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  • A Hybrid Collaborative Algorithm to Solve an Integrated Wood Transportation and Paper Pulp Production Problem Jos Eduardo Pcora Angel Ruiz Patrick Soriano

    September 2014

    CIRRELT-2014-45 Document de travail galement publi par la Facult des sciences de ladministration de lUniversit Laval, sous le numro FSA-2014-006.

  • A Hybrid Collaborative Algorithm to Solve an Integrated Wood Transportation and Paper Pulp Production Problem

    Jos Eduardo Pcora1, Angel Ruiz2,3,*, Patrick Soriano2,4

    1 Departamento de Administrao Gera e Aplicada, Universidade Federal do Paran, rua XV

    de Novembro, 1299, Centro, Curitiba, PR, 80060-000, Brazil 2 Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation

    (CIRRELT) 3 Department of Operations and Decision Systems, 2325 de la Terrasse, Universit Laval,

    Qubec, Canada G1V 0A6 4 Department of Management Sciences, HEC Montral, 3000 chemin de la Cte-Sainte-

    Catherine, Montral, Canada H3T 2A7

    Abstract. This paper proposes a hybrid algorithm to tackle a difficult real world problem

    arising in the context of pulp and paper production. This situation is modeled as a

    scheduling problem where one has to decide which wood goes to each available

    processing unit (wood cooker) in order to minimize the variance of wood densities within

    each cooker for each period of the planning horizon. The proposed hybrid algorithm is

    built around two distinct phases. The first phase uses two interacting heuristic methods to

    identify a promising reduced search space which is then thoroughly explored in the

    second phase. This hybrid algorithm produces high quality solutions in reasonable

    computation times, especially for the largest test instances. Extensive computational

    experiments demonstrated the robustness and efficiency of the method.

    Keywords. Vehicle routing problem with pauses, exact formulation, heuristic.

    Acknowledgements. This research was partially supported by Grants OPG 0293307 and

    OPG0177174 from the Natural Sciences and Engineering Research Council of Canada

    (NSERC) and grant [2671/04-2] from Coordenao de Aperfeioamento de Pessoal de

    Nvel Superior (CAPES) - Brazil. Their support is gratefully acknowledged.

    Results and views expressed in this publication are the sole responsibility of the authors and do not necessarily reflect those of CIRRELT.

    Les rsultats et opinions contenus dans cette publication ne refltent pas ncessairement la position du CIRRELT et n'engagent pas sa responsabilit.

    _____________________________

    * Corresponding author: Angel.Ruiz@cirrelt.ca

    Dpt lgal Bibliothque et Archives nationales du Qubec Bibliothque et Archives Canada, 2014

    Pcora, Ruiz, Soriano and CIRRELT, 2014

  • 1. Introduction

    The problem considered here arises in the context of a large Brazilian pulpand paper producer. The paper pulp's manufacturing process is based on thetransformation of wood into a brous material. This material is known aspaste, pulp or industrial pulp. Paper pulp is obtained by a thermochemicalprocess (Kraft process) in which wood chips and chemicals are fed into apressure vessel. The Kraft process basically consists in submitting the chipsto the combined action of sodium hydroxide, sodium sulte and steam insidethe vessel in order to separate the lignin that binds the bre in the wood.This liberated bre is the industrial pulp. For more information on the Kraftprocess see Biermann (1996).

    The basic density of the wood chips (i.e density of dry wood) plays animportant role during the Kraft process, as mentioned in Foelkel et al. (1992)and Williams (1994). If the range of the basic densities of the chips presentin a cooker is wide, setting the parameters for the thermochemical process(i.e. quantities of chemicals, pressure and temperature) to values maximizingthe quality of the produced pulp will not be possible. Consequently, thecooker will contain a mix of under and over cooked wood chips, and thetransformation will be inecient: lower percentages of lignin will be extractedfrom the wood while requiring increased energy consumption and generatinga lower quality pulp. In addition, pulp produced with high density wood hasa dierent purpose than pulp produced with low density wood. The formeris mostly used to manufacture cardboard while the latter is used for tissues,as reported by Kennedy et al. (1989). For these reasons, the homogeneityof the basic density of wood chips is a highly desired factor in the pulp andpaper industry.

    Therefore, in order to meet pulp quality requirements while minimizingproduction costs, one needs to use the most homogeneous mix of wood chips.To this end, plant managers need to carefully set the cooker's parameters.Even if we assume that the average basic density in a cooker is known, values'setting for each parameter maximizing the production yield is an extremelycomplicated task. Since there is no known analytical relationship betweenparameters, companies have empirically developed specic recipes for whichspecic parameters values are suggested. These recipes will be referred to asworking levels.

    On the other hand, wood supply plays a key role in the paper pulp'smanufacturing process. At every moment, plant managers must decide which

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  • wood, from what is available at the wood yard, should be used at each cooker.In the Brazilian context studied here, pulp production is based on the trans-formation of farm growned eucalyptus. The farms are divided into homoge-neous parcels of land, known as harvest areas, producing enough wood to feeda pulp digester for one day. Once a parcel is harvested, the logs are trans-ported to the factory yard. Until very recently, wood yards were managed ina rather simplistic manner: trucks dropped the harvested wood into heaps,then wood-cranes moved the logs to the chippers which feed the cookers.However, the eorts made to increase the productivity of forestry operationshave led to a more ecient, yet challenging context. The previous practice,where yard desynchronized forests and production, has evolved towardsmodern yards separated into zones, where each zone assigned to a dierentcooker. In other words, the harvested wood is transported by a number offulltruckload trips to the yard zone corresponding to a specic cooker. Thisnew practice requires that plant manager determines in advance to whichyard zone, and therefore to which cooker, the wood from the harvested for-est will be assigned. It follows that both transportation and transformationactivities are synchronized by the transportation and production plan. Also,in order to simplify wood yard operations, this new management model re-quires that all the wood coming from the same harvested area be used beforeusing the one coming from another area. Indeed, this strategy minimizesboth trac handling at the wood yard and the amount of wasted wood.

    Taking this into account, our industrial partner's production is managedin the following way. First, he considers the available wood within a xedplanning horizon, each period being a working week. Then, he considers vepotential working levels, each corresponding to a specic basic density. Basedon these inputs, he simultaneously sets the working levels for every cookerduring each planning period, and selects the harvested wood to transport tothe factory and its assignment to cookers. This is done in such a way that