e s y s t e m m a y b e o b t a i n e d f r o m T a b l e 3 w h e r e m e a n s a n d s t a n d a r d d e v i a t i o n s a r e p r e s e n t e d f o r t h e s a m e d i s t r i b u t i o n s . T A B L E i i i M e a n V a l u e s a n d S t a n d a r d D e v i a t i o n s ( S D ) f o r A r r i v a l  D i s t r i b u t i o n s t o S a w s a n d G r e e n c h a i n ( P i e c e s p e r m i n u t e ) S a w s T r i m m e r #1 R e s a w P o n y e d g e r #2 R e s a w G r e e n c h a i n M o d e l M e a n : 8 . 6 6 7 . 3 1 1 . 7 8 5 . 6 6 1 2 . 2 2 S D : 5 . 7 3 6 . 4 4 2 . 4 2 4 . 4 0 7 . 6 6 S y s t e r n M e a n : 1 3 . 6 6 6 . 6 8 2 . 3 8 8 . 9 6 1 3 . 9 7 S D : 9 . 2 1 5 . 2 8 7 . 3 0 6 . 0 8 9 . 8 9 N o d a t a a r e p r e s e n t e d f o r t h e d o u b l e t r i m s a w . T h i s u n i t f u n c t i o n s p a r t l y a s a r e c e i v e r o f m i s j u d g e d p i e c e s f r o m s a w s t h r o u g h o u t t h e s y s t e m , p i e c e s t h a t w e r e t h o u g h t t o y i e l d a b o a r d b u t d i d n o t . L e n g t h o f q u e u e , t h e r e f o r e , b u i l t u p t o 1 0 t i m e s t h e m a x i m u m e n c o u n t e r e d t h r o u g h t h e m o d e l . - 82 -The m i l l productivity w i l l to some extent depend on the lumber yield from each log class. For this system, yield i s considered to be of prime importance. The simulation output includes a log sample where the lumber yield for each log is recorded. By comparing this yield with that found by empirical studies, the breakdown logic for each saw can be verified. In Figure 18 the overall yield range, as recorded during the simulation, is compared with that recorded during the processing of the 400 logs referred to previously. 80 70 9 60 O o o o o o -LU o or UJ O Actual average yield from processed logs 40 Yield range obtained from the simulation model Forest Products Laboratory recovery study, and the simulated yield for the m i l l under study. - 83 -The simulated y i e l d s f o r diameter classes less than 15 inches are s i m i l a r to those found i n t h e o r e t i c a l c a l c u l a t i o n s . * Within a diameter c l a s s , the v a r i a t i o n i s mainly due to v a r i a t i o n i n the breakdown pattern. The breakdown l o g i c i n the simulation w i l l use only those boardwidths that have not exceeded t h e i r volume constraint l i m i t . For any equal sized cant a r r i v i n g at the bulledger, d i f f e r e n t combinations of boardwidths w i l l c onstitute the "maximum" volume y i e l d according to the varying set of av a i l a b l e widths. This method of producing a constrained output w i l l probably amplify the lumber y i e l d v a r i a t i o n for each diameter c l a s s . The f a c t that the lumber i s cut to square edges w i l l contribute considerably to the discrepancy between act u a l and simulated y i e l d values f o r the lower diameter classes. The reverse r e l a t i o n s h i p found f o r the higher diameter classes i s mainly due to recovery reductions because of rot i n the processed logs. 2. Considerations for V a l i d a t i o n The u n v e r i f i e d a r r i v a l rates make any attempt to v a l i d a t e the produc t i v i t y of the model meaningless. Several explanations for th i s w i l l be suggested i n Discussion. At t h i s point, however, i t should be noted that the average output to the greenchain for the model comes close to the system's average. A further analysis of the s e n s i t i v i t y of t h i s f i g u r e as the log supply and product d i s t r i b u t i o n c h a r a c t e r i s t i c s change, shows a v a r i a t i o n i n the a r r i v a l rate too small to embrace the model average. For example, i f a l l logs with top diameter less than 14 inches were excluded from the * Unpublished data, Western Forest Products Laboratory. - 84 -process, the number of pieces arriving per minute to the greenchain would average 12.24. On the other hand, if less of smaller widths