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h 61 (2008) 669–677

Journal of Business Researc

Upstream or downstream in the value chain?☆

Marcos Singer ⁎, Patricio Donoso

Escuela de Administración, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Macul, Santiago, Chile

Received 1 February 2007; received in revised form 1 April 2007; accepted 1 June 2007

Abstract

Companies in the natural resources industry (e.g., mining, timber, farming and fishery) face the dilemma of whether to focus upstream ordownstream in the value chain. The literature provides arguments and empirical evidence for either position. This paper presents an analyticalframework based on the neoclassical theory of the firm, for which the best competitive advantage is the one that maximizes production efficiency.It serves to formulate an optimization model for the sawmill industry, and draws the data from the largest sawmilling company in the southernhemisphere. Although one conclusion is that the company should concentrate on the upstream activities, such conclusion is not applicable to otherfirms, since the analysis of the upstream–downstream dilemma must focus on the individual capabilities of each firm.© 2007 Elsevier Inc. All rights reserved.

Keywords: Strategic planning and management; Production and inventory systems; Optimization modeling

1. Introduction

Latin American countries have specialized in the productionof commodities. In 2004, the main Chilean exports were copper(46%), timber products (6%) and fishery (5%). Argentina'smain exports were agricultural products (62%) and petroleum(26%). Peru's main exports were mining and petroleum (65%)and fishery (10%). Uruguay's second main export was leather(8%) and Brazil's second and third main exports wereagricultural products (22%) and raw materials (19%). Eachfirm participating in those industries faces the dilemma ofwhether to invest upstream or downstream in the value chain.Upstream activities are those close to the exploitation of naturalresources, whose output is a primary commodity or virginmaterial (Van Beukering et al., 2000). Downstream activitiesadd value to the products, through manufacturing or customiza-tion, which outflow is a final commodity. Several firms arevertically integrated, so each must decide where to focus theireffort.

☆ This research has been partially sponsored by FONDECYT projectnumber 105/1021. The authors wish to thank the executives from AserraderosArauco S.A.⁎ Corresponding author.E-mail addresses: singer@faceapuc.cl (M. Singer), pdonoso@facepuc.cl

(P. Donoso).

0148-2963/$ - see front matter © 2007 Elsevier Inc. All rights reserved.doi:10.1016/j.jbusres.2007.06.043

The literature provides arguments in one direction or theother. The theory of comparative advantages explains interna-tional trade by relative differences in productivity of labor andcapital (Keuschnigg, 1999). Productivity varies betweencountries due to technological knowledge and natural condi-tions such as climate, natural resources, soil conditions andgeographical location. According to the author's argumentation,firms in Latin America should pursue upstream activities, giventhe relative abundance of natural resources in the region. Manycountries can build a factory of copper wire, but very few candeploy a copper mine with the production yields observed inChile or Peru, and with a relatively mild environmental impact.Consistently, several recent mining projects, such as BHP-Billiton's Escondida, the largest copper mine in the world,focus on extraction and concentration (upstream activities),forfeiting the refinement (downstream activities) to plants in thenorthern hemisphere. Wooden furniture can be manufacturedalmost anywhere in the world, but while in the northernhemisphere trees reach maturity in half to one century, insouthern Chile and Argentina trees mature in an average of just25years. Thus, Latin America's comparative advantage is in theforest itself. By contrast, the comparative advantage of sawmillsin the northern hemisphere is their closeness to the consumptioncenters. This situation justifies the empirical evidence obtainedby Roos, et al. (2001) for the Swedish sawmilling industry,

670 M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

which shows that customization is the most successful strategyto increase profits. In summary, if the firm's advantage is in theavailability of natural resources, its competitive strategy shouldfocus on how to exploit them.

Challenging the above, there is empirical evidence showingthat those countries that have pursued downstream activitieshave grown much faster than those that have specialized in theexploitation of natural resources (Sachs and Warner, 1995).Japan and Korea have become world-class steel producersdespite their lack of iron ore, while some of the main iron oreexporters like Brazil and the Russian Federation show a muchslower economic development. The apparent contradiction thathaving fewer natural resources leads to stronger economicgrowth can be explained by the absence of positive externalitiescoming from natural resource sectors. Industrialization, asopposed to natural resource exploitation, entails a morecomplex division of labor. This condition translates into ahigher capability of knowledge creation, which is essential forsustaining the firm's competitive advantage (Powell andSnellman, 2004). Manufacturing skills are flexible, whichallows companies to adapt to changes in the markets withinnovative products (Anand and Ward, 2004). Commodityproduction is extremely specific, and has little room to react tovolatile world prices. In a nutshell, companies that engage indownstream activities increase rents by developing their corecompetences for adding higher value to their products andadapting to the market's fluctuations.

