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The influence of cut-block size and adjacency rules on harvest levels and road networks Finn, Steven Terence 1994

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The Influence Of Cut-Block Size And AdjacencyRules On Harvest Levels And Road NetworksbySteven Terence FinnB.S.F., The University Of British Columbia, 1987A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF FORESTRYinTHE FACULTY OF GRADUATE STUDIESDepartment of ForestryWe accept this thesis as conformingto the required St dariTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1994© Steven Terence Finn, 1994Signature(s) removed to protect privacyIn presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)____________________Department of FO,ESTRYThe University of British ColumbiaVancouver, CanadaDate 5DE-6 (2/88)Signature(s) removed to protect privacy11ABSTRACTPrevious harvesting practices in coastal British Columbia generally favouredlarge opening sizes with relatively short regeneration periods before adjacent blockswere removed. These large openings were both criticized for being aestheticallyunpleasing and for not providing a proper age class distribution for wildlife habitat. Tocombat these problems, smaller opening sizes with longer times between harvesting ofadjacent blocks have been proposed.It is believed that smaller opening sizes and more rigid adjacency constraints willimpact cutting levels and harvesting and transportation costs. An area-basedscheduling model was developed between 1989 and 1991 which quantifies theseimpacts and provides a better understanding of the harvest levels and costs associatedwith different cut block sizes and adjacency constraints.The effect on the Annual Allowable Cut (AAC) due to block size and exclusionperiod showed that the delay period had a greater effect on the AAC than did blocksize. As the block size decreased while keeping the delay period constant, thereduction in AAC ranged from 6.0% to 23.5%.As the delay or exclusion period increased, adjacency constraints limited thenumber of blocks available for harvest and therefore reduced the harvest volume.Increasing the delay period from I to 2 and from I to 3 caused volumes to drop anaverage of 18.6% and 40% respectively. Increasing the delay period and decreasingthe block size resulted in large reductions in harvest volume of up to 50%.Another effect of increasing the delay period and decreasing the block size isthat a large number of blocks may never be harvested. Values ranged from 6.8% to43.8% of blocks not eligible for harvesting.A stumpage calculation showed that there is a drastic difference in the amount ofstumpage payable when comparing the different sized blocks and adjacencyrequirements. Values ranged from $119.7 million to $52.8 million, a reduction of nearly$67 million as the block size was decreased and the adjacency requirementsincreased.111TABLE OF CONTENTSABSTRACT iiLIST OF TABLES ivLIST OF FIGURES VACKNOWLEDGEMENTS viINTRODUCTION IPROBLEM BACKGROUND IOBJECTIVES ILITERATURE REVIEW 2LITERATURE RELATING TO STRATA BASED PLANS 3LITERATURE RELATING TO AREA BASED PLANS 5METHODOLOGY 6DATA FORMULATION AND COMPILATION 6MCIP FORMULATION I INFORMATION REQUIRED 8THE RANDOM SEARCH TECHNIQUE - BASIC STEPS 12RESULTS AND DISCUSSION 14PROGRESSIVE CLEAR CUT SOLUTION 14UNCONSTRAINED ROAD SOLUTIONS 15CONSTRAINED ROAD SOLUTION 19CONSTRAINED VERSUS UNCONSTRAINED SOLUTION 23THE EFFECT ON THE AAC DUE TO BLOCK SIZE AND EXCLUSION PERIOD 25ECONOMIC ANALYSIS 29IMPACT ON STUMPAGE 35CONCLUSION 37BIBLIOGRAPHY 40APPENDIX I. DESCRIPTION OF ANALYSIS AREAS 42APPENDIX 2. ANALYSIS AREA MAP I ZONE MAP 45APPENDIX 3. DBASE PROGRAM TO MAKE TABLES OF BLOCK VOLUMES 48APPENDIX 4. BLOCK LAYOUT AND ROAD NETWORKS BY BLOCK SIZE 52APPENDIX 5. INPUT FILE EXAMPLES 56APPENDIX 6. MCIP FLOW CHART 70APPENDIX 7. MAIN PROGRAM FILE 72APPENDIX 8. OUTPUT FILE EXAMPLES 94APPENDIX 9. TYPICAL PROGRAM SOLUTIONS 98ivLIST OF TABLESTable 1: Summary Of Files Used In The MCIP Model 9Table 2: Zone Number And Earliest Possible Entry 13Table 3: Average Harvest Volumes And Percent Reductions For TheUnconstrained Road Construction Solutions 16Table 4: Average Harvest Volumes And Percent Reductions For TheConstrained Road Construction Solutions 19Table 5: Difference In Volumes Harvested Between The ConstrainedAnd Unconstrained Solutions 23Table 6: Total Amount Of Road Constructed (In Kilometers) ForBlock Size And Delay Period Combinations 24Table 7: Percentage Of Blocks Not Harvested During The Planning Period 26Table 8: Range Of Road Construction, Hauling And MaintenanceCosts Per Cubic Meter Harvested By Block Size And Delay Period 29Table 9: Range Of Tree To Truck Costs Per Cubic Meter By BlockSize And Delay Period 30Table 10: Range Of Total Delivered Cost Of Wood ($1M3) By BlockSize And Delay Period 30Table 11: Range Of Operating Costs ($1M3) By Block Size And Delay Period 35Table 12: Range Of Indicated Stumpage ($1M3) By Block Size AndDelay Period 36Table 13: Range Of Stumpage Revenues (in millions of $) By BlockSize And Delay Period 37VLIST OF FIGURESFigure 1: Road Construction Schedule For The Progressive Clear-Cut Solution 15Figure 2: Road Maintenance Schedule For The Progressive Clear-Cut Solution 15Figure 3: Road Construction Schedule For The Unconstrained RoadSolution - I Decade Exclusion Period 16Figure 4: Road Construction Schedule For The Unconstrained RoadSolution -2 Decade Exclusion Period 17Figure 5: Road Construction Schedule For The Unconstrained RoadSolution -3 Decade Exclusion Period 17Figure 6: Road Maintenance Schedule For The Unconstrained RoadSolution - I Decade Exclusion Period 18Figure 7: Road Maintenance Schedule For The Unconstrained RoadSolution -2 Decade Exclusion Period 18Figure 8: Road Maintenance Schedule For The Unconstrained RoadSolution - 3 Decade Exclusion Period 19Figure 9: Road Construction Schedule For The Constrained RoadSolution - I Decade Exclusion Period 20Figure 10: Road Construction Schedule For The Constrained RoadSolution -2 Decade Exclusion Period 20Figure 11: Road Construction Schedule For The Constrained RoadSolution - 3 Decade Exclusion Period 21Figure 12: Road Maintenance Schedule For The Constrained RoadSolution - I Decade Exclusion Period 21Figure 13: Road Maintenance Schedule For The Constrained RoadSolution -2 Decade Exclusion Period 22Figure 14: Road Maintenance Schedule For The Constrained RoadSolution - 3 Decade Exclusion Period 22Figure 15: Total Delivered Cost By Decade -80 ha Blocks, IDecade Exclusion Period 31Figure 16: Total Delivered Cost By Decade - 80 ha Blocks, 2Decade Exclusion Period 31Figure 17: Total Delivered Cost By Decade - 80 ha Blocks, 3Decade Exclusion Period 32Figure 18: Total Delivered Cost By Decade -40 ha Blocks, IDecade Exclusion Period 32Figure 19: Total Delivered Cost By Decade -40 ha Blocks, 2Decade Exclusion Period 33Figure 20: Total Delivered Cost By Decade -40 ha Blocks, 3Decade Exclusion Period 33Figure 21: Total Delivered Cost By Decade -20 ha Blocks, IDecade Exclusion Period 34Figure 22: Total Delivered Cost By Decade -20 ha Blocks, 2Decade Exclusion Period 34Figure 23: Total Delivered Cost By Decade -20 ha Blocks, 3Decade Exclusion Period 35viACKNOWLEDGEMENTSI would like to thank the following people for their help with this thesis. First, Iwould like to thank Dr. John Nelson of the Faculty of Forestry at UBC for his initial topicsuggestion, computer programming skills, proof reading of drafts and finally hisguidance and support throughout my graduate work at UBC. Second, Ian Thomas andDave Daust of the UBC Harvest Research Group were of great assistance with theirskills in computers and Geographical Information Systems.Appreciation is also extended to the Staff and Management of the RenewableResources Technology at the British Columbia Institute of Technology for theircomputer and educational leave support.Finally, to my wife and children, I thank you for your never ending patience andsupport.INTRODUCTIONPROBLEM BACKGROUNDPrevious harvesting practices in coastal British Columbia generally favouredlarge opening sizes with relatively short regeneration (“free to grow”) periods beforeadjacent blocks were removed. Sometimes viewed as a progressive clear-cut, theselarge openings were criticized for being aesthetically unpleasing and for not providing aproper age class distribution for wildlife habitat. With the growing importance ofenvironmental and other non-timber issues, it is likely that todays harvesting practiceswill have to be changed or modified to reflect these concerns. In some areas this maymean a switch to an alternative to clear-cutting, such as selection cutting. However, inmany areas of the coast selection cutting is not viable from a silvicultural prospective.Therefore, clear-cutting will likely continue but with smaller opening sizes and withlonger times between harvesting of adjacent blocks.OBJECTIVESIt is believed that smaller opening sizes and more rigid adjacency constraints willimpact cutting levels and harvesting and transportation costs. An area-basedscheduling model was developed which quantifies these impacts and provides a betterunderstanding of the harvest levels and costs associated with different cut block sizesand adjacency constraints.Using a case study approach, this paper will quantify the effect on the AnnualAllowable Cut (AAC) due to the reduction of block size in conjunction with more rigidadjacency constraints when:1) there is no limit on road construction and;2) there is a road construction limit.-2-Specifically, this paper will:1) compare the constrained and unconstrained road budget model solutions withregard to volume harvested and road construction and maintenance schedules.2) determine the effect on the AAC due to block size and exclusion period through acomparison of volume harvested;3) quantify the total delivered wood cost for combinations of block and exclusionperiods and;4) determine the impact of smaller cut-blocks on stumpage revenues.LITERATURE REVIEWForest planning models can be segregated into two main categories according tothe length of the planning horizon and the level of detail required to address resourceallocation issues (Nelson and Brodie, 1990). First, there are the long-range strategic orstrata based plans that look ahead over one or more rotations. Strata based plans giveminimal area resolution with no operational detail. Second, there are the tactical orarea based plans that cover a shorter planning horizon than those of the strata basedplans. Area based plans are area specific with operational detail.LITERATURE RELATING TO STRATA BASED PLANSThe most widely used technique for timber harvest scheduling in the UnitedStates is linear programming (LP) (O’Hara et al., 1989). One of the earliest modelsdeveloped was Timber RAM (Resource Allocation Model) which did not include anyspatial considerations. This was followed by other models such as MUSYC (MultipleUse Sustained Yield Calculator) and FORPLAN (Forest Planning Model) whichattempted to deal more effectively with site-specific environmental questions.-3-Armel (1986) noted that one of the most frequently asked questions by forestmanagers concerns how the allocations represented by the standard, strata basedFORPLAN solution, in which homogeneous forest units are aggregated, can beimplemented within a heterogeneous area represented by a given parcel of nationalforest land. Complications result from the specific placement and management ofhabitats for wildlife such as spotted owls or pileated woodpeckers, and from the need toconsider harvest adjacency constraints. The standard FORPLAN solution does notconsider these factors. Approaching the problem by the means of the “coordinatedallocation choices” option in FORPLAN version II does not lead to a satisfactorysolution to this problem because representation of the problem at the harvest-unit levelproduces a problem of unmanageable size.O’Hara et al. (1989) state that a problem shared by all LP approaches to solvingspatially constrained timber harvest scheduling problem is that the solutions are notintegral. Commonly units are split to meet the spatial constraints. In a mathematicalsense, the constraints are met, but in practical terms, field implementation of thesolution is not possible unless the solution is integral.Bare et al. (1984) note that explicit recognition of spatial relationships and theconsequent constraints on timber harvest scheduling are important for a number ofreasons. First, management for multiple use requires that managers know thegeographic location of specific outputs and how much of the output to produce in agiven time period. Second, failure to recognize spatial relationships can also result inenvironmental problems. Where a buffer strip is to be retained, such as aroundstreams, lakes, recreation areas, roads, or wilderness areas, or where the buffer strip isnecessary for regeneration purposes, the spatial relationship between the timberscheduled for harvest and the adjacent stand or feature needs to be recognized. Third,the spatial relationship between harvest units must be recognized so that specificwildlife habitat objectives, such as maintenance of adequate degrees of habitatdiversity can be met.