{"http:\/\/dx.doi.org\/10.14288\/1.0075540":{"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool":[{"value":"Forestry, Faculty of","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider":[{"value":"DSpace","type":"literal","lang":"en"}],"https:\/\/open.library.ubc.ca\/terms#degreeCampus":[{"value":"UBCV","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/creator":[{"value":"Huang, Ye","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/issued":[{"value":"2012-07-16T16:48:02Z","type":"literal","lang":"en"},{"value":"2012-04","type":"literal","lang":"en"}],"http:\/\/purl.org\/dc\/terms\/description":[{"value":"This essay develops prototypes of linear programming-based models to project the harvesting level, lumber production, and net revenue of a harvesting plan in order to support forest operation decision-making in the Malcolm Knapp Research Forest (MFRF) in Maple Ridge, British Columbia. Field data were collected from 3 different biogeoclimatic zones within the research forest. Growth and yield of the forest was modeled by Table Interpolation Program for Stand Yields (TIPSY) which is a stand- and forest-level model developed by the British Columbia Ministry of Forest and Range. Then, the growth and yield data were imported into a forest estate linear programming model to forecast the volume of logs harvested from the forest. A sawing pattern model was used to design the sawing pattern and generate Lumber Recovery Factors by log diameter. Subsequently, a log-to-product linear programming model was used to estimate the final lumber production, mill working hours and the net profit for the forest. The results predict that the mill can earn $3,110,141 by producing 141,229 MBF of lumber and 298,818 m\u00b3 of chips over a 60-year planning horizon. Sensitivity analysis included different sawing patterns, price fluctuations and limited mill operating hours. Some potential improvements in model structure, efficiency, availability for big diameter log, and carbon credits are also discussed. Although the forest data and the sawmill configuration used in the models are different from reality, it will not be difficult to modify the model for MKRF.","type":"literal","lang":"en"}],"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO":[{"value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/42711?expand=metadata","type":"literal","lang":"en"}],"http:\/\/www.w3.org\/2009\/08\/skos-reference\/skos.html#note":[{"value":" A DECISION SUPPORT SYSTEM FOR HARVEST SCHEDULING AND LOG PROCESSING AT THE MALCOLM KNAPP RESEARCH FOREST IN MAPLE RIDGE, BRITISH COLUMBIA by Ye Huang B.Sc., The University of British Columbia, 2012 A GRADUATING ESSAY SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE in The Faculty of Forestry FRST 497 THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2012 \u00a9 Ye Huang, 2012 i Abstract This essay develops prototypes of linear programming-based models to project the harvesting level, lumber production, and net revenue of a harvesting plan in order to support forest operation decision-making in the Malcolm Knapp Research Forest (MFRF) in Maple Ridge, British Columbia. Field data were collected from 3 different biogeoclimatic zones within the research forest. Growth and yield of the forest was modeled by Table Interpolation Program for Stand Yields (TIPSY) which is a stand- and forest-level model developed by the British Columbia Ministry of Forest and Range. Then, the growth and yield data were imported into a forest estate linear programming model to forecast the volume of logs harvested from the forest. A sawing pattern model was used to design the sawing pattern and generate Lumber Recovery Factors by log diameter. Subsequently, a log-to-product linear programming model was used to estimate the final lumber production, mill working hours and the net profit for the forest. The results predict that the mill can earn $3,110,141 by producing 141,229 MBF of lumber and 298,818 m3 of chips over a 60-year planning horizon. Sensitivity analysis included different sawing patterns, price fluctuations and limited mill operating hours. Some potential improvements in model structure, efficiency, availability for big diameter log, and carbon credits are also discussed. Although the forest data and the sawmill configuration used in the models are different from reality, it will not be difficult to modify the model for MKRF. Key words: linear programming model, forest operations, Malcolm Knapp Research Forest ii Table of Contents Abstract ................................................................................................................................................... i List of Tables ........................................................................................................................................ iv List of Figures ........................................................................................................................................ v List of Acronyms and Abbreviations ................................................................................................... vii Acknowledgements ............................................................................................................................. viii 1. Introduction .................................................................................................................................... 1 1.1 Foreword ...................................................................................................................................... 1 1.2 Introduction of Malcolm Knapp Research Forest ........................................................................ 1 1.3 Goals and Objectives.................................................................................................................... 2 2. Method ........................................................................................................................................... 3 2.1 Study Site ..................................................................................................................................... 3 2.2 TIPSY modeling........................................................................................................................... 4 2.3 Linear programming modelings ................................................................................................... 8 2.3.1 Forest Estate Model ............................................................................................................. 10 2.3.2 Sawing Pattern Model ......................................................................................................... 14 2.3.3 Log-to-product model.......................................................................................................... 19 3. Results .......................................................................................................................................... 23 3.1 Forest Estate Model.................................................................................................................... 23 3.2 Log-to-product model ................................................................................................................ 26 4. Discussion .................................................................................................................................... 29 4.1 2 8-oriented sawing pattern ...................................................................................................... 29 4.2 Lumber price fluctuation ............................................................................................................ 31 4.3 Limited mill working time ......................................................................................................... 34 4.4 Possible Improvements of Models ............................................................................................. 35 4.4.1 Combine 2 LP Models ......................................................................................................... 35 4.4.2 Improve Available Log Diameter Range of Sawing Pattern Model ................................... 36 iii 4.4.3 Introduce a Carbon Credit Section ...................................................................................... 36 5. Conclusion .................................................................................................................................... 37 6. Reference ...................................................................................................................................... 38 7. Appendices ................................................................................................................................... 41 7.1 Appendix A: Forest Estate Model .............................................................................................. 41 7.1.1 Stand One ............................................................................................................................ 42 7.1.2 Stand Two ........................................................................................................................... 43 7.1.3 Stand Three.......................................................................................................................... 