are to be produced, e.g., reducing the proportion of 4-inch from 19 percent to 8 percent, the arrivals drop to 10.08 per minute. To test the model's reaction to changes in exogenous variables, the log supply was cut off at 10-inch and 14-inch top diameters. The minimum of 10-inch top diameter leads to an increase in productivity of 4 percent when product distribution constraints were kept constant, but to a 6 percent increase i f the product distribution was shifted towards larger widths. A minimum top diameter of 14 inches lead to productivity increases of 20 percent and 23 percent, respectively, from the i n i t i a l value. For the original top diameter distribution, a shift towards larger widths reduced the productivity by 7 percent. Should the maximum top diameter be reduced from 26 inches to 22 inches, the system productivity is predicted to drop 17 percent. This shows that, when a particular sawmill is studied with respect to validation of the productivity, as found from a simulation model of that mill, thorough registration of the constraints governing the manufacturing process is important. Figure 19 shows the productivity in thousand boardfeet as the average top diameter in the log supply changes. According to the steep ascent of the points as diameter increases, this type of mill is highly sensitive to changes in its log supply. Because of the underestimation of log yield for smaller diameter classes, however, the actual productivity would probably be higher than shown for these. - 85 -^ 2001 1 1 r >*-if) L . A J . I I _ J I ^ 10 12 14 16 18 20 AVERAGE TOP DIAMETER IN LOG SUPPLY (inches) Figure 19. Estimated r e l a t i o n s h i p between sawmill p r o d u c t i v i t y and average top diameter i n log supply. S o l i d l i n e i s hand drawn. Another factor which should be subject to v a l i d a t i o n , e s p e c i a l l y when the design of b u f f e r storages becomes c r i t i c a l , i s the system's queues. When the processing rate and the a r r i v a l s are recorded simultaneously, and " i n i t i a l queue length i s known, the queuing development can be followed. Once v a l i d a t e d , changes i n p r o d u c t i v i t y by varying buffer storage lengths may be c a l c u l a t e d . Only i f the a r r i v a l rates, processing rate, delay and interdelay time d i s t r i b u t i o n s have a l l been v e r i f i e d , and the queue length - 86 -d i s t r i b u t i o n s validated, can the queuing s i t u a t i o n at each saw, as predicted by the model, be completely accepted. DISCUSSION Before a f i n a l conclusion as to r e j e c t i o n or acceptance of the model i s reached, several factors possibly contributing to the discrepancies between the model and the actual system should be discussed. When data were sampled from the system, manpower was not a v a i l a b l e to sample log supply and product output. Should, for example, the product width d i s t r i b u t i o n have been s h i f t e d towards a lower average, more pieces would have been generated, y i e l d i n g greater s i m i l a r i t y between model and system d i s t r i b u t i o n s . The average values f o r the yearly log supply may also very w e l l d i f f e r from those processed at the time of data c o l l e c t i o n . A better explanation f o r the differences between the observed data, p a r t i c u l a r l y at the trimmer, and the model's data, may be found by exploring a s i g n i f i c a n t d i f f e r e n c e i n operating procedure between model and system. The model searches each slab coming off the headrig as to i t s p o s s i b i l i t y of producing a minimum sized board. Only i f the answer i s af f i r m a t i v e w i l l the slab be passed on to the bulledger queue. The system, on the other hand, w i l l process a larger number of slabs mainly because of three f a c t o r s : 1. As logs often have an i r r e g u l a r shape, one slab may be rejected, whereas the d i a m e t r i c a l l y opposite slab w i l l be accepted and w i l l y i e l d a board. The model w i l l e i t h e r r e j e c t or accept a l l the slabs from a log. - 87 -2. The first log from a tree usually has a butt swell, whereas a truncated cone has none. Frequently this swell will make the difference between the yield of a board and no yield. Consequently, the model will reject too many slabs. 