-4-The lack of spatial resolution and site specific data is the major disadvantage ofstrata based models (Nelson and Brodie, 1990). They further state that the principaladvantage of strata based models is that individual timber stands with similar physicaland economic characteristics can be aggregated, making forest wide planning a taskthat is computationally feasible. Therefore these models are only adequate for settingstrategic harvest goals within a temporal context.LITERATURE RELATING TO AREA BASED PLANSIn an area based plan individual harvest units (blocks) and road systems arespecified creating the ability to define a spatially feasible solution.Since area based plans require integer solutions, these problems are generallysolved using mixed integer programming (MIP) techniques (Nelson, 1988). Integervariables are needed to specify if a road is or is not built, and to specify if a harvest unitis or is not cut. This alleviates the problem of splitting harvest units between timeperiods. However, due to these integer restrictions only very small problems can besolved using MIP.As an alternative to MIP and simulation, a random search algorithm calledMonte-Carlo Integer Programming (MCIP) has been used to generate feasible solutionsto area based problems (Nelson and Brodie 1990). According to Clements et al. (1990),“a typical MCIP algorithm begins by generating random solutions to a mixed-integerprogramming (MIP) problem. These solutions are tested against a set of spatial andtemporal constraints, and solutions meeting all of the constraints are designatedfeasible. Each feasible solution is evaluated relative to an objective function. After alarge number feasible solutions have been identified, the solutions best satisfying theobjective function are selected for further analysis.” Unlike MIP, MCIP does notguarantee optimality, however, it is capable of quickly generating feasible solutions tothe complex integer problems associated with planning. Nelson and Brodie (1990) were-5-able to find a MCIP solution with a objective function solution that was within 3% of thetrue optimum. They concluded that by using MCIP, it is relatively easy to find severalsolutions with values that lie within 10% of the optimum.METHODOLOGYA 4500-hectare subunit of MacMillan Bloedel’s Stillwater Logging Division wasused as a case study area. This study is broken into two major components, the firstbeing the data formulation and compilation and the second being the MCIP analysis.DATA FORMULATION AND COMPILATIONNelson (1988) utilized the same study area and therefore most of the inventorydata used were taken from his paper. There are 109 individual stands grouped into 62analysis areas (AA’s). An analysis area is a timber stratum based on zone, loggingsystem, site, species and age. See Appendix I and 2, pages 42 and 45 for a completedescription of the analysis areas and an analysis area map.Using a 1:20,000 scale map of the study area in conjunction with the analysisareas, cut blocks of 80-hectares were formulated using the following guidelines:- average yarding distance of 200-m.,- maximum yarding distance of 250-rn.,- blocks to be made up of similar age classes.The 80 ha. blocks were split in half to make 40 ha. blocks. The 40 ha. blockswere subsequently split in half to make 20 ha. blocks. The blocks were split so that thesame logging system, and the same main roads could be used in all cases. The resultswere the formulation of forty-eight 80 ha. blocks, ninety-six 40 ha. blocks and onehundred ninety-two 20 ha. blocks. (Block layout and road network maps are included inAppendix 4, page 52). The blocks were then input into a Geographic Information-6-System (GIS). GIS processing was carried out with the result being themes that givethe total area of each block and the area of each analysis area within the block.A stand growth model, Stand Projection System (SPS), was used to generatetimber volumes by analysis area. These were then input into a database file and a GIStheme was created to produce the volume per hectare by analysis area by decade.This process was done for both the existing stands and for the projected regeneratedstands. The block theme was overlaid onto the yield theme to generate the area andvolume per hectare per decade for each block.An small dBase program (Appendix 3, page 48) was then written that produced,for each block size, a table of existing and regenerated volumes per block per decade.At the same time as the blocks were formulated, a road network was created(Appendix 4, page 52). As previously stated, the same main roads were used for allthree block sizes. For each block, the road needed to log that particular block wastracked by noting the road links required to access that block. While the total length ofthe road network remained constant, shorter and more numerous road links wereneeded as the block size decreased. The number of road links required were 162, 185and 292 for the 80, 40 and 20 ha. blocks respectively. For a limited number of blockssecondary roads were also required. Secondary roads are defined as roads that areneeded only to harvest the block that contained them.-7-MCIP FORMULATION/INFORMATION REQUIREDBLOCK DATAFor each block, the area, current age, zone and adjacent block numbers arerequired. The area is calculated from the GIS data processing. The existing stand ageis an average ,to the closest 10 years, of the stands that make up the block. The entireforest was broken into 8 zones to help the block selection process (Appendix 2, page45). Each block, therefore, has a zone number. For each block the adjacent blockswere identified. An adjacent block is a cut block whose boundary touches the selectedcut block, regardless of the length of common boundary. All the block data wereincorporated into a file called blockdat.txt. For examples of all the input files used, seeAppendix 5, page 56.EXISTING AND REGENERATION BLOCK VOLUME TABLEThe total existing and regeneration volume per block per period wasincorporated into files called exvoltab.txt and rgvoltab.txt, respectively.EXISTING AND REGENERATION BLOCK REVENUE TABLEFor each block the estimated logging cost was calculated using the formuladerived by Nawitka Resource Consultants (1987):LOGGING COST ($/M3) = -0.3316(age) + 43.482-8-The above formula was derived for a site of average logging difficulty. As thestands covered such a wide variety of topography, each block was assigned a loggingdifficulty of high, medium or low based on topography and expected logging difficulty.The logging cost formula was revised to reflect the high and low difficulty classes byadding or subtracting $11m3 respectively. The block revenue tables were incorporatedinto the files exrevtab.txt and rgrevtab.txt.MAIN ROAD ACCESSThe road links required to access a particular block were incorporated into a filecalled mraccess.txt. Also included in this file was the transportation cost for eachparticular block. The transportation cost formula used was (Hackett, 1990):TRANS COST ($1M3) = 2.971 + .0575(average weighted haul distance (oneway))The haul distance for each block was calculated from the center of each block tothe main access point of the valley.ROAD LENGTHS AND CONSTRUCTION COSTSFor each main and secondary road to be constructed, the roads length and totalconstruction cost were calculated and saved in a file called mrlinks.txt or srlinks.txt.Three categories of road construction cost were used, with the criteria being based onthe topography. The estimated road costs were:LOW $ 30, 000/kmMEDIUM $ 45,000/kmHIGH $60,000/km-9-Table 1: Summary of files used in the MCIP modelFile Name Contentsblockdat.txt area, existing stand age, zone andadjacent block numbers of eachblockconstrai.txt sets the parameters for use withinthe harvest planner (see below)exrevtab.txt estimated logging cost per blockper period for existing standsexvoltab.txt existing volume per block perperiodrgrevtab.txt estimated logging cost per blockper period for regenerated standsrgvoltab.txt regenerated volume per block perperiodmraccess.txt transportation costs and road linksrequired to access each blockmrlinks.txt main road lengths and constructioncostssrlinks.txt secondary road lengths andconstruction costs-10-CONSTRAINTSThe constraint file (constraints.txt) is the file that sets the parameters for usewithin the harvest planner. The information required to run the program is:HABITAT DELAY - the number of periods (decades) required to pass before theadjacent block can be harvested.MAXIMUM NUMBER OF BLOCKS - either 48, 96 or 192 depending on the block sizebeing modelled.MAXIMUM NUMBER OF PERIODS - the total length of the modelling period in decades(i.e. planning horizon).MAXIMUM NUMBER OF ZONES - set at 8 for this model.MINIMUM AGE - the minimum harvest age, in decades, for an existing or regenerationstand.MAINTENANCE COST - the maintenance cost per meter for an previously constructedroad. This was set at $5100 per kilometer per year (Hackett,1990) or $51 per meter per period.MAXIMUM ROAD - the maximum number of kilometers of road that can be constructedper period.CUT I - the minimum volume that must be harvested in period 1.CUT 2 - the minimum volume that must be harvested in period 2.MINIMUM VOLUME - the minimum volume that must be harvested in any period otherthan periods I and 2.MAXIMUM VOLUME - the maximum volume per period that can be harvested in anyperiod.MINIMUM COST - the minimum net revenue per period.MAXIMUM COST - the maximum cost per period.MAXIMUM GRADE COST - the maximum road construction and maintenance budgetper period.—11 —ZONE AND PERIOD OF FIRST ENTRY - the period of first entry into each particularzone. To prevent the early harvesting of cut-blocks at the far reaches of the roadnetwork, the forest was divided into 8 zones with each zone assigned a first entry time.(See appendix 2 page 45 for a map of the zones).The objective function maximized the total volume produced over the planninghorizon, subject to the constraints outlined above.-12-THE RANDOM SEARCH TECHNIQUE - BASIC STEPSAs the planning problems had approximately 2000 - 5000 integer variables,depending on block size, direct optimization techniques were impractical. As analternative, a random search technique was used to find feasible solutions. Thismethod is displayed on a flow chart in Appendix 6 ,page 70. The basic steps used bythis technique are:1) Set the planning period to 1.2) All the blocks that are available for harvest in this period are assigned a random 0/1variable. I identifies blocks that can harvested in this period and 0 identifies blocks notto be harvested.3) Let count be a variable to identify the number of attempts at finding a feasiblesolution for this period. Set count = count +1.4) Queue the list of blocks available for harvest in step 2 according to decreasingaccessibility. The blocks with the minimum number of main road links will be at thehead of the queue.5) Randomly select a block near the front of the queue and add its volume to the periodharvest. The adjacent blocks to the selected block are made unavailable for harvestuntil the adjacency delay age has been met. The next available block is then selectedand the process continues until the minimum harvest level in that period is met. If theminimum harvest level cannot be satisfied from the available blocks, return to the startof step 2 and try another random block selection. If the count variable exceeds 20, it isunlikely a solution exists and the harvest constraints must be reduced.6) The road links needed to provide access to the harvested blocks are identified. Theroad links are checked to determine whether or not they have been constructedpreviously. If so they are assigned a maintenance cost. If not the road links areconstructed, and the grade construction cost is calculated for this period.