44 7.1.4 Harvesting, Inventory and Result ........................................................................................ 45 7.2 Appendix B: Sawing Patterns for Each Type of Log ................................................................. 46 7.2.1 2x10-oriented Lumber Recovery Factor ............................................................................. 43 7.2.2 2x8-oriented Lumber Recovery Factor ............................................................................... 52 7.3 Appendix C: Log-to-product Model .......................................................................................... 54 iv List of Tables Table 2-1. Site conditions for three study sites .................................................................................. 3 Table 2-2. Volume and log DBH class by age for site one ................................................................ 6 Table 2-3. Volume and log DBH class by age for site two ................................................................ 6 Table 2-4. Volume and log DBH class by age for site three ............................................................. 7 Table 2-5. Volume and age classes for existing stands .................................................................... 11 Table 2-6. Volume and age classes for future stands ...................................................................... 11 Table 2-7. Harvest yield (m3\/ha) at harvesting for different stands .............................................. 12 Table 2-8. Ending inventory (m3\/ha) of different stands ................................................................ 12 Table 2-9. Finished thickness and width value of corresponding nominal lumber ..................... 16 Table 2-10. Lumber and Chips Recovery Factor ............................................................................ 16 Table 2-11. Headsaw Productivity .................................................................................................... 20 Table 2-12. Trimmer Productivity ................................................................................................... 21 Table 2-13. Price of Lumber and Cost of Sawmill Operation ....................................................... 22 Table 3-1. Harvesting area in each period for each stand .............................................................. 24 Table 3-2. Harvesting volume in each period .................................................................................. 24 Table 3-3. Logs available and used in each period for each stand ................................................ 26 Table 3-4. Logs sorted by diameter in each period (m3) ................................................................. 27 Table 3-5. Lumber (MBF) and chips (m3) produced in each period ............................................. 28 Table 4-1. Difference between 2x8 and 2x10 production, price and net revenue ......................... 30 Table 4-2. Lumber price, production and net revenue for three scenarios .................................. 33 Table 4-3. Net revenue comparison of 92.6% of the original price and 92.7% of the original price ..................................................................................................................................................... 34 v List of Figures Figure 1-1. Location of UBC Malcolm Knapp Research Forest ...................................................... 2 Figure 2-1. Growth and yield curve for three sites ........................................................................... 8 Figure 2-2. Flow of model analysis ..................................................................................................... 9 Figure 2-3. Display portion of sawing calculator ............................................................................ 18 Figure 2-4. Summary Portion of Sawing Calculator ...................................................................... 19 Figure 3-1. Inventory and harvest in each period ........................................................................... 25 Figure 3-2. Stand composition of harvesting stands ....................................................................... 25 Figure 3-3. Log composition and volume for each period sorted by diameter ............................. 28 Figure 3-4. Final lumber production and composition ................................................................... 29 Figure 4-1. Production distribution of 2x8-oriented and 2x10-oritented sawing patterns .......... 31 Figure 4-2. Quarterly lumber prices from 2007 to 2011 ................................................................ 32 Figure 7-1 Stand One portion ........................................................................................................... 42 Figure 7-2. Stand Two portion .......................................................................................................... 43 Figure 7-3. Stand Three portion ....................................................................................................... 44 Figure 7-4. Harvesting, inventory and result portion ..................................................................... 45 Figure 7-5. 2x10-oriented sawing pattern and LRF for 15cm log ................................................. 43 Figure 7-6. 2x10-oriented sawing pattern and LRF for 20cm log ................................................. 44 Figure 7-7. 2x10-oriented sawing pattern and LRF for 25cm log ................................................. 45 Figure 7-8. 2x10-oriented sawing pattern and LRF for 30cm log ................................................. 46 Figure 7-9. 2x10-oriented sawing pattern and LRF for 35cm log ................................................. 47 Figure 7-10. 2x10-oriented sawing pattern and LRF for 40cm log ............................................... 48 Figure 7-11. 2x10-oriented sawing pattern and LRF for 45cm log ............................................... 49 Figure 7-12. 2x10-oriented sawing pattern and LRF for 50cm log ............................................... 50 Figure 7-13. 2x10-oriented sawing pattern and LRF for 55cm log ............................................... 51 vi Figure 7-14. 2x8-oriented sawing pattern and LRF for 35cm log ................................................. 52 Figure 7-15. 2x8-oriented sawing pattern and LRF for 55cm log ................................................. 53 vii List of Acronyms and Abbreviations BEC: Biogeoclimatic Ecosystem Classification Cw: Coastal Western redcedar CWH: Coastal Western Hemlock CWHdm: Coastal Western Hemlock, Dry Maritime CWHvm1: Coastal Western Hemlock, Submontane Very Wet maritime CWHvm2: Coastal Western Hemlock, Montane Very Wet maritime CRF: Chips Recovery Factor DBH: Diameter at Breast Height DWB: Decay, Waste and Breakage Fd: Coastal Douglas-fir Hw: Western hemlock LB: Lower Bound LP: Linear Program LRF: Lumber Recovery Factor MBF: Thousand Board Feet MKRF: Malcolm Knapp Research Forest Ha: Hectare Hr: Hour OAF: Operational Adjustment Factor Regen: regenerated RHS: Right Hand Side TIPSY: Table Interpolation Program for Stand Yields UBC: University of British Columbia viii Acknowledgements Here I avail myself of this opportunity to express enduring gratitude to the faculty, staff and my fellow students at the UBC, who have inspired and encouraged me to complete my undergraduate education in UBC forestry. I am greatly indebted to Dr. John Nelson for his knowledge, patience and precious supervision throughout the whole process of this essay. Without his help and guidance, this essay would never be finished. I am also greatly indebted to Dr. Guangyu Wang, who has shown much consideration for my composition and provided me many valuable suggestions. Moreover, I would like to express my thanks to Laura Cottle, RPF, who has given me many valuable suggestions and advices, and made necessary corrections. My heartfelt thanks also go to Danielle Fleury for her instructive corrections and useful suggestions. My hearty appreciation also goes to Jun Li for his help in building the model. Special thanks are owed to my parents, Zhijian Huang and Yiqin Wang, and relatives for their continuous support and encouragement. 1 1. Introduction 1.1 Foreword Forest models are a tool for foresters and ecologists to predict and analyze the state, dynamics and productivity of forests (Clark & Clark, 1999). Models can be applied in forest management, climate change, forest dynamics and the entire biogeochemical cycle (Lischke, 2001). Moreover, forest models can be applied to different aspects of forestry on local, sub-regional, regional and global levels. For instance, forest dynamics models can be utilized in prediction of single trees and forest stands (local level), changes in tree species and age distributions of forests (sub-regional level), stages in biomass redistribution in the regional ecosystem (regional level) and the importance of forests within the global energy cycle (global level) (Vladimirov & Chudnenko, 2009). Therefore, models, which can provide better understanding of forests in the future, can support the decision-making process in long-term forest management and operations (Clark & Clark, 1999). 