3. Large logs may have considerable butt swell, which will be too short to yield boards when sawn but, at the same time, too wide or thick to pass through the limited-sized access to the chipper. These slabs will not occur in the model, but will be added to the edger queue in the system. After the bulledger has split the slabs the trimmer cuts the pieces to 2-foot length for the chipper. Undoubtedly these 3 points may in fact be the explanation for the entire difference in the trimsaw arrival patterns. The model does not make erroneous decisions. In other words, there is a zero probability of pieces having to be re-edged because the bulledger sawyer judged the piece wrongly and set the sawblades incorrectly. This frequently happens in the system, which leads to more remanufacturing. Steady state in the system may therefore be reached later than the indicated 6 to 8 hours, but once reached, the actual output to the greenchain should stay the same. The model confirms this hypothesis to a certain extent, as arrivals to the greenchain is the variable corresponding best to the recorded value. From the lumber yield data in Figure 18 i t is obvious that the productivity of the mill, as described by the model, is not valid when - 88 -average top diameter i s less than 15 inches. For larger diameters, sound and s t r a i g h t logs are necessary conditions. On the other hand, the breakdown l o g i c need not be pushed to p e r f e c t i o n . Its main function i s to generate the correct number of pieces, not the exact volume produced. As sawing to allow maximum wane w i l l y i e l d r e l a t i v e l y more board volume when average log diameter i s small than when large, the f i r s t step to improve the r e l i a b i l i t y of the lumber y i e l d figures would be to include wane as a factor i n the breakdown l o g i c . It should be noted that within a computer-run the product width and log c h a r a c t e r i s t i c d i s t r i b u t i o n s are stationary. If the system's constraints, notably the log supply c h a r a c t e r i s t i c s , undergo a se r i e s of changes not r e f l e c t e d by the random s e l e c t i o n of logs from an assumed d i s t r i b u t i o n , the model l o g i c must be modified to accommodate t h i s . Then the e f f e c t on p r o d u c t i v i t y of moving from one d i s t r i b u t i o n to the next with a constant set of d e c i s i o n rules can be more c l o s e l y studied. When d i f f e r e n t systems are to be compared with respect to p r o d u c t i v i t y , i t must be r e a l i z e d that the r e s u l t of the comparison depends on how well the m i l l management i s able to synchronize t h e i r order f i l e , log breakdown decisions and log c h a r a c t e r i s t i c d i s t r i b u t i o n s . Great care should therefore be taken i n assuring that the most l i k e l y "management "environment" i s documented f o r each investigated system. The development of t h i s one model has led to greater i n s i g h t s into the problem of serving the sawmilling industry as a whole. A few recommendations, hopefully showing a r a t i o n a l path towards a more - 89 -acceptable and applicable model f o r the industry, are given and discussed below. C a ) Rather than looking at d i f f e r e n t m i l l systems as separate and highly s p e c i a l i z e d cases, whose c h a r a c t e r i s t i c s require the development of t a i l o r e d models, one general assembly-system, which regards sawmills as a c o l l e c t i o n of interconnected components, should be viewed as