Paper Forestal

Copyright q 1999, Institute for Operations Researchand the Management Sciences0092-2102/99/2901/0007/$5.00This paper was refereed.

INDUSTRIES—LUMBER/WOODDECISION ANALYSIS—APPLICATIONS

INTERFACES 29: 1 January–February 1999 (pp. 7–29)

Use of OR Systems in the Chilean ForestIndustries

Rafael Epstein Department of Industrial Engineering, Universityof Chile, Republica 701—Santiago, Chile

Ramiro Morales Department of Industrial Engineering, Universityof Chile

Jorge Seron Bosques Arauco Los Horcones s/n, Concepcion,Chile

Andres Weintraub Department of Industrial Engineering, Universityof Chile

The Chilean forestry sector is composed of private firms thatcombine large timber-land holdings of mostly pine plantationsand some eucalyptus with sawmills and pulp plants. Since1988, to compete in the world market, the main Chilean forestfirms, which have sales of about $1 billion, have started imple-menting OR models developed jointly with academics fromthe University of Chile. These systems support decisions ondaily truck scheduling, short-term harvesting, location of har-vesting machinery and access roads, and medium- and long-term forest planning. Approaches used in solving these com-plex problems include simulation, linear programming withcolumn generation, mixed-integer LP formulations, and heuris-tic methods. The systems have led to a change in organiza-tional decision making and to estimated gains of at least US$20 million per year.

The Chilean forestry sector generatesabout 13 percent of all exports. For-

estry exports include timber logs, pulp,and sawtimber. It is the second largest sec-tor in the country after mining. The sectorhas grown at a rate of 12 percent a year

during the last seven years and has goodpotential for further expansion during thenext 20 years. The forest sector has beenone of the drivers of Chile’s amazing eco-nomic development during the last 15years.

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The Chilean forestry sector is com-pletely private, based mainly on largefirms that own pine plantations (some eu-calyptus too) and are vertically integratedwith pulp plants, sawmills, and papermarkets. Holding Arauco and ForestalMininco (CMPC), the two largest compa-nies, are among the 50 largest forestryfirms in the world. Holding Arauco, whichconsists of Bosques Arauco and ForestalCelco, has 740,000 hectares of plantationsand annual timber sales of about $300 mil-lion. In addition, it purchases timber val-ued at about $100 million. With its indus-trial products (pulp and sawtimber) itstotal sales are about $1 billion a year.CMPC, the other large firm, owns 490,000hectares and has annual timber sales of$180 million. Timber purchases add an-other $120 million, and total sales are $1.3billion a year when pulp, paper, and saw-timber are added. Other important forestfirms are Forestal Bio-Bio, owned by theNew Zealand group Fletcher (50,000 hec-tares); Forestal Millalemu (60,000 hec-tares); Forestal Monteaguila, owned byShell (30,000 hectares); and Forestal Copi-hue (20,000 hectares).

Chilean forestry firms have always hada high level of cooperation. In 1988, theywere organized into an association calledForestry Production Group (GPF), coordi-nated by Fundacion Chile, a nonprofit in-stitution formed by the Chilean State andITT, to promote the development of Chile.Within this initiative, the management ofthe Chilean forestry firms has changedthrough the introduction of optimizationsystems at different decision levels. Mostof the systems were developed by the for-estry firms in a joint effort coordinated by

Fundacion Chile. We will describe the sys-tems we developed, the problems wesolved, the process we used in developingthe systems, the methodology used, its im-plementation, and finally the results ob-tained in each case. The systems devel-oped deal with three operationalproblems: daily truck scheduling, locationof harvesting machinery, and short-termharvesting. A typical distribution of oper-ating costs is 30 percent for harvesting, 42percent for transportation, 14 percent forroad building, four percent for loading,and 10 percent for other processes[Weintraub et al. 1996]. The fourth prob-lem the systems deal with is medium-range tactical harvest scheduling, and thefifth problem is long-range strategicplanning.

All of these systems have evolved overtime as the firms’ needs have changed andthe systems have become more sophisti-cated. At the moment, each system is inversion 2 or 3. The systems are designedon PCs for ease of use and run in smallCPU times consistent with time managersallocate for decision-making meetings. Thesystems have had an organizational im-pact. Decision making at each level has re-lied on these systems, and successful man-agement is seen as associated with the useof these systems.

Use of systems has led to annual sav-ings of at least US $20 million a year. Thisamount is significant given the size of thefirms. For instance, due to the use of threeOR systems, Bosques Arauco reports totalsavings of $8 million a year over a totalannual timber production worth $140 mil-lion. The firm considers its use of thesesystems a strategic competitive advantage.

CHILEAN FOREST INDUSTRIES

January–February 1999 9

The systems have also had an importantimpact on management organization andhave in some cases contributed to environ-mental protection. This work has been rec-ognized in other countries: South Africaand Brazil have implemented some ofthese systems, and New Zealand has ex-pressed interest in them.

Their joint development ofthese systems means that thesoftware has become jointproperty, evidence of thewillingness of the firms . . . toshare technical developments.

Starting in 1993, a state agency that sup-ports applied research, Fondef, funded thedevelopment of basic tools, which werelater transfered to forestry firms. This sup-port came through a grant obtained by thegroup.

The positive impact of these systems hasled forestry firms to increase their profes-sional development and training in the useof these quantitative tools. Some of theprofessionals who directed successful im-plementations of these systems have beenpromoted to higher positions within theirorganizations. As Jorge Seron, CEO ofBosques Arauco, said, “Our firm has beenusing three systems developed by thisgroup. These systems have had a deep im-pact on our firm, as they have become ba-sic tools in our forest planning and man-agement. Any new professional we hire isrequired to learn the use of these systemsand make them part of their regular work.This has allowed us to handle a largenumber of timber stands, multiple prod-

ucts, hauled from many origins to destina-tions, using 200 trucks with a small num-ber of engineers. In this way, eachengineer is capable of managing about500,000 cubic meters of production peryear, leading to a very productive man-agement. Through better use of the har-vesting machinery, we reduce erosion.This reduction in environmental harm isvital though difficult to quantify. Overall, Ifeel that the use of these systems has givenus a strategic competitive advantage in theglobal timber markets, where our firm,which is significantly oriented toward ex-ports, competes in a very competitivesetting.”