1.2 Introduction of Malcolm Knapp Research Forest The 5,157 hectare Malcolm Knapp Research Forest (MKRF), is located in Maple Ridge, British Columbia, approximately 60 km east of Vancouver. Figure 1-1 shows the location of the MKRF. It was established in 1949 as an affiliated facility of the University of British Columbia (UBC) for academic research in forestry and related sciences. Besides its research function, MKRF also provides services in recreation, education and timber production (UBC Malcolm Knapp Research Forest, 2011b). MKRF holds a 250 hectare woodlot license (Woodlot W0037). It also owns a small sawmill, located in the MKRF, so that the MKRF is able to produce wood products within the forest to obtain revenues for the regular operation of the research forest (UBC Malcolm Knapp Research Forest, 2011c). Due to the economic downturn, in 2010 the harvested volume was reduced by 60% compared to 2009 and Woodlot W0037 was not harvested (UBC Malcolm Knapp Research Forest, 2 2011d). This essay is aimed at developing a decision supports system to predict the harvesting and log processing practices in the MKRF. Figure 1-1. Location of UBC Malcolm Knapp Research Forest (Source: UBC Malcolm Knapp Research Forest, 2011a) 1.3 Goals and Objectives This essay will use a forest estate linear programming (LP) model, a sawing pattern model, and a log-to-product LP model to project and analyze the forest products production chain for the MKRF and to examine the feasibility of using an LP model in providing optimized solutions for timber harvesting and lumber production. The models will also be used to predict net revenue for the forest operations. The ecological conditions of experiment plots will be introduced and the structure of the 3 model will be described. The optimum result that is obtained through the model will be presented and discussed in terms of the type and volume of harvested tree and lumber to obtain maximum revenue. Then, different scenarios, including sawing pattern, lumber price and limited mill working time, will be discussed. Finally, recommendations will be made for assisting forest management and log processing in MKRF. 2. Method 2.1 Study Site In this study, three sites were established in the MKRF and the ecological conditions and stand data were collected for the modeling growth and yield with the Table Interpolation Program for Stand Yields program (TIPSY). Table 2-1 summarizes ecological conditions for three study sites. Table 2-1. Site conditions for three study sites Sites Species Composition Site Index (m) Stock Height (cm) Site One Fd, Cw, Hm 40% Fd, 30% Cw, 30%Hm 18 for Fd, 18 for Cw, 15.75 for Hw 30 for Fd, 27 for Cw, 22 for Hw Site Two Fd, Cw, Hm 30% Fd, 40% Cw, 30%Hm 18 for Fd, 18 for Cw, 15.75 for Hw 30 for Fd, 27 for Cw, 22 for Hw Site Three Fd, Cw, Hm 20% Fd, 50% Cw, 30%Hm 18 for Fd, 18 for Cw, 15.75 for Hw 30 for Fd, 27 for Cw, 22 for Hw There are some general ecological conditions that are common among all three sites: \uf0b7 Geography: the forest region for all three sites is \u201ccoast\u201d and the forest district is 4 \u201cChilliwack\u201d; the biogeoclimatic zone (BEC zone) is \u201cCoastal Western Hemlock (CWH)\u201d; and the average slope is 10%; \uf0b7 Stand establishment: the type of stand regeneration is planted; the density is 1600 stems\/ha and there is no delay for regeneration; and \uf0b7 Coastal Douglas-fir (Fd), Coastal Western Redcedar (Cw) and Coastal Western Hemlock (Hw) are the leading species in the three sites. Site Index for Douglas-fir and Western Redcedar is 18m; Site Index for Western Hemlock is 15.75m Site One is within the Coastal Western Hemlock, Dry Maritime (CWHdm) zone. The CWHdm is characterized by warm-to-dry summers and mild-to-moist winters with little snow (Pojar& Stewart, 2007a). The site consists of 40% Coastal Douglas-fir, 30% Coastal Western Redcedar and 30% Coastal Western Hemlock. Site Two is within the Coastal Western Hemlock, Submontane Very Wet Maritime (CWHvm1) zone. This BEC zone has cool summers and mild winters with very little snow (Pojar& Stewart, 2007b). The site is composed of 30% Coastal Douglas-fir, 40% Coastal Western Redcedar and 30% Coastal Western Hemlock. Site Three is within the Coastal Western Hemlock, Montane Very Wet Maritime (CWHvm2) zone. Different from site 2 (CWHvm1), it has short, cool summers and cool winters with a large amount of snow (Pojar& Stewart, 2007c). Site 3 is 20% Coastal Douglas-fir, 50% Coastal Western Redcedar and 30% Coastal Western Hemlock. 2.2 TIPSY Modeling The collected data were processed by TIPSY version 4.2. Growth and yield data that are related 5 to volume and wood products were generated by TIPSY. Since TIPSY does not model multiple species, for each site three TIPSY runs were conducted for three different species, and the volumes of each species were summed up and multiplied by their corresponding composition in order to make adjustments for the correct volume for each site. In the data entry process, two TIPSY parameters were applied to the ecological data: \uf0b7 Operational Yield Adjustments: two default TIPSY medium examples of Operational Adjustment Factors (OAF), which are parameters to reflect the yield loss with regards to insects and disease, non-merchantable wood, stocking gaps and other factors, were applied in order to mimic real growth and yield (British Columbia Ministry of Forest and Range, 2005). In example 1, the total age was 0-300, and the factors were 0.85-0.85; in example 2, the total age was 0-300, and the factors were 1-0.95-0.85. \uf0b7 Decay, Waste and Breakage losses (DWB) factors were applied as the default value in TIPSY. After data entry and TIPSY analysis, growth and yield curves were created. There are two assumptions that were made in growth and yield tables: \uf0b7 Only \u201cmerchantable volume\u201d, which refers to the volume of trees that are greater than 12.5 cm in DBH excluding non-merchantable trees, was considered as available volume. \uf0b7 Based on the sawmill capacity, logs that are less than 15cm or greater 55 cm in diameter would not be shipped to the sawmill. Based on the TIPSY projections, Western Redcedar in all three sites would have logs that are greater than 55 cm in diameter after 120 years of age, which exceeded the maximum capacity of the sawmill, so only data from 0 to 120 years old were used. The merchantable volume and composition 6 of different log diameter classes of each age class for the three sites are listed in Table 2-2, Table 2-3 and Table 2-4. The growth and yield curves for the three sites are shown in Figure 2-1. Table 2-2. Volume and log DBH class by age for site one Age \/ yrs Merchantable volume \/ m3 Proportion of Merchantable Volume 15 20 25 30 35 40 45 50 55 0 0 NA NA NA NA NA NA NA NA NA 10 0 NA NA NA NA NA NA NA NA NA 20 0 NA NA NA NA NA NA NA NA NA 30 11 0.95 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 40 52 0.53 0.40 0.07 0.00 0.00 0.00 0.00 0.00 0.00 50 101 0.28 0.47 0.20 0.04 0.01 0.00 0.00 0.00 0.00 60 144 0.16 0.40 0.30 0.10 0.03 0.01 0.00 0.00 0.00 70 181 0.10 0.31 0.34 0.17 0.06 0.02 0.00 0.00 0.00 80 210 0.08 0.24 0.31 0.22 0.09 0.04 0.01 0.00 0.00 90 237 0.06 0.19 0.28 0.25 0.12 0.06 0.03 0.01 0.00 100 264 0.05 0.15 0.25 0.24 0.16 0.08 0.05 0.01 0.00 110 286 0.05 0.13 0.22 0.23 0.18 0.10 0.06 0.03 0.01 120 304 0.04 0.11 0.19 0.22 0.19 0.12 0.07 0.05 0.01 Table 2-3. Volume and log DBH class by age for site two Age \/ yrs Merchantable volume \/m3 Proportion of Merchantable Volume 15 20 25 30 35 40 45 50 55 0 0 NA NA NA NA NA NA NA NA NA 10 0 NA NA NA NA NA NA NA NA NA 20 0 NA NA NA NA NA NA NA NA NA 30 11 0.95 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 40 53 0.51 0.41 0.08 0.00 0.00 0.00 0.00 0.00 0.00 50 104 0.27 0.47 0.21 0.05 0.01 0.00 0.00 0.00 0.00 60 148 0.15 0.38 0.31 0.11 0.04 0.01 0.00 0.00 0.00 70 187 0.09 0.29 0.34 0.18 0.07 0.02 0.00 0.00 0.00 80 217 0.07 0.23 0.30 0.23 0.10 0.05 0.01 0.00 0.00 90 246 0.06 0.18 0.27 0.24 0.13 0.07 0.03 0.01 0.00 100 274 0.05 0.15 0.24 0.23 0.16 0.09 0.06 0.02 0.01 110 296 0.04 0.12 0.21 0.22 0.18 0.11 0.07 0.04 0.01 7 120 315 0.04 0.11 0.18 0.21 0.19 0.13 0.08 0.06 0.01 Table 2-4. Volume and log DBH class by age for site three Age \/ yrs Merchantable volume \/m3 Proportion of Merchantable Volume 15 20 25 30 35 40 45 50 55 0 0 NA NA NA NA NA NA NA NA NA 10 0 NA NA NA NA NA NA NA NA NA 20 0 NA NA NA NA NA NA NA NA NA 30 11 0.95 0.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 40 55 0.49 0.41 0.09 0.00 0.00 0.00 0.00 0.00 0.00 50 107 0.25 0.46 0.22 0.06 0.01 0.00 0.00 0.00 0.00 60 153 0.14 0.37 0.31 0.12 0.05 0.01 0.00 0.00 0.00 70 194 0.09 0.28 0.34 0.19 0.08 0.03 0.00 0.00 0.00 80 225 0.07 0.22 0.29 0.23 0.11 0.06 0.01 0.00 0.00 90 254 0.05 0.17 0.26 0.24 0.14 0.08 0.04 0.01 0.00 100 284 0.05 0.14 0.22 0.23 0.17 0.10 0.07 0.02 0.01 110 307 0.04 0.12 0.20 0.21 0.18 0.12 0.08 0.04 0.01 120 326 0.04 0.10 0.17 0.20 0.18 0.14 0.09 0.07 0.02 8 Figure 2-1. Growth and yield curve for three sites 2.3 Linear Programming Models Linear programming models were built with Microsoft Excel for determining the optimal harvest schedule and the optimal sawmill production. The Solver analysis tool embedded in Excel was used to calculate the optimum solution. A sawing pattern model was used to determine Lumber Recovery Factors for various dimensions of lumber. Figure 2-2 shows the flow of the analysis process. 