Tactical supply chain planning in the forest products industry through optimization and scenario-based analysis Daniel Beaudoin, Luc LeBel, and Jean-Marc Frayret Abstract: A mixed integer programming model that aims at supporting the tactical wood procurement decisions of a multifacility company is presented. This model allows for wood exchanges between companies. Furthermore, the mate- rial flow through the supply chain is driven by both a demand to satisfy (���pull��� strategy) and a market mechanism (���push��� strategy), enabling the planner to take into consideration both wood freshness and the notion of quality linked to the age of harvested wood into log, chips, and end-product demands. An inability to consider alternative plans for implementation, and the difficulty of assessing the performance of these plans in an uncertain environment, are two shortcomings of the manual planning process. A planning process, based on human planner ��� decision support system interactions that allows a company to overcome these shortcomings is therefore presented. The process combines Monte Carlo methods and an anticipation mechanism that will, in the long term, enable the company to take into ac- count equipment transportation costs. The proposed planning process leads to a multicriteria decision-making problem where the human planner has to select a plan to implement from a set of candidate plans. A hypothetical test case shows that it is possible to manage the wood flow from stump to end market in such a way as to preserve freshness and extract higher value from the logs processed in the mills. The test case also shows that the proposed planning pro- cess achieves an average profitability increase of 8.8% compared with an approach based on a deterministic model us- ing average parameter values. Finally, a sensitivity analysis reveals that the accuracy of standing inventory on harvest blocks and the anticipated market conditions are the most important parameters to consider in selecting a good wood procurement plan. R��sum�� : Cet article pr��sente un mod��le qui utilise la programmation lin��aire mixte pour r��soudre le probl��me de pla- nification tactique des approvisionnements forestiers d���une entreprise propri��taire de plusieurs usines. Le mod��le per- met les ��changes de bois entre compagnies. Les flux de mat��riaux �� travers le r��seau d���approvisionnement sont dict��s tant par la demande �� satisfaire (strat��gie en flux tir��s) que par un m��canisme de march�� (strat��gie en flux pouss��s). Ces strat��gies permettent de tenir compte de la fra��cheur du bois et de la notion de qualit�� associ��e �� l�����ge du bois dans les demandes de billots, de copeaux et de produits finis. L���incapacit�� de consid��rer l���implantation de plans alter- natifs et la difficult�� d�����valuer la performance de ces plans dans un environnement incertain sont deux points faibles d���un processus manuel de planification. Un processus de planification permettant de surmonter ces lacunes est pr��sent��. Ce processus est bas�� sur les interactions entre une personne et un syst��me d���aide �� la d��cision. Il combine les m��tho- des Monte Carlo et un m��canisme d���anticipation qui permet �� l���entreprise de tenir compte des co��ts associ��s au d��pla- cement des ��quipements. Le processus de planification propos�� prend la forme d���un probl��me de prise de d��cision multicrit��re pour lequel le planificateur s��lectionne un plan �� implanter parmi un ensemble de plans candidats. Une ��tude de cas d��montre qu���il est possible de g��rer le flux de bois de la for��t jusqu���au march��, de mani��re �� pr��server sa fra��cheur et extraire plus de valeur des billots transform��s aux usines. Aussi, les r��sultats d���une simulation d��montrent que le processus de planification propos�� permet d���augmenter les profits de 8,8 % en moyenne par rapport �� une ap- proche bas��e sur un mod��le d��terministe utilisant la valeur moyenne des param��tres. Finalement, une analyse de sensi- bilit�� r��v��le que la pr��cision de l���inventaire des volumes sur pied pr��sents sur les parterres de coupe et l���anticipation des conditions de march�� sont les param��tres les plus importants pour ��tablir un bon plan d���approvisionnement. [Traduit par la R��daction] Beaudoin et al. 140 Can. J. For. Res. 37: 128���140 (2007) doi:10.1139/X06-223 �� 2007 NRC Canada 128 Received 19 October 2005. Accepted 11 August 2006. Published on the NRC Research Press Web site at cjfr.nrc.ca on 4 April 2007. D. Beaudoin.1 Laboratoire d���Op��rations Foresti��res, Facult�� de Foresterie et de G��omatique, Pavillon Abitibi���Price, Universit�� Laval, Qu��bec, QC G1K 7P4, Canada. L. LeBel. D��partement de Science du Bois et de la For��t, Facult�� de Foresterie et de G��omatique, Pavillon Abitibi���Price, Universit�� Laval, Qu��bec, QC G1K 7P4, Canada. J.-M. Frayret. D��partment de math��matiques et g��nie industriel, ��cole polytechnique de Montr��al, 2500, chemin de Polytechnique, Montr��al, QC H3T 1J4, Canada. 1Corresponding author (e-mail: daniel.beaudoin.1@ulaval.ca).