We will comment on the relationshipbetween all the participants in developingthese systems: the University of Chile, theforest firms, and Fundacion Chile, whichcoordinated the firms in the Forest Pro-duction Group. Their joint development ofthese systems means that the software hasbecome joint property, evidence of thewillingness of the firms in this industry toshare technical developments. This will-ingness exists not only among forest firmswithin Chile, which could be explained bytheir need to collaborate in marketing andtechnological development to competewith other timber-producing countries,such as New Zealand, South Africa, andCanada, but also extends to firms in othercountries. Visits of Chilean professionalsto forest areas in other countries are com-mon, and a culture of sharing knowledgeis far stronger than in other fields. Thishas made the extension of the systems wedeveloped to multiple firms in Chile, andlater to firms in other countries, mucheasier.

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While forest professionals within thefirms have become quite proficient in un-derstanding and using the systems, nofirm has hired technical personnel in OR.Thus, all systems development dependson the expertise of the university group.ASICAM: A Truck-Scheduling System

An important problem in forestry opera-tions is deciding how to transport timbereach day from different stands (origins orsources), with known supplies, to destina-tions, such as pulp mills, sawmills, sortingyards, and ports, to meet their daily de-mands. The timber products transportedare characterized basically by the lengthand diameter of each log. The productsavailable are usually stocks remainingfrom the previous day plus productionthroughout the day. Trucks transportloads of logs from origins to destinations.At origins and destinations cranes loadand unload the trucks. Although the firmstypically subcontract trucks and cranes,they usually organize their schedules. Thebasic decisions a log-transport managermakes each day concern (1) the originsfrom which to transport product to satisfyeach demand, (2) what trucks and cranesare needed at origins and destinations tosatisfy all demands, and (3) the workschedule for each truck and crane.

Besides satisfying demands for prod-ucts, forestry firms must consider (1) thecharacteristics of trucks and cranes, basi-cally described by the time and costs in-volved in trips and in loading and unload-ing; (2) the arrival time of trucks atdestinations, which determines the num-ber of cranes needed for unloading andfor coordinating deliveries of logs withdownstream operations; (3) the income

levels of truck drivers; and (4) the startingand ending points of each truck’s dailyroute.

The basic objective is to satisfy the de-mand for different products at each desti-nation, while minimizing transportationcosts within technical, policy, and laborconstraints. A typical forestry firm oper-ates with approximately 10 to 90 origins,five to 30 destinations, and between 50and 300 trucks. Depending on the distanceinvolved, each truck can make from one tofour trips per day. Since transportationcosts account for about 40 percent of oper-ating costs, it is important to define andcontrol truck schedules efficiently.

The traditional log-transport systemsused in the Chilean forest industry wereinefficient and poorly organized. Essen-tially truck drivers had no well-definedschedules. This led to failures to meet de-mand, long waiting times in queues, fric-tion among drivers, long working days,low utilization of equipment, and poor co-ordination with downstream operations,such as the conveyor belt at the mill. In1988, Bosques Arauco produced 600,000cubic meters of timber per year, whichwas transported with a fleet of approxi-mately 90 trucks. Jorge Seron, at the timehead of production, and Pier Traverso,head of transportation, worried becausetruck operations were difficult to handleand expansion plans called for almost tri-pling production by 1990. They were con-vinced that their manual scheduling sys-tem, based on a magnetic board, could nothandle the expansion in volume. Thatmagnetic board was the first effort to or-ganize transportation in the forestry sec-tor. The managers realized the limitations



of their manual scheduling, which only al-lowed them to define rigid trip cycles withschedules that had to be kept for manydays and which limited their capacity torespond to variations in production. Theyneeded a new and better tool to improvethe efficiency of the operation and to han-dle the expansion. They were unable tofind a system that handled forest-transportation scheduling in high technol-ogy countries with forestry sectors, includ-ing the USA, Canada, and New Zealand.To improve this situation, they asked theteam at the University of Chile, AndresWeintraub, Rafael Epstein, and RamiroMorales, to develop an administrative andcomputerized system for Chilean forestfirms to program and manage an efficientdaily schedule of truck trips. This was thefirst such joint project of GPF, which wasat the time directed by Marcelo Kunz, whois now CEO of Forestal Millalemu.

ASICAM took about a year to develop,but a preliminary version was operativeafter six months. The system was imple-mented in January 1989 at Bosques Ar-auco. Weintraub and Epstein designed thealgorithm for ASICAM to be very robust,so that all firms could use it. Later ArielSchilkrut, who also supported the othersystems, participated in maintaining anddeveloping newer versions of the system.Jaime Catalan and Jorge Gatica also con-tributed to this project.

ASICAM had a dramatic impact on for-est transportation. A main reason the pro-ject succeeded was that Jorge Seron andPier Traverso became directly involved indeveloping and implementing the systemand had a clear understanding of theproblem and objectives. This close collabo-

ration between academics and managersof the forestry firms was a common factorin the successful implementation of all thesystems that we developed. The success ofASICAM showed the potential of opera-tions research tools for forestmanagement.

Eight Chilean firms haveimplemented ASICAM, andthey report savings of 15 to 35percent of transportationcosts.

ASICAM is based on two notions: a cen-tralized administrative system that sched-ules and controls all trips, and a simula-tion model for generating such decisions.The administrative overhaul was essentialto centralize and coordinate decisions andto schedule trips efficiently. Determiningefficient truck schedules is a complex com-binatorial problem, which clearly couldnot be solved well with a manual ap-proach using a magnetic board. We basedthe computational system on a simulationmodel driven by heuristic rules that assigntrips to trucks. The system, which is rundaily, takes the following as its main in-puts: the supply of timber products at ori-gins or sources, demands at destinations,truck fleet and crane equipment character-istics, costs and times for the differenttrips and for loading and unloading, plusan additional set of relevant constraints.As outputs, the system yields require-ments for trucks and cranes, a schedule foreach, and basic statistics to evaluateperformance.

Given the high combinatorial complex-

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ity of the problem, we chose an approachthat simulates daily operations. We triedto replicate real-time scheduling, given thevolumes of products that have to behauled from origins to destinations andthe trucks available. In the simulation pro-cess, we assign trucks following specificrules. The simulation starts, for example,at 6:30 AM as the first group of trucksstarts loading and later are dispatched totheir destinations. As the cranes at originsbecome available again, new trucks enterthe system. After trucks unload at destina-tions, they are assigned new trips. Thesystem moves along in this manner duringthe day.

To assign trips in a coordinated way, wechose a moving time horizon of one hour.Given a starting time t0, the system evalu-ates all possible trips for all trucks thatwill become free before t0 ` 1 hour. Onlythose trips that are assigned by the simu-lation process during the first 15 minutesare actually fixed. Then the starting timemoves to t0 ` 15 minutes and the trip as-signment process is repeated (Figure 1).The assignment of trips is based on evalu-ating every feasible option a truck has af-ter unloading. An option is a trip to anorigin to load a product and another tripto a destination for unloading. An optionis feasible depending on truck-frame andengine characteristics, and on policy deci-sions. These options are evaluated basedon priorities and desirability of the trips.