0 50 100 150 200 250 300 350 400 0 10 20 30 40 50 60 70 80 90 100 V o lu m e ( m 3 \/h a) Age\/years Site 1 Site 2 Site 3 9 TIPSY Growth and Yield Tables - Provide merchantable volume by age - Offer log diameter by age Forest Estate Linear Programming Model - Maximize total harvesting volume (m3) and harvesting size (ha) of each stand to cut in each decade - Project volume harvested in each period by 15cm to 55cm in diameter Sawing Pattern Model - maximize Lumber Recovery Factor (mbf\/m3) for 2x4, 2x6, 2x8 and 2x10 lumber by log diameter Log to Product Linear Programming Model - Maximize Net Present Value from sawing logs into lumber over six periods Outcomes - Optimize lumber production schedule - Present lumber production level (mbf) and volume (m3) of chips Figure 2-2. Flow of model analysis 10 2.3.1 Forest Estate Model The Forest Estate model was used to optimize the harvesting schedule. The model is shown in Appendix A. 2.3.1.1 Model assumptions and data input Some assumptions and constraints for harvesting were set up for this model: \uf0b7 Area of site: because the original areas of the study sites were too small to conduct harvesting economically, the size of each site is assumed to be 1000 hectares. \uf0b7 Period: each period is 10 years; the total planning horizon is 6 periods. \uf0b7 Period of harvesting: due to the limited merchantable volume of wood and limited capacity of the sawmill, this model only assumes 60 years of stand growth (age 60 to age 110). \uf0b7 Time of harvesting: trees at age 60 would be harvested in period 1; trees at age 70 would be harvested in period 2 etc. \uf0b7 Minimum ending inventory: in order to have enough trees left to provide other services, the minimum harvesting inventory is 10,000 m3. \uf0b7 Minimum ratio of ending inventory: the ending inventory must be at least equal to one-fourth of the beginning inventory. \uf0b7 Minimum harvesting per period: in order to ensure harvesting occurs in every period, the minimum harvesting per period is 110,000 m3. \uf0b7 Maximum changes of harvesting flow: the maximum change of harvesting level for each period is 20%, which means that the harvesting level for period 2 is between 80% and 120% of the harvesting level for period 1. \uf0b7 The objective function maximizes to total harvest over the planning horizon. 11 \uf0b7 Decision variables are the size (ha) of stand i cut in period j. Derived from the volume tables (Table 2-2 to Table 2-2) and the growth and yield curve (Figure 2-1), the volume and age classes data for existing stands and future stands were entered, and are shown in Table 2-5 and Table 2-6. Harvested volume of existing and future stands in different periods is shown in Table 2-7. The ending inventory of different periods is shown in Table 2-8. Table 2-5. Volume and age classes for existing stands Existing Stands Stand 1 Stand 2 Stand 3 Age Volume Volume Volume 60 144 148 153 70 181 187 194 80 210 217 225 90 237 246 254 100 264 274 284 110 286 296 307 Table 2-6. Volume and age classes for future stands Future (Regenerated) Stands Stand 1 Stand 2 Stand 3 Periods Stand Age volume before harvest volume cut volume before harvest volume cut volume before harvest volume cut 0 0 0 0 0 0 0 0 1 10 0 0 0 0 0 0 2 20 0.4 0 0.5 0 0.6 0 3 30 17 0 18 0 18 0 4 40 62 0 67 0 68 0 5 50 124 124 130 130 134 134 12 Note: Xij refers to number of hectares of stand I first cut in period j 2.3.1.2 Model Structure The forest estate model follows the typical structure of an LP model. There are five series of columns (decision variables) and seven series of rows (constraints) in the model. As for columns, the model has six periods for each of the three stands, harvest of each period and beginning and ending inventory. In terms of rows, the model has yields at harvesting, ending inventory, existing volume, regenerated volume, minimum harvesting level, harvesting flow and size of each stand. The names of each variable are shown in the \u201cVariable name\u201d row; total harvested volume per ha for each period of each stand is shown in the \u201cObjective\u201d row; the areas that would be harvested are calculated by Solver and put into the \u201cAnswer\u201d row; \u201cSign\u201d and \u201cRight Hand Side (RHS)\u201d columns are designated for constraints; the final result, total volume of harvesting, is shown at top of the \u201cResult\u201d column. Other rows of the \u201cResult\u201d column are used to check if the answer that was obtained fits with Table 2-7. Harvest yield (m3\/ha) at harvesting for different stands Table 2-8. Ending inventory (m3\/ha) of different stands 13 constraints (\u201cSign\u201d and \u201cRHS\u201d columns) by the \u201csumproduct\u201d function and the Solver. Yields (m3\/ha) at harvesting for different stands (Table 2-7) are shown in the \u201charvest 1\u201d to \u201charvest 6\u201d rows. Harvested volumes in each period are summed into a total volume variable. Taking period 1 as an example, the total harvested volume of period 1 consists of harvesting in 3 stands. Therefore, the total volume of wood can be calculated by Equation 1: Vij=\u2211 [1] Where i represents the harvesting period; Vij represents the available volume stand I in period j (m3\/ha), and Ai represents the area of the stand i. Subsequently, Solver automatically fills the harvest volume into the \u201charv 1\u201d column of the \u201cAnswer\u201d row. This method is applied to the entire LP model. The inventory section of the model shows the beginning inventory and ending inventory for each period of each stand and the minimum ratio of ending inventory. Beginning inventory was calculated by the sum of the products of the initial volume (volume at age 60) of each stand and its corresponding harvesting area. Ending inventory of each period is the same as Table 2-8. The \u201cexisting-ha\u201d and \u201cregen-ha\u201d rows are the constraints for Solver which state that all values in the harvesting area are positive. The \u201cAbsolute-LB-Harvest\u201d rows are used to set constraints for the minimum harvesting level per period, which is 110,000 m3 in the model. The \u201cLB Harvest flow\u201d rows are used to constrain the change of harvesting level for each period. The mechanism of limiting changes is also linked to Solver by applying a limit factor. Specifically, it is assumed that the allowable change of harvesting from period 1 to period 2 is \u00b1X%, so the limiting factor in the model is - (1-|X|). Therefore, if the change of harvesting level is within \u00b110%, the harvesting level for the 14 first period, multiplied by the limiting factor plus harvesting level for the second period, will be equal to or greater than 0. For example, assuming the harvesting level for the first period is 10,000 m3 and the harvesting level for the second period is 9,500 m3, the change in harvesting level is = - 5%, and the limiting factor is - (1- |-0.05|) = -0.95. The harvesting level for the first period is multiplied by the limiting factor is 10,000 (-0.95) = -9500. Finally, the \u201cha available stand\u201d rows limit the sum of harvested area and uncut area for each stand to the total area of the stand, which is 1000 hectares. 2.3.2 Sawing Pattern Model The Sawing Pattern Model is used for computing the Lumber Recovery Factor (LRF), which is an important component of the Log-to-product model. The sawing pattern model used in this essay is a Microsoft Excel-based model provided by Dr. Thomas Maness from Oregon State University at Corvallis, Oregon. This sawing pattern model can calculate the LRF based on diameters of logs and dimensions of lumber produced. For the detailed sawing patterns for each diameter of log, refer to Appendix B. 2.3.2.1 Model assumptions and data input The strategy of this model is to maximize the usage of the log, producing lumber of as large dimensions as possible. Some assumptions of the input log and the designated products are applied in this study: \uf0b7 Small end diameter: logs accepted range from 15 cm to 55 cm in the log small end diameter with an interval of 5cm (e.g. 15cm, 20cm, 25cm etc.); \uf0b7 Length: due to the balance of log diameter and economic value, all the lumber it produces 15 is 8 feet in length; \uf0b7 Taper: the value of taper is 1%, which means that for every 100 inches of log length, the large end diameter will be 1 inch more than the small end diameter; \uf0b7 Large end diameter: it is assumed that for an 8-foot-long log, the larger end is 1 inch greater than the small end; \uf0b7 Trim Allowance: 0.25 foot is set for trim allowance for the loss from end injuries or uneven cuts in processing; \uf0b7 Log sweep: there is no log sweep assumed; \uf0b7 Side shift and horns angle: side shift and horns angle will not be applied in the model \uf0b7 Saw kerf, wane allowance, infeed mechanism, log class size and other parameters are set at default values; \uf0b7 Volume of log: the volume of log is calculated by Equation 2: [2] where 0.001818 is a constant, Ds is the log small end diameter, Dl is the log large end diameter and log length is in feet (Grosenbaugh, 1963). \uf0b7 Volume of lumber: The volume of a board can be calculated by Equation 3: Volume of lumber (MBF) = [3] where the units for length, width and thickness are inches and the thickness and width of lumber used in the calculation are the finished value. The corresponding finished value of different dimensional lumber is shown in Table 2-9. 