Since the debate in the aggregate is inconclusive, managersfacing the upstream–downstream dilemma must look foranswers at the firm level. No related academic literature exists,with the exception of Gaudet, van Long and Soubeyran (1999).These authors model a partially integrated industry in order toillustrate the separate effects of strategic interaction and theupstream cost, in the determination of the integrated firm's netsales to the nonintegrated sector. This paper proposes amethodology based on the neoclassical theory of the firm, forwhich markets progressively approach perfect competition(Stoelhorst and van Raaij, 2004). Companies are price takers,there is no room for product differentiation, resources aredivisible and mobile, and market entry and exit are frictionless.There is also perfect information, sellers maximize their profit,and transactions are costless. Some decades ago, most of theseassumptions sounded overly simplistic. Today, the globalizationof markets, the free-trade agreements, the international free-flow of capital and the development of the Internet have drivenseveral industries close to perfect competition (Van Beukeringet al., 2000).

Some of the assumptions of the neoclassical theory of thefirm are especially valid for primary commodities or virginmaterials. These are non-differentiable products by definition,traded on efficient and well-informed global markets (seeWårell, 2005 for the case of the coking coal). Several studies oncommodity trade assume that firms face perfect competition(Hens, 1997; Schwarz, 2006), especially in the case of naturalresources. According to McLaren (1999) “the overwhelmingmajority of existing studies [about primary commodities] as-sume perfect competition.”

Recent studies have acknowledged that in some industriesthere exist producers with market power (Gellert, 2003). In sucha case, firms may engage in strategic behavior to reducecompetition and increase prices. Johnsen (1991) reports the caseof major oil companies that were buying above their ownmarginal cost at the upstream market, in order to harm theirdownstream competitors. In addition, when commodities comefrom non-renewable resources, firms may foresee a futuremonopoly status and decide not to maximize current profits asassumed by the perfect competition model. Such may be thecase of oil and natural gas, where reserves will last for around41 and 67 years more, respectively (Egging and Gabriel, 2006).

As Kolstad and Wolak (1983) assert, the markets of primarycommodities lie somewhere between the two extremes ofperfect and imperfect competition. The closer the market to theperfect competition extreme, the more valid this approach. Suchis the case with the timber, fruit and salmon industries, whichhave hundreds of producers worldwide, and depend onrenewable resources. This paper also considers copper, forwhich mild market power exists: the largest five producersaccount for less than 40% of the global supply.

Under perfect competition, the best competitive strategy isthe set of actions that maximize the firm's efficiency, whichimplies generating the maximum economic value consumingthe least amount of resources (Grifell-Tatjé and Lovell, 1999).To do so, firms must offer the most valuable mix of productsand services, given current prices. Firms must do so at minimumcosts, which is achievable by transforming and mobilizinginputs and resources in an optimal manner. From its origin,mathematical programming has focused on the decision-makingproblems that intend to reach the firm's efficiency (Dantzig,2002). Most of those problems have the necessary structure toallow mathematical tools to solve them and describe themformally. That is how mathematical programming has beengaining relevance for strategic decision-making, as Schwarz(2003) reports for the aluminum industry and Singer andDonoso (2005) do for the steel industry. The conclusion fromthe above is that mathematical programming should be apractical tool for assisting strategic decision-making for thenatural resource industries in Latin America. In particular,programming can solve the upstream–downstream dilemma interms of the specific features of each firm.

The objective of this paper is to assist managers in solvingthe above strategic decision. Section 2 shows how the decisionapplies to mining, timber, fruit farming and fishery. Section 3describes some general principles regarding how to translate thestrategic decision-making process, as understood by theneoclassical theory of the firm, into a mathematical program.Section 4 applies those principles to the sawmilling industry,and Section 5 presents a case study. Section 6 explains thepaper's conclusions, limitations and some possible extensions.

2. The exploitation of natural resources

The copper industry produces three main products: concen-trate, anodes and cathodes. Copper concentrate is a sort ofdust with a 33% content of copper. Such concentrate may be

Fig. 1. Chilean production of copper at three stages. Fig. 3. Chilean production of timber.