To evaluate the desirability of each fea-sible trip, we define an index that consid-ers the total real cost plus a congestionpenalty. The typical contracts with truckowners link payment with the length ofthe loaded trips carried out (salaries to

truck drivers are managed by the truckowners, not the forest firms). However,the firms realized that in the long run theyneeded to consider the real costs the truckowners faced (for example, to consideralso queuing and empty trips). So the ob-jective was defined to minimize the realcosts of transportation. Total real costsfaced by truck owners include operationalcosts (fuel, tires, maintenance) and fixedcosts (capital depreciation, insurance, sala-ries). The penalty for congestion at originsis a heuristic estimate that depends on (1)the trucks that may load at the same timeat a given origin, (2) the alternative tripsavailable for those trucks, and (3) theprobability of selecting a conflicting trip.The simulation process estimates the con-gestion effect as it analyzes possible futuretrips to origins to be made in addition tothose already scheduled. The congestionpenalty is not a real cost; it is just a deviceto reflect the loss of efficiency some tripassignments cause to other trucks, and it isnot included in the reports.

The selection of the next trip to be as-signed is based on the desirability indexjust described but in the context of trippriorities. Priorities are based on themodel’s perception of urgency in schedul-ing trips. Thus, the first priority is for tripsto destinations with urgent requirements.For example, if a destination requires fourtruckloads per hour, and the simulationhas assigned only two between 14:00 and15:00 with few options available to pro-vide the remaining two truckloads, thosetrips become first priority. The scheduleprograms efficient trips to minimize trans-portation costs and reduces queuing atorigins and destinations.



Figure 1: Between t0 and t0 ~ 1, trucks 1 and 2 arrive at destination D1, and trucks 3 and 4arrive at destination D2. At t0 the simulation model assigns a trip for trucks 1, 2, 3, and 4. Deci-sions for trucks 1 and 3 are performed while decisions for trucks 2 and 4 are released. Thesimulation time is increased by 15 minutes and the process is then repeated at t0 ~ 15*. A deci-sion consists of an unloaded trip to an origin and a loaded trip to a destination. For instance, adecision for truck 1 could be loading at origin O2 and unloading at destination D2.

Because destinations and downstreamoperations have limited unloading capac-ity, arrivals at destinations must be regu-lar. This is not trivial because complete cy-cles (trip to origin, load, trip todestination, unload) can vary significantly(1.5 to five hours) depending on the loca-tions of the origins and destinations. Dur-ing the simulation, the system dynami-cally determines when a destination willbe in critical need of supply in order tocontinue regular operations.

The development and fine-tuning ofthese heuristic rules took over a year, in-cluding tests in different firms. The finalalgorithm turned out to be robust for allfirms and situations. Weintraub et al.[1996], give a detailed description of thesystem. The system runs on a PC andtakes approximately three minutes to finda solution. The operators need to havegood knowledge of the transportation sys-

tem but not a high level of technical prep-aration. Typically, the operator needsthree or four runs of the system to evalu-ate several scenarios before choosing asolution.

The implementation of the system hasprovided significant benefits, both quanti-tative and qualitative. The quantitative im-provements have been measured in termsof numbers of trucks, numbers of cranes,operational costs, and total transportationcosts. More efficient assignment of tripsleads to shorter trips and less queuing. Astrucks’ productivity increases, fewertrucks are needed (Table 1). This allows adecrease in capital investments. Becausethe firms usually share the savings withthe trucking firms, the trucks that remainin the system have improved the incomethey produce for their owners. In mostcases, reorganizing the administrative sys-tem was responsible for a significant frac-

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CompanyBeforeASICAM

AfterASICAM

Bosques Arauco 156 120Forestal Millalemu 80 50Forestal Bio-Bio 118 76Forestal Rıo Vergara 120 80

Table 1: The number of trucks four forestryfirms required for hauling similar volumes oftimber decreased with the implementation ofASICAM.

tion of the improvement. As peak arrivalsat destinations flattened, the number ofcranes needed for loading and unloadingdecreased by about 20 percent.

Eight Chilean firms have implementedASICAM, and they report savings of 15 to35 percent of transportation costs, equiva-lent to total annual savings of more than$8.5 million a year [Weintraub et al. 1996].

The firms also achieved qualitative im-provements, such as improved overallcontrol of the system, by organizing tim-ber stocks at origins, keeping trucks andcranes in good shape, and handling dis-ruptions that occur during the day, andsmoother downstream operations by mak-ing regular deliveries at demand nodes. Inaddition, the system has improved thequality of life of workers, reducing theirworkdays from 14 to 11 hours, and in-creasing their salaries because of higherproductivity. Managers of forestry firmshave commented on these improvements[Weintraub et al. 1996]. ClaudioRodriguez, head of the Division of TimberSupply at Forvesa (presently Forestal Min-inco), noted, “We have reduced our fleetby 32 percent, but the most positive as-pects, in my judgment, are the qualitativebenefits concerning people.” Bosques Ar-auco tripled its operations in 1990; Pier

Traverso, head of transportation, said in1992, “ASICAM has been in operation forthree years in Bosques Arauco with verysignificant benefits, which were especiallyevident when a new plant came intooperation. We went from 120 trucks to 300trucks in a peak month, and in spite ofthis expansion, there was no chaos, no dis-order. In addition, the quality of work ofthe drivers improved as well as the con-trol over the system, especially with re-spect to loading and unloading.”

Leonidas Valdivieso, head of the De-partment of Harvesting and Transport atMininco, said, “We have been able to opti-mize not only transport, reducing thenumber of trucks, favoring the remainingwith more trips, but we have alsoachieved better coordination between har-vesting operations and demand centers.”Mauricio Pena from Forestal Millalemucommented, “The most visible and imme-diate effect was the reduction in the truckfleet from 80 to 50 trucks. Additionally,the number of internal personnel dedi-cated to programming and supervisingtransportation was reduced. Further bene-fits obtained have included the detectionof equipment shortages, a reduction ofwood stock at origins, and the subsequentdecrease in losses due to degradation.”

The system has proved to be extremelyportable to different realities. For instance,Sawmills Arauco, a subsidiary of HoldingArauco that handles sawtimber produc-tion through eight sawmills, has used aversion of ASICAM to schedule its truckfleet since 1997. Mondi in South Africa im-plemented ASICAM; we are developing aversion of ASICAM for Aracruz, a largeBrazilian forest firm; and according to



Figure 2: In this analysis of the use of two different bucking patterns, pattern 1 first tries toobtain a piece 12.10 m long and at least 24 cm in diameter. After that, the pattern looks for apiece 4.10 m and 20 cm. Finally, the remainder of the tree goes to pulp. Similarly for pattern 2.The diameters shown in each schematic figure are actual values obtained. Since in pattern 2, at8.10 m long the diameter obtained (29 cm) is larger than the minimum required (24 cm), thefirst piece can be cut.