16 Table 2-9. Finished thickness and width value of corresponding nominal lumber Nominal Finished Thickness Width Thickness Width 2 4 1.5 3.5 2 6 1.5 5.5 2 8 1.5 7.5 2 10 1.5 9.5 \uf0b7 LRF: the LRF can be computed by Equation 4 and the summary of LRF is demonstrated in Table 2-10: LRF (MBF\/M3) = [4] Table 2-10. Lumber and Chips Recovery Factor Lumber Recovery (MBF\/m3) Lumber 15 cm 20 cm 25 cm 30 cm 35 cm 40 cm 45 cm 50 cm 55cm 2x4 - 8' 0.1305 0.1526 0.0500 0.0176 0.0262 NA NA NA NA 2x6 - 8' NA NA 0.1570 0.1938 0.1440 0.0476 0.0379 NA NA 2x8 - 8' NA NA NA NA NA 0.1466 NA NA NA 2x10 - 8' NA NA NA NA 0.1153 0.0890 0.3541 0.3782 0.3614 sum LRF 0.1305 0.1526 0.2070 0.2114 0.2855 0.2832 0.3920 0.3782 0.3614 Chips 0.6421 0.5899 0.4615 0.4512 0.2763 0.2817 0.0250 0.0575 0.0972 \uf0b7 Chip Recovery Factor (CRF): chip recovery factors are shown in Table 2-10. An assumption is made that there is 5% sawdust loss in this sawmill, and anything besides lumber and sawdust loss can be converted into wood chips. The CRF can be calculated by Equation 5: Chip Recovery Factor = 1 \u2013 sawdust loss \u2013 sum LRF x 2.360 m3 \/ MBF [5] Where the sawdust loss is 5%. 17 The 2.360 m3 \/ MBF is the conversion factor for LRF. 1 board foot has 12 inches in length, 12 inches in width and 1 inch in thickness. To convert cubic meters into MBF, use the formula 1000 = 2.360m3\/MBF. The sum of LRF includes the LRF for 2x4x8, 2x6x8, 2x8x8 and 2x10x8. 2.3.2.2 Model Structure Figure 2-3 and Figure 2-4 show the structure of the sawing pattern model. Figure 2-3 shows the display portion of the model, including log parameters mentioned above, log volume and LRF for different dimensions of lumber. Figure 2-4 shows the summary portion of the model, including the number of different dimensions of lumber produced from this log and the corresponding volume of each product. The volumes of different dimensional lumber are already built into the model. When the log small end diameter is entered, a graph showing the cross-sectional area of the log will be generated, as can be seen in the Figure 2-3. The blue line represents the small end of the log, the red line represents the large end of the log. The dotted line is the average of the small end and the large end. Lumber of various dimensions are arranged in the circle by manually entering the type of products (e.g. 2x4, 2x6) and the length, which is all 8 feet in this case. In order to have a sufficient amount of wood to produce lumber, the dimensions of the lumber must fit the small end of the log (the blue circle). When the number of lumber boards that can be produced is maximized, the volume of lumber (board foot) will be computed by summing up all the volumes of lumber in different dimensions. In this study, the strategy for lumber production optimization is to produce as much larger dimension lumber as possible in order to get higher profits. 18 Figure 2-3. Display portion of sawing calculator 19 Figure 2-4. Summary portion of sawing calculator However, this model is not fully capable of handling larger logs, such as 50cm and 55cm logs, because the graph representing the cross-sectional area of the log cannot be shown appropriately. In order to adjust this situation, the half of the log that can be seen in the graph is filled in by cant lumber, and then the volume of cant lumber is doubled to calculate the total volume of lumber. 2.3.3 Log-to-product model The log-to-product model optimizes the sawing of logs (by small end diameter) into various dimensions of lumber products. Chips are a by-product of the sawing process. The model has six time periods and the log distributions for each period were provided by the forest estate model. The model is shown in the Appendix C. 20 2.3.2.1 Model assumptions and data input Assumptions that were applied to this model are: \uf0b7 Cost: the stumpage cost for MKRF is $50\/ m3; haul cost is $10 \/ m3. Therefore, the total cost is $60\/ m3 (data provided by Dr. John Nelson, UBC Faculty of Forestry). \uf0b7 Headsaw productivity: a headsaw is a machine used to cut the log into a narrower canted log to adjust for other sawing equipment. (Jadeja, 2007). The headsaw productivity for this mill is shown in Table 2-11. Based on the capacity, the headsaw can process 1125 8-foot logs in 1 hour. The volume of log can be calculated by the Average End Method. Therefore, the productivity of headsaw (hours\/m3) can be calculated by Equation 6: Productivity of headsaw (hour\/m3) = [6] Table 2-11. Headsaw productivity Headsaw Productivity Table Log dia (cm) Logs\/hr Volume \/log Volume \/hr hrs\/m3 15 1125 0.0525 59.08 0.0169 20 1125 0.0896 100.79 0.0099 25 1125 0.1365 153.61 0.0065 30 1125 0.1934 217.55 0.0046 35 1125 0.2601 292.61 0.0034 40 1125 0.3367 378.80 0.0026 45 1125 0.4232 476.11 0.0021 50 1125 0.5196 584.53 0.0017 55 1125 0.6259 704.08 0.0014 \uf0b7 Trimmer productivity: A trimmer is the machine that cuts the lumber to form square ends (Mardikar, 2007). The trimmer productivity can be seen in Table 2-12. The trimmer can process 4617 boards per hour. Therefore, the productivity of the trimmer (hour\/MBF) can be 21 calculated by Equation 7: Productivity of trimmer (hour\/MBF) = [7] However, the ratio of headsaw productivity to trimmer productivity is 1.69. In order to balance the productivity of both machines, adjustments are made such that all the trimmer productivities are divided by 1.32. The trimmer productivities after adjustment are used in the model. Table 2-12. Trimmer productivity Trimmer Productivity Size Boards \/ Hr MBF\/Board MBF \/ Hr Hr \/ MBF(before adjustments) Hr \/ MBF(after adjustments) 2x4-8' 4617 0.0035 16.1595 0.06190 0.0469 2x6-8' 4617 0.0055 25.3935 0.0394 0.0298 2x8-8' 4617 0.0075 34.6275 0.0289 0.0219 2x10-8' 4617 0.0154 71.1788 0.0140 0.0106 \uf0b7 Cost and Revenue: The price of lumber in different dimensions, the cost of shipping, finishing, hourly headsaw and trimmer operations, and maximum hours for the headsaw and the trimmer are shown in Table 2-13. The 8-foot lumber price is based on the 2001-2011 average lumber prices for random length (TradingCharts, 2011). This price, which is $273 \/ MBF, is used for the price of 2x4 lumber. Values for the 10-year averages for 2x6, 2x8 and 2x10 were determined using the current value relative to the price of 2x4 lumber. Based on the patterns of current lumber price (Madison's Canadian Lumber Reporter, 2011), The prices for 2x6, 2x8 and 2x10 are all higher than 2x4, 15%, 14%, and 17% respectively. For instance, 22 the price for 2x6 is 15% higher than the price of 2x4, so the price for 2x6 can be calculated by: The price of chips is the courtesy of Tony Peiffer, the general manager of fibre supply for Interfor Ltd. Other cost information is assumed based on the previous data provided by Dr. John Nelson. The sawmill is scheduled to run 4600 hours to finish the processing of these logs. When the headsaw is running, $500 per hour will be charged for operation. If the headsaw is in the \u201cdown\u201d status, it also incurs costs of $250 per hour. The trimmer costs are $422 and $211 per hour, respectively. Table 2-13. Price of Lumber and Cost of Sawmill Operation Revenue Costs Product Price Units Shipping -$10 \/ MBF Headsaw Run $500 \/hr 2x4 - 8' $273 \/ MBF \/ MBF Headsaw Down $250 \/hr 2x6 - 8' $314 \/ MBF 2x8 - 8' $311 \/ MBF Finishing -$35 \/ MBF Trimmer Run $422 \/hr 2x10 - 8' $319 \/ MBF Trimmer Down $211 \/hr CHIPS $36 \/ m 3 Maximum hours\/week for Head saw & Trimmer 4600 \uf0b7 Minimum production level for each period: in order to have a relatively even production flow, the minimum of production is set at 100,000 m3 for each diameter of log. 2.3.2.2 Model Structure Similar to the tree-to-log model, the log-to-product model is an LP model in Microsoft Excel. It has 5 series of columns: stand & period, logs sorted by diameter (m3), produced lumber (MBF) & 23 chips (m3), headsaw hours and trimmer hours, and 5 corresponding rows plus a series of maximum production levels. Specifically, since there are 6 harvesting periods, there are 18 columns and rows for the \u201cstand & period\u201d series (6 harvesting periods for 3 stands), 54 columns and rows for the \u201clog sorted by diameter\u201d series (9 categories of log diameter for 6 periods), 30 columns and rows for the \u201clumber & chips\u201d series (1 chip and 4 types of lumber for 6 periods), 2 columns and rows for \u201cheadsaw\u201d series, 2 columns and rows for \u201ctrimmer\u201d series and 6 rows for \u201cmaximum production level\u201d series. As in the forest estate model, the \u201cvariable name\u201d row contains the name for each variable; the \u201canswer\u201d row shows the value for each variable; the \u201cobjective\u201d row shows the cost and revenue for each variable. Constraints are checked by the \u201csumproduct\u201d function and the Solver in the \u201cresult\u201d, \u201csign\u201d and \u201cRHS\u201d columns. The result of each series of variables will be shown in the \u201canswer\u201d row in corresponding columns and the final result (net revenue) will be shown in the \u201cnet revenue\u201d cell. 3. Results 3.1 Forest Estate Model The results of the forest estate model are shown in Table 3-1 and Table 3-2. All hectares in stand 1 and stand 2 are harvested and 206 hectares of stand 3 are not harvested. In terms of harvesting periods, 110,000 m3 of wood, which is the minimum level of harvesting, are harvested during each period, from period 1 to 5. For the final period, besides the minimum harvesting level, an additional 16,752 m3 of wood are harvested. In total, 676,752 m3 of wood are harvested out of the forest. In terms of ending inventory, from period 1 to period 6, the ending inventory decreases, reaching the lowest point in period 6, which is 111,353 m3. Figure 3-1 graphically shows the harvesting and inventory volumes for each period. The graph shows that as the time goes by, the ending inventory is decreasing. Figure 3-2 shows harvest by existing and regenerated stands. The regenerated stand is only harvested in period 6. 