-13-7) The total cost for each period is calculated by summing the main and secondaryroad construction costs and the maintenance costs from each block harvested.8) The constraints are checked. If the solution does not meet the constraints, return tostep 3.9) Adjust the block ages for harvest and growth and increment the planning period by 1.If the planning period is greater than the planning horizon, stop, otherwise go to step 2.Preliminary program runs using the same constraints were executed todetermine the suitable length of time for the program to complete a successful run. Itwas decided that runs should be kept to a maximum of 40, 60 and 90 seconds persolution for the 80, 40 and 20 hectare plans respectively. These were deemedreasonable times for a 80386 computer running at 20 Mhz. Refer to Appendix 7, page72 for the main program file.Many combinations of zones and entry times are possible and trial runs werecarried out to provide a solution that seemed to maximize the annual allowable cut.Once identified, this zone/entry time frame was kept constant throughout the rest of thecomputer runs.Table 2: Zone number and earliest possible entryzone I entry time (period)I I I2 I 53 I I4 I I5 I I6 I 27 I 18 I 4The minimum and maximum AAC were steadily increased until a set of 10feasible solutions could not be found within the pre-determined time limits. Generally,-14-the minimum AAC was found by increasing the minimum AAC while keeping themaximum AAC large. When the minimum AAC was bounded, the maximum AAC wasreduced in the direction of the minimum AAC until the solution was no longer feasibledue to time constraints or no feasible solutions existed. See Appendix 8, page 94 fortypical program solutions.Feasible solutions were saved to files and their minimum and maximum AACconstraints, solution time, average AAC, AAC standard deviation and AAC range wererecorded. The ‘best’ solution was determined as the solution with: 1) the smallestdifference between the minimum and maximum AAC; 2) the largest average AAC and3) the smallest standard deviation. Once the ‘best’ solution was identified, 50 solutionsusing the same constraints were generated. Finally, these 50 solutions were averagedfor comparison purposes. Because MCIP is a random procedure, it was felt that theaverage of 50 solutions would provide a better bench mark than only the best solution.While the average is useful for evaluating trends, it does not represent a solution that ismapable. In hindsight, perhaps acceptance of the best solution is a preferred method.See Appendix 9, page 98 for typical block solutions by block size and delay periodcombinations.Initially, no constraints were placed on the length of road that could beconstructed during any one period. For comparison, the problem was re-solved with anadditional constraint that limited road construction to 25 kilometers per period (ie 2.5km. per year).RESULTS AND DISCUSSIONPROGRESSIVE CLEAR CUT SOLUTIONTo provide a datum, a progressive clear cut solution was generated using the 80ha blocks. The blocks were progressively harvested from the beginning of the road-15-network without regard for adjacency constraint rules. For this particular blockarrangement, the solution generated set the volume harvested per decade at 360 000m3.Figures 1 and 2 show the road construction and maintenance schedules for theprogressive clear-cut solution.ROAD CONSTRUCTIONPROGRESSIVE CLEARCUT70K6°Ho4030DECADEFigure 1: Road construction schedule for the progressive clear-cut solutionROAD MAINTENANCEPROGRESSIVE CLEARCUT70S101 2 3 4 5 6 7 8 9 10DECADEFigure 2: Road maintenance schedules for the progressive clear-cut solution-16-UNCONSTRAINED ROAD SOLUTIONSTable 3 summarizes the harvest volume by block size and exclusion period forthe unconstrained road solutions.Figures 3, 4 and 5 show the road construction schedules for each block size andexclusion period combination. Figures 6, 7 and 8 show the road maintenanceschedules for each block size and exclusion period combination.ROAD CONSTRUCTION NO LIMITI DECADE EXCLUSION PERIODL0METERSDECADE-- 8OHA -•- 4OHA -+- 2OHAFigure 3: Road construction schedule for unconstrained road solution - I decadeconstruction solutionsTable 3: Average harvest volumes and percent reductions for the unconstrained road80 ha blocks 40 ha blocks% reduction from % reduction fromdelay period harvest volume clear cut delay I harvest volume clear cut delayl1 339910 5.5 0 332460 7.7 02 269963 25 21 264830 26 203 218621 39 36 192608 46 42.harvest volume33467324122317149720 ha blocks% reduction fromclear cut delay I7.0 033 2852 49The percent reduction is calculated to :1) compare each solution to the progressive clear cut solution; and 2) compare the effect ofncreasing the exclusion period while maintaining the same blocksize.1 2 3 4 5 6 7 8 9 10exclusion periodL0METERS-17-ROAD CONSTRUCTION NO LIMIT2 DECADE EXCLUSION PERIODDECADE-- 8OHA --- 4OHAFigure 4: Road construction schedule for unconstrained road solution - 2 decadeexclusion period70ROAD CONSTRUCTION NO LIMIT3 DECADE EXCLUSION PERIOD60502 3 4 5DECADE6 7 8 9 1080 HA I 40 HA -+- 20 HAFigure 5: Road construction schedule for the unconstrained road solution - 3 decadeexclusion period2 3 4 5 6 7 8 9 10-- 2OHAL0METERS40302010-18-ROAD MAINTENANCE NO LIMITI DECADE EXCLUSION PERIOD70K60—..!30E20RS 10n I1 2 3 4 5 6 7 8 9 10DECADE—- 8OHA -- 4OHA -+- 2OHAFigure 6: Road maintenance schedule for the unconstrained road solution - 1 decadeexclusion periodROAD MAINTENANCE NO LIMIT2 DECADE EXCLUSION PERIOD70K 60S 102 3 4 5 6 7 8 9 10DECADE80 HA 40 HA + 20 HAFigure 7: Road maintenance schedule for the unconstrained road solution -2 decadeexclusion period-19-ROAD MAINTENANCE NO LIMIT3 DECADE EXCLUSION PERIOD70K60S 100 I I I I I1 2 3 4 5 6 7 8 9 10DECADE-- 8OHA -- 4OHA -- 2OHAFigure 8: Road maintenance schedule for the unconstrained road solution -3 decadeexclusion periodCONSTRAINED ROAD SOLUTIONSTable 4 summarizes the harvest volume by block size and exclusion period forthe constrained road solutions.Table 4: Average harvest volumes and percent reductions for the constrained roadconstruction solutions80 ha blocks 40 ha blocks 20 ha blocks% reduction fromdelay period harvest volume clear cut delay I harvest volume clear cut delayl harvest volume clear cut delay 11 340691 5.4 0 326556 9.3 0 321402 11 02 276952 23 19 271697 24 17 255928 29 203 221062 39 35 196498 45 40 179044 50 44The percent reduction Is calculated to :1) compare each solution to the progressive clear cut solution; and 2)compare the effect ofincreasing the exclusion period while maintaining the same block size.-20-Figures 9, 10 and 11 show the road construction schedules for each block sizeand exclusion period combination. Figures 12, 13 and 14 show the road maintenanceschedules for each block size and exclusion period combination.ROAD CONSTRUCTION LIMITEDI DECADE EXCLUSION PERIOD701<60iHo4030__________I56789DECADE-- 80 HA -- 40 HA -+- 20 HAFigure 9: Road construction schedule for the constrained road solution - I decadeexclusion periodROAD CONSTRUCTION LIMITED2 DECADE EXCLUSION PERIOD701(60Ho40E 30I____DECADE-- 80 HA -- 40 HA —+- 20 HAFigure 10: Road construction schedule for the constrained road solution - 2 decadeexclusion period-21-ROAD CONSTRUCTION LIMITED3 DECADE EXCLUSION PERIOD-- 80 HA -a- 40 HA -+- 20 HAFigure 11: Road construction schedule for the constrained road solution - 3 decadeexclusion periodK60L0METERSROAD MAINTENANCE LIMITEDI DECADE EXCLUSION PERIOD-- 8OHA -a- 4OHA -+- 2OHAFigure 12: Road maintenance schedule for the constrained road solution - I decade70605040302010L0METERS1 2 3 4 5 6 7 8 9 10DECADE702 3 4DECADE5 6 7 8 9 10exclusion oeriod-22-ROAD MAINTENANCE LIMITED2 DECADE EXCLUSION PEROD70MFFFZEEEES 10CI I1 2 3 4 5 6 7 8 9 10DECADE-- 80 HA —- 40 HA +- 20 HAFigure 13: Road maintenance schedule for the constrained road solution -2 decadeexclusion periodROAD MAINTENANCE LIMITED3 DECADE EXCLUSION PERIOD70K 60S 100 I I I1 2 3 4 5 6 7 8 9 10DECADE—s- 80 HA —- 40 HA -4- 20 HAFigure 14: Road maintenance schedule for the constrained road solution - 3 decadeexclusion period-23-CONSTRAINED VERSUS UNCONSTRAINED SOLUTIONSComparison between Tables 3 and 4 shows that limiting the amount of roadconstruction has very little effect on the overall periodic harvest volume. The differencebetween the volumes harvested was a low of 0.2 % (delay 1, 80 ha. blocks) to a high of5.7 % (delay 2, 20 ha. blocks).Table 5: Percent increase in harvest volume of the constrained road solutions (basevolumes are unconstrained road solutions)Delay Period 80 ha blocks 40 ha blocks 20 ha blocks1 0.2 -1.8 -4.02 2.6 2.6 6.13 1.1 2.0 4.4The reason for this low variation of harvest levels is that the 25 kilometer roadconstruction constraint wasn’t binding on volume, If the road constraint was lowered to15 or 20 kilometers, one would expect the harvest volumes to decrease for theconstrained road solutions. Though in our particular case the 25 kilometer roadconstruction constraint wasn’t binding on volume, the results in Table 5 show that witha road constraint, higher volume blocks may have been selected as a result of the roadconstraint. This in turn related to a small increase in harvest volumes of the constrainedroad solutions.-24-Table 6 shows the total amount of road constructed for each block size anddelay period combination. It shows that the delay period reduces the amount of roadconstructed, which may limit the amount of volume eligible for harvest. Table 6 alsoshows that some roads are never constructed when long delays are specified.Figures 3, 4 and 5 show that the unconstrained solutions tended to build largeamounts of road during the first construction period (up to a high of 48.1 km of roadconstructed in period 1, 20 ha blocks, delay 1). After this initial peak, road constructionfell below the maximum level set in the constrained model. After periods 4-5 the roadconstruction schedules for both the constrained and unconstrained models were verysimilar for all combinations of block size and delay period.Comparison between the road maintenance schedules show that except forperiod 1, there is very little difference between the maintenance schedules of theconstrained and the unconstrained models. Both models display a relatively uniformschedule. The period I difference is caused by the lower road construction that takesplace in the constrained model. There is a greater difference when the maintenanceschedules for the two period delay models are compared. The maintenance schedulefor the constrained model is still relatively uniform whereas the unconstrained modelstarts to display a two period cyclic pattern for all block sizes. The cyclic pattern in theperiod combinationsTable 6: Total amount of road constructed (in kilometers) for block size and delay80 HA BLOCKSROAD CONSTRUCTEDDELAY PERIOD NO LIMIT LIMITED1 113.3 113.92 106.2 107.13 99.1 99.140 HA BLOCKSROAD CONSTRUCTEDNO LIMIT LIMITED112.2 111.61062 107.995.9 97.120 HA BLOCKSROAD CONSTRUCTEDNO LIMIT LIMITED112.7 112.0106.5 109.095.9 98.7-25-unconstrained model results from the combination of the large initial road constructionduring the first two periods, and the need to maintain rather than construct these roadsas the model progresses through its two period adjacency delay constraint.Comparison between the road maintenance schedules for the three period delaymodels shows that both the constrained and the unconstrained models show a cyclicpattern directly attributable to the three period adjacency delay constraint.THE EFFECT ON THE AAC DUE TO BLOCK SIZE AND EXCLUSION PERIODA comparison can be done between the progressive clear cut solution and theconstrained road construction solutions to determine the effect on the Annual AllowableCut due to the reduction of block size and exclusion period. As shown above, due tothe low variation in harvest levels, either the constrained or the unconstrained roadconstruction data could be used for this comparison.The results in table 4 show that the delay period had a greater effect on the MCthan did reducing the block size. The smallest reduction (5.4%) is observed betweenthe progressive clear cut solution and the 80 ha, I period delay solution. As theprogressive clear cut model is based on 80 ha blocks and the I period delay is notoverly restrictive, this small difference is expected.As previously discussed, the 40 ha and 20 ha blocks were created by dividingthe original 80 ha blocks. Keeping the exclusion period constant, one would expect thatthere would be no reduction in harvest volumes as the block size decreased becauseeven though the block size is smaller, more blocks are created and eligible for harvest.The results show that there was a reduction in harvest volumes as the block sizedecreased while keeping the delay period constant. The values ranged from adifference of 6.0 % (delay period I) to 23.5 % (delay period 3). These volumereductions associated with block size were due to irregularly shaped blocks with a largenumber of adjacent blocks. Since an adjacent block was defined as a block that shared-26-any part of a common boundary with another block, situations arose with some blockshaving from between 7, 8 or 9 adjacent blocks for the 80, 40 and 20 ha formulationsrespectively. As the block size decreased, adjacency constraints actually reduced thenumber of available blocks, thus reducing the harvest volume available.As the delay or exclusion period is increased, adjacency constraints limit thenumber of blocks available for harvest and therefore reduce the harvest volume.Increasing the delay period from I to 2 and from I to 3 caused volumes to drop anaverage of 18.6 % and 40 % respectively. Simultaneously increasing the delay periodand decreasing the block size results in large reductions in harvest volume of up to 50% in the case of 20 ha blocks and delay period 3.Another effect of increasing the delay period and decreasing the block size isthat a large number of blocks may never be harvested. Values ranged from 6.8 % to43.8 % of blocks not harvested for 20 ha delay period 1 and 20 ha delay period 3respectively.