671M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

refined at high temperatures by smelters, supplying blistercopper and other products 99% pure, known as anodes. Anodesmay be electro-refined at high voltages, delivering 99.9999%-pure cathodes. Cathodes can also be obtained directly bybleaching copper oxide ore with sulfuric acid, which is abyproduct from the smelters. Fig. 1 (www.prochile.cl) showsthe Chilean production measured in tons of copper content,from 1997 to 2005. Although the volume of concentrates andcathodes is larger than the volume as anodes, the threeproduction stages show a similar growth rate, so from thecountry's viewpoint, the upstream, the downstream and theintermediate strategies seem all profitable.

Firms in the copper industry face the decision of how far intothe value chain to invest. Those that are vertically integrated—that have already invested in the infrastructure to perform theentire refining process—still have to decide whether to sell

Fig. 2. Main product f

intermediate goods along with final products. Consider the caseof the Chilean Copper Corporation Codelco, the largest producerof copper and molybdenum in the world. Fig. 2 summarizes theoutbound logistics of its products, as well as the internal transfersamong its five productive divisions. As the divisions arehundreds of kilometers apart, it is sometimes more convenientto export the product before being refined as a cathode. Forinstance, the Andina division may transfer concentrate forrefining to the smelter at the El Teniente division, export theproduct through the port of Ventanas. El Teniente may transferits production to be refined as cathodes by the Ventanas division,or may export it through the port of Valparaíso.

Sawed timber may be exported as a “green” product, orfurther processed at drying and sanding plants. Fig. 3 (www.infor.cl) shows the Chilean production of timber at both stages,measured in millions of dollars free on board (FOB).

lows at Codelco.

Table 1Main features of the units of a fruit- (timber-) exporting firm

Unit Function Key resource Operationaldecisions

Strategicdecisions

Sales Marketingproducts

Sales force Sales targets ineach market

Marketdevelopment

Shipping Movingproducts

Transportationfleet

Origin-destination ofshipments

Fleetconfiguration

Operations Packing fruit(processingtimber)

Packing plants(sawmills)

Production goalsat different stages

Productioninfrastructure

Acquisitions Purchasingfruit (timber)

Capital Purchases anddelivery points

Long-termprovisiondeals

Logistics Monitoringinventory

Warehouses Where to storeproducts

Storagedevelopment

Fig. 4. The value chain of a fruit- (timber-) exporting firm.

672 M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

The fruit industry may freeze and export its productionwithout further processing, or may prepare and export the fruit ascanned food. The salmon and trout farming industries sell theirproduce at twomain stages of the value chain. Exportersmay sellthe fish “as is” when harvested, or without head and tail.

The data on the above charts, and from the fruit and the salmonindustry, show a similar growth rate for the upstream and thedownstream production, suggesting that there is not one singlestrategy to follow. According toGaudet, van Long and Soubeyran(1999), this situation occurs because upstream–downstreamspecialization decision depends on the firm's cost advantage,and there are persistent cost differences amongst firms in naturalresource industries, exogenously determined by nature. Becauseof those differences, in 1993 the ratio between the refiningcapacity and the extraction capacity of themain state-owned LatinAmerican oil producers was diverse: 48% for Pemex (Mexico),80% for PDV (Venezuela), 193% for Petrobras (Brazil), 118% forYPF (Argentina), 123% for Petroecuador (Ecuador).

Therefore, a solution to the upstream–downstream dilemma atan aggregated level is unlikely. Different firmsmay be better suitedto execute different strategies, as a result of both the country'scomparative advantages and the firm's individual infrastructure.

3. Modeling the value chain

This paper models the activity of the firm as a value chain,which obtains its raw material from its providers, and generatesproducts and services for its clients (Porter, 1985). Fig. 4 showsthe value chain of a firm that exports agricultural products, suchas fruit or timber. The departments or units upstream in thechain deliver to the next downstream unit, until the productreaches the final client. The logistics unit is transversal,interacting with all the echelons in the value chain.

Each unit has a specific value-adding function, which itperforms by managing the key resources of the firm (Peteraf,1993). The remaining of this section takes as an example a fruit-exporting company (Lowe and Preckel, 2004), and in parenthe-sis shows the example of a timber-exporting company (Carlssonand Rönnqvist, 2005), as the two work in a similar manner.

• The Sales unit is in charge of marketing the products byusing its sales force and other commercial channels. In theshort term, this unit must decide how much to sell of eachproduct at each market. In the long run, it must develop newmarkets, that is, find new clients and fruit varieties (timberproducts) to sell.