preferable. Cb) The input and output f a c i l i t i e s of a general model, should be made much more f l e x i b l e than i n t h i s a p p l i c a t i o n . In p a r t i c u l a r , the a b i l i t y to change pieces of equipment, to r a p i d l y model new configurations and to vary the constraints described e a r l i e r , would be assets greatly appreciated by those who are faced with investment decisions. Cc) As the amount of data needed to make general conclusions i n i t s e l f represents a sizeable investment, p r i o r i t i e s should be c a r e f u l l y established i n order to a s s i s t the industry where needed most. For example, the considerable i n t e r e s t i n chipping equipment, for the processing of small logs, points to chipping/sawing combinations as high p r i o r i t y systems. The advantages of one general model include the f a c i l i t y of component c h a r a c t e r i s t i c s v a r i a t i o n as w e l l as maximum f l e x i b i l i t y i n r a p i d l y redesigning system a l t e r n a t i v e s . Through the development of an appropriate addressing routine and standard a r r i v a l and departure submodels f o r each group of components, new pieces of machinery can be tested, as to t h e i r impact on e x i s t i n g systems, immediately a f t e r t h e i r operating - 90 -c h a r a c t e r i s t i c s have become known. New concepts and systems may be studied at a minimal cost compared to that experienced through the t r i a l and error sequence. CONCLUSION This thesis has attempted to demonstrate the f e a s i b i l i t y of pr o d u c t i v i t y estimation for a dimension sawmill. To that end, i t may be claimed that: (a) A d e t a i l e d d e s c r i p t i o n of how the separate components of a sawmill work, and of the variables i n f l u e n c i n g them, i s f e a s i b l e , even for the most complex m i l l s . (b) The r e s u l t of the i n t e r a c t i o n between the components, the product output stream, can be accurately predicted provided a d d i t i o n a l e f f o r t s are put into the data c o l l e c t i o n . From the few r e s u l t s presented, some general conclusions as to t h i s p a r t i c u l a r m i l l system may be drawn. (a) System p r o d u c t i v i t y i s highly s e n s i t i v e to changes i n constraints, and the optimum mix of breakdown decisions f o r a given set of constraints i s not e a s i l y a t t a i n a b l e . (b) Given a large v a r i a t i o n i n constraint d i s t r i b u t i o n and stationary decisions according to one or a few order f i l e s only, the system w i l l f o r most of i t s time be working below capacity. - 91 -(c) A considerable e f f o r t i n synchronizing order f i l e , breakdown decisions, and log c h a r a c t e r i s t i c d i s t r i b u t i o n s i s necessary to push pr o d u c t i v i t y closer to maximum. - 92 -BIBLIOGRAPHY Arthur, W. To simulate or not to simulate: That is the question. Educational Data Processing Newsletter 2(4):9. (Original not seen). Dobie, J. 1970. Advantages of log sorting for chipper headrigs. Forest Prod. J. 20(l):19-24. Jan. Dunmire, D.E., and G.H. Englerth. 1967. Development of a computer method for predicting lumber cutting yields. U.S. Forest Service Research Paper. Nth. Cent. For. Exp. Sta. No. NC-15. pp. 7. Emshoff, J.R., and R.L. Sisson. 1970. Design and Use of Computer Simulation Models. 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Pritsker, A.A.B., and P.J, Kiviat. 1969. Simulation with GASP II. Prentice-Hall, Inc., Englewood C l i f f s , New Jersey, pp. 332, Reynolds, H.W., and C.J. Gatchell. 1969. Sawmill simulation: Concepts and computer use. U.S. Forest Service Research Note Nth east. For. Exp. Sta. No. NE-100. pp. 5. Riikonen, R., and J. Ryhanen. 1965. Tietokone sahan £uotannon optimoinnissa. [Electronic data-processing in the optimization of sawmill production.] Pap. ja Puu 47(9):497-502. Sept. (Transl. Dep. For. Can. No. 258). Row, C , C. Fasick, and S. Guffenberg. 