(Table 7). This is due partially to adjacency constraints making theseblocks ineligible for harvest during the length of the simulation. Also the unloggedblocks may require a large amount of road to be constructed to access a relatively lowvolume of timber. Though not directly investigated during the simulation, a maximumgrade cost per period is built into the program. Chances are that a road with a largeconstruction cost would be built if that road accessed a large amount of timber oraccessed a large number of blocks, whereas a road that accessed little timber mightnot be built.-27-Table 7: Percentage of blocks not harvested during the planning periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 8.3 7.3 6.82 18.8 19.8 24.43 33.3 36.5 43.8Figures land 2 show the road construction and maintenance schedules for theprogressive clear cut solution. After the first rotation (decade 7), road constructiondropped since most of the road network had been constructed. The construction peakin decade 2 was due to the development of branch roads. Road maintenance closelyparallelled the progressive clear cut model with the amount of maintenance increasingas the cut progressed towards the back of the valley. Once the end of the first rotationwas reached, maintenance decreases as the harvest again moves closer to thebeginning of the road network. Road maintenance peaks were related to themaintenance and subsequent abandonment of branch roads.Figures 9, 10 and 11 show that the smaller cut blocks require more roadconstruction during the first 3 or4 decades in order to develop enough volume to meetthe allowable cut. As the simulation progressed beyond that period, the smaller cutblocks required slightly less construction as the majority of the road network hadalready been developed. Observation of Table 6 shows with the delay period heldconstant, the total amount of road constructed is fairly constant throughout the range ofblock sizes. As the delay period is increased, the total amount of road constructeddecreases. These declines in road construction are directly attributable to the increasein blocks not eligible for harvest due to spatial restrictions.Figures 12,13 and 14 show a definite trend that the smaller cut blocks require agreater amount of road maintenance than did the larger cut blocks, even though the-28-volume of timber harvested was less for the smaller cut blocks. As the delay periodincreased, the total amount of road maintenance decreased, with the 20 ha blocks stillrequiring the greatest amount of road maintenance. As the delay period is increased,adjacency constraints decreases the number of available blocks for harvesting, thusthe amount of road maintenance decreases.The road maintenance schedules for the 1 and 2 period delay are fairly uniformwith a large increase in maintenance during the first three decades, decreasing slightlyor staying constant until around the seventh decade and increasing slowly beyond thatpoint. This shows the need to maintain the large initial road construction phase and tore-access previously harvested blocks once the rotation age has passed.The road maintenance schedule for the 3 period delay. shows a definite cyclicpattern not displayed in the I and 2 period delay models. The cyclic pattern follows the3 period delay constraint where the road maintenance schedule has peaks and valleysevery three periods. This pattern is not evident in the I and 2 period delay models asthe I and 2 period delays are not overly binding and do not force such a widelydispersed harvest.The results show that current harvesting levels within a fixed area cannot bemaintained if smaller cut blocks in combination with longer exclusion periods are used.Either additional forested land must be made available or harvest levels will drop. Otheralternatives include designating land within a best-use policy whereby certain lands areset aside primarily as timber production areas or increasing timber production on alimited land base through intensive management.-29-ECONOMIC ANALYSISAn economic analysis was done comparing the construction, hauling, roadmaintenance, tree to truck and delivered cost per cubic meter for the block size anddelay period combinations. Costs were averaged across the decades. Periodic costsare addressed in Figures 15 through 23.For each block size the typical pattern was for the road construction, hauling andmaintenance (con/haul/main) cost to be the lowest for a one period delay and toincrease for delay periods two and three. Values ranged from a high of $16.01/m3 for20 ha blocks delay period 3 to a low of $1 0.741m3 for 80 ha delay period 1. This trendwas expected even though the actual cost of road construction, maintenance andhauling decreases as the delay period increases, due to the lower volumes harvestedwhen the delay period increases.Table 8: Average road construction, hauling and maintenance costs ($1m3) harvestedby block size and delay periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 10.74 11.75 13.232 11.06 13.02 14.913 11.75 13.51 16.01The tree to truck cost per cubic meter showed no trend. The values ranged from$14.70/m3 for 20 ha delay period 2 to a high of $15.34/m3 for 80 ha delay period 1.This was expected as the only variables that change the tree to truck cost are loggingdifficulty and harvest age, and there was no clearly identifiable pattern for thedistribution of logging systems throughout the study area.-30-Adding of the con/haul/main and tree to truck costs per cubic meter shows thetotal delivered cost per cubic meter. Following the trend of the con/haul/main costs, thetotal delivered cost was the lowest for delay period I and increased as the delay periodincreased. The values ranged from $25.09/m3 for 80 ha delay period I to $30.75/m3for 20 ha delay period 3 (22.6% increase). Graphically, the total delivered costs areshown in Figures 15 through 23.35.0030.0025.0020.0015.0010.005.000.00Table 9: Average tree to truck costs ($/m3) by block size and delay periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 14.35 15.07 15.002 14.57 14.72 14.703 14.80 14.84 14.72Table 10: Average total delivered cost of wood ($/m3) by block size and delay periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 25.09 26.82 28.232 25.63 27.74 29.613 26.55 28.35 30.7580 HADELAY 1C0STPERCUCMETER5 6DECADECONMAULIMAIN TREE TO TRUCKFigure 15: Total delivered cost by decade - 80 ha blocks, I decade exclusion periodm-Imo—wcOimu-40)00m-lni0—wcomu—1(0000 8UI088888880UI0888p.)8888C,)11 D - -‘I -1 ) I) D D D D. 0 ) I) 4. a 0 a 0 0 0 j) a 0 a 0 3 ., 0 aNNNNflNNllINIIIOlIHIIrAIrj:11C) 0 z I > CUIm 0 > ci m11 D 3.) -I ) 4. I) 2. D D 2 ) 0 3- 0 ) T 0 0 .3 a 0 a 3 D ) 2.ci00-<IC.)>Lii C) 0 I > C I:U)> Zm C) > cim m 0 -l C 0UIci00rn0-.11•11-‘ D--I ) 1 D D CD a C, 0 Ci) a CD 9 a ) 7 LU c3. 0 C) C’) r\) a CD C) LU CD > •1 0 a.r.mO11 D-& D -I ) -I. I) a CD D D 1 ) I) a CD C, LU a CD L D F C’) - c C’) 0 CD )m-4mC)—wC0mU-4(000ec,’88888888IIIII3m—Im0—wC0mo-4000DC,’88888888IIIIIIMIII IIIII1NNINUIC) 0 z >lID C) 0 I C I::m 0 > Q m-I m m C C)(A)NNNHHNHNllflNHIIIIIIIIIr0m-ImC—wcOmD-noOPu,888888881•m-4mO—wtc)mu-4(1,00Pu,$88888888IC.)1•p..)11 2 --I D a CD D 2. 0 I) -I. CD C) B) a r’s) 0 - a CD C) B) a CD CD x C) C’) D 0 :2-ll 0 0 z I > C > z0 -.4 m m d C 011 2 D -I ) U 2 CD CD -‘ CD :2- C•) ) I) -I. :- :2- CD B) a CD 0 J B) (p.) a CD C, B) a CD 9 D D a0 m0Ifl 0 0 1 > C0zom 0 0 mm m C 011flHV411o ICp.)m-mO—wcC)mo—10000$fl08??888881•I’)m—ImO—wCOmo-(nOC)PU’t)$88888888IIIIIIIC)Do•<Co.—LUCD — :-C) CDCDCl)(C)o—.CDE<0CDCCD-‘-‘-‘z IN (0) -‘.0 o; 9. LU 3go LU D D. < 0 CD—CD -. •CDD CDCD CD-o• —CD— ‘J -‘LU —LU— -‘—.NNNNNNNNNNIIHIUNNNUf1II1IIIIIII-o C) -I 0 z Cl) -1 0 0 mn ) 3 p.) - ) •1. I D C •1 1 ) D r) 4. T a 0 ) D -r r I) •1 0 0 0 I8 z > C I:(7.Zm C) > ci mm m11 -I ) - U I CD CD -‘ 0 a D j) - C ) ) 1 CD 3 D 3- 3. ) ) 3 1 CD C, 0) 0. CD ) ) 3 3 D 0 0.m0LED4.C) 0 z > C LZU’Zci ci mm m d-IcimO_<I.r.(0 00-35-overhead, crew transportation, crew accommodation, sort/scale and forestrycosts.(Shaw, 1993). Average operating cost values ranged from $41 .071m3 to$45.501m3 for the 80 ha, I delay period and 20 ha, 3 delay period respectively. (Table11). For simplicity it was assumed that the calculated operating costs were equal to theoperating allowances for use in the stumpage calculation.Table 11: Average operating cost ($1m3) by block size and delay periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 41.07 41.96 43.232 41.22 42.35 44.173 41.42 43.48 45.50The values in Table 11 are reasonable given the variation in road constructionand road maintenance requirements for each combination. Also, the smaller cut-blocksolutions would be expected to have a higher operating cost due to the greater numberof machine set-ups and moves required.Stumpage revenue was calculated using the following formula (MOE, 1991):IS = BR + ((SP - OC) -VI)where:IS = indicated stumpageBR = base rate (assumed $14.03/m3). The base rate is a quarterlyadjusted value to ensure that the average of all coniferous sawlog rates isequal to the target rate set by the ministry for that quarter.SP = stand as a whole selling price (assumed $80/m3)OC = operating allowance-36-VI = mean value index (assumed $17.751m3). The mean value index is avolume weighted average of the value indexes for all harvests that haveoccurred in the last twelve months. It provides a benchmark against whichindividual stands are compared.The calculated indicated stumpage values (Table 12) ranged from $35.211m3 to$30.781m3 for the 80 ha, I delay period and 20 ha, 3 delay period respectively.Table 12: Average indicated stumpage values ($/m3) by block size and delay periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 35.21 34.32 33.052 35.06 33.93 32113 34.86 32.80 30.78As stumpage is the amount of money that a logging company must pay to theprovince for the “right” to harvest timber on a tract of land, there is a drastic differencein the amount of money payable when comparing the different sized blocks andadjacency requirements (Table 13). Comparison between the 80 ha, I delay period andthe 20 ha, 3 delay period shows the stumpage payable (indicated stumpage multipliedby the total harvest volume) of the 20 ha, 3 delay period is only 44% of the 80 ha, Idelay period. This is a reduction of nearly $67 million . These figures represent thedramatic economic impacts associated with block size and adjacency rules. It shouldalso be noted that due to the high road construction costs in the first few decades, theshort-term impacts on stumpage are probably greater than the average figurescalculated.-37-Table 13: Average stumpage revenues (in millions of $) by block size and delay periodDelay Period 80 ha blocks 40 ha blocks 20 ha blocks1 119.7 114.1 110.62 94.6 89.9 77.53 76.2 63.2 52.8CONCLUSIONAn area-based scheduling model was developed to evaluate the impacts andcosts associated with various cut-block sizes and adjacency constraints. Specifically,this paper: 1) determined the effect on the AAC and road network activity due to blocksize and the exclusion period for both unconstrained and constrained road budgets ; 2)quantified the delivered wood costs; and 3) forecasted the impacts on stumpagerevenues.Comparison between the constrained and unconstrained road budgets showedlittle effect on the overall periodic harvest volumes. The increase of the constrainedharvest volume ranged from -4.0% to 6.1% of the unconstrained harvest volume. Thisdifference is low because the road construction constraint of 25 kilometers was notparticularly binding.The effect on the MC due to block size and exclusion period showed that thedelay period had a greater effect on the AAC than did reducing the block size. As theblock size decreased while keeping the delay period constant, the reduction in harvestvolume ranged from 6.0% to 23.5%. As the block size decreased, adjacencyconstraints actually reduced the number of available blocks, thus reducing the volumeavailable for harvest.