Introduction Wood procurement planning is a complex task, as a multi- tude of factors must be taken into account. It is even more complex in a multifirm environment, where firms may sup- ply each other, and where forest stands are composed of sev- eral tree species. Yet planning is still largely done on the basis of intuition and without mathematical programming support. Furthermore, the considerable amount of time re- quired to build a single plan precludes the evaluation of al- ternative plans. The contributions of this paper are (i) a detailed tactical model to support centralized annual planning by an inte- grated forest company that may own many mills, and allows for wood exchanges between companies (ii) an extension of the market mechanism presented in Maness (1989) to antici- pate market needs, taking wood freshness into account (iii) a planning process, that is, a process for generating and evaluating candidate plans. The remainder of this paper is organized as follows: a lit- erature review is presented in the next section, followed by a description of the problem. The planning process is then in- troduced with its different components. Then the mathemati- cal formulation of the tactical wood procurement model is shown. Following this is a description of a hypothetical test case. Finally, the results and concluding remarks are pre- sented. Literature review Models The use of mathematical models to deal with wood pro- curement problems can be traced back to the early 1960s. Since that time, a large body of models has been developed to address different aspects of wood procurement. Some have been designed for specific activities such as skidding (Carlsson et al. 1998) or transportation (Wightman and Jor- dan 1990 Weintraub et al. 1996). Others have integrated several activities within a single model to capture possible synergies between them. For instance, Burger and Jamnick (1995) integrated harvest, storage, and transportation deci- sions, while Karlsson et al. (2004) included allocation of harvest teams in addition to these factors. To our knowledge, no attempt has been made to address these decisions while taking into account mills��� anticipated production decisions, even though significant gains could be achieved through an increase in fiber freshness (i.e., a decrease in time elapsed between harvesting and processing at the mill). Deteriorating items In the last decade the industry has come to realize the im- portance of procuring fresh fiber. Common problems associ- ated with log storage are check development due to drying, and sap stain. Even if sap stain does not change the struc- tural integrity of the wood, it can severely affect its appear- ance, resulting in serious loss of value (Kreber et al. 2001). Lagani��re and Defo (2002) looked at the impact of timber freshness for sawmill operators. They identified problems associated with the log yard, debarking, sawing, drying, planing, and grading. They concluded that for all activities, older fiber is detrimental to a sawmill���s performance. Simi- larly, Bicho (2002) and Wood (2002) discussed the impact of storage duration on pulp yield, pulp brightness, and pro- cessing costs of pulp mills. Production planning and scheduling of deteriorating items have long been the subject of articles, but such consider- ations have appeared only recently in models dealing with the problem of harvest and distribution planning. Karlsson et al. (2003) were among the first to introduce age-related stor- age costs. In their model, fiber deterioration is taken into ac- count by associating a reduction in value for different log assortments and different total storage times. Two improve- ments can be made to this approach. First, the reduction in value does not take into consideration the seasonal variation in the rate of deterioration of the fiber. It is not only the time elapsed between the moment a tree is harvested and the mo- ment it is transformed into diverse products that should be considered, but also the periods or seasons over which the elapsed time occurs. Second, their model considers the rate of deterioration to be the same regardless of the storage lo- cation and the end products to be manufactured. Storage lo- cations are sometimes far apart, and even if the seasonal rate of deterioration is the same, the season may begin at differ- ent times across the land base. Furthermore, mills may use different technologies and may not be affected in the same way by the freshness of the resource. The mathematical for- mulation proposed in this paper takes these considerations into account. Uncertainty Forest managers and researchers are increasingly con- cerned with uncertainty and would like to account for it when making decisions. Weintraub and Bare (1996) and Martell et al. (1998) identify wood procurement planning under uncertainty as a new challenge for researchers. To date, the majority of models tackling the wood procurement problem have focused on deterministic formulations of the problem. A fundamental property of deterministic models is that all required data are supposed to be known with cer- tainty. This is an important assumption that limits the valid- ity of any linear programming solution to a supply chain problem (Shapiro 2001). The main criticism of these appli- cations concerns not necessarily the use of deterministic de- cision models in nondeterministic environments but rather the lack of focus on analysis and validation of the so-called optimal solution. Contingency analysis is a necessary step before any decision is made. Relatively few studies that consider the role of stochastic conditions in addressing wood procurement problems have been undertaken. For a review of stochastic parameters and approaches adopted in order to take uncertainty into consid- eration, we refer the reader to Weintraub and Bare (1996) and Martell et al. (1998). The most commonly used method- ologies are ���one at a time��� sensitivity analysis and scenario- based analysis. One at a time sensitivity analysis is a point-by-point change that consists of varying the value of a parameter to find the extent to which the change affects the outcome, while scenario-based analysis is a process of ana- lyzing potential future events by considering possible alter- native outcomes. Major drawbacks of these two methods are their inability to evaluate the impact of the interactions be- tween the various stochastic parameters and a lack of knowl- �� 2007 NRC Canada Beaudoin et al. 129