1965. Improving sawmill profits through operations research. U.S. Forest Service Research Paper South. For. Exp. Sta. No. SO-20. pp. 26. Tsolakides, J.A. 1969. A simulation model for log yield study. Forest Prod. J. 19(7):21-6. July. Woodzinski, C , and E. Hahm. 1966. A computer program to determine yields of lumber. U.S. Forest Products Laboratory, pp. 33. - 94 -APPENDIX: INITIAL INPUT VALUES TO THE MODEL Log Top-Diameter Distribution (%) Top diam. (inches): 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Distribution (%) 1 4 8 11 11 8 9 7 7 6 4 4 3 3 5 2 21 22 23 24 25 26 2 1 1 1 1 1 Log Length Distribution (%) Diam.\ Inches Length \ feet 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 5 3 - - 5 3 3 5 3 23 10 12 6 7 12 1 7 6 1 1 1 6 3 3 5 6 12 6 10 11 8 13 4 10 7 - 2 3 8 4 5 2 4 11 6 11 14 7 9 5 9 8 - 1 2 11 7 8 3 6 11 8 9 8 5 9 4 8 9 - 3 1 13 5 7 4 8 8 7 7 11 6 6 5 9 10 1 2 2 22 4 4 2 3 8 7 8 7 5 8 5 12 11 1 2 1 20 5 6 3 4 10 7 5 8 6 7 4 11 12 1 ^  4 4 22 4 2 3 3 10 6 6 8 5 7 5 10 13 - 3 4 26 4 3 2 4 9 7 4 5 5 7 5 12 14 2 2 2 28 3 3 2 2 8 7 6 6 5 6 4 14 15 1 1 2 26 3 2 2 2 9 7 5 7 5 7 4 17 16 - 2 2 29 2 3 2 3 8 7 5 6 5 6 4 16 17 - 1 1 28 3 2 1 3 8 7 6 7 4 8 6 15 18 - 1 2 33 1 2 2 2 9 7 4 6 4 2 5 20 19 - - - 15 1 2 1 1 10 7 3 6 6 9 7 32 20 - - - 43 1 1 1 2 7 4 3 5 4 5 4 20 21 - - 1 38 2 1 1 2 7 6 4 5 6 4 3 20 22 - - - 41 1 1 1 2 6 5 2 6 3 6 5 21 23 - - - 36 3 1 1 2 7 6 3 6 4 7 5 19 24 - - 5 37 1 1 - 1 5 5 3 5 4 7 5 21 25 - - - 32 1 2 1 - 7 3 5 4 6 7 6 26 26 1 1 1 31 — 2 2 3 5 3 3 8 2 4 10 24 Log Taper Distribution Taper (inches per linear feet): .05 .10 .15 .20 .25 Distribution (%) 14 34 37 14 1 I n t e r d e l a y T i m e D i s t r i b u t i o n ( % ) , a l l t i m e s i n 1 / 1 0 0 m i n u t e . B u l l e d g e r T i m e : 2 5 7 5 1 2 5 1 7 5 2 2 5 2 7 5 3 2 5 3 7 5 4 2 5 4 7 5 5 2 5 5 7 5 6 2 5 6 7 5 8 2 5 9 2 5 D i s t r i b u t i o n ( % ) : 3 1 5 6 6 9 6 1 5 9 9 3 4 3 3 3 3 3 T r i m m e r T i m e : 1 0 3 0 5 0 7 0 9 0 1 1 0 1 3 0 1 5 0 1 7 0 1 9 0 2 1 0 2 3 0 2 5 0 2 7 0 2 9 0 3 1 0 3 3 0 3 5 0 4 1 0 4 3 0 4 7 0 D i s t r i b u t i o n ( % ) : 2 3 7 1 5 2 5 7 8 2 7 6 1 1 5 3 3 3 3 1 3 3 5 1 0 5 5 0 6 3 0 6 5 0 2 3 2 2 #1 R e s a w T i m e : 2 5 7 5 1 2 5 1 7 5 2 2 5 2 7 5 3 7 5 5 2 5 5 7 5 7 2 5 9 2 5 9 7 5 1 0 7 5 1 1 7 5 D i s t r i b u t i o n (%) : 4 1 4 1 1 7 4 7 1 1 1 1 1 1 3 4 3 3 7 P o n y e d g e r T i m e : 1 5 4 5 7 5 1 0 5 1 3 5 1 6 5 D i s t r i b u t i o n ( % ) : 3 2 2 6 2 6 6 5 5 D o u b l e T r i m s a w T i m e : 1 0 0 3 0 0 5 0 0 7 0 0 9 0 0 1 3 0 0 D i s t r i b u t i o n ( % ) : 1 3 3 1 2 5 1 9 6 6 #2 R e s a w T i m e : 5 0 1 5 0 2 5 0 3 5 0 4 5 0 5 5 0 6 5 0 7 5 0 8 5 0 9 5 0 D i s t r i b u t i o n (%) : 5 3 0 2 0 5 5 1 0 1 0 5 5 5 - 96 -5. Delay Time Period Length, Distribution {%), a l l times in 1/100 minute. Bulledger Time : 15 45 75 105 135 165 195 285 345 585 % 10 21 24 14 3 3 14 4 4 3 Trimmer Time : 10 30 50 70 90 110 130 150 170 190 % 2 43 20 10 6 6 4 4 3 2 #1 Resaw Time : 10 30 50 70 90 130 % 13 29 17 8 4 29 Ponyedger Time : 50 150 250 750 % 71 18 6 5 Double Trimsaw Time : 20 60 100 140 180 220 % 29 21 14 14 8 14 #2 Resaw Time : 10 30 50 70 110 150 230 290 % 7 40 20 7 7 7 6 6 6. Sawkerf (inches) Headrig Bulledger Trimmer #1 ; 0.259 0.238 0.250 0 7. Cant Thickness Array (inches) Nominal measure : 2 3 Actual measure : 1.87 3.05 8. Product Width Array (inches) Nominal measure : 3 4 Actual measure: 3.05 4.05 9. Product Width Distribution (%), Nominal measure : 3 4 Distribution (%): 2 19 esaw Ponyedger Double Trim #2 Resaw 180 0.220 0.250 0.180 4 6 8 10 12 3.74 6.11 8.03 10.11 11.75 6 8 10 12 12x12 6.11 8.03 10.11 11.75 12.00 measures in inches 6 8 10 12 12x12 20 23 15 2 19 Cutting Pattern Codes Butt D i s t r i b u t i o n diam. within diam. inches class (%) Codes 11 100 112 001 099 112 066 004 12 100 269 077 099 269 066 004 13 60 212 077 099 212 001 066 004 13 40 116 001 099 116 066 005 14 50 253 077 099 253 066 005 14 10 369 