-38-Increasing the delay period from I to 2 and from I to 3 caused volumes to dropan average of 18.6% and 40% respectively. Increasing the delay period anddecreasing the block size simultaneously resulted in large reductions in harvest volumeof up to 50%.Another effect of increasing the delay period and decreasing the block size isthat a large number of blocks are never harvested. Values ranged from 6.8% to 43.8%of blocks being ineligible for harvest.Road construction schedules showed that the smaller cut-blocks required moreroad construction during the first 3 or 4 decades in order to develop enough volume tomeet the allowable cut. Beyond that point, the smaller cut-blocks required lessconstruction as the majority of the road network was already developed. The roadmaintenance schedules clearly show that the smaller cut-blocks require a greateramount of road maintenance than did the larger cut-blocks. This was due to the greateramount of road access required to service the dispersed harvest of small blocks.The economic analysis showed that road construction, hauling and maintenancecosts were the lowest for the I period delay and increase for delay periods 2 and 3.A stumpage calculation showed that there is a drastic difference in the amount ofstumpage payable when comparing the different sized blocks and adjacency options.Values ranged from $119.7 million to $52.8 million, a reduction of nearly $67 million asthe block size was decreased and the adjacency constraints increased.As the block size decreased,, the forest became more and more fragmented asgroupings of different age classes began to emerge over time. While this may be moreaesthetically pleasing than a large clear cut, a highly fragmented forest is not ideal inproviding habitat for most species of wildlife. Most wildlife do require a specific ageclass distribution throughout the forest in order to provide habitat for protection, foodproduction and migration. These particular habitats may exist in the fragmented forestbut they must be accessible to the animals and in sufficient quantities through time.Further research must be done to examine the benefits of maintaining a specific age.39...class distribution for wildlife habitat. For example, different adjacency rules could be setfor different areas within a study area so that designated migration corridors would bemaintained with a predefined age class distribution of timber.If we are to follow other countries in the world, further research must be done todetermine the impacts on harvest levels and road networks of going to cut blocks evensmaller than 20 ha. Additional work is also required to investigate the use of selectionsystems and their economic, social and forest structure impacts.-40-BIBLIOGRAPHYArmel, N.B. 1986. Area analysis and Version II of FORPLAN. In Proceedings of theWorkshop on Lessons From Using FORPLAN, Denver, CO, April 29 - May 1.USDA Forest Service, Land Management Planning Systems Section,Washington, D.C.Bare, B.B., Faaland, B.H., and Gupta, I. 1984. Timber harvest scheduling in thepresence of spatial constraints. Paper presented at the Joint National Meeting ofthe Institute Of Management Sciences and the Operations Research Society ofAmerica, San Francisco, CA, May 14-16.Clements, S.E., Dallain, P.L., and Jamnick, M.S. 1990. An operational, spatiallyconstrained harvest scheduling model. Can. J. For. Res. 20: 1438-1447.Hackett, J. MacMillan Bloedel Corporate Forestry, Vancouver, B.C. PersonalCommunication, 1990.Johnson, K.N., and Jones, D.B. 1991. Multiple Use Sustained Yield Calculation TimberHarvest Scheduling Model Users Guide. Pacific Forestry Center, Victoria, B.C.Johnson, K.N., Stuart, T.W., and Crim, S.A. 1986. FORPLAN Version 2 : An overview.USDA Forest Service, Land Management Planning Systems SectionWashington, D.C.Ministry Of Forests, 1991. Stumpage Appraisal Information Paper No. I ComparativeValue Timber Pricing, Valuation Branch, Victoria, B.C.Nawitka Resource Consultants. 1987. Impact Of Intensive Forestry Practices On NetStand Values In British Columbia. Forestry Economic and RegionalDevelopment Agreement Report 014, Victoria, B.C.Nelson, J.D. 1988. Integrating Short-term Spatially Feasible Harvest Plans With Long-term Harvest Schedules Using Monte-Carlo Integer Programming And LinearProgramming. Ph.D. dissertation, Oregon State University, Oregon.Nelson, J., and Brodie, J.D. 1990. Comparison of a random search algorithm and mixedinteger programming for solving area-based forest plans. Can. J. For. Res. 20:934-942.Nelson, J.D., and Finn, S.T. 1991. The influence of cut-block size and adjacency ruleson harvest levels and road networks. Can. J. For. Res. 21: 595-600.O’Hara, A.J., Faaland, B.H., and Bare, B.B. 1989. Spatially constrained timber harvestscheduling. Can. J. For. Res. 19: 715-724.-41-Shaw, N. British Columbia Institute of Technology, Burnaby, B.C. PersonalCommunication, 1993.-42-APPENDIX IDESCRIPTION OF ANALYSIS AREAS-43-Description of the Analysis Areas (from Nelson, 1988)ANALYSIS AREA SITE/SPECIESIAGE HA VOL/HAI HCJ7 45 6902 MCJ7 13 4003 MFJ7 40 3304 HHJ6 120 6105 HCJ8 36 7606 MFJ8 19 4707 LCJO 17 4408 HHJ8 67 8009 HHJ6 55 61010 LFJ6 12 10011 MFJ7 95 41012 LFJ6 17 10013 MFJ7 28 41014 MFJO 37 71015 MHJ7 233 41016 LHJ6 18 9017 MFJO 137 71018 MFJC 21 62019 LFJ7 45 20020 MFJC 31 62021 HHJB 71 97022 MHJA 202 57023 HFJO 82 117024 HHJC 80 101025 HHJA 39 93026 HHJB 29 97027 HHJA 16 93028 HHJC 28 101029 HCJ9 20 84030 MHJA 44 57032 HFJI 368 034 HFJ7 15 68035 HFJB 35 94036 HFJC 12 99037 HFJO 92 117038 HHJ7 59 72039 HHJ8 56 80040 HHJB 70 80041 HHJC 40 101043 HCJ4 26 33044 MFJI 148 045 MFJ2 64 046 MFJ3 295 14-44-47 MFJ7 65 41048 MFJ8 27 47049 MFJC 33 61550 MFJ0 58 71051 MHJ4 20 12552 MHJ6 62 33053 MHJ7 270 41054 MHJ8 60 48058 MCJ3 99 2059 MCJ4 205 12060 MCJO 14 75061 LFJI 47 062 LFJ6 46 100Codes Used To Define Site/Species/Age:- the first character is the site classH = HighM = MediumL = Low- the second character is the species groupF = FirH = HemlockC = Cedar- the third and fourth characters are the 10 year age classesJI = 10J2 = 20J3 = 30J4 =40J5 = 50J6 =60J7 = 70J8 = 80J9 = 90JA = 100JB = 110JC = 130JO = 200+-45-APPENDIX 2ANALYSIS AREA MAP I ZONE MAP-46-ANALYSIS AREA MAPdWI]NOZc37&-48-APPENDIX 3DBASE FILE TO MAKE TABLES OF BLOCK VOLUMES-49-* MAKETAB* CREATES A TABLE OF VOLUMES PER BLOCK PER PERIOD TO BE USED BYMCIP (NELSON)* WRITTEN BY STEVE FINN AND IAN THOMASMAH29, 1990* FOR INTERNAL USE ONLY**AA***A****A******INSTRUCTIONS FOR** THE FIELD NAMES AND LENGTHS SHOULD CORRESPOND TO THOSE IN THIS* FILE** USE C:TERRAUSERSTILLWTR.DB_** TO RUN THE PROGRAM TYPE “DO MAKETAB” AT THE DOT PROMPT IN DBASE* THE VOLUME TABLE WILL BE WRITTEN TO THE FILE “SUMS”.************A.AAAA**AAAAAAAAAAAAAAAAAAAAA1.A.LAAA*SORT ON POLY_LABEL TO C:\TMPTENT.DBFCLOSE ALLUSE C:TMPTENT.DBFGO TOPSELECT BUSE C:\TMP\SUMSZAPSELECT ADO WHILE .NOT. EOFOSUMOI = 0SUMO2 =0SUMO3 =0SUMO4 =0SUMO5 =0SUMO6 =0SUMO7 = 0SUMO8 = 0SUMO9 = 0SUMIO = 0SUMII =0SUMI2 = 0SUMI3 = 0SUMI4 = 0SUMI5 = 0-50-SUMI6 = 0SUMI7 = 0SUMI8 = 0SUMI9 = 0SUM2O =0SUM2I =0SUM22 =0SUM23 =0SUM24 =0SUM25 =0SUM26 =0SUM27 =0SUM28 =0SUM29 =0SUM3O =0CURRENT_BLK = POLY_LABELDO WHILE POLY_LABEL = CURRENT_BLKSUMOI = (POLY_AREA * EX_YLDOI) + SUMOISUMO2 = (POLY_AREA * EX_YLDO2) + SUMO2SUMO3 = (POLY_AREA * EX_YLDO3) + SUMO3SUMO4 = (POLY_AREA * EX_YLDO4) + SUMO4SUMO5 = (POLY_AREA * EX_YLDO5) + SUMO5SUMO6 = (POLY_AREA * EX_YLDO6) + SUMO6SUMO7 = (POLY_AREA * EX_YLDO7) + SUMO7SUMO8 = (POLY_AREA * EX_YLDO8) + SUMO8SUMO9 = (POLY_AREA * EX_YLDO9) + SUMO9SUMIO = (POLY_AREA * EX_YLDIO) + SUMICSUMI I = (POLY_AREA * EX_YLDI I) + SUMI ISUMI2 = (POLY_AREA * EX_YLDI2) + SUMI2SUMI3 = (POLY_AREA * EX_YLDI3) + SUMI3SUMI4 = (POLY_AREA * EX_YLDI4) + SUMI4SUMI5 = (POLY_AREA * EX_YLDI5) + SUMI5SUMI 6 = (POLY_AREA * REG_YLDOI) + SUMI 6SUMI7 = (POLY_AREA * REG_YLDO2) + SUMI7SUMI8 = (POLY_AREA * REG_YLDO3) + SUMI8SUMI9 = (POLY_AREA * REG_YLDO4) + SUMI9SUM2O = (POLY_AREA * REG_YLDO5) + SUM2OSUM2I = (POLY_AREA * REG_YLDO6) + SUM2ISUM22 = (POLY_AREA * REG_YLDO7) + SUM22SUM23 = (POLY_AREA * REG_YLDO8) + SUM23SUM24 = (POLY_AREA * REG_YLDO9) + SUM24SUM25 = (POLY_AREA * REG_YLDI 0) + SUM25SUM26 = (POLY_AREA * REG_YLDI I) + SUM26SUM27 = (POLY_AREA * REG_YLDI2) + SUM27SUM28 = (POLY_AREA * REG_YLDI3) + SUM28SUM29 = (POLY_AREA * REG_YLDI4) + SUM29SUM3O = (POLY_AREA * REG_YLDI5) + SUM3OSKIP-51 -ENDDOSELECT BAPPEND BLANKREPLACE BLOCK_NUM WITH CURRENT_BLKREPLACE EX_VOLOI WITH SUMOIREPLACE EX_VOLO2 WITH SUMO2REPLACE EX_VOLO3 WITH SUMO3REPLACE EX_VOLO4 WITH SUMO4REPLACE EX_VOLO5 WITH SUMO5REPLACE EX_VOLO6 WITH SUMO6REPLACE EX_VOLO7 WITH SUMO7REPLACE EX_VOLO8 WITH SUMO8REPLACE EX_VOLO9 WITH SUMO9REPLACE EX_VOLIO WITH SUMIOREPLACE EX_VOLI I WITH SUMI IREPLACE EX_VOLI2 WITH SUMI2REPLACE EX_VOLI3 WITH SUMI3REPLACE EX_VOLI4 WITH SUMI4REPLACE EX_VOLI5 WITH SUMI5REPLACE REG_VOLOI WITH SUMI6REPLACE REG_VOLO2 WITH SUMI7REPLACE REG_VOLO3 WITH SUMI8REPLACE REG_VOLO4 WITH SUMI9REPLACE REG_VOLO5 WITH SUM2OREPLACE REG_VOLO6 WITH SUM2IREPLACE REG_VOLO7 WITH SUM22REPLACE REG_VOLO8 WITH SUM23REPLACE REG_VOLO9 WITH SUM24REPLACE REG_VOLIO WITH SUM25REPLACE REG_VOLI I WITH SUM26REPLACE REG_VOLI2 WITH SUM27REPLACE REG_VOLI3 WITH SUM28REPLACE REG_VOLI4 WITH SUM29REPLACE REG_VOLI5 WITH SUM3OSELECT AENDDOAAAAAAAALAAAAAAAAEND OF FILE*-52-APPENDIX 4BLOCK LAYOUT AND ROAD NETWORKS BY BLOCK SIZE-53-- “••.•1- \.1ci/I.......&.••// . • . .. .80 HECTARE BLOCKS AND ROAD NETWORK-54-...‘..I....IF/I .•40 HECTARE BLOCKS AND ROAD NETWORK-55-1:.. ••S I• .. ...‘ ... ...•.; .20 HECTARE BLOCKS AND ROAD NETWORKS-56-APPENDIX 5EXAMPLES OF INPUT FILES-57-1 782 863 934 835 986 747 668 799 7710 8411 9012 7713 7914 9815 8916 6717 7118 7719 8420 7721 7822 8923 8024 6525 8426 8327 10028 8129 8130 7731 8132 8733 7234 7835 7936 8137 8638 7339 7940 8741 8442 8643 7144 8145 7345000005630000670000058900002 4 6 8 9 10 03 7 11 10 5 0 06 11 16 0 0 0 05 9 12 0 0 0 05 8 10 12 13 0 06 11 14 13 9 0 07 16 15 14 13 10 09 13 20 19 0 0 010 11 14 21 20 12 011 15 13 21 0 0 016 17 23 22 14 0 011 15 22 23 17 0 015 22 23 18 0 0 023 0 0 0 0 0 020 0 0 0 0 0 019 13 21 0 0 0 013 14 24 0 0 0 016 17 23 31 30 25 017 16 15 22 31 0 025 26 0 0 0 0 022 30 32 0 0 0 027 28 0 0 0 0 000000000000000035 34 33 32 035 36 0 0 038 37 0 0 038 37 0 0 039 38 0 0 036 40 39 0 0000005 32 33 38 42 41 0 0 07 37 32 33 34 39 42 0 0738343540434542 08 39 35 36 43 0 0 0 05 37 42 0 0 0 0 0 07 41 37 38 39 45 44 0 08 39 40 46 45 0 0 0 07 42 39 45 47 0 0 0 08 44 42 39 43 46 47 0 0BLOCKDAT.TXTblock ha age zone adjacent blocks323132112122331424252618194 104 11373 164 171 121 126 204 154 186 215 246 246 26 28 296 26 27 296 27 28 05 25 22 314 23 22 305 25 30 337 32 30 347 33 30 358 34 30 318 31 35 40787777787778872020787777777777777720121111772012720102010-58-46 69 11 8 45 43 47 48 0 0 0 047 74 10 8 44 45 46 48 0 0 0 048 82 20 8 46 47 0 0 0 0 0 0-59-CONSTRALTXTHAB_DELAY MAX_BLOCKS MAX_PERIODS MAX_ZONES MIN_AGE MAX_ADJAC2 48 10 8 6 8MAX_MRD MAX_ACCESS COST_MAINT MAX_ROAD CUT_I CUT_2162 51 51 25 210000. 210000.DISC MINVOL MAXVOL MINCOST MAXCOST MAXGRADECOST1. 265000. 275000. 0. 50000000. 50000000.ZONE FIRST_ENTRYI I2 53 14 15 16 27 18 4-60-EXREVTAB.TXT1 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.882 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.883 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.884 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.885 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.886 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.887 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.888 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.889 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8810 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8811 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8812 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8813 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8814 20.11 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8815 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8816 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8817 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8818 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8819 20.11 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8820 20.11 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8821 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8822 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8823 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8824 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8825 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8826 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8827 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8828 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8829 21.11 18.00 14.88 14.88 14.88 14.88 14.88 14.88 14.88 14.8830 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8831 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8832 20.11 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8833 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8834 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8835 12.88 12.88 12.88 12.88 - 12.88 12.88 12.88 12.88 12.88 12.8836 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8837 20.11 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8838 19.11 16.00 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8839 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8840 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8841 20.11 17.00 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8842 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8843 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8844 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.88 13.8845 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8846 