• The Shipping unit must move the products between packing(production) plants and cooling (storage) facilities and fromthere to the port, using a transportation fleet. This unit mustalso schedule and supervise loading of the vessels. In its

daily operation, it decides the origin and destination of theshipments. Its strategic decisions are about what size andtype of truck fleet to have, and what type of vessels tocontract.

• The Operations unit is in charge of the packing (sawing)plants, where the raw material is processed according to theclients' requirements. The operational decisions are theproduction goals at both the upstream and the downstreamlevel. The strategic decisions define investments in produc-tion plants, personnel and technology.

• The Acquisitions unit is in charge of purchasing the fruit(timber) from the farmers (forestry providers). The fruitacquisition process starts long before the fruit is delivered inthe packing plant, since farming is a capital-intensiveactivity, and farmers must be financed throughout theseason. Banks and other sources of capital are inefficient,given the strong information asymmetry and the moralhazard problem that may arise (Rasmusen, 2001). Fruit-exporting firms are a more knowledgeable—and thereforemore efficient—lender. Their operational decisions focus onwhich crops to purchase, and at which packing plants todeliver them. Their strategic decisions are about what long-term deals should be worked out with which farmers, inorder to guarantee the provision of fruit.

• The Logistics unit, sometimes regarded as the managementdepartment of the supply chain, is in charge of coordinatingthe value chain. The tasks include monitoring inventories, toguarantee that goods are available as an input to theproductive tasks, delivered on-time and in-full for theclients. Inventories are stored in warehouses and distributioncenters. In the case of a fruit-exporting firm, warehouses areespecially costly, because of expensive cooling systems thathelp preserve products for a long time. Some varieties ofapples and pears are stored in Chilean cooling chambersalmost a full year before being exported to the northernhemisphere.

Table 1 summarizes the function, key resource, operationaldecisions and strategic decisions of the five units depicted byFig. 4.

Fig. 5. Sawmill model.

673M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

As the actions performed at each unit influence other units, intheory operational and strategic decisions should be made in acoordinated fashion. Defining sales targets at the operationallevel that exceed product availability given by currentinventories, raw material purchases and production capacitymakes no sense. At the strategic level, it is convenient to alignfleet configuration with markets and production infrastructure.Consistently, whether the operations unit decides to focus onupstream or on downstream activities depends on all the units.This dilemma generalizes the approach by Gaudet et al. (1999),which considers production cost only. Besides cost, this paperconsiders business constraints at all the stages of the value chain.

4. Mapping the sawmill value chain into a model

Mathematical programming can coordinate the operationaland strategic decisions within the firm, as it makes explicit the

Fig. 6. Actual sales and suggested optim

interactions among its internal units. This paper models theinternal process of the sawmill in terms of two transformationstages: sawing and drying-sanding (finishing). There are alsotwo stock stages: “green” inventory (after sawing) and “dried”inventory (after drying and sanding). Fig. 5 is a simplifiedrepresentation of the products' flow and stocks within a sawmill.

The first stage begins with the purchase of raw material, thatis, logs from both thinned and regular (unthinned) stands.Thinning is a treatment usually carried out at year 6 in the life of astand, which includes cutting branches in order to yield betterquality timber. Regular and thinned logs go to differentcategories based on diameter and according to the characteristicsof the forest that supplies each sawmill. The productivity of thesawing process, measured in terms of the volume of logsprocessed per hour, is different for each log type and diameter.Depending on the type of cut made, three kinds of primary or“green” products result: G1, G2 and G3 (GR1, GR2 and GR3

al sales of green and dried timber.

674 M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

denote the products obtained from regular logs; GT1, GT2 andGT3 refer to those from thinned logs). There are maximumproportions for the utilization of the raw material that result fromarranging rectangular sections in the cylindrical logs. Inaddition, the cutting process loses raw material in the form ofsawdust. Once the sawing process finishes, products G1, G2 andG3 go either to the drying and sanding stage, for sale in themarket or to storage.

The second stage (kiln-drying and sanding) converts thegreen products into finished products F1 and F2 in certainestablished proportions that depend on the type of green andfinished products and on the sawmill. For example, for eachcubic meter of thinned G1 logs cut in sawmill A2, a total of0.8m3 is allotted for the production of F1 and the remaining0.2m3 for the production of F2. There is a loss of product yieldduring the drying and sanding process of the green material dueto cracking, splitting and chipping off. For this reason, it isnecessary to assume a certain percentage of loss of materialduring the process of drying and sanding.