Cossens [1992, p. 18], “ASICAM appearsto have good potential for use in NewZealand.” (However, it has not been im-plemented in New Zealand.)

Mondi’s implementation of ASICAM re-quired minor modifications to account forthe fact that Mondi works around theclock. ASICAM was one of the tools thatled to Mondi Forests being awarded the1996 South African Logistics AchievementAward. As Don Alborough, supplies andlogistics manager of Mondi-Natal, ex-plains, “Over a period of years ASICAMwas purchased and implemented verysuccessfully into our Natal operations. Thecontrol over our and contractor fleet in-

creased dramatically, and Mondi saw dou-bling of vehicle utilization and a halvingof the fleet transporting some 400,000 tonsper annum. The system now forms thecornerstone of a quality initiative where itis essential that we feed the merchant millwith a consistent supply of timber withsimilar properties.”OPTICORT: A Short-Term HarvestingSystem

After implementing ASICAM, the fo-resty firms initiated a project to supportshort-term harvesting. For the purpose ofharvesting decisions, forests are dividedinto reasonably homogeneous stands,similar mainly in tree age, site quality, and

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management state. Short-term harvest de-cisions can be viewed as follows: for a pe-riod of typically three months, demandsfor timber products, defined by length anddiameter of each piece, are known. Attimes, the average diameter of all thepieces making up a complete sale is alsoimportant. Typical demands are (in orderof decreasing commercial value) exportlogs (long pieces of high diameter), saw-timber (shorter logs of high diameter), andpulp timber (any diameter).

In harvesting, firms use different typesof machinery for different types of terrain.They harvest areas with steep slopes usingtowers or cable logging, and they harvestflat areas using tractors or skidders. Whenloggers harvest trees they cut them intoseveral products or pieces to respond todemand. This cutting operation is calledbucking. Bucking can be carried out on theground and individual pieces are trans-ported to their separate destinations fromthere, or the whole log can be transportedto a sorting center, where the bucking iscarried out.

The bucking instructions are given as aset of lengths and diameters to be ob-tained in sequence, of decreasing diameterand value. Loggers are instructed to ob-tain as many pieces as possible of each de-fined piece, in the given order. Thus, frombucking pattern 2 in Figure 2, the loggerfirst tries to get a piece which at 8.10 mhas a diameter of at least 24 cm. If at thatlength the diameter falls below 24 cm, thelogger then tries to obtain a piece of length4.10 m and diameter 20 cm. After that, therest of the tree is used for pulp, which hasa minimum diameter of 8 cm.

Each forestry firm has developed a

forest-inventory system based on sampleplots, which indicate for each stand andgiven bucking pattern how much volumecan be expected for each product. Figure 3shows how a sample tree might be visual-ized by the inventory system before buck-ing, while Figure 2 shows a schematic so-lution for two given bucking patterns.

Short-term harvest planning takes intoaccount harvesting and transportation de-cisions. Transportation costs used in OPTI-CORT are based on observed-average orestimated transportation costs for differentorigin-destination pairs. Traditionally, anexperienced planner did short-term har-vest planning manually. The planner ana-lyzed the demands for different productsin the near future (one to three monthsahead), the standing timber available inthat period, and the firm’s capacity forharvesting, which depends mainly on theavailability of harvesting equipment (tow-ers, skidders) and trucks for transporta-tion. With this information, the plannerscheduled a sequence of stands to be har-vested and the machinery to be allocated.The planner defined bucking patterns soas to yield the products needed, includingstocks, to satisfy each period’s demand,typically a week. The information onstanding timber came from preharvest-inventory systems.

Matching standing timber with productdemand turned out to be a difficult combi-natorial problem, which led to significantlosses as mismatches led to harvestingmore timber than was really needed andto the degradation of much of the excess.An additional problem, though of lesserimpact, was that less than optimal deci-sions were made in the use of machinery



Figure 3: In this representation of simulation criteria in bucking patterns, the bottom part ofthe tree, below the defect, leads to an export piece, with some residual timber useful only aspulp. The six-meter section above the defect can be used as sawtimber.

and transportation.OPTICORT seemed a logical way to get

better schedules. The development wasled by Jorge Seron and Enrique Nieto,head of planning from Arauco. SergioAlvarez, regional chief, and EduardoTapia, a senior manager from ForestalMininco, also played important roles. De-velopment of the system took about twoyears, and its implementation at Arauco,Mininco, and Bio-Bio was very successful.

OPTICORT is based on an LP modelwith a column-generation procedure (ap-pendix). The main decisions the modelcovers are which stands to harvest amongthose with mature trees ready for harvest-ing that are already accessible by existingroads, what type of machinery to use ineach operation, what volume to cut eachweek or period (with the correspondingbucking patterns to be used), and whatproducts should be delivered to differentdestinations to satisfy demand (stocks canalso be accumulated for future use).

A main methodological point was the

definition of bucking patterns. The num-ber of such patterns is exponentially high.At first, we built the model with a pre-defined, moderate set of such patterns foreach stand, trying to cover a reasonablerange of options. When the model wassuccessfully implemented, we developed acolumn-generation approach to automati-cally generate the bucking patterns. Thisnew feature overcame two main draw-backs: first, for users it was too time con-suming to generate a “good” set of pat-terns, and second, the sets of initialbucking patterns were probably missingbetter options. We based the column-generation scheme on a specially devel-oped branch-and-bound algorithm linkedto each firm’s forest-inventory system.

The basis of the column-generationscheme is shown in Figure 4. At the rootnode, the scheme chooses a first cut. Forexample, it cuts a piece 12.10 m long and24 cm in diameter. From each node, thescheme defines new branches according tothe next cuts that are possible. Thus, after

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Figure 4: In this branch-and-bound tree for generating bucking patterns, an arc leaving the rootnode corresponds to the first cut in the bucking pattern (level 0), and a path from the root nodeto the bottom of the tree represents a bucking pattern. Each arc represents a product defined bylength and diameter, while its level indicates the position of the product in the bucking pat-tern.

a cut 12.10 m long and 24 cm in diameter,a next cut 8.10 m long and 20 cm in diam-eter is one logical alternative. The value ofeach branch is defined by the sale value ofthe corresponding piece, given its lengthand diameter, and the dual variables ofthe present solution. Each path from theroot node to the bottom of the tree corre-sponds to a bucking pattern. The scheme,including branching and stopping rules,has been implemented at Bosques Arauco.Tests showed that using column genera-tion improved the objective value by threeto six percent over just using a limitednumber of bucking patterns in the LP

model.The system has been in use since 1991 at

Bosques Arauco, Forestal Celco, ForestalMininco, and Forestal Bio-Bio. They typi-cally run the model about every twoweeks, in a rolling horizon of threemonths. The model runs on a commercialLP code on a PC in about 10 minutes.Quantitative savings, obtained mainlythrough a better fit of supply of standingtimber to demand for specific products,have been estimated at about $3 millionper year for the larger firms, and a total of$7.7 million for all firms [Epstein et al.forthcoming]. Using OPTICORT, they



make better use of timber to satisfy de-mand by reducing the amount of timberdegradation. The better match has reducedthe need for cutting extra volume.