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8847 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.8848 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88 12.88-61 -EXVOLTAB.TXT1 26968 30580 34285 36950 40374 41129 42436 43270 44577 454102 35161 38696 42838 45470 49268 49825 51380 52722 53799 551403 37989 44259 47976 52457 55207 57911 59745 61575 63360 643224 42415 47372 52588 56550 59298 62067 64089 65811 67345 681855 41578 46832 52077 56290 58809 62054 63971 65367 67263 686516 37262 41293 45086 47722 50043 52323 53909 54947 56238 570207 29032 33010 35620 38450 40263 42076 43314 44332 45481 460578 50175 55695 60451 64031 66918 69671 71902 73429 74874 759179 48546 53895 58805 62785 65591 68393 70995 72941 74359 7570010 49578 55678 60617 65080 68042 71011 73672 75689 77323 7865211 33990 37858 41531 44401 46581 48760 50162 51128 52408 5318612 52837 57779 61803 64635 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990 2970028 440 1320029 915 2745030 965 2895031 1315 3945032 500 2250033 1770 7965034 270 1215035 170 765036 430 1935037 1125 5062538 305 1372539 310 1395040 260 1560041 810 4860042 785 3532543 1530 6885044 1420 6390045 185 832546 380 1710047 300 1350048 240 1080049 705 3172550 700 3150051 275 1237552 915 2745053 615 1845054 380 1140055 360 1080056 1080 3240057 280 8400-65-58 290 870059 225 675060 700 2100061 1045 3135062 930 2790063 385 2310064 270 1620065 860 5160066 975 2925067 220 660068 205 922569 1120 3360070 285 855071 825 3712572 825 3712573 1340 4020074 175 525075 165 495076 640 3840077 190 1140078 920 5520079 605 1815080 410 2460081 680 2040082 380 2280083 425 2550084 150 900085 505 3030086 1690 10140087 405 2430088 795 4770089 810 4860090 1350 8100091 1755 10530092 175 1050093 535 3210094 460 2760095 265 1590096 1055 6330097 1290 7740098 475 2850099 470 28200100 975 29250101 950 28500102 755 22650103 100 3000104 530 15900105 180 5400106 300 9000107 160 4800108 555 24975109 1210 54450110 1250 56250111 200 9000112 1600 72000113 1180 35400114 160 4800115 945 28350116 210 6300-66-117 205 6150118 360 10800119 575 17250120 655 19650121 215 6450122 245 7350123 975 43875124 435 13050125 500 15000126 150 4500127 315 9450128 130 3900129 170 5100130 495 14850131 545 16350132 250 7500133 485 14550134 870 26100135 390 11700136 255 11475137 1385 62325138 1225 36750139 660 19800140 510 15300141 265 7950142 785 23550143 125 3750144 675 20250145 710 21300146 940 28200147 360 10800148 630 18900149 610 18300150 540 16200151 790 23700152 270 8100153 225 6750154 140 4200155 995 29850156 240 7200157 370 11100158 895 26850159 710 21300160 1105 33150161 1085 32550162 830 24900-67-RGREVTAB.TXT1 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.882 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.883 0.00 0.00 0.00 0.00 0.00 22.23 19.1.1 16.00 12.88 12.884 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.885 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.886 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.887 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.888 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.889 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8810 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8811 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8812 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8813 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8814 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8815 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8816 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8817 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8818 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8819 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8820 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8821 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8822 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8823 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8824 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8825 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8826 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8827 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8828 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8829 0.00 0.00 0.00 0.00 0.00 24.23 21.11 18.00 14.88 14.8830 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8831 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8832 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8833 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8834 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8835 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8836 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8837 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8838 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8839 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8840 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8841 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8842 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8843 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8844 0.00 0.00 0.00 0.00 0.00 23.23 20.11 17.00 13.88 13.8845 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8846 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8847 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.8848 0.00 0.00 0.00 0.00 0.00 22.23 19.11 16.00 12.88 12.88-68-RGVOLTAB.TXT1 0.0 204.0 881.3 6073.3 12935.8 19986.9 26968.3 30579.7 34285.4 36950.22 0.0 22.9 1210.5 8134.9 16935.6 24565.4 31814.5 36779.4 40446.5 44034.83 0.0 21.7 1870.2 11055.1 22055.9 30304.9 37639.8 44051.3 47724.9 52305.04 0.0 2804.7 6396.8 16596.0 26572.5 34794.8 42415.4 47371.9 52588.4 56550.25 0.0 1667.5 3857.7 12758.8 22417.5 32022.0 41567.7 46826.2 52069.3 56285.46 0.0 1754.2 4148.8 12344.2 20906.3 28057.8 35000.6 39400.0 43400.4 46611.87 0.0 0.0 1016.5 7638.5 15589.4 21867.6 27180.2 31510.7 34473.4 37479.58 0.0 3638.6 8078.6 20428.7 31757.8 40155.2 47796.1 53364.0 58566.7 62774.79 0.0 4294.2 9244.3 21322.5 31982.2 39948.6 48157.9 53541.1 58508.1 62587.210 0.0 3629.3 8245.6 21076.8 32942.7 41450.0 49528.7 55634.9 60579.3 65054.911 0.0 0.0 689.9 6969.9 15336.6 23493.0 31286.0 35669.7 39855.4 42983.112 0.0 3735.9 8212.7 20129.8 31011.8 39052.2 46599.2 52087.3 57165.6 61294.113 0.0 1796.9 4583.7 13127.0 22295.4 29246.0 36051.2 41544.9 45440.8 49310.514 0.0 0.0 1714.0 10377.0 21199.4 29548.2 37012.1 43697.8 47501.7 52134.715 0.0 10.5 1227.5 10102.5 20742.6 29286.9 36380.3 42019.8 46135.6 50004.016 0.0 0.0 646.4 7064.4 14835.6 21411.4 26777.8 30679.6 33976.8 36595.017 0.0 0.0 1403.0 8441.0 16886.6 23225.4 28855.8 33777.8 36597.6 40112.018 0.0 3801.0 8536.3 21111.3 32508.9 40574.4 48353.8 54218.1 58982.6 63309.319 0.0 0.0 1655.2 9931.2 19862.4 27310.8 33548.0 39341.2 43035.2 47173.220 0.0 433.3 2329.9 10513.0 19911.8 26899.0 32486.3 37886.4 41821.7 45696.621 0.0 0.0 1441.8 8650.8 17518.0 24276.6 29845.6 35216.5 38731.1 42497.922 0.0 2100.0 5318.3 16902.6 28768.7 37750.3 45752.8 51900.9 56752.7 61143.723 0.0 4049.5 8901.7 21827.8 33457.6 42012.5 49871.4 55560.2 60964.5 65318.524 0.0 0.0 1296.4 7778.4 15556.8 21390.6 25934.2 30471.6 33706.4 36947.425 0.0 6.0 1678.1 10029.6 20042.7 27552.9 34226.3 40065.9 43405.6 47577.626 0.0 0.0 816.8 8953.8 18718.2 26852.1 33358.6 38243.9 42312.4 45570.327 0.0 0.0 985.4 10839.4 22664.2 32518.2 40401.4 46313.8 51240.8 55182.428 0.0 0.0 801.3 8814.3 18429.9 26442.9 32853.3 37661.1 41667.6 44872.829 0.0 0.0 1511.4 9478.4 19038.8 26291.1 31950.0 37444.9 41428.4 45329.930 0.0 2979.3 6746.0 21178.5 34187.9 44146.8 51834.9 58721.7 64069.3 69406.131 0.0 2168.5 5142.9 17601.1 29644.8 39028.0 46523.9 52754.6 57761.7 62380.632 0.0 3427.6 7715.1 24011.2 38596.5 49749.7 58330.7 66053.3 72057.6 78063.433 0.0 2762.5 6213.3 19291.0 30989.0 39930.7 46816.8 53008.4 57826.5 62641.534 0.0 5413.4 11610.9 26495.3 39056.5 47723.3 56322.3 62613.7 68099.4 72822.635 0.0 5513.1 11816.4 26802.4 39423.9 48128.3 56786.6 63086.5 68645.7 73393.036 0.0 2523.5 6304.7 17640.2 28791.4 36794.3 44348.6 50372.8 54690.7 59096.737 0.0 2438.0 5722.2 19669.7 32871.6 43162.1 51150.7 58056.4 63506.4 68719.738 0.0 1455.2 3640.4 14141.7 24669.4 33014.9 39577.1 45013.4 49374.8 53351.139 0.0 2900.3 6662.2 20941.2 33937.9 43844.0 51595.3 58511.3 63803.1 69141.340 0.0 5986.4 12849.9 29093.5 42787.9 52330.5 61679.8 68459.7 74667.3 79872.541 0.0 222.8 1285.5 10185.8 20543.1 29109.2 35939.8 41146.3 45457.2 48983.942 0.0 396.0 1706.2 11198.2 22014.4 30858.3 37937.1 43448.8 47893.2 51684.743 0.0 2763.4 6551.1 17211.8 27315.5 34505.7 41366.3 46730.7 50766.0 54716.244 0.0 0.0 872.5 9009.5 18773.9 26852.1 33361.7 38302.7 42312.4 45626.045 0.0 324.8 2066.5 9816.1 18800.1 25494.8 31499.6 36675.3 39750.4 43459.746 0.0 3824.0 8441.5 20530.4 31171.3 38670.5 45826.3 51292.9 55780.4 59873.447 0.0 1430.6 4141.8 13432.1 23184.8 30299.0 36864.2 42278.8 45873.0 49799.848 0.0 3958.7 8734.2 24253.4 37908.5 48065.9 56464.4 63585.1 69302.7 74789.8-69-SRLINKS.TXT1 625 187502 0 03 1365 409504 230 69005 0 06 0 07 1220 366008 245 73509 0 010 0 011 100 300012 335 1507513 0 014 1395 6277515 400 1200016 895 2685017 360 1080018 2130 6390019 425 1912520 825 3712521 0 022 0 023 0 024 140 840025 0 026 0 027 0 028 .0 029 0 030 340 1020031 0 032 0 033 650 1950034 505 1515035 0 036 290 870037 215 967538 0 039 555 1665040 843 2529041 0 042 415 1245043 60 180044 400 1800045 315 945046 0 047 555 1665048 165 4950-70-APPENDIX 6MCIP FLOW CHART-71-MCIP BLOCK SCHEDULER FLOW CHARTSTART_______‘I,_________LAST SOLUTIOIyes no4->PERIOD =44,INITIALIZE ALL VARIABLES_____________1>COUNT= 0COUNT = COUNT + IINITIALIZE PERIOD VARIABLES <1COUNT> 20yes no1-ASSIGN BLOCKS 0/I1IF BLOCK= I, SETADJACENT BLOCKS =0 VASSIGN ROADS‘I,ELIMINATE REDUNDANT ROADSSUM VOLUME“SUM REVENUE‘IfCHECK CONSTRAINTSPASS CONSTRAINTSesADJUST AGES, ETC‘If__________PERIOD= PERIOD + ILAST PERIOD_> FEASIBLE SOLUTIONno yes-72-APPENDIX 7MAIN PROGRAM FILE-73-(* Monte Carlo Integer Program(* trans.PAS MCIP WITH ROADS minvol as constraint,transportation *)(* DATE: February 1993 *)(* For MB -StiliwaterPROGRAM MCIP (INPUT, OUTPUT,DISKFILE);USESDOS, CRT, PRINTER;CONSTMOSTBLOCK =230; { max no of blocks)MOSTZONES =10;MOSTPERIOD =10; { max time periods)MOSTACCESS =100; { MAX NUMBER OF ROADS TO ACCESS BLOCK)MOSTADJAC =10; { MAX NUMBER OF ADJACENT BLOCKS)MOSTMRD =300; { MAXIMUM NUMBER OF MAIN ROADS }MAXREPS =100; (MAXIMUM NUMBER OF REPETITIONS }TYPEZONEARRAY ARRAY[1 .MOSTZONES] OF INTEGER;ZCOUNTERPTRZONEARRAY;FIRSTENTRYPTRZONEARRAY;INTZONEBLOCKARRAYARRAY[1 ..MOSTZONES,1 ..MOSTBLOCK] OF INTEGER;BLOCKINZONEPTR=”INTZONEBLOCKARRAY;ZONEPERIODARRAY=ARRAY[1..MOSTZONES,1..MOSTPERIOD] OF REAL;ZVOLPTR=’ZONEPERIODARRAY;VOLREVARRAY =ARRAY[1 ..MOSTBLOCK,1 ..MOSTPERIOD,1 .2] OF REAL; (vol and rev tables)volumePtr Avolrevaffay;revenuePtr =Avolrevarray;REALARRAY ARRAY[0..MOSTBLOCK,1 ..MOSTPERIOD] OF REAL;PERIODARRAY =ARRAY[1 ..MOSTPERIOD] OF real;BLOCKARRAY =ARRAY[1 . .MOSTBLOCK] OF REAL;areaPtr Ablockan.ay;blockPtr Ablockaffay;MRLENARRAY ARRAY[1 . .MOSTMRD] OF REAL;MAINROADARRAY=ARRAY[1 . .MOSTMRD, 1. .MOSTPERIOD] OF REAL;mrPtr =Amajnroadan..ay;mrmaintPtr =Amalnroadan.ay;DNRARRAY =ARRAY[1 . .maxreps] OF REAL; {number of solutions)ADJACARRAY ARRAY[1 . .MOSTBLOCK,0. . MOSTADJAC] OF INTEGER;(integers needed for adjacprocdure}adjacPtr Aadjarray;ACCESSARRAY =ARRAY[1 ..MOSTBLOCK,1 ..MOSTACCESS] OF INTEGER; {access roads for eachblock)accessPtr Aaccessan.ay;INTBLOCKARRAYARRAY[1 ..MOSTBLOCK] OF INTEGER; (for vtable and r table)starlagePtr Ajntblockan.ay;vtablePtr Aintblockarray;rtablePtr Aintblockarray;ZONEPTR AINTBLOCKARRAY;INTARRAY ARRAY[1 . .MOSTBLOCK,0. .MOSTPERIOD] OF INTEGER;agePtr Ajntarray;VARZVOL :ZVOLPTR;BLOCKINZONE:BLOCKINZONEPTR;ZCOUNTER :ZCOUNTERPTR;ZONE :ZONEPTR;FIRSTENTRY:FIRSTENTRYPTR;-74-COSTMAINT :REAL; (MAINTENANCE COST/KM/YR)MAXZONE :INTEGER;MAXBLOCK, (max no of blocks)MAXPERIOD, (max time periods }MAXACCESS, { MAX NUMBER OF ROADS TO ACCESS BLOCK)MAXADJAC, { MAX NUMBER OF ADJACENT BLOCKS)MAXMRD, { MAXIMUM NUMBER OF MAIN ROADS)MINAGE :INTEGER; { MINIMUM HARVEST AGE }HABDELAY,CUTI ,CUT2 :REAL;DISKFILE :TEXT;AGE :agePtr;STARTAGE :startagePtr;ACCESS :accessPtr;ADJ :adjacPtr;SRCOST :BLOCKARRAY;BLOCK :blockPtr;AREA :areaPtr;VOLUME :volumePtr;NETVAL :revenuePtr;VTABLE :vtablePtr;RTABLE :rtablePtr;5,SR :REALARRAY;SRLENGTH :BLOCKARRAY;SRBUILT :BLOCKARRAY;SECLENGTH :PERIODARRAY;SRMAINT :REALARRAY;SECMAINT :BLOCKARRAY;TRANS, LOGCOST, BLKVOL :blockarray;mr :mrPtr;mrmaint :mm,aintPtr;MRLENGTH :MRLENARRAY;MRBUILT :MRLENARRAY;MAINLENGTH :PERIODARRAY;MAINMAINT :MRLENARRAY;MRCOST :MRLENARRAY;TOTALLENGTH :PERIODARRAY;TOTALMAINT :PERIODARRAY;GRADECOST :PERIODARRAY;MAXGRADECOST :PERIODARRAY;DISC,MAINRDS, SECRDS,VOL, HARVCOST,TAREA,MINVOL, MAXVOL, MAXROAD,MINREV, MAXREV,NETREV,NET,ROADMAI NT,MARGIN, HAUL :PERIODARRAY;CURSORX,C U RSORY,CODE,REP,REPSDESIRED,J,R :INTEGER;SEED :Iongint;RANDSEEDS,DNR :DNRARRAY;HIGHSOFARDNR,HIGHESTDNR :REAL;-75-ASKPRINT :CHAR;A,B,C,D,E,X,Y,Z :TEXT;OUTFILE :STRING;HOURI ,MINI ,SECI ,I-IUNDRETHI :WORD;Resp,passroad,Test, passvol,passrev,passgrade :Boolean;zx,SEEDY :double;(*=============================SCREEN DI SPLAY=====================*)PROCEDURE DRAWBOX; { Draws a header for the screen }varW : Integer;BEGINCLRSCR;GOTOXY(1 ,l);WRITE (#201);FOR W:= I TO 78 DOWRITE (#205);WRITE (#187);WRITE (#186,’ MCIP Block Scheduler);WRITE (‘ ‘#186);WRITE (#200);FOR W: ITO 78 DOWRITE (#205);WRITE (#188);WRITELN;END;(*— screen display(*________.