24 Table 3-1. Harvesting area in each period for each stand Harvesting in each period (ha) 1 2 3 4 5 6 Uncut Stand 1 339 0 524 28 0 109 0 Stand 2 412 588 0 0 0 0 0 Stand 3 0 0 0 406 388 0 206 Table 3-2. Harvesting volume in each period period Harvesting Inventory\/m3 Total (m3) Existing (ha) Regen (ha) 1 110000 751 0 335410 2 110000 588 0 313051 3 110000 524 0 253529 4 110000 434 0 190251 5 110000 388 0 146396 6 126752 109 751 111353 summary 676752 2794 751 1349990 25 Figure 3-1. Inventory and harvest in each period Figure 3-2. Stand composition of harvesting stands 0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 1 2 3 4 5 6 V o lu m e \/ m 3 Period\/decade Inventory Harvest 0 100 200 300 400 500 600 700 800 900 1000 1 2 3 4 5 6 A re a\/ H a Period\/decade Regen Ha Exist Ha 26 3.2 Log-to-product model The final result of the tree-to-log model is shown in Table 3-5. The optimal solution is for the sawmill to produce 141,229 MBF of lumber and 298,818 m3 of chips with a net revenue of $3,110,141. The final result is derived from the data shown in Table 3-3 and Table 3-4. Table 3-3 illustrates the log volume available and used for processing. The upper part is the available log volume in each period for each stand, as derived from the forest estate model; the lower part is the log used for processing, as calculated by MS Excel Solver. Comparing the two parts, it can be seen that all the logs are processed except for 10,000 m3 of log in stand 1 for period 1. This is due to the optimization process by Solver. The logs that are subject to processing are sorted by diameter, which is shown in Table 3-4. The table indicates that logs ranging from 25cm to 30cm in diameter comprise the biggest portion of the log volume, comprising 45% of the total. From period 1 to period 6, the number of small logs declines steadily, whereas the number of bigger logs increases (Figure 3-3). Table 3-5 shows the 4 different dimensions of lumber and chips produced from the logs in each period, and it illustrates that the lumber production increases from period 1 to period 6. Moreover, it can be seen that 2x6 and 2x4 are produced in the largest volume. 2x8 is the least in production because only 40cm logs are used to produce 2x8 lumber. Figure 3-4 illustrates the lumber composition and volume and indicates that as the log diameter increases, a greater amount of larger-dimension lumber is produced. Table 3-3. Logs available and used in each period for each stand Logs available in each period for each stand (m3) 1 2 3 4 5 6 Stand 1 48,786 0 110,000 6,587 0 73,153 Stand 2 61,214 110,000 0 0 0 53,599 Stand 3 0 0 0 103,413 110,000 0 Logs used in each period for each stand (m3) 1 2 3 4 5 6 Stand 1 38,786 0 110,000 6,587 0 73,153 Stand 2 61,214 110,000 0 0 0 53,599 Stand 3 0 0 0 103,413 110,000 0 27 Table 3-4. Logs sorted by diameter in each period (m3) Perio d SED-1 5 SED-20 SED-25 SED-30 SED-3 5 SED-4 0 SED-4 5 SED-5 0 SED-5 5 sum 1 15,38 8 38,776 30,612 10,612 3,612 1,000 0 0 0 100,00 0 2 9,900 31,900 37,400 19,800 7,700 2,200 0 0 0 108,90 0 3 8,800 26,400 34,100 24,200 9,900 4,400 1,100 0 0 108,90 0 4 5,566 18,832 28,732 26,466 15,26 8 8,668 4,334 1,100 0 108,96 6 5 5,500 15,400 24,200 25,300 18,70 0 11,00 0 7,700 2,200 1,100 111,10 0 6 5,802 15,942 27,349 28,617 22,81 5 13,21 1 8,141 4,339 1,268 127,48 3 sum 50,95 5 147,24 9 182,39 3 134,99 5 77,99 6 40,47 9 21,27 5 7,639 2,368 665,34 9 28 Figure 3-3. Log composition and volume for each period sorted by diameter Table 3-5. Lumber (MBF) and chips (m3) produced in each period Period 2x4_8 2x6_8 2x8_8 2x10_8 chips Sum lumber 1 9,737 7,430 147 505 52,950 17,820 2 8,580 10,923 323 1,084 54,116 20,909 3 7,567 11,720 645 1,923 51,882 21,855 4 5,902 12,415 1,271 4,483 46,715 24,071 5 5,213 12,211 1,613 7,091 43,891 26,128 6 5,659 14,063 1,937 8,788 49,264 30,446 Sum 42,659 68,762 5,934 23,874 298,818 141,229 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 1 2 3 4 5 6 V o lu m e \/m 3 Period\/decade SED-55-1 SED-50-1 SED-45-1 SED-40-1 SED-35-1 SED-30-1 SED-25-1 SED-20-1 SED-15-1 29 Figure 3-4. Final lumber production and composition 4. Discussion The preceding models are appropriate tools for predicting production and net revenue of forest operations. In order to have a better understanding of the system, three scenarios, 2x8-oriented sawing pattern, lumber price fluctuation and limited mill working time, were applied to the model to evaluate its performance and assess these assumptions. 4.1 2 8-oriented sawing pattern 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 1 2 3 4 5 6 P ro d u ct io n \/ M B F Period \/ decade 2x10_8 2x8_8 2x6_8 2x4_8 30 In the previous Sawing Pattern Model application, the strategy was to produce as much larger-dimension lumber as possible (2x10-oriented). However, if the 2x8 lumber markets improve, increasing 20% over the current price, the mill would like to use another sawing pattern (2x8-oriented) to increase its customer share in the 2x8 market. In order to begin 2x8 lumber production, the sawing pattern has to be changed to 2x8-oriented. Since logs less than 35cm in diameter are not big enough to produce 2x8 lumber, and logs greater than 50cm are more valuable in producing 2x10 lumber, logs ranging from 35cm to 45cm are applicable for the LRF change. Table 4-1 shows the difference between the 2 LRF types in production, price and net revenue. Based on the table, in 2x10-oriented sawing type, 35cm, 40cm and 45cm logs would all be used to produce 2x10 whereas only 40cm logs would be used to produce 2x8. As the result, the final volume of lumber is different. According to the production distribution of 2x8-oriented and 2x10-oriented sawing patterns (Figure 4-1), the 2x8-oriented sawing pattern results in 4.5 times larger volume of 2x8 lumber; however, except for 2x8 lumber, the volume of other dimensions of lumber produced under the 2x8-oriented sawing pattern is less, especially 2x10 lumber; it is about 3 times less than the level of the 2x10-oriented sawing pattern. However, since the price of 2x8 lumber has increased 20%, the net revenues of the two sawing patterns are similar. Table 4-1. Difference between 2x8 and 2x10 production, price and net revenue 2x8-oriented 2x10-oriented 35 cm 40 cm 45 cm 35 cm 40 cm 45 cm 2x4 - 8' NA NA NA 0.0262 NA NA 2x6 - 8' NA 0.0476 NA 0.144 0.0476 0.0379 2x8 - 8' 0.2169 0.1466 0.2165 NA 0.1466 NA 2x10 - 8' NA 0.089 NA 0.1153 0.089 0.3541 sum LRF 0.2169 0.2832 0.2165 0.2855 0.2832 0.392 Chips 0.4382 0.2817 0.4391 0.2763 0.2817 0.025 2X8 price $373 $311 Net revenue $3,108,753 $3,110,141 31 Figure 4-1. Production distribution of 2x8-oriented and 2x10-oritented sawing patterns Based on the previous analysis, it is clear that the sawing pattern is a key factor in the mill operation and it is directly related to profitability. Mill managers should clearly identify the market direction beforehand, and then implement the corresponding sawing pattern. 4.2 Lumber price fluctuation Price has important effects in terms of production and marketing. It is directly linked to supply and demand of commodity products (Rewoldt et al., 1973). Since lumber is a type of commodity product, price plays a pivotal role in the sawmill operational decisions. Figure 4-2 shows the lumber price from the 4th quarter of 2006 to the 2nd quarter of 2011 (Council of Forest Industries, 2012). It illustrates that, with the US housing crash in 2008, the price experienced a significant decrease. The price dropped 30%-40% in the second half of the 2008. However, the industry has shown a trend of rebounding (Cross, 2011). Ebner and Grant (2011) claimed that the recovery of the forest sector 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 2x4 2x6 2x8 2x10 V o lu m e \/ M B F Product 2x8-oriented 2X10-oriented 32 could even contribute to Canadian exports hitting the pre-recession level in 2012. Figure 4-2. Quarterly lumber prices from 2007 to 2011 (Source: Council of Forest Industries, 2012) Therefore, two price fluctuation scenarios were applied to the model, assuming there is a \u00b120% change of price without any change in other parameters. -20% change represents the lumber price during the recession period; +20% change represents the price before recession and the price that can be reached in the future. Table 4-2 shows the lumber price, production and net revenue