The productivity of the drying and sanding process,measured in cubic meters per hour, depends on the greenproduct utilized in each sawmill. The parameters are related tothe input, without considering the associated volume losses.The capacity of the milling, drying and sanding stages dependson each sawmill and on the given time period. Production cost isexpressed in terms of output. Transportation cost to the port isconstant for each plant. Storage cost depends on the sawmill,the product and the period (being higher in the winter seasonbecause of humidity). Minimum sales also depend on thesawmill, the product and the period, while prices dependexclusively on the product and the period. Once the drying andsanding process has finalized, the plant may either sell theproduction or store the products. Transferring green productsamong plants optimizes the production capacity utilization.Transferring final products optimizes the use of the storagecapacity. Transferring logs, the raw material, may also beadvantageous if technology at one mill is more productive thanat another due to the characteristics of the raw material.

An extension of the model by Singer and Donoso (2006) (seeAppendix) permits to model the sawmill operation with a linearprogram. The range of the decision variables is in months, so boththe location of the facilities and the production capacities are given.The assumptions include unlimited availability of raw material,following Troncoso and Garrido (2005), and that the raw materialmarkets are integrated (Toivonen et al., 2002), so log prices aregiven. Sincemost of the production is for the global market, pricesfor final products are given. The above suppositions are crucial;otherwise, there is no perfect competition and one should considerstrategic behavior to reduce competition and gain market power inone or more stages of the value chain (Johnsen, 1991).

Parameter classification depends on which unit is in charge ofproviding the data to calculate its value. The variablescorrespond to the operational decisions in Table 1. The objectivefunction maximizes revenues minus production cost, minusinventory costs, minus costs of raw material and minus transfercosts. This study groups constraints according to which unit ismore directly related to them. Some constraints affect the unit's

performance directly, such as the sawing, drying and sandingcapacity constraints that limit the production throughput of theOperations unit (Gupta, 2001). Other constraints requiresupervision by the unit. For instance, the Sales unit must verifythe minimum sales constraint, and the Logistics unit mustsupervise that the inventory equation holds, that is, that productsdo not disappear. The sensitivity analysis guides the strategicdecisions. The marginal benefit of relaxing the maximum salesconstraint shows which markets need to be developed. Themarginal benefit of relaxing the sawing, drying and sandingcapacity constraints shows the type of infrastructure in which thefirm must invest.

5. The case of a Chilean sawmill holding

Aserraderos Arauco Sociedad Anónima (AASA) is the largestsawmilling corporation in the southern hemisphere. As of 2004,AASA consisted of twelve companies, each one managing aproduction plant (eleven in Chile and one in Argentina) with anaggregate annual processing capacity of 4.3million cubic metersof saw logs. The above translates into an aggregate productioncapacity of 2.5million cubic meters of lumber. The sawn timber'smarkets cover packaging, pallets, construction, and decorativeproducts for the furniture and design industries. AASA also hasfive companies for remanufactured wood products (e.g., windowmoldings, clear rips, decking balusters) aswell as several facilitiesfor manufacturing plywood and fiber panels (Casadesus-Masanell, Tarziján and Mitchell, 2005). High-level planningconsists of assigning customer orders to the different plants. Inaddition to capacity and productivity, planners at headquartersmust take into account a fairness criterion.

One can adapt the mathematical model described in Section 4and Appendix to the specific conditions of each of AASA'seleven plants. Instead of two diameter categories, plantsmay havefour or five. Plants may produce about seven types of greenproducts and 21 final products. Assuming only one time periodsimplifies the problem to a static model. In total, there are 453decision variables and 483 constraints, not including non-negativity. Approximately 50 constraints account for specificassignments and other considerations that are not included in thegeneral model, which ensures that the solution arrived at is arealistic one. Implementing the optimizationmodel in aMicrosoftExcel spreadsheet using a Frontline System Solver permits tosolve the problem in a few seconds using a Pentium III processor.

A comparison of the actual monthly sales for Septem-ber, October and November 2003 with the model's optimalsolution—omitting results for other periods for reasons ofconfidentiality—yields similar conclusions. Fig. 6 compares theaverage actual sales with the sales suggested by the modelfor both green and dried timber. Note that eight of the elevenplants are equipped for drying and sanding timber, while theothers must subcontract these tasks. The aggregate quantitiesturned out to be similar: 158,533m3 for the real-life situationand 164,244m3 for the model's solution. Total cost was alsosimilar: US$18,578,777 actual and US$18,436,626 for themodel. Revenues, on the other hand, displayed an increase fromUS$21,500,529 actual to US$21,804,388 for the model, which

675M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

implies a 15.3% increment in profits, from US$2,921,752 to US$3,367,762. This result derives from shifting the productionfocus upstream the value chain. The aggregate production ofgreen products should grow by 48.5%, while the aggregateproduction of final products should fall by 21.6%.