077 099 369 066 004 14 40 166 001 099 166 066 005 15 50 216 077 099 216 001 066 005 15 30 110 001 099 110 001 066 005 15 20 216 001 099 216 066 005 16 40 266 001 099 266 066 005 16 50 166 001 099 160 001 066 005 16 10 149 001 001 077 099 149 001 066 004 17 30 106 001 099 106 001 066 006 17 60 210 001 099 210 001 066 005 17 10 209 001 001 077 099 209 001 066 004 18 40 260 001 099 260 001 066 005 18 40 156 001 099 156 001 066 006 18 20 260 001 088 260 001 088 260 001 066 005 19 30 124 001 088 124 001 088 124 001 066 007 19 40 251 002 099 251 001 066 005 19 30 100 001 001 077 099 100 001 066 006 20 20 246 001 099 246 001 066 006 20 20 174 001 088 174 001 088 174 001 066 007 20 60 253 001 088 253 001 088 253 001 001 066 005 21 50 210 001 099 210 001 003 066 005 21 40 193 001 077 088 193 001 088 193 001 066 006 21 10 117 001 001 077 099 117 001 066 007 22 30 274 001 088 274 001 088 274 001 066 007 22 20 143 001 001 077 088 143 001 088 143 001 001 066 006 22 50 166 003 088 166 001 088 166 001 003 066 005 Butt D i s t r i b u t i o n diam. within diam. inches class (%) Codes 23 30 216 001 088 216 003 088 216 003 003 066 005 23 20 206 001 088 206 001 088 206 001 003 066 006 23 50 124 001 088 124 001 088 124 001 003 066 007 24 10 149 001 088 149 001 088 149 001 001 003 066 006 24 70 174 001 088 174 003 088 174 001 003 066 007 24 20 253 001 001 077 088 253 077 088 253 001 003 066 005 25 30 224 001 088 224 001 001 077 088 224 001 003 066 007 25 20 195 001 088 195 001 003 001 088 195 001 005 066 005 25 50 271 002 088 271 002 088 271 002 088 271 002 003 066 007 26 30 166 001 003 077 088 166 001 088 166 003 003 066 005 26 60 274 003 088 274 001 088 274 001 001 066 007 26 10 131 001 003 077 088 131 077 088 131 001 001 004 066 004 1 27 20 396 001 001 077 088 396 001 088 396 003 066 006 » 27 30 310 001 001 077 088 310 001 001 077 088 310 003 003 066 005 i 27 50 265 001 088 265 002 001 077 088 265 002 003 066 007 28 30 245 001 088 245 001 003 077 088 245 001 004 066 007 28 20 162 001 003 088 162 001 003 077 088 162 003 003 066 006 28 50 345 001 001 077 088 345 001 003 077 088 345 005 066 005 29 20 199 001 003 077 088 199 001 001 077 088 199 001 001 003 066 006 29 30 224 001 003 077 088 224 001 088 224 001 003 066 007 29 50 279 002 001 077 088 279 001 002 002 088 279 002 003 001 066 005 30 30 274 003 088 274 003 088 274 001 001 003 066 007 30 40 294 002 001 077 088 294 002 088 294 001 003 003 066 005 30 30 274 001 003 077 088 274 001 003 077 088 274 001 003 066 007 31 30 124 001 001 003 088 124 001 001 001 088 124 003 003 066 007 31 60 285 001 003 077 088 285 001 088 285 001 001 004 066 005 31 10 297 001 003 077 088 297 001 001 077 088 297 003 001 004 066 004 32 20 280 001 003 077 088 280 001 001 077 088 280 003 003 066 007 32 20 208 001 002 077 088 208 001 088 208 001 003 003 066 007 32 60 160 001 003 003 088 160 001 001 077 088 160 001 003 003 066 005 33 50 076 001 001 077 088 076 001 001 001 001 077 088 076 001 003 077 088 076 001 003 005 066 005 33 30 198 001 003 003 088 198 001 003 077 088 198 001 088 198 003 005 066 006 Butt D i s t r i b u t i o n diam. within diam. inches class (%) Codes 33 20 211 001 001 34 40 139 001 003 34 20 377 001 003 34 40 459 001 003 35 30 544 001 003 35 20 085 001 002 35 50 216 001 003 36 30 195 077 001 36 30 302 077 001 36 40 067 001 003 001 003 077 088 211 001 002 077 088 139 001 001 003 088 077 088 377 002 003 077 088 077 088 459 001 003 077 088 003 001 077 088 544 002 001 002 088 085 001 002 002 088 077 088 216 001 003 077 088 077 002 077 088 195 001 003 001 002 002 088 302 077 001 003 088 067 001 003 001 088 077 088 211 001 003 066 007 139 001 003 001 005 066 005 377 001 001 003 066 007 459 001 001 003 066 006 077 088 544 002 077 088 544 085 001 001 002 003 004 066 216 003 005 066 007 001 003 077 088 195 001 001 077 001 002 001 077 099 302 067 001 003 003 001 066 007 003 001 003 066 005 004 001 003 003 066 007 003 003 066 007 

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