under three scenarios. Lumber production did not undergo significant change as the prices changed, but the net revenue underwent dramatic changes. In the 20% increase scenario, the sawmill can obtain an additional $8,576,137 in net revenue by only increasing lumber production by 651 MBF. A similar situation occurs with the 20% decrease scenario. After running the model, the production only 33 decreased approximately 10% from the original production level, but net revenue decreased dramatically, falling 268% from the baseline. Table 4-2. Lumber price, production and net revenue for three scenarios Baseline 20% increase 20% decrease 2x4 \/ MBF $273 $328 $218 2x6 \/ MBF $314 $377 $251 2x8 \/ MBF $311 $373 $249 2x10 \/ MBF $319 $383 $256 Net revenue $3,110,141 $11,686,278 -$5,238,221 Total lumber production \/MBF 141,229 141,880 126,689 As these results show, price is very sensitive for commodity products, so knowing the critical point of the lumber price in terms of earning or losing money is essential for the sawmill. A sensitivity analysis was conducted to examine this critical point for lumber price in the model. The sensitivity report shows that 92.6% to 92.7% of the original price is the critical point. Table 4-3 shows the price and net revenue at 92.6% of the original price and 92.7% of the original price. The table shows that if the price drops 0.1 %, from 92.7% to the 92.6% of the original price, the mill will suffer a $42,197.97 loss in net revenue. Considering the importance of price and the downturn in the lumber market, the decision of the MKRF to reduced harvesting by 60% in 2010 helped the sawmill operation avoid potential loss in the lumber market (UBC Malcolm Knapp Research Forest, 2011d). However, since the US market is recovering and the Chinese market is rising, it is more likely that there is future opportunity for the mill to gain profit (British Columbia Ministry of Jobs, Tourism and Innovation, 2011). Therefore, mill managers have to be aware of the current price and its trends to adjust the mill operation. 34 Moreover, knowing the critical point of the lumber price is also essential for mill operation. Since the price and cost information keeps changing, the critical point of price also changes consequently. Hence, the current critical point of lumber price is important information. Table 4-3. Net revenue comparison of 92.6% of the original price and 92.7% of the original price 92.6% of original price 92.7% of original price 2x4 - 8' $252.80 2x4 - 8' $253.07 2x6 - 8' $290.72 2x6 - 8' $291.03 2x8 - 8' $288.19 2x8 - 8' $288.50 2x10 - 8' $295.77 2x10 - 8' $296.09 Net revenue -$36174 Net revenue $6024 4.3 Limited mill working time Mill working time is directly linked to the labour cost, which constrains lumber production and therefore is a vital factor in the profit optimization process. Canada has one of the highest labour costs in the world, which poses challenges for many Canadian companies, especially small companies (Van Liemt, 1992). The sawmill in MKRF has a small capacity, so working time has to be taken into consideration in terms of general operation and cost-saving. In the previous analysis, the sawmill was scheduled running 4,600 hours in order to process as many logs as possible. In this limited mill working time scenario, the mill has 1 year to process those harvested logs. Generally the mill will shut down for 4 weeks within 1 year, so the mill operates about 48 weeks per year and 2 shifts per week. For 1 shift, a mill worker works 8 hours per day and 5 days per week. Therefore, the total mill working time is 8 hours 5 days 2 shifts 48 weeks = 3840 hours. The ratio of headsaw and trimmer productivity was re-adjusted to 1.3 because the available time for both of the machines changed. After running the model, no feasible answer could be obtained with a mill working time of 3840 hours. In order to explore the reason, 2 sensitivity analyses were conducted. One examined the 35 critical point for the working time that is feasible for the LP model; the other one removed the constraint on minimum production level of each period and kept the mill working hour as 3840 hours to explore the feasible minimum production level for each period. As for feasible mill working time, the sensitivity analysis showed that the mill can have positive net revenue only if the mill working time is greater than 4156 hours. The main reason for the model generating this number is the minimum production level constraint. In the original analysis, in order to have an even production flow, the assumption was made to produce 100,000 MBF lumber per period for the mill. Therefore, if the mill working time is less than 4156 hours, the mill will not be able to meet this requirement, so the LP model cannot provide a feasible result for the processing. Another sensitivity analysis was conducted to test the critical point for the minimum production level. It was necessary to assume that the mill working time is 3840 hours, and there is a change in the minimum reduction level. The sensitivity analysis indicates that if the minimum production level is less than 92000 MBF per period, the mill is able to maintain its production. The previous analyses for the mill working time illustrate that mill working time and minimum production level are linked closely. The mill manager has to determine the minimum production level carefully based on the projected mill working time, or vice versa. 4.4 Possible Improvements of Models Throughout this research, the series of models projected the volume of harvested trees, lumber production, mill working time and net revenue. However, the model has room for improvement. These possible improvements include combining the tree-to-log and forest estate models together; increasing the upper limit of log diameter of sawing pattern model and introducing a section for carbon credit consideration into the model. 4.4.1 Combine 2 LP Models In this study, two linear programming models, forest estate model and log-to-product model, 36 were built separately. However, the two models have similar structures and they both need Microsoft Excel Solver to run, so there may be a way to appropriately design an LP model that combines the two models together. There are two main reasons for this improvement. Primarily, one Excel spreadsheet is more efficient and more manageable for mill managers. Currently, the forest estate model must be run first, then the data output (available log volume for each period) has to be copied and pasted manually into the log-to-product model. There is more probability of error in this \u201ccopy-and-paste\u201d process. If the model can incorporate the two parts together, it is more user-friendly for a mill manager. Additionally, what the Solver does now is optimize the value for each separate model. However, an optimized answer for one part is not necessarily the best answer overall. If this situation happens, the mill manager may be misled by model outcomes and therefore the mill will suffer some unnecessary losses. Hence, if models can be consolidated, it will be more beneficial for the model users. 4.4.2 Improve Available Log Diameter Range of Sawing Pattern Model In the sawing pattern model, logs that are greater than 50cm in diameter encounter some design problems due to the inappropriate graphing of the log cross-section. The reason for this problem is the insufficient coordinates of the graph. Based on the size of the log and the product selected, some default coordinates are already embedded in the Excel spreadsheet so that the cross-section of a log and the products can be shown when the information is entered. Although an adjustment was used to generate the LRF for the study, it is expected to have some error compared to a full view design for sawing patterns. Therefore, more default coordinates are needed to be built into the model; however, currently there is a technical deficiency in this study so coordinates are not able to be set up. However, if the sawing pattern model is intended to be used by mill managers in reality, this problem should be fixed. 4.4.3 Introduce a Carbon Credit Section 37 With the increasing awareness of climate change issues and the establishment of formal carbon credit legislations, carbon credits are considered another important \u201cproduct\u201d from forests additional to traditional lumber production. British Columbia is leading in greenhouse gas reduction in Canada as it is the first province in Canada to establish carbon tax (Greig & Bull, 2009). Therefore, conserving forest to obtain carbon credits is a serious option for forest managers. As for the MKRF, some projects examining carbon credits for the forest are ongoing in the UBC Faculty of Forestry. Therefore, it is worth exploring some methods to incorporate a carbon section into the LP model, which will give the forest manager more choice. For example, constraints can be added to lower harvesting level, resulting in high growing stock and therefore revenue from carbon credits. However, more research is needed to be done in this field. 