OPTICORT also produced savings intransportation. For instance, Bosques Ar-auco saved $250,000 per year when themodel indicated that it was better to trans-port directly to destination about 50 per-cent of the volume that was being trans-ported through intermediate sortingcenters. Enrique Nieto, head of planningfor Arauco, explains that OPTICORT hasbeen useful in evaluating the overall planfor each season and in estimating the like-lihood of satisfying the demand for the re-mainder of the season. As far we know[Weintraub and Bare 1996], this is the firstsystem developed that optimizes detailedshort-term harvesting decisions. We aredeveloping a similar system for Aracruz-Brazil.PLANEX: A Machine-Location and Road-Design System

The third system deals with the optimallocation of harvesting equipment and ac-cess roads. Harvesting planners allocateharvesting machinery and design the roadnetwork to reach that machinery. Whenthe firm plans to harvest a defined area of400 hectares in the next three to sixmonths, the planner must decide how toallocate harvesting machinery to most effi-ciently carry out the harvesting operations.Cable-logging or towers are used for steepareas and skidders or tractors for flat ar-eas. Cable-logging operations, which aremore expensive than tractor operations,have longer reach and thus require lessroad building and hauling. The plannermust decide where to place towers and

what type of tower to use. Towers typi-cally range from 300 to 1,000 m, with thedirection of pull upwards or downwards.Finally, the planner must design roads toaccess tower landings, where a small, flatarea in necessary to store logs and loadthem into trucks. Also, skidders shouldwork near roads. It is most economical forskidders to work no farther than 300 mfrom the road. Harvesting operations us-ing skidders and towers and building theaccess roads account for about 45 percentof the total operating cost, so this is an im-portant problem.

The main decisions in planning are (1)which areas to harvest by skidders andwhich by towers, (2) where to locate thelandings for towers, (3) what area shouldbe harvested by each tower, (4) whatroads to build, and (5) what volume oftimber to harvest and transport.

In addition, since Chilean forests aremostly in mountainous areas, the designof harvesting systems is complex andmust take into account a variety of techni-cal constraints that govern (1) locating thelandings for towers according to topo-graphical conditions; (2) locating eachtower to comply with its range of reach,depending on the type of tower, operatingconditions, and the characteristics of theterrain (for example, ensuring that thereach of the cable for logging is not inter-rupted by a river); (3) ensuring that topo-graphical conditions permit skidder opera-tions, basically determined by the terrainslope; (4) building roads with appropriatecharacteristics, including acceptable slopeand minimum radius of turn for trucks;and (5) availability of equipment. Cable-logging operations from a specific location

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are carried out by moving the cable intoset positions in a radial sequence, so as toharvest all the timber that is within thereach of the cable and is topographicallyfeasible.

Traditionally, planners allocated ma-chines manually by analyzing topographi-cal maps in a laborious exercise, which al-lowed the planner to evaluate only a verylimited range of options. Jorge Seron ofBosques Arauco led an effort to mechanizethese decisions. The best-known systemsavailable were PLANS, developed by theUS Forest Service [Twito et al. 1987] andPLANZ [Cossens 1992], a similar systemdeveloped for New Zealand. Both inter-acted with a geographic information sys-tem (GIS) and worked basically as simula-tors. The user defines the location ofharvesting machinery on a screen, and thesystem, based on GIS information, thengenerates the road to link the machinerywith the existing roads and to allocate thetimber to be harvested by each machine.Not satisfied with the existing systems,Jorge Seron met with Epstein andWeintraub and asked for a “system to tellme where to locate the towers and skid-ders and the complete road network.”

We developed PLANEX to supportthese decisions. Arauco senior managersEnrique Nieto and Pedro Sapunar werealso heavily involved. Later, FernandoBustamante and Hugo Musante, seniormanagers from Bio-Bio and Mininco, re-spectively, worked on the project for theirfirms.

PLANEX requires a large amount of in-formation provided by the GIS that eachfirm has developed, such as altitude-levelcurves, timber volume, existing road loca-

tions and characteristics, and topographicaccidents, such as rivers or ravines. Thereare two main standards for storing geo-graphic data, the raster format, which di-vides the area into small polygons, usuallysquares, to which all the information is as-sociated; and the vector format, whichstores the data using the exact coordinatesof each graphic element (Figure 5). Eachhas advantages and disadvantages. Man-aging information is usually easier in ras-ter format, particularly when designing aroad. In this case, information that comesfrom the GIS in vector format is trans-formed into raster format in cells of 10 2

10 square meters, to cover topographicconditions, existing roads, and standingtimber.

We have developed, jointly with Johnand Bren Sessions of Oregon State Univer-sity, a friendly, interactive, graphic userinterface that allows the user to visualizeand modify solutions. The system incorpo-rates the information from the GIS, plusadditional information obtained throughthe interactive interface regarding possiblelocations for towers, relevant costs, andsuch technical parameters as maximumslope for designing roads. The system de-signs an approximately optimal allocationof machinery based on a heuristic algo-rithm. The objective of the system is toharvest all volume that is profitable to har-vest while minimizing costs. Basic costsconsidered are installing and operatingtowers, operating skidders, road building,and transportation, often of little signifi-cance given the short distances within theharvesting area.

The system has an internal heuristic al-gorithm that obtains a solution based on



Figure 5: GIS data are stored and presented in raster format or in vector format. The squaresrepresent the raster pixels. The bold line shows a road in a vector format while the thin linesrepresent isometric altitude curves in vector form. The shaded area represents areas with stand-ing timber in raster form.

first defining the areas to be harvestedwith skidders and towers according toslopes. The most attractive locations for in-stalling machinery are then sequentiallydetermined based on a criterion of mini-mum cost per cubic meter, where costs in-clude harvesting, road building, and trans-portation. A shortest-path algorithmdetermines the best new roads to build tolink machine locations to existing roads. Alocal search routine looks for changes ofmachine locations to improve the solution.Once all locations are defined, a heuristicroutine finds a road network of minimumcost.