The sensitivity analysis confirms that increasing theupstream capacity of sawmilling is highly profitable, especiallyin Horcones I and Colorado. A similar analysis shows a limitedbenefit of investing in downstream capacity.

6. Conclusions

This paper has dealt with the question of whether companiesin the natural resources industries should focus on activitiesupstream or downstream in the value chain. The macroeco-nomic argumentation and the country-level empirical evidenceare inconclusive, so managers can derive little help. This studyproposes to examine the upstream–downstream dilemma fromthe point of view of the neoclassical theory of the firm, whichassumes that companies are price takers, there is no room forproduct differentiation and there is perfect information. Due tothe globalization of markets and Internet, most of theseassumptions are becoming realistic, leading markets toapproach perfect competition. In such a scenario, the bestcompetitive advantage is the one that maximizes productivity,subject to the constraints facing the firm.

In the above decision-making setup, mathematical program-ming can provide crucial insight. By identifying the mainparameters, decision variables and constraints of each unit in thevalue chain, it was possible to map the operational and strategicdecisions into a lineal program and test the model at AASA, acorporation consisting of eleven sawmilling plants located insouthern Chile. To evaluate how close the company was to aglobal optimum, it was necessary to simulate the conditions inSeptember, October and November 2003 to derive the optimaloperating plan. Interestingly, there is an opportunity to increaseprofits by more than 15% if the firm orients its productionupstream the value chain. While conclusions for AASA arerobust for a relatively wide range of values, the same should notbe directly applied to other companies. The timber industry inChile is the aggregation of individualities, and there is doubtthat there could be a one-size-fits-all strategy for all the firms.Whether the competitive advantages theory prevails over thebenefits of the higher-value-adding activities depends on a case-by-case analysis. The results will most likely be mixed, as thestrengths of different firms are diverse.

This upstream–downstream dilemma is not only relevant forthe competitive strategy of the firm; it is also crucial inthe development strategy of countries based on the exploitationof natural resources, as are in most countries in Latin America.As several governments have been following a more proactiveattitude, where to invest the resources becomes a matter ofpublic policy. Just like the managers of individual companies,the authority will face the contradicting prescriptions. To avoidsuch confusion, it seems convenient to study each industry atthe firm level and, in the case of the sawmilling industry, toreplicate the method to several companies. This process will

reveal the exact place in the value chain where the country mustinvest to increase its worldwide competitiveness.

Appendix

Index definition:r ∈ {regular, thinned} Type of raw materiald ∈ {16–18, 20–22} Diameter of logsg ∈ {G1, G2, G3} Green productsf ∈ {F1, F2} Finished products (kiln-dried and sanded)t ∈ {1, 2, 3,…} Time periodsp ∈ {P1, P2} Plants

Parameter classification reflects which unit is in charge ofproviding the data to calculate its value. The following sixparameters relate to the Sales unit:

MGg,t maximum quantity of green product g for sale inperiod t

MFf,t maximum quantity of finished product f for sale inperiod t

QGg,t minimum quantity of green product g for sale inperiod t

QFf,t minimum quantity of finished product f for sale inperiod t

Gg,t sale price of green product g at time tFf,t sale price of finished product f at time t

The following parameters relate to the Shipping unit:

TRp transportation cost to the port from plant pTp,q transportation cost from plant p to plant q, with

Tp,p = ∞

The following parameters relate to the Operations unit:

MHt,p sawmilling hours available during period t at plant pDHt,p kiln-drying hours available during period t at plant pSHt,p sanding hours available during period t at plant pMPr,d,p sawmilling productivity of type r logs of diameter d at

plant pDPr,g,p kiln-drying productivity of type r logs of product g at

plant pSPr,g,p sanding productivity of type r logs of product g at

plant pMr,d,g,p maximum proportion of type r logs of diameter d

converted into g at plant pMr,d,+,p maximum proportion of type r logs of diameter d

converted into G1 + G2 at plant pMr,d,p maximum proportion of type r logs of diameter d for

converting into green product at plant pYr,g,f indicating (1 = yes; 0 = no) if green product g from type

r logs must go for drying and sanding to make product fAf,p volume loss of product f at plant pMCp sawmilling cost for product g obtained at plant pDCp kiln-drying cost for product f obtained at plant pSCp sanding cost for product f obtained at plant p