5. Conclusion This study provides a prototype decision support system to project forest operations and log processing in the Malcolm Knapp Research Forest. Actual forest area and sawmill specific parameters were not used for MKRF, but the system could be modified to make it suitable for the research forest. Growth and yield data were simulated by TIPSY, based on information collected in the field. Cost and revenue data were either derived from the market or defined by reasonable assumptions. Models were developed by Microsoft Excel and model simulations were conducted by the Microsoft Excel Solver add-in. The result shows that the mill can obtain $3,110,141 by producing 141,229 MBF of lumber and 298,818 m3 of chips. Additionally, three scenarios, 2x8-oriented sawing pattern, lumber price fluctuation and limited mill working time, were tested by changing data inputs to the model. The results indicated that market-preferred type of lumber, price trend and mill operation time are three important things of which mill managers need to know. Therefore, the mill manager must continually update and optimize the model. 38 6. Reference British Columbia Ministry of Forest and Range. (2005). OAF1 Project | Project Home Page. Ministry of Forests Home Page. Retrieved January 17, 2012, from http:\/\/www.for.gov.bc.ca\/hfp\/silviculture\/OAF1\/default.htm British Columbia Ministry of Jobs, Tourism and Innovation. (2011). B.C. sets yearly China lumber export record. Province of British Columbia News Archive. Retrieved March 15, 2012, from http:\/\/www2.news.gov.bc.ca\/news_releases_2009-2013\/2011JTI0121-001313.htm Clark, D., & Clark, D. (1999).Assessing the Growth of Tropical Rain Forest Trees: Issues for Forest Modeling and Management.Ecological Applications, 9(3), 981-997. 39 Council of Forest Industries. (2012). Softwood Lumber Indicators 2006 to 2010. Council of Forest Industries. Retrieved March 13, 2012, from www.cofi.org\/wp-content\/uploads\/2012\/01\/sla_indicators_2006-2010.pdf Cross, P. (2011). Canadian Economic Observer: Section 3: Feature article. Statistics Canada: Canada's national statistical agency \/ StatistiqueCanada :Organismestatistique national du Canada. Retrieved March 13, 2012, from http:\/\/www.statcan.gc.ca\/pub\/11-010-x\/2011009\/part-partie3-eng.htm Ebner, D., & Grant, T. (2011). Canadian exports forecast to hit prerecession levels in 2012. The Global and Mail. Retrieved March 13, 2012, from http:\/\/www.theglobeandmail.com\/report-on-business\/economy\/canadian-exports-forecast-to- hit-prerecession-levels-in-2012\/article2016485\/ Greig, M., & Bull, G. (2009). Carbon Management in British Columbia\u2019s Forests: Opportunities and Challenges. FORREX Series 24. Retrieved March 15, 2012, from http:\/\/www.forrex.org\/publications\/forrexseries\/fs24.pdf Grosenbaugh, L. (1963). Some suggestions for better sample-tree-measurement.Society of American. Foresters, Proceedings, 1, 36-42. Jadeja, J. (2007). Introduction and Literature Review.A model for increasing yield in sawmills based on detection of subsurface defects in canted logs using ground penetrating radar (GPR) system (pp. 1-16). Morgantown, W. Va.: [West Virginia University Libraries]. Lischke, H. (2001). New Developments in Forest Modeling: Convergence Between Applied and Theoretical Approaches. Natural Resource Modeling, 14(1), 71-102. Madison's Canadian Lumber Reporter. (2011). The source for Canadian and U.S. lumber and panel prices. Madison's - Canada's Leading National Lumber Publication. Retrieved February 25, 40 2012, from www.madisonsreport.com\/assets\/mclr121611.pdf Mardikar, Y. (2007). Introduction.Establishing baseline electrical energy consumption in wood processing sawmills a model based on energy analysis and diagnostics (pp. 1-21). Morgantown, W. Va.: [West Virginia University Libraries]. Pojar, J., & Stewart, A. (2007a). CWHdm - Coast Forest Region BEC.British Columbia Ministry of Forests. Retrieved March 7, 2012, from http:\/\/www.for.gov.bc.ca\/rco\/research\/eco\/bec_web\/docs\/CWHdm.htm Pojar, J., & Stewart, A. (2007b). CWHvm1 - Coast Forest Region BEC.British Columbia Ministry of Forests. Retrieved March 7, 2012, from http:\/\/www.for.gov.bc.ca\/rco\/research\/eco\/bec_web\/docs\/CWHvm1.htm Pojar, J., & Stewart, A. (2007c). CWHvm2 - Coast Forest Region BEC.British Columbia Ministry of Forests. Retrieved March 7, 2012, from http:\/\/www.for.gov.bc.ca\/rco\/research\/eco\/bec_web\/docs\/CWHvm2.htm Rewoldt, S., Scott, J., &Warshaw, M. (1973).Introduction to marketing management; text and cases (Rev. ed.). Homewood, Ill.: R. D. Irwin. TradingCharts.(2011). Lumber Historical Prices.TradingCharts. Retrieved February 12, 2012, from http:\/\/futures.tradingcharts.com\/historical\/LU\/2011\/0\/continuous.html UBC Malcolm Knapp Research Forest. (2011a). Location and Ecology | Malcolm Knapp Research Forest. Home | Malcolm Knapp Research Forest. Retrieved March 20, 2012, from http:\/\/www.mkrf.forestry.ubc.ca\/about\/location-and-ecology\/ UBC Malcolm Knapp Research Forest. (2011b). Malcolm Knapp Research Forest: About Us. Malcolm Knapp Research Forest. Retrieved March 13, 2012, from http:\/\/www.mkrf.forestry.ubc.ca\/about\/ 41 UBC Malcolm Knapp Research Forest. (2011c). Malcolm K\/napp Research Forest: Operations. Malcolm Knapp Research Forest. Retrieved March 13, 2012, from http:\/\/www.mkrf.forestry.ubc.ca\/operations\/ UBC Malcolm Knapp Research Forest. (2011d). 2010 Annual Report.Malcolm Knapp Research Forest. Retrieved March 13, 2012, from http:\/\/www.mkrf.forestry.ubc.ca\/2011\/11\/2010\/ Van Liemt, G. (1992). Economic Globalization: Labour Options and Business Strategies in High Labour Cost Countries;.International Labour Review, 131(4-5), 453-470. Vladimirov, I., &Chudnenko, A. (2009).Multilevel Modeling of the Forest Resource Dynamics.Mathematical Modelling of Natural Phenomena, 4(5), 72-88. 7. Appendices 7.1 Appendix A: Forest Estate Model Appendix A (Figure 7-1 to Figure 7-4) show the structure of the forest estate model. The forest estate model is a linear-programming based model, which is used to project the volume of logs that need to be harvested for the processing in this study. The assumptions and structure of the model were described in the 2.3.1 section of this article. The numbers in the matrix are the optimized solutions for operation. 42 7.1.1 Stand One 43 7.1.2 Stand Two 44 7.1.3 Stand Three 45 7.1.4 Harvesting, Inventory and Result 46 7.2 Appendix B: Sawing Patterns for Each Type of Log Appendix B (Figure 7-5 to Figure 7-15) illustrates the different sawing patterns used in the Sawing Pattern Model, referred to in 2.3.2 section of this essay. Appendix B also contains the Lumber Recovery Factor for logs ranging from 15cm to 55cm in the 2x10-oriented pattern and different sawing patterns for 35cm log and 45cm log in the 2x8-oriented pattern. However, due to the design limitation of the sawing pattern model, logs greater than 50cm could not be shown in the cross-section appropriately. Therefore, an adjustment was used, so that only half of the cross-section was filled, in the centre cant, then the volume of that lumber was doubled and the LRF was calculated. 47 43 7.2.1 2x10-oriented Lumber Recovery Factor 7.2.1.1 15cm log Figure 7-5. 2x10-oriented sawing pattern and LRF for 15cm log 44 7.2.1.2 20cm log Figure 7-6. 2x10-oriented sawing pattern and LRF for 20cm log 45 7.2.1.3 25cm log Figure 7-7. 2x10-oriented sawing pattern and LRF for 25cm log 46 7.2.1.4 30cm log Figure 7-8. 2x10-oriented sawing pattern and LRF for 30cm log 47 7.2.1.5 35cm log Figure 7-9. 2x10-oriented sawing pattern and LRF for 35cm log 48 7.2.1.6 40cm log Figure 7-10. 2x10-oriented sawing pattern and LRF for 40cm log 49 7.2.1.7 45cm log Figure 7-11. 2x10-oriented sawing pattern and LRF for 45cm log 50 7.2.1.8 50cm log Adjustment: there are 5 2x10 lumber in the centre cant and 4 2x10 lumber in the side board, which is 138.75 board feet. It was tested that 4 more 2x10 can be filled into the upper part of the centre cant. Therefore, the volume of lumber from this log is 138.75+ 4 15.42 = 200.43 board feet. LRF (MBF\/m3) = = 0.3782 Figure 7-12. 2x10-oriented sawing pattern and LRF for 50cm log 51 7.2.1.9 55cm log Adjustment: there are 6 2x10 lumber in the centre cant and 4 2x10 lumber in the side board, which is 154.17 board feet. It was tested that 5 more 2x10 can be filled into the upper part of the centre cant. Therefore, the volume of lumber from this log is 138.75+ 5 15.42 = 231.27 board feet. LRF (MBF\/m3) = = 0.3614 Figure 7-13. 2x10-oriented sawing pattern and LRF for 55cm log 52 7.2.2 2x8-oriented Lumber Recovery Factor Since logs less than 35cm in diameter are too small to produce 2x8 lumber; logs greater than 50cm are more suitable in producing 2x10 lumber and the sawing pattern for 40cm log is well-designed; only 35cm log and 45cm log are subject to change. 7.2.2.1 35cm log Figure 7-14. 2x8-oriented sawing pattern and LRF for 35cm log 53 7.2.2.2 45cm log Figure 7-15. 2x8-oriented sawing pattern and LRF for 55cm log 54 7.3 Appendix C: Log-to-product Model Appendix C shows the structure of the log-to-product LP model. This model is also a linear-programming based model, and is used to simulate the volume of logs that need to be used for processing, lumber production, machine working time and net revenue in this study. The assumptions and structure of the model were described in section 2.3.3 of this essay. The numbers in the ANSWER row are the optimized solution. 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