The machine-location and road-designmathematical problem behind PLANEXcan be reduced to an uncapacitated net-work design (UND) problem (appendix).Moreover, if we discard the transportationcost, which is small compared to the othercosts, the problem can be reduced to thewell-known Steiner tree problem. Thegreedy heuristic can be thought of as adual ascent algorithm, which has provedto be very efficient for solving UND prob-lems [Balakrishnan, Magnanti, and Wong1989]. We attempted to solve small in-stances of this UND problem as a mixed-integer LP. To improve the solution speed

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of the algorithm, we implemented andtested several options: strengthening thelinear relaxation and using Lagrangian re-laxation and Bender’s decomposition tech-niques. These exact approaches were notcompetitive with the heuristic approach,because they required much more CPUtime. For real-life large-scale instances,these exact approaches were unable tohandle the problems.

“Good harvesting planningwill be critical to ensure thatharvesting is profitable whileenvironmental quality ismaintained.”

The system presents the solution in twoforms. A graphic menu shows on screenall the relevant aspects of the solution,such as the locations of towers, the areasthat are harvested by each tower, the areasharvested with skidders, the areas notreachable or not harvested, new roads, oldroads used, and old roads not used (Fig-ure 6). The system generates conventionalreports that contain location (coordinatesx-y) of installed towers, volumes har-vested, average costs of harvesting (towersor skidders), road-building cost, and trans-portation cost.

PLANEX is operated by a forest engi-neer. With its use, the planner can spendmore time analyzing different scenarios in-stead of generating maps. The graphic in-terface allows the planner to analyze pos-sible modifications to solutions. Using themouse on the screen, the user can, for ex-ample, choose towers that should be se-lected or design a road that should be

built. The system then optimizes the re-maining part of the problem and presentsa new global solution. Using this option,the user can analyze different scenarios ina simple and visual way. PLANEX runson a PC with 128 Mb of RAM memoryand needs 15 minutes to solve an instanceof 1,000 hectares.

The system has been used since 1996 byHolding Arauco, Forestal Bio-Bio, ForestalMininco, and Forestal Copihue. Its use hasmade life easier for planners, and it hasled to an improved use of harvestingequipment over previous manual ap-proaches. The companies are still evaluat-ing the quantitative savings. Preliminaryestimates from Forestal Bio-Bio suggestsavings ranging from 0.5 to 1.5 dollars percubic meter (Bio-Bio harvests 400,000 cubicmeters per year). The experience of Hold-ing Arauco and Forestal Mininco showsgains of 0.5 dollars per cubic meter. For-estal Bio-Bio reported instances in whichPLANEX reduced the road network by asmuch as 50 percent. The cost reduction isdue mainly to less road building. Theseestimates translate roughly into a totalannual saving of at least $2 million.

In addition, use of the system benefitsthe environment because fewer roads leadto less damage during the harvesting pro-cess. We believe PLANEX, an interestingapplication combining OR tools with GIS,is the most advanced system of its kindand the only one that automatically gener-ates a solution to the harvesting problem,indicating the locations of machinery andthe road networkOPTIMED: A Tactical Forest PlanningTool

In making tactical decisions, forestry



Figure 6: In this PLANEX output example, the light shaded area shows the area harvested withskidders, while the dark shaded area represents tower harvesting. The full lines show the con-necting road network, while the black dots indicate the position of the towers.

companies look ahead at two to five yearsof planning divided into summer andwinter seasons. They decide which standsto harvest and in what order, how muchtimber they will be need to satisfy pro-jected demands, and what roads they willneed to gain access to the areas to be har-vested. At this level, managers view pro-duction in an aggregate form divided intoexport logs, various classes of sawtimber,and pulp logs. Usually forests are nearpaved public roads, but firms need tobuild internal roads. These can either begravel roads that can be used year round

or cheaper, dirt roads that can be usedonly in the dry summer season. Usuallythe firms store timber in stockyards dur-ing the summer for later use in winter.Each firm has growth-simulation modelsthat estimate timber yields in futureperiods.

To support these decisions, we devel-oped OPTIMED, a 0–1 mixed-integer LPmodel. The 0–1 variables correspond toroad building or to upgrading road stan-dards from dirt to gravel, and they takeinto account the fixed costs of harvestingoperations. We handle fixed costs by re-

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INTERFACES 29:2 24

quiring that any harvested tract be of acertain minimum area. This model is simi-lar to models the US Forest Service devel-oped for long-range planning [Kirby,Hager, and Wong 1986; Weintraub et al.1996]. Solving this mixed-integer LPmodel poses difficulties because of road-building variables. To overcome this dis-advantage, we need a combination ofschemes, including strengthening the LPformulation and heuristic rounding off ofvariables. The model runs on a PC using acommercial LP code and takes about 30minutes for a typical run. Lagrangian re-laxation was useful in some cases but wasnot implemented for the users. MoniqueGuignard of the University of Pennsylva-nia collaborated with us in developing thealgorithms. Andalaft et al. [1998] describethe model and its solution approach indetail.

Marcelo Kunz at Millalemu first sug-gested the development of a tactical plan-ning system. Alexis Wainer, regional man-ager for operations, and Cesar Lagos, asenior manager, worked very closely withthe academic group in developing the sys-tem. Forestal Millalemu has used OP-TIMED regularly since 1994, running itevery few months. Improvements in thiscase are difficult to estimate because of thelong planning horizon, but it does help thefirm to make better use of standing timber.Alexis Wainer, regional head at Millalemu,estimates revenue gains of about $200,000per year from improvements in this area.

In addition, Millalemu has used OP-TIMED to evaluate the purchase of landwith mature timber, an option large for-estry firms frequently face. Once a forest isoffered, Millalemu incorporates its stands

into the model. The difference in net bene-fit between runs with and without thesestands indicates their value to Millalemu.Because of transportation costs, the loca-tion of these potential timberlands is im-portant. Also, tree age may make a standof timber more valuable to one firm thanto another. A firm with a shortage of ma-ture trees will have more urgent need oftimberland purchases to satisfy productdemand. We are developing a tactical-planning tool, somewhat similar to OP-TIMED, for Aracruz, Brazil.MEDFOR: A Strategic Planning Tool

MEDFOR deals with long-range strate-gic decisions, in a typical horizon of 50years, which corresponds to two forest ro-tations. The model is designed to supportdecisions on the sustainable production oftimber through the planning horizon,maintaining a consistent supply for the in-dustrial plants (mainly sawmills and pulpplants), and to estimate the volume of logexports, to select silviculture regimes forplantations, to establish policies for thepurchase, sale, and rental of timber lands,and to project cash flows. The main prob-lem is to maintain a consistent relationshipover time between timber availability anddemands from sawmills, pulp plants, andexport opportunities.