;p

676 M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

The following parameters relate to the Acquisitions unit:

Cr,p cost of type r logs at plant pPr,d,p proportion of type r logs of diameter d at plant p

The following parameters relate to the Logistics unit:

ICf,t,p inventory cost of final product f at time t at plant pIGr,g,p initial inventory of green product g from type r logs at

plant pIFf,p initial inventory of final product f at plant p

The following variables relate to the Sales unit:

gsr,g,t,p green product sales of type g from logs type r inperiod t from plant p

fsf,t,p finished product sales of type f in time period t fromplant p

The variables related to the Shipping unit are:

tgr,g,t,p,q green product g from logs r transferred from plant p toq at time t

tff,t,p,q final product f transferred from plant p to plant q at time t

The variables related to the Operations unit are:

or,d,g,t,p product g obtained from type r logs of diameter d inperiod t at plant p

mr,g,t,p product g from type r logs moved to drying andsanding in period t at plant p

The variables related to the Acquisitions unit are:

ar,t,p acquisitions of type r logs at time t at plant p

The variables related to the Logistics unit are:

igr,g,t,p inventory of green product g from type r logs at time tat plant p

iff,t,p inventory of final product f at time period t at plant p

The linear program considers the following objective function:Maximize revenues discounting the transportation cost– sawmilling, draying and sanding costs– inventory costs – costs of raw material – transfer costs

¼ Pr;g;t

Gg;t � TR� � � gsr;g;t þ

Pf ;t

Ff ;t � TR� � � fsf ;t

�MC �Pr;d;g;t

or;d;g;t � DCþ SCð Þ �Pr;f ;g;t

mr;g;t � Yr;g;f � 1� Af

� �

�Pf ;t

ICf ;t � if f ;t �Pr;t

Cr � ar;t �P

r;g;t;p;qTp;q � tgr;g;t;p;q

þPf ;t;p;q

T p;q�tf f ;t;p;q ;

Constraint classification reflects which unit constraints relatemore directly to. The maximum sales constraints directly affectthe performance of the Sales unit. The Sales unit is in charge of

supervising the minimum sales constraints.

X

r;p

gsr;g;t;pVMGg;t

8 g, t Max. sales of g

X

p

fsf ;t;pVMFf ;t

8 f, t Max. sales of f

X

r;p

gsr;g;t;pzQGg;t

8 g, t

Min. sales of g

X

p

fsf ;t;pzQFf ;t

8 f, t Min. sales of f

The following constraints affect the Operations unit:

X

r;d;g

or;d;g;t;pMPr;d;p

VMHt;p

8 t, p

Sawing capacity

X

r;g

mr;g;t;p

DPr;g;pVDHt;p

8 t, p

Drying capacity

X

r;g

mr;g;t;p

SPr;g;pVSHt;p

8 t, p

Sanding capacity

or;d;g;t;pVPr;d;p � ar;t;p �Mr;d;g;p

8 r, d, g, t, p Max. prop.

or;d;G1;t;p þ or;d;G2;t;p

VPr;d;p � ar;t;p �Mr;d;þ;p

8 r, d, t, p

Max. prop.

or;d;G1;t;p þ or;d;G2;t;p þ or;d;G3;t

VPr;d;p � ar;t;p �Mr;d;p

8 r, d, t, p,

Max. prop.

The following constraints relate to the Logistics unit,because this unit is in charge of detecting any deviation.

igr;g;t�1;p þX

d

or;d;g;t;p

þX

q

tgr;g;t;q;p ¼ igr;g;t;p þ gsr;g;t;p

þ mr;g;t;p þX

q

tgr;g;t;p;q

8 r, g, t, p

Inventory of g

igr;g;0;p ¼ IGr;g;p

8 r, g, p Initial

inventory of g

if f ;t�1;p þX

r;g

mr;g;t;p � Yr;g;f ;p � 1� Af ;p

� �þX

q

tf f ;t;q;p

¼ if f ;t;p þ fsf ;t;p þX

q

tf f ;t;p;q

8 f, t, p

Inventory of f

if f ;0;p ¼ IFf ;p

8 f, p Initial

inventory of f

677M. Singer, P. Donoso / Journal of Business Research 61 (2008) 669–677

Finally, the non-negativity constraints follow.

ar;t;p;or;d;g;t;p;gsr;g;t;p;fsf ;t;p;mr;g;t;p; igr;g;t;p;if f ;t;p;tgr;g;t;p;q;tf f ;t;p;q

z0; 8r; d; g; f ; t; p; q

References

Anand G, Ward PT. Fit, flexibility and performance in manufacturing: copingwith dynamic environments. Prod Oper Manag 2004;13:369–85.