______=___________introducllon=____=_____====______.._______PROCEDURE INTRODUCTION;varPAUSE :STRING;PROCEDURE COLLECT;varRESP, TESTSEED, TESTREP : BOOLEAN;SEEDRESPONSE : CHAR;BEGINDRAWBOX;TESTREP:FALSE;WRITE (‘PLEASE TYPE IN THE DESIRED NUMBER OF REPETITIONS OF THE PROGRAM: ‘);REPEAT {TESTREP}READLN (REPSDESIRED);IF REPSDESIRED >0 THENBEGINIf repsdesired <= maxreps then BEGINTESTREP:=TRUE;ENDELSEWRITE (‘PLEASE ENTER A NUMBER BETWEEN I AND’, MAXREPS:5,’ :ENDELSEWRITE (‘PLEASE ENTER A NUMBER BETWEEN I AND’, MAXREPS:5,’:UNTIL TESTREP;WRITE (‘PLEASE ENTER SEED:);-76-READLN(zx); (seed for random numer generator)END;(*—------u introduction—(*========================clear result files==========================*)PROCEDURE CLEARFILES; { EMPTIES RESULT FILES)BEGINASSIGN (X,’SEEDDNR.txt);RESET (X);REWRITE(X);CLOSE (X);END;end result files(*____=___________._._=========read input files constraints===__====__=========*)PROCEDURE READCONSTRAINTS; { READS IN VOLUME REV CONSTRAINT DATA FILE }VARI :INTEGER;TITLEI ,TITLE2,TITLE3,TITLE4 :STRING;ZONENUM :ARRAY[1 .MOSTZONES] OF INTEGER;BEGINASSIGN (E, ‘CONSTRAINTS.bct);RESET(E);READLN(E,TITLEI);READLN (E, HABDELAY,MAXBLOCK,MAXPERIOD,MAXZONE,MINAGE,MAXADJAC);READLN(E,TITLE2);READLN (E, MAXMRD,MAXACCESS,COSTMAINT,MAXROAD[1J,CUTI ,CUT2);READLN(E,TITLE3);READLN (E, DISC[1 ],MINVOL[1 ],MAXVOL[1 ],MINREV[1 ],MAXREV[1 ],MAXGRADECOST[1 ]);READLN (E,TITLE4);FOR I: I TO MAXZONE DOBEGINREAD(E,ZONENUM[I], FIRSTENTRYALI])END;CLOSE (E);FOR I:1 TO MAXPERIOD DOBEGINDISC[IJ:=DISC[I];MINVOL[I]:MINVOL[1 1;MAXVOLII]: MAXVOL[1 J;MINREV[l]:MINREV[I j;MAXREV[I]:MAXREV[I 1;MAXGRADECOST[IJ:=MAXGRADECOST[I 1;MAXROAD[I]:=MAXROAD[I];END;MINVOL[1]:=CUT1;MINVOL[2]:CUT2;END;(* end read constraints *)-77.-beginREADCONSTRAINTS;DRAWBOX;WRITELN;WRITELN (‘TO PROMPT THE PROGRAM TO CONTINUE JUST PRESS THE TMRETURN” KEY.);WRITELN;WRITELN (‘THE CONSTRAINTS USED IN THE MODEL ARE:’);WRITELN;WRITELN (‘PLANNING HORIZON: ‘,MAXPERIOD:8,’ (MAX TIME PERIODS));WRITELN (‘NUMBER OF BLOCKS: ‘,MAXBLOCK:8,’ (MAX NO. BLOCKS ));WRITELN (‘NUMBER OF ZONES: ‘,MAXZONE:8,’ (NO. ZONES ));WRITELN (‘NUMBER OF MAIN ROADS: ‘,MAXMRD:4,’ { MAX NO. ROADS ));WRITELN (‘MIN HARVEST AGE : ‘,MINAGE:8,’ { MINIMUM HARVEST AGE ));WRITELN (‘MAX ACCESS LINKS :‘,MAXACCESS:8, ‘{ ACCESS LINKS PER BLOCK });WRITELN (‘ADJAC DELAY AGE : ‘,HABDELAY:8:0,’ (MINIMUM AGE OF ADJAC BLOCKY);WRITELN (‘MINIMUM VOLUME := ‘,MINVOL[3]:8:0,’ (MIN VOLUME HARVESTED PER PERIODWRITELN (‘MAXIMUM VOLUME := ‘,MAXVOL[1]:8:O,’ { MAX VOLUME HARVESTED PER PERIODWRITELN (‘MAXIMUM COST : ‘,MAXREV[1]:8:0,’ (MAX COST PER PERIOD )‘);WRITELN (‘MAX GRADE COST := ‘,MAXGRADECOST[1]:8:0,’ (MAX GRADE BUDGET PERPERIOD));WRITELN (‘MAINTENANCE COST/KM : ‘,COSTMAINT:8:0,’ (MAINT. COST!M));WRITELN (‘MAX ROAD COSTRUCTION: ‘,MAXROAD[1J:8:0,’ {MAX KM. ROAD CONST. PERPERIOD ));WRITELN (‘MIN VOL PERIODI :=‘,CUTI :8:0);WRITELN (‘MIN VOL PERIOD2 :‘,CUT2:8:0);pause:=READKEY;COLLECT;CLEARFILES;END;(* end read constraints(*============================read in block data============================*)PROCEDURE READBLOCKDATA; (READS IN BLOCK,AREA,AGE AND ADJACENT BLOCKS)VARI,K :INTEGER;TITLEI :STRING;BEGINASSIGN (A, ‘BLOCKDAT.txt);RESET(A);FOR I:1 TO MAXZONE DOBEGINZCOUNTERA[I]:0;END;readln(A,TITLEI);FOR I : I TO MAXBLOCK DOBEGINREAD (A, BLOCKA[I],AREAA[I],STARTAGEi[I],ZONEA[I]);ZCOUNTERA[ZONE[I]]:=ZCOUNTERA[ZONEA[I]]+I;BLOCKI NZONEA[ZONEA[I],ZCOUNTERA[ZONEA[I]]]:1;FOR K:1 TO MAXADJAC DOBEGIN-78-READ (A, ADJ”[l,KJ);END;END;CLOSE (A);END;(*—----— end block data *)(*==================read in existing block volume taL, ,PROCEDURE EXISTVOLUME;VARl,K :INTEGER;BEGINASSIGN (A, ‘EXVOLTAB.TXT’);RESET(A);FOR I : I TO MAXBLOCK DOBEGINREAD (A, BLOCKA[I]);FOR K:1 TO MAXPERIOD DOBEGINREAD (A, VOLUMEA[I,K,1J);END;readln(a);END;CLOSE (A);END;end existing volumes *)(*===================_==read in regen block volume tab1es*)PROCEDURE REGENVOLUME;VARI,K :INTEGER;BEGINASSIGN (A, ‘RGVOLTAB.TXT);RESET(A);FOR I : I TO MAXBLOCK DOBEGINREAD (A, BLOCKA[I]);FOR K:=1 TO MAXPERIOD DOBEGINREAD (A, VOLUME’[I,K,2]);END;readln(a);END;CLOSE (A);END;— end regen volumes —-79-(*=====================read in existing block revenue tabIes===========*)PROCEDURE EXISTREVENUE;VARI,K :INTEGER;BEGINASSIGN (A, ‘EXREVTAB.TXT);RESET(A);FOR I : I TO MAXBLOCK DOBEGINREAD (A, BLOCKA[I]);FOR K:1 TO MAXPERIOD DOBEGINREAD (A, NETVALA[I,K,1]);END;readln(a);END;CLOSE (A);END;(*— end existing revenues *)(*readin regen block revenues tables==================,PROCEDURE REGENREVENUE;VARI,K :INTEGER;BEGINASSIGN (A, ‘RGREVTAB.TXT’);RESET(A);FOR I : I TO MAXBLOCK DOBEGINREAD (A, BLOCKA[I]);BEGINFOR K:1 TO MAXPERIOD DOREAD (A, NETVALA[I,K,2]);END;readln(a);END;CLOSE (A);END;(* end regen volumes(*.....=========================read in main roads to access blocks============*)PROCEDURE ACCESSROADS;VARI,K,MARKER :INTEGER;BEGINASSIGN (E, ‘MRACCESS.TXT’);RESET (E);FOR I:1 TO MAXBLOCK DOBEGINREAD (E, BLOCKA[I], TRANS[I]);K:0;WHILE NOT EOLN(E) DOBEGIN-80-K:K+1;READ (E, ACCESS’[I,K]);END;END;READLN(E);MARKER:=K;WHILE NOT EOF(E) DOBEGINFOR I:1 TO MAXBLOCK DOBEGINK:=MARKER;WHILE NOT EOLN(E) DOBEGINK:K+1;READ (E, ACCESS’[I,K]);END;READLN(E);END;END;CLOSE (E);END;end read road access(*=====================read main road lengths and const’n costs============*)PROCEDURE READMRCOST;VARM :INTEGER;BEGINASSIGN (B, ‘MRLINKS.TXT);RESET (B);FOR M : I TO MAXMRD DOBEGINREAD (B,MRALM,J] ,MRLENGTh[M],MRCOST[M]);END;CLOSE (B);END;(*— end main road const’n costs(*===================read secondary road lengths and const’n costs==========*)PROCEDURE READSRCOST;VARI :INTEGER;BEGINASSIGN (B, ‘SRLINKS.TXT);RESET (B);FOR I := I TO MAXBLOCK DOBEGINREAD (B,BLOCKA[I],SRLENGTH[I] ,SRCOST[Ij);END;CLOSE (B);END;(* end secondary road const’n costs-81 -ii flJIl II I lull lIJI .ieratoiPROCEDURE RANNUM;VARI,k :INTEGER;XETA :REAL; (XDECIMAL, S=O or)KX,ALPHA,MU,MM,ZZX :DOUBLE;BEGINALPHA:=EXP(LN(7)*5); (alpha,mu,mm for random generator)MU:=EXP(LN(2)*31);MM:=EXP(LN(2)*31)1;{ZX= seed)FOR I:1 TO MAXBLOCK DOBEGINZZX:=INT(ALPHA*ZX/MU); (whole number from division)ZZX:=(ALPHA*ZX)(ZZX*MU); (modulus arithmetic)KX:INT(ALPHA*ZXIMU); (whole number)IF (ZZX+KX) < MM THEN ZX:ZZX+KXELSEZX:=ZZX+KX-MM;XETA:ZX/MU;S[IJ]: INT(XETA+O.5);IF AGEA[I,J1 < MINAGE THEN S[I,J]:0; (if unit immature..set to zero)END;(set zones zero if before first entry)FOR I:1 TO MAXZONE DOif j < FIRSTENTRYA[I1 thenbeginfor K:=1 to ZCOUNTERA[I] doS[BLOCKINZONEA[I ,KJ,jJ:0END;END;(* end random number generator *)(*==============================set blocks to zero===PROCEDURE SETTOZERO;VAR1K :INTEGER;BEGINVOL[J]:=O;NET[J]:=O;FOR K:1 TO MAXPERIOD DO DNR[K]:0;FOR I:1 TO MAXBLOCK DO S[I,J] :0;END;(* end blocks to zero-82-(*__==________._.__===================set roads to zero=====================!)PROCEDURE INITROADS;VARM,K :INTEGER;BEGINFOR M:=1 TO MAXMRD DO (*main roads to zero*)BEGINMRAEM,J1 :0;MRMAINT”[M,JJ:=O;END;FOR K:=1 TO MAXBLOCK DOBEGINSR[K,J]:= 0; (* initialize secondary roads *)SRMAINT[K,J]:0;END;END;—-------— end roads to zero(*_____________________________.. roads================================*)(* assign roads for each period *)PROCEDURE ASSIGNROADS;VARI,K :INTEGER;BEGIN(main roads)FOR I:=1 TO MAXBLOCK DOBEGINIF S[I,J] = I THENBEGIN(should use repeat until k=maxaccess or access[i,k]=0)FOR K:1 TO MAXACCESS DOBEGINIF ACCESSA[I,K] >0 THENBEGINMRALACCESSA[I K],Jj:=I;MRMAINTA[ACCESSA[I,K],J]:=I;END;END;END;END;(secondary roads)FOR I: I TO MAXBLOCK DOBEGINIF S[I,J] =1 THENBEGINSR[IJJ:=I;SRMAINT[I,JJ:1;END;END;END;(* end assign roads(*checkredundancies in road assignments==========PROCEDURE REDUNDANTCHECK;-83-VARI,K,M :INTEGER;BEGINIFJ>1 THENBEGINFOR M:1 TO MAXMRD DOBEGINFOR K:1 TO J-1 DOBEGINIF MRALM,K1 1 THEN MR’jM,JJ:O;END;END;(* check secondary roads for redundancy and correct *)FOR I:1 TO MAXBLOCK DOBEGINFOR K:1 TO J-1 DOBEGINIF SR[I,K] 1 THEN SR[I,J]:0;END;END;END;END;— end road redundancy check *)(*======================check for adjacent blocks and set to zero===========*)PROCEDURE ADJAC;VARI,K :INTEGER;ADJACDELAY :BOOLEAN;BEGINFOR I:=1 TO MAXBLOCK DOBEGINIF S[I,J] = I THENbegink:0;ADJACDELAY:TRUE;repeatk:k+1;IF (ADJA[I,K]> 0) AND (AGEALADJALI,K],J] < HABDELAY) THENBEGINADJACDELAY: FALSE;S[I,Jj:0;END;UNTIL (ADJACDELAYFALSE) OR (ADJ”[I,K]O) OR (KMAXADJAC);END;END;FOR I:=1 TO MAXBLOCK DOBEGINIF S[I,J] = I THENFOR K:1 TO MAXADJAC DOBEGINIF ADJ’[I,K] >0 THEN S[ADJA[I,KJ,J]:0;END;-84-END;END;(*—end adjacency check *)(*====================che net revenue of period solution================*)PROCEDURE REVENUE; (* first the undiscounted main road costs*)VARI,M,PERIOD :INTEGER;BEGINMAINRDS[J] :0;MAINLENGTH[J]:=O;MAINMAINT[J]:0;FOR M:1 TO MAXMRD DOBEGINMAINRDS[J]:MAINRDS[J] + MRCOST[M] * MRA[M,J];MAINLENGTH[J]:MAINLENGTH[J] + MRLENGTH[M] * MRA[M,J];MAINMAINT[JJ:MAINMAI NT[J] + MRLENGTH[M]*MRMAINTA[M,J];END;(* then the undiscounted secondary road costs in each period *)SECRDS[J]:=O;SECLENGTH[J]:0;SECMAINT[J]:0;FOR l:=l TO MAXBLOCK DOBEGINSECRDS[J]:SECRDS[J] + SRCOST[I] * SR[I,Jj;SECLENGTH[J]:SECLENGTH[J] +SRLENGTH[I] * SR[I ,J];SECMAINT[J] :SECMAI NT[J]+SRLENGTH[I] *SRMAI NT[I ,J];END;(* caic total length (and costs) of roads constructed and maintained*)TOTALLENGTH[JJ:MAINLENGTH[J] + SECLENGTH[JJ;TOTALMA1NT[J]: MAINMAINT[J] + SECMAINT[J];GRADECOST[J]:MAINRDS[J] + SECRDS[JJ;(* calculate the area harvested *)TAREA[J]:0;FOR I:1 TO MAXBLOCK DOTAREA[J]:TAREA[J]+(S[I ,JJ*AREA[I]);(* now calculate the gross margin from each sale *)MARGIN[J] :0;HAUL[J]:0;FOR I:1 TO MAXBLOCK DOBEGINIF RTABLEA[I] = 1 THEN PERIOD:=AGEA[I,JISTARTAGE[l]+1;IF RTABLEA[I] 2 THEN PERIOD:=AGEA[l,JJ;MARGIN[J]:MARGIN[J]+(S[l,J]*VOLUMEA[l,PERIOD,VTABLEA[l]]*(NETVALA[I,PERIOD,RTABLEj ]+TRANS[l]));HAUL[J]: HAUL[J]+(S[l ,J1*VOLUMEA[I PERlOD,VTABLEl[I]J*TRANS[l]);END;(* CALCULATE THE ROAD MAINTENANCE COSTS PER PERIOD *)ROADMAINT[JI:=TOTALMAINT[J]*COSTMAINT;-85-(* CALCULATE THE TOTAL COST FOR THE PERIOD *)NET[JI:=0;NT[JJ:=MARGIN[J]+MAINRDS[J]+SECRDS[J]+ROADMAlNT[Jj;END;(* end revenue *)(*______.____________________IcuIate DNR==============================*)PROCEDURE SUMSALES; (* sum discounted roads and sales to get DNR *)VARJ :INTEGER;BEGINDNR[RI:0;FOR J:1 TO MAXPERIOD DODNR[R]:=DNR[R]+NET[J]*DISC[J];END;(* end DNR(*=====_.________...____._=====_======screen display of results==================*)PROCEDURE DISPRESULTS; (* display solutions to screen *)VARI,J :INTEGER;BEGIN{ clrscr;}TEXTBACKGROUND(blue);WINDOW(1 ,1 ,80,25);drawbox;GOTOXY(1 ,12);WRITELN (‘REP: ‘,R-l :3,’ COST: ‘,DNR[R]:8:0);WRITELN (‘BLOCKS HARVESTED BY PERIOD’);FOR J =1 TO MAXPERIOD DOBEGINWRITE (‘PERIOD ‘,J:2,’I);FOR I:-1 TO MAXBLOCK DOBEGINIF S[I,JJ1 THEN WRITE (1:4);END;Wnte(’WRITELN;END;WRITELN;WRITELN(’ PERIOD VOLUME CONST_N LEN MAINT LEN CONST_N COST MAINT COSTTOTAL COST’);FOR J:1 TO MAXPERIOD DOBEGINWRITELN(J:5,VOL[J]:1 0:0,TOTALLENGTH[J]/1 000:10:1 ,TOTALMAINT[JjI1 000:11:1,GRADECOST[J]!vol[j]:13:2, ROADMAtNT[J]/vol[j]:1 3:2,NET[J]/vol[j]: 13:2);END;END;(* end display(*=====...signoff screen display===========================*)PROCEDURE SIGNOFF;BEGIN-86-CLRSCR;DRAWBOX;WRITELN C The program MCIP.exe has completed its run.);WRITELN (‘The results have been written to the following files:’);Readln;exit;END;(* end sionon *)(*===__======_================pnnt results—======——===PROCEDURE PRINT;VARI,J,L :INTEGER;Procedure Configurepage;VARI,J,L :INTEGER;ANS :STRING;Begin { configurepage)_______________VVRITELN (LST,IA FEASIBLE SOLUTION A);writeln(Ist);WRITE (LST,’COST=’,DNR[RJ: 10:2);WRITELN (LST,’ SEED ‘,SEEDY:15:0);WRITELN (LST);FOR J:1 TO MAXPERIOD DOBEGINWrite (LST, ‘Period ‘,J:2,’: );FOR I:1 TO MAXBLOCK DOIF S[I,J]=1 THEN WRITE (LST,’ ‘,I);Writeln(Ist);END;WRITELN (LST);WRITELN (LST,’HECTARES VOLUME SEC ROADS MAIN ROADS TOTAL COST SEC LENMAIN LEN TOTLEN);FOR J:1 TO MAXPERIOD DOBEGINWRITELN(LST,TAREA[Jj:8:0,VOL[J]:8:0,SECRDS[J]: I 0:0,MAINRDS[J]:1 2:0,NET[J]: 12:0,SECLENGTH[J]/1 000:10:1 ,MAINLENGTH[J]/1 000:10:1 ,TOTALLENGTH[J]/1 000:10:1);END;WRITELN (LST);WRITELN (LST,’SEC MAINT MAIN MAINT TOT MAINT GRADE COST RD MAINT COSTTRANSCOST);FOR J:1 TO MAXPERIOD DOBEGINWRITELN (LST,SECMAINT[J]/1 000:8:1 ,MAINMAINT[J]/1 000:10:1,TOTALMAINT[J]/1 000:12:1 ,GRADECOST[J]:14:1,ROADMAINT[J]:14:1, HAUL[J]:14:1);END;(*pnnts out road links constructed and maintained over time*)WRITELN;WRITELNCDO YOU WANT THE ROADS PRINTED IN DETAIL ? ANSWER Y);READLN(ANS);IF (ANS’Y’) OR (ANS’y’) THENBEGINWRITELN (LST);WRITELN (LST,’ ROADS TO BE CONSTRUCTED);WRITELN (LST);-87-WRITELN (LST,’ 1 2 3 4 5 6 7 8 9 10);WRITELN (LST,’—-----_________________FOR L =1 TO MAXMRD DOBEGINFOR J:1 TO MAXPERIOD DOBEGINIF (MRA[L,J] =1) AND (J1) THEN WRITELN(LST,L:5);IF (MRALL,J] =1) AND (J2) THEN WRITELN(LST,L:10);IF (MRALL,J] =1) AND (J3) THEN WRITELN(LST,L:1 5);IF (MRA[L,J] =1) AND (J4) THEN WRITELN(LST,L:20);IF (MRA[L,J] =1) AND (J=5) THEN WRITELN(LST,L:25);IF (MR’[L,J] =1) AND (J=6) THEN WRITELN(LST,L:30);IF (MRA[L,JJ =1) AND (J7) THEN WRITELN(LST,L:35);IF (MRA[L,J] =1) AND (J=8) THEN WRITELN(LST1L:40);IF (MRALL,J1 =1) AND (J=9) THEN WRITELN(LST,L:45);IF (MR”[L,J] =1) AND (J=10) THEN WRITELN(LST,L:50);END;END;WRITELN (LST);________________________________VVRITELN (LST,IAAAAAAAAAA***AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAWRITELN (LST);WRITELN (LST,’ ROADS TO BE MAINTAINED);WRITELN (LST);WRITELN (LST,’ 1 2 3 4 5 6 7 8 9 10 ‘);WRITELN (LST,’ I);FOR L :1 TO MAXMRD DOBEGINFOR J:1 TO MAXPERIOD DOBEGINIF (MRMAINTALL,JJ =1) AND (J1) THEN WRITE(LST,L:5);if (mrrnaintA[I,jj =0) and (j=1) then write(Ist,’ ‘);IF (MRMAINTAEL,J] =1) AND (J=2) THEN WRITE(LST,L:5);if (mrmaintA[I,j] =0) and 0=2) then write(Ist,’ );IF (MRMAINTA[L,J] =1) AND (J3) THEN WRITE(LST,L:5);if (mrmaint’[IJJ =0) and (j=3) then write(Ist,’ );IF (MRMAINTALL,J] =1) AND (J4) THEN WRITE(LST,L:5);if (mrmaintA[I,j] =0) and 0=4) then write(Ist,’ );IF (MRMAINTALL,J] 1) AND (J5) THEN WRITE(LST,L:5);if (mrmaintA[I,j] =0) and 0=5) then write(Ist, );IF (MRMAINTA[L,J] =1) AND (J6) THEN WRITE(LST,L:5);if (mrmaintA[I,jj =0) and 0=6) then write(Ist,’ );IF (MRMAINTA[L,JJ =1) AND (J7) THEN WRITE(LST,L:5);if (mrmaintA[I,j] =0) and 0=7) then wiite(Ist,’ );IF (MRMAINTA[L,J1 =1) AND (J=8) THEN WRITE(LST,L:5);if (mrmaintA[I,j] =0) and 0=8) then write(Ist,’ ‘);IF (MRMAINTA[L,J1 =1) AND (J9) THEN WRITE(LST,L:5);if (mrmaintA[I,j] =0) and 09) then write(Ist,’ );IF (MRMAINTA[L,J1 =1) AND (J10) THEN WRITE(LST,L:5);{if (mrmaint’[I,j] =0) and 0=10) then write(Ist,’ );}END;WRITELN(LST);END;WRITELN (LST);______________________________________VVRITELN (LST,AJ);END;END; { configurepage }-88-Procedure Askforprint;varresp :boolean;Begin { askforprint)Resp:=false;DRAWBOX;WRITELN;If repsdesired = I thenbeginWRITE (‘DO YOU WANT A PRINTOUT OF THE FEASIBLE SOLUTION ?: ‘);RepeatASKPRINT: READKEY;If askpnnt in [#89,#121 ,#78,#1 10] then Resp:= true; (yes or no)Until resp =true;end;END; { askforprint }BEGIN (procedure print main)Askforprint;CASE ASKPRINT OF#89,#121:beginConfigurepage; { Y OR y)end;#78,#1 10: exit;end; { case)end; (print)end print results(*_=write DNR and seed to fiIe==================*)PROCEDURE WRITESEEDTOFILE;VARI,J :INTEGER;TOTALVOL,LENGTH :REAL;BEGINTOTALVOL:=0;LENGTH:0;FOR J:1 TO MAXPERIOD DOBEGINTOTALVOL:=TOTALVOL+VOL[J];LENGTH:=LENGTH+TOTALLENGTH[J]/1 000;END;ASSIGN (X,’SEEDDNR.txt);APPEND (X);RANDSEEDS[R] : RANDSEED;BEGINWRITE (X,SEEDY:1 2:0,DNR[R]:1 0:0,TOTALVOL:1 O:0,LENGTH:1 0:1);FOR I:1 TO MAXPERIOD boWRITE(X,TOTALLENGTH[I]/1 000:5:1);FOR I:= I TO MAXPERIOD DOWRITE(X,TOTALMAINT[I]/1 000:5:1);WRITELN(X);CLOSE (X);END;END;(* end DNR and seed to file-89-(*_________======_._....._=========calc run time================================*)Procedure CalcElapsedTime;varELAPSEDHOUR, ELAPSEDMIN,ELAPSEDSEC, ELAPSEDTIME : Word;HOUR2,MIN2,SEC2,HUNDRETH2 :WORD;beginGETTIME(HOUR2,MIN2,SEC2,HUNDRETH2);IF SEC2 < SEC1 THENBEGINELAPSEDSEC := 60+ SEC2 -SECI;MIN2 :=MIN2 - I;ENDELSEELAPSEDSEC :SEC2-SECI;IF MIN2 < MINI THENBEGINELAPSEDMIN : 60+ MIN2 -MINI;HOUR2 := HOUR2-I;ENDELSEELAPSEDMIN :MIN2-MIN1;ELAPSEDHOUR:HOUR2-HOURI;ELAPSEDTIME:(ELAPSEDHOUR*3600+ELAPSEDMIN*60+ELAPSEDSEC);WRITELN LOWEST COST IS:’,HIGHESTDNR:l 0:0);WRITELN CELAPSED TIME:’);WRITELN (ELAPSEDTIME:8,’ sec);WRITELN(ELAPSEDHOUR:3,’ hr,ELAPSEDMIN:3,’ min’,ELAPSEDSEC:3,’ s’);end;(*—---end run time(*initia1ize vol & rev tables and flags for constructed roads====*)PROCEDURE INITTABLES;VARI :INTEGER;BEGINFOR l:1 TO MAXBLOCK DOBEGINAGEA[I, I ]:STARTAGEA[l];VTABLEA[l]:=I;RTABLE”[l]:I;END;END;(* end initialize tables and const’n flags(*===============__===========INCREMENT BLOCK AGES===========================*)PROCEDURE INCREMENTAGE;VARI :INTEGER;BEGINIFJ> 1 THENBEGINFOR l:1 TO MAXBLOCK DO-90-AGE’jI,J]:AGE”[I,J-l] + 1;END;END;(*— end increment block ages- -(*.__.....============_==========set age of blocks cut to zero================PROCEDURE ADJUSTAGE;VARI :INTEGER;BEGINFOR I:1 TO MAXBLOCK DOIF SfI,J] =1 THENBEGINSTARTAGEA[I]:0;AGE’[I,J]:=O;VTABLE’[I]:2;RTABLE”[l]:2;END;END;end setting ages to zero(*===========_===_===========sum volumes for periodj*)PROCEDURE SUMVOL;VARI,PERIOD,K :INTEGER;BEGINFOR I:1 TO MAXZONE DOBEGINFOR K:1 TO ZCOUNTERA[I] DOBEGINIF VTABLEA[BLOCKINZONEALI,K]]1 THEN PERIOD:AGE”[BLOCKI NZONEALI ,K],J]STARTAGE[BLOCKINZONEA[I ,K]]+1;IF VTABLEA[BLOCKINZONEA[I , K]]2 TI-lEN PERIOD:AGE”[BLOCKI NZONEA[I ,K],J];(check if volume is above lower bound, if so,)(set the rest of the blocks in the zone(s) to zero)IF VOL[J] >= minvol[j] THENBEGIN(current zone)FOR K:=K TO ZCOUNTERA[I] DOSLBLOCKINZONEA[I ,K],J]:0;END;BLKVOL[BLOCKINZONEA[I ,K]] :VOLUMEA[BLOCKINZONEALI , K],PERIOD,VTABLEA[BLOCKINZONEA[I , K]]]* S[BLOCKINZONEA[I,K1,J];VOL[J]:VOL[J] + BLKVOL[BLOCKI NZONEA[I ,K]];END;END;END;(* end sum volumes—---------------- _*)-91-check the constrIIL—,PROCEDURE CHECKCONSTRAINTS;BEGINIF (TOTALLENGTH[J]/1 000 <= MAXROAD[J] ) THENPASSROAD:TRUE;IF (VOL[J] >= MINVOL[J]) AND (VOL[J] <= MAXVOL[J]) THENpassvol:=true;IF (NET[J] >= MINREV[J]) AND (NET[J] <= MAXREV[J]) THENpassrev:=true;IF (GRADECOST[J] < MAXGRADECOST[J]) THENpassgrade:=true;writeIn vol ‘,vol[j]:lO:O,’ cost ‘,net[j]:lO:O,’ grade ‘,gradecost[j]:lO:O,’ road‘,totallength[j]/l 000:2:0);END;(* end check constraints(*============================n==================__====__==============*)PROCEDURE BEEP;BEGINSOUND (500);DELAY (75);NOSOUND;END;(* end beep *)(*==========================sta period by period Ioop=====================*)PROCEDURE PERIOD2;VarExitProcPrem2 : Boolean;counter : array[1 . .50] of integer;BEGINJ:=0;INITrABLES;REPEATBEGINJ:J+1;COUNTER[J] :0;INCREMENTAGE;ExitProcPrem2 := False;REPEATinitroads;settozero;passvol:= false;passrev:= false;passgrade:=false;passroad:=FALSE;COUNTER[J] :COUNTER[J]+1;IF COUNTER[J] >30 THENBEGINTest : False;-92-ExitProcPrem2 True;EXIT;END;RANNUM;ADJAC;SUMVOL;ASSIGNROADS;REDUNDANTCHECK;REVENUE;WINDOW(1 ,1 ,80,25);TEXTBACKGROUND(red);gotoxy(45,5);writeITERATIONS PERIOD : ‘,J,COUNTER[J]:lO);CHECKCONSTRAINTS;UNTIL (passvol AND passrev AND passgrade AND passroad);ADJUSTAGE;END;UNTIL J > MAXPERIOD;END;(* end period loop-(*===========================sta the main program=======================*)BEGIN(* MAIN PROGRAM *)J:0;new(volume);new(netval);new(startage);new(age);new(adj);new(access);new(vtable);new(rtable);new(mr);new(mrmaint);new(area);new(block);new(zcounter);new(zone);new(zvol);new(flrstentry);new(blockinzone);INTRODUCTION;GETTIME(HOURI ,MINI ,SECI ,HUNDRETHI);EXISTVOLUME;REGENVOLUME;EXISTREVENUE;REGENREVENUE;ACCESSROADS;READMRCOST;READSRCOST;HIGHSOFARDNR :9999999999.;DRAWBOX;FOR R:=2 TO REPSDESIRED+1 DOBEGINWINDOW(2,2,76,24);-93-TEXTBACKGROUND(red);GOTOXY(1 ,1);WRITELN(’REP: ‘,R-1 :5);REPEATTest: True;SEEDY:ZX;READBLOCKDATA;PERIOD2;IF test=TRUE THENBEGINSUMSALES;WRITESEEDTOFILE;END;UNTIL test;IF DNR[R] < highsofardnr THENHIGHSOFARDNR:=DNR[Rj;HIGHESTDNR:HIGHSOFARDNR;DISPRESULTS;END;CALCELAPSEDTIME;BEEP;READLN;PRINT;{signoff;}END.(* end of main program *)L1-94-APPENDIX 8EXAMPLES OF OUTPUT FILES-95-.COST = 83366009.86PERIOD 1:PERIOD 2:PERIOD 3:PERIOD 4:PERIOD 5:PERIOD 6:PERIOD 7:PERIOD 8:PERIOD 9:PERIOD 10:FEASIBLE SOLUTIONSEED = 1436013131 78 13 15 192 4 12 17 3014 16 18 20 24 31 4122 27 32 34 423 9 21 25 28 335 29 37 40 446 8 15 19 26 36 382 4 7 12 17 30 45 481 10 16 20 24 35 4613 18 31 32 34 41 43HECTARES VOLUME SEC ROADS MAIN ROADS TOTAL COST SEC LEN MAIN LEN TOTLEN475 233369 93825 720300 6619883 2.9 19.5 22.4394 236534 42975 335250 5992715 1.3 10.9 12.1549 335679 199050 715050 8780604 5.4 16.6 22.0440 344762 27600 625425 8513922 0.9 13.1 14.0485 343111 60450 321750 8231911 2.0 7.5 9.5433 342277 52965 453150 8928417 1.5 11.1 12.5563 335729 8700 147450 8736617 0.3 4.0 4.2615 342859 14400 211650 9527481 0.5 7.1 7.5519 344760 0 122400 8424133 0.0 4.1 4.1557 343351 1800 21300 9610326 0.1 0.7 0.8SEC MAINT MAIN MAINT TOT MAINT GRADE COST RD MAINT COST TRANS COST2.9 19.5 22.4 814125.0 1142145.0 740996.81.3 24.5 25.7 378225.0 1312995.0 760174.15.4 37.9 43.3 914100.0 2208300.0 1131632.20.9 38.6 39.5 653025.0 2015265.0 1216631.72.0 37.0 39.0 382200.0 1990785.0 1155298.31.5 49.0 50.4 506115.0 2572848.0 1207249.21.4 39.7 41.0 156150.0 2092020.0 1128142.63.0 35.3 38.3 226050.0 1950750.0 1176189.22.5 34.4 36.9 122400.0 1880370.0 1164064.42.7 38.8 41.5 23100.0 2116500.0 1190865.7TYPICAL SOLUTION FOR A 80 HECTARE DELAY PERIOD I-96-COST = 67810904.24PERIOD 1:PERIOD 2:PERIOD 3:PERIOD 4:PERIOD 5:PERIOD 6:PERIOD 7:PERIOD 8:PERIOD 9:PERIOD 10:HECTARES3 8 13 16 3118 19 24 28 392 14 22 33 414 12 27 407 23 25 38 445 20 35 463 15 26 29 371 9 19 36 45FEASIBLE SOLUTIONSEED= I6 16 18 24 30 414 13 28 39 48VOLUME SEC ROADS MAIN ROADS TOTAL COST SEC LEN MAIN LEN TOTLEN75150 660375 6313897 2.5 20.0 22.5108075 865875 7332786 3.3 17.7 20.982275 537750 6908205 2.0 14.7 16.847265 321450 6448749 1.4 7.2 8.654600 237150 6314494 1.6 6.2 7.837125 263850 5932608 0.8 7.9 8.821675 303000 7667755 0.6 5.9 6.536900 130500 6129366 1.2 4.4 5.610200 70800 7548646 0.3 2.4 2.74950 117300 7214399 0.2 3.9 4.1399386429347384323432393444404SEC MAINT2.53.32.01.41.60.82.01.73.51.0221443253252272760269928273481273012273819272331271999272616MAIN MAINT20.030.232.328.525.821.643.023.238.335.8TOT MAINT22.533.434.429.927.422.444.924.841.836.8GRADE COST735525.0973950.0620025.0368715.0291750.0300975.0324675.0167400.081000.0122250.0RD MAINT COST1148265.01704165.01753635.01524033.01397400.01141125.02291430.01266330.02133330.01876290.0TRANS COST713764.8881859.0927975.6904328.9944458.8923469.8957742.8905348.6919287.8958412.5TYPICAL SOLUTION FOR A 80 HECTARE DELAY PERIOD 2-97-P.AA*AAAAAAAAAA.AAAAAAAFEASIBLE SOLUTIONCOST = 58274230.45 SEED =810616507PERIOD 1: 1 3 13 15 18PERIOD 2: 8 25 26 29 31PERIOD3: 193339PERIOD 4: 2 7 14 17 41PERIOD 5: 24 28 36 46PERIOD 6: 4 12 34PERIOD 7: 15 18 32 42PERIOD 8: 10 21 40PERIOD 9: 1 3 19 31 47PERIOD 10: 8 25 29 37HECTARES VOLUME SEC ROADS MAIN ROADS TOTAL COST SEC LEN MAIN LEN TOTLEN416 211663 135600 711300 6266347 4.5 20.3 24.8408 225899 7350 968550 7007142 0.2 19.1 19.3235 210556 55275 258450 4770470 1.6 7.5 9.1405 225614 110175 382800 6029787 3.0 10.2 13.1296 227497 17100 313050 5893739 0.4 8.8 9.3238 220125 37125 44100 4551109 1.1 1.2 2.2339 223015 12450 155175 6179895 0.4 4.8 5.2249 226034 25290 270750 5597294 0.8 7.1 7.9410 211288 16650 32400 5640978 0.6 1.1 1.6330 213422 9675 72000 6337470 0.2 1.6 1.8SEC MAINT MAIN MAINT TOT MAINT GRADE COST RD MAINT COST TRANS COST4.5 20.3 24.8 846900.0 1266585.0 687567.50.2 31.0 31.2 975900.0 1591965.0 767151.91.6 17.4 19.0 313725.0 969510.0 732239.03.0 31.9 34.9 492975.0 1779390.0 750005.80.4 31.8 32.2 330150.0 1643220.0 817869.21.1 15.6 16.7 81225.0 849660.0 715300.62.9 28.8 31.8 167625.0 1619505.0 779601.20.8 29.2 30.0 296040.0 1529643.0 758966.63.0 23.6 26.5 49050.0 1353540.0 711642.60.5 41.2 41.6 81675.0 2123385.0 737639.1TYPICAL SOLUTION FOR A 80 HECTARE DELAY PERIOD 3-98-APPENDIX 9TYPICAL BLOCK SOLUTIONS-99-48_____________4746423q 4337 40::382q2733 3528624 2521HARVEST PERIOD22/23JA 80 HECTARE, DELAY PERIOD I SOLUTION-100-484748• 42HAPVEST) 43/ 4034I.363025,PERIOD123A 80 HECTARE, DELAY PERIOD 2 SOLUTION-101-4844 45 47464142HARVEST PERIOD4337 40 1353622/23 1M;\10 11/ 7541 2—A 80 HECTARE, DELAY PERIOD 3 SOLUTION-102-41 ‘iq35j36J-ç2 Yi1 I \—m)7778\ I 84( 90 8879 8786HARVEST8081828584PERIOD123A 40 HECTARE, DELAY PERIOD I SOLUTION-103-PERIODA 40 HECTARE, DELAY PERIOD 2 SOLUTION-104-86 ]\/ HARVEST PERIOD144 1 ‘\85 \—(;/ & 4Lf1I LI 41\ 72I I \ k )( \c, //‘%%%/ R 3KI\‘v )64 4%%% J68 70I - I / \ /6 I40’\,)38 ? 82Ir5c605635— 348 /333126 4824 2720 21 22is12 14108 6:.:.:.:.:.:.7S53A 40 HECTARE, DELAY PERIOD 3 SOLUTION-105-17qh\J’X”7fr_______74)%72\1 >i’__(147L(JX-/tY \r-)140 rioleees 143169 tes163146 159 181 182 Ij] 1140 157 186154 111521532tee 133 •so 1271 135 131 12•,.121:: 17112_i3 114HARVEST PERIODA 20 HECTARE, DELAY PERIOD I SOLUTION-106-101 192177 182 190149 172 173 174 176183 187147 . 171 i’m 184148 170 107 163 HARVEST PERIOD• 143 189 toe 105eq14.142 159 181 162 [jjjj] 1• 141•53 lj: 282 e3 138131• :......132 13 S 37.5.’.71 72 ..70 h 1L1••115113U •...106 104 1GO ••• 10$.:..57 i0363 62 •.•:• •. ..:.::54 ::.•::••.•..47 5148 4446- 37 9141 40 33G32 ii30 31 Ii2124 22 17284 5:-:.:t:.:.:• 2A 20 HECTARE, DELAY PERIOD 2 SOLUTION-107-160iqi iqi.,. 177182 591q 172 173 174 176193 187147 175 184l-_ •i7g 196 184163 HARVEST PERIOD189 169 285159 160141142 159 1,82 :::99 . 164— 157 151 152 L 292•3 84 138 134 133 132 13 • 3cç81 1371 135. 131 129•19 .122 •Z.• 178 123125 12718 74 •:. 126‘75 120 1177 1270 . Liioi—./106 104 1,8684 57 103 .øt:::.96 7q963 62 81.•.•:: ..“•:•.5448 4e 4437...41 404232 1831 Ii29 1421282423 201710 1229 1125 4 57•::• 2 ::::3:A 20 HECTARE, DELAY PERIOD 3 SOLUTION

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