The model was developed by RamiroMorales. Simon Berti, CEO of Forestal Bio-Bio, Mariana Lobel, senior manager ofForestal Bio-Bio, and Carlos Granier, se-nior manager of Cholguan, participated indeveloping and implementating the sys-tem. The model considers both data anddecisions in a very aggregate form and isa moderate-sized LP model. It is run sev-eral times a year. An important aspect in



defining the model is the process of aggre-gation, in which stands with similar char-acteristics (site quality, tree age, density ofplanting, geographical location) aregrouped into macro-stands and timberproducts are grouped into export, sawmill,or pulp type. Information on future yieldsis obtained through inventory-growth sim-ulators. Costs, revenues, and technicalproduction coefficients corresponding tothese aggregate activities must be esti-mated with care. It is difficult to evaluatequantitative gains obtained from the useof the system, given the very long-rangeplanning horizon. Simon Berti estimatessavings of between $2.5 and $5.0 million ayear due to better use of the timber.

The system is being used successfully byForestal Bio-Bio and Cholguan and par-tially by Masisa. We are currently imple-menting a similar model for Aracruz, Bra-zil. It explicitly includes industrial-plantdecisions, such as building, expanding,and closing processing installations, in amixed-integer LP model.Conclusion

These five systems have had a profoundorganizational impact on the forestry firmsand have led to savings the firms estimateto be at least $20 million annually. We feelthat ASICAM, OPTICORT, and PLANEX,in particular, have been pioneering effortsin the forestry-management field. We con-tinue to collaborate with the forestry firmsto enhance these systems by including ad-ditional management options and improv-ing the user interface. The systems OP-TIMED and MEDFOR have not been usedextensively in the industry, because thelarge firms had established systems fordealing with these problems.

In addition to the present implementa-tions in Chile, South Africa, and Brazil, weare planning a joint venture with the For-est Research Institute (FRI) of New Zea-land to combine PLANEX, our machine-location system, with MARVL, a NewZealand advanced inventory system. AsBruce Manley, portfolio manager at FRI,explains, “Good harvesting planning willbe critical to ensure that harvesting is prof-itable while environmental quality ismaintained. Consequently I anticipate thatPLANEX will have great applicability forharvest planning in New Zealand. I alsobelieve that there are real opportunities forlinking PLANEX in with our MARVL pre-harvest inventory system, with environ-mental data, and with harvesting cost in-formation to provide an integrated harvestplanning system.” Interest in some ofthese systems has also been expressed inCanada, Zimbabwe, and Colombia.

Chile is now structuring more stringentenvironmental controls for implementa-tion in the near future. There is an obviouseconomic cost in implementing environ-mental protection measures, such as costsassociated with avoiding the use of heavymachinery on fragile soils to limit erosionor avoiding harvesting near river banks tolimit water sedimentation. The impact ofthese controls is typically reflected in anincrease in harvesting costs or in a de-crease in harvested timber. One presentline of development, started in 1997 andsupported by the forestry firms and agrant from Fondef, is to modify our mod-els to evaluate the trade-offs betweenthese costs and environmental protectionsto support the political discussion on theseissues. Once the government has defined

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environmental protection rules, we will in-corporate these environmental protectionconstraints into the systems that supportthe planning processes of the forestryfirms, allowing them to comply with therules in an optimal way.Acknowledgments

We wish to acknowledge the participa-tion for this project of the Chilean ForestCompanies in the Forestry ProductionGroup headed by Fundacion Chile and thesupport of Conycit through its programsFondecyt and Fondef. We wish to thankLynne McCullough, our coach for the Ed-elman presentation, for her very valuableadvice, and Carmen Ortiz, Pablo Santiba-nez, and Glen Murphy for their help inpreparing the Edelman presentation andthis paper.APPENDIXMathematical Formulation of the Short-Term Harvesting Model

We show a simplified version of themodel solved by OPTICORT.ParametersVOLi: Volume available in stand i (m3).RENijk: Fraction of product k obtained pereach cubic meter bucked using buckingpattern j in stand i.

, : Minimum and maximummin maxDD DDktd ktd

demand for product k in period t at desti-nation d (m3).DIdt: Average diameter required at desti-nation d in period t (cm).DMk: Diameter of product k (cm).CACt: Production capacity in period t (m3).PVdk: Sale price for product k at destina-tion d ($).COSTi: Cost of harvesting in stand i($/m3).CTAidk: Transportation cost for product kbetween stand i and destination d ($/m3).VariablesYidkt: Volume of timber transported from

stand i to destination d, of product k in pe-riod t (m3).Kijt: Volume of timber produced in stand iusing bucking pattern j in period t (m3).Objective function

Max (PV 1 CTA ) Yo dk idk idkti,d,k,t

1 COST K .o i ijti,j,t

Constraints(1) Total volume harvested is bounded byexisting timber.

K # VOL for all i.o ijt ij,t

(2) Timber harvested is bounded by pro-duction capacity.

K # CAC for all t.o ijt ti,j

(3) Volume transported is bounded byproduction of each product in each standand period.

REN K 1 Y > 0 for all i, k,t.o kij ijt o idktj d

(4) Demand must be satisfied for eachproduct at each destination during eachperiod.

min maxDD < Y < DDktd o idkt ktdi

for all k, d, t.

(5) For the set of products at destination din period t, a minimum average diametermust be satisfied.

DM Y > DI Yo o k idkt dtoo idkti k[s i k[s

for all d, t.

(6) Nonnegativity.

K > 0, Y > 0 for all i, d, k, j, t.ijt idkt

The actual model is more complex. Forexample, the model considers the use ofdifferent types of harvesting machinery,the grouping of neighboring stands fortransportation purposes (this significantly



reduces the size of the model), and theconstraining of the supply to ensure that aspecific demand is regular over several pe-riods (a shipment for export for example).

A cost of standing timber, which is not afinancial one, is added to the objectivefunction to avoid nearsighted solutions, inwhich more valuable trees could be har-vested to save, for example, on transporta-tion costs. While this would improve theshort-term profits, it would decrease thevalue of the firm in the long run.The Scheme for Generating BuckingPatterns

Given the solution to the LP problem,with a given set of bucking patterns, newbucking patterns are defined as follows. Inthe LP model, constraints (1), (2), and (3)involve bucking patterns. Let ci, di, and bikt

be, respectively, the dual variables of con-straints (1), (2), and (3). Then the reducedcost of a bucking pattern variable Kijt willbe

C 4 c ` d 1 b REN 1 COST .ijt l t o ikt kij ik

We need to find bucking patterns withvalue Cijt . 0 to improve the current solu-tion. Note that bucking patterns are gener-ated for each stand and period. If wedefine

a 4 c ` d ,it i t

the dual variables ait represent the valueassigned to one cubic meter of a mix ofproducts already defined for stand i in pe-riod t, while bikt represents the value of acubic meter of product k obtained in pe-riod t in stand i.