Carlsson D, Rönnqvist M. Supply chain management in forestry—case studiesat Södra Cell AB. Eur J Oper Res 2005;163:589–616.

Casadesus-Masanell R, Tarziján J, Mitchell J. Celulosa Arauco: forwardintegration or horizontal expansion? Harvard Business School, teaching caseN9-705-474; 2005.

Dantzig GB. Linear programming. Oper Res 2002;50:42–7.Egging RG, Gabriel SA. Examining market power in the European natural gas

market. Energy Policy 2006;34:2762–78.Gaudet G, van Long N, Soubeyran A. Upstream–downstream specialization by

integrated firms in a partially integrated industry. Rev Ind Organ 1999;14:321–35.

Gellert PK. Renegotiating a timber commodity chain: lessons from Indonesia onthe political construction of global commodity chains. Sociolo Forum2003;18:53–84.

Grifell-Tatjé E, Lovell CAK. Profits and productivity. Manag Sci 1999;45:1177–93.

Gupta M. Activity-based throughput management in a manufacturing company.Int J Prod Res 2001;39:1163–82.

Hens T. Exchange rates and perfect competition. J Econ 1997;65:151–61.Johnsen DB. Property rights to cartel rents: the Socony–Vacuum story. J Law

Econ 1991;34:177–203.Keuschnigg M. Comparative advantage in international trade: theory and

evidence. Studies in empirical economies. Springer-Verlag Company; 1999.Kolstad CD, Wolak Jr FA. Competition in interregional taxation: the case of

western coal. J Polit Econ 1983;91:443–60.Lowe TJ, Preckel PV. Decision technologies for agribusiness problems: a brief

review of selected literature and a call for research. Manuf Serv Oper Manag2004;6:201–8.

McLaren J. Speculation on primary commodities: the effects of restricted entry.Rev Econ Stud 1999;66:853–71.

Peteraf MA. The cornerstones of competitive advantage: a resource-based view.Strateg Manag J 1993;14:179–91.

Powell WW, Snellman K. The knowledge economy. Annu Rev Sociol2004;30:199–220.

Porter ME. Competitive advantage. New York, NY: Free Press; 1985.Rasmusen E. Games and information. Cambridge: Blackwell Publishing; 2001.Roos A, FlinkmanM, Jäppinen A, Lönner G, Warensjö M. Production strategies

in the Swedish softwood sawmilling industry. For Policy Econ 2001;3:189–97.

Sachs JD, Warner AM. Natural resource abundance and economic growth.National Bureau of Economic Research Working paper, vol. 5398.Cambridge, MA: National Bureau of Economic Research; 1995.

Singer M, Donoso P. Strategic decision-making at a Chilean integrated steelmanufacturer aided by an activity-based optimization system. J Bus Res2005;59:387–90.

Singer M, Donoso P. Internal supply chain management in the Chilean sawmillindustry. Forthcoming in International Journal of Operations & ProductionManagement; 2006.

Schwarz HG. Modelling investment and implementation of technologicalprogress in metal industries. Theory and application to the German primaryaluminium industry. Resour Policy 2003;29:99–109.

Schwarz H-G. Economic materials-product chain models: current status, furtherdevelopment and an illustrative example. Ecol Econ 2006;58:373–92.

Stoelhorst JW, van Raaij EM. On explaining performance differentials:marketing and the managerial theory of the firm. J Bus Res 2004;57:462–77.

Toivonen R, Toppinen A, Tilli T. Integration of roundwood markets in Austria,Finland and Sweden. For Policy Econ 2002;4:33–42.

Troncoso JJ, Garrido RA. Forestry production and logistics planning: ananalysis using mixed-integer programming. For Policy Econ 2005;7:625–33.

Van Beukering, P.J.H., van den Bergh, J.C.J.M., Janssen, M.A., Verbruggen, H.,2000. International material-product chains: an alternative perspective oninternational trade and trade theories. Tinbergen Institute Discussion Papers00-034/3, Tinbergen Institute.

Wårell L. Defining geographic coal markets using price data and shipments data.Energy Policy 2005;33:2216–30.