To generate improving patterns, we de-veloped a branch-and-bound algorithm asshown in Figure 4 in the text. In thebranch-and-bound tree, in each branch,the length and minimum diameter of aproduct is defined. For example, branch 1–2 defines a product of length 12.10 m andminimum diameter 24 cm.

The value at each node is determined by

the addition of the values of each branchleading to that node, that is, the value ofnode 14 is defined by the value of prod-ucts (12.10,24 / 4.10,30 / pulp). The yieldsof each product are determined by thepreharvest-inventory system. Suppose theyields for node 14 in the example haveproportions (50%, 30%, 20%), then forgiven dual values b1, b2, b3 for these threeproducts and a for the correspondingstand, all in period t, the value of node 14will be

a 1 0.5b 1 0.3b 1 0.2b .1 2 3

The column-generation feature was im-plemented mainly by Jaime Gabarro andPhilippe Chevalier. The rules for branch-ing and bounding are described by Ep-stein et al. [forthcoming]. The search withthis column-generation scheme can be car-ried on to optimality or stopped after anumber of improving patterns have beenfound. Figure 7 shows the variation in ob-jective value in a test problem for twostrategies: the column generation carriedon to optimality or stopped after three im-proving patterns are found.Mathematical Formulation for PLANEX

We show a mathematical model formu-lation for the problem behind PLANEX.ParametersV: Set of pixels or points in the study area,as shown in Figure 5.E: Set of road links in the form (i,j) where iand j are pixels of V.X , V: Set of exit points. We consider thetimber to be outside the study area whenreaching one of these points. One of theexit points is a dummy pixel to which wesend timber that is not worth harvesting.Q: Set of machine types.Tq: Total harvesting capacity of machinetype q.

, V: Set of pixels that can be harvestedqGi

from pixel i with a machine type q.ni: Timber volume on pixel i.D 4 Total demand on the studyn :o i

i[V

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INTERFACES 29:2 28

Figure 7: The pattern generation approach produces improvements on the objective functionvalue. The full line represents increments in the objective value when the column-generationscheme is stopped after three improving patterns have been found. The dotted line shows re-sults when the column-generation scheme is run to optimality. The solutions show steep im-provements at some iterations followed by a number of iterations with negligible improve-ment. The approach of stopping the column-generation scheme when three improving patternsare found appears superior.

area.ce: Fixed cost of building link e.

: Fixed cost of locating a machine type qqai

on pixel i.be: Transportation cost, per cubic meter, onlink e [ E.

: Cost, per cubic meter, of harvestingqgij

pixel j from pixel i using machine type q.Variablesxe: 1 if link e 4 (i,j) is built, 0 otherwise.

: 1 if machine type q is located on pointqyi

i, 0 otherwise.: Timber volume harvested on pixel jqwij

from pixel i using machine type q.fe: Timber flow on arc e 4 (i,j).si: Timber exiting the forest at pixel i [ X(si 4 0 for all i [ V\X).Objective function

q qMin c x ` g wqo e e o o o ij ijie[E q[Q i[Vj[G

q q` a y ` b fo o i i o e eq[Qi[V e[E

Constraints(1) Flow balance constraint at each pixel.

qf 1 f ` w 4 so ji o ij oo ji ij j q j

for all i[V.

(2) All the timber must be harvested. Adummy exit point represents the unreach-able or uneconomical harvesting pixels.

S 4 D.o ii[X

(3) To harvest pixel j from pixel i using amachine type q, we have to locate such amachine on the pixel.

q qw < v y for all i, j [ V, q [ Q.ij j i

(4) The harvesting is bounded by the tim-ber supply of each pixel.

qw < v for all j [ V.oo ij jq i

(5) Each machine type has a maximumvolume capacity.

q qw < T for all q [ Q.oo iji j

(6) To carry timber on a link, we have tobuild the link beforehand.

f < Dx for all e [ E.e e

(7) Nonnegativity and integrality of thedecision variables.

x, y [ {0,1}w, f > 0.

In this formulation, since the road ca-



pacity D defined in constraint (6) is neverexceeded (D is the total timber to be har-vested), the problem corresponds to anuncapacitated-network-design probem.ReferencesAndalaft, N.; Andalaft, P.; Guignard, M.;

Magendzo, A.; Wainer, A.; and Weintraub,A. 1998, “A problem of forest harvesting androad building,” Working paper.

Balakrishnan, A.; Magnanti, T. L.; and Wong,R. 1989, “A dual-ascent procedure for large-scale uncapacitated network design,” Opera-tions Research, Vol. 37, No. 5, pp. 716–740.

Cossens, P. 1992, “Planning and control ofshort-term log allocation in New Zealand,”Integrated Decision-Making in Planning andControl of Forest Operations, Proceedings ofIUFRO Conference, School of Forestry, Uni-versity of Canterbury, Christchurch, NewZealand, pp. 46–56.

Epstein, R.; Nieto, E.; Weintraub, A.; Gabarro,J.; and Chevalier, P. forthcoming, “A systemfor short term harvesting,” European Journalof Operations Research.

Kirby, M. W.; Hager, W.; and Wong, P. 1986,“Simultaneous planning and wildland trans-portation alternatives,” TIMS Studies in theManagement Sciences, Vol. 21, Elsevier SciencePublishers, New York, pp. 371–387.

Twito, R. H.; Reutebuch, S. E.; McGaughey,R. J.; and Mann, C. N. 1987, “Preliminary log-ging analysis system (PLANS): Overview,”Technical report, USDA Forest Service,PNW-199, Portland, Oregon.

Weintraub, A. and Bare, B. 1996, “New issuesin forest land management from an opera-tions research perspective,” Interfaces, Vol.26, No. 5, pp. 9–25.

Weintraub, A.; Epstein, R.; Morales, R.; SeronJ.; and Traverso, P. 1996, “A truck schedulingsystem improves efficiency in the forest in-dustries,” Interfaces, Vol. 26, No. 4, pp. 1–12.

Weintraub, A.; Jones, G.; Magendzo, A.;Meacham, M. L.; and Kirby, M. W. 1994, “Aheuristic system to solve mixed-integer forestplanning models,” Operations Research, Vol.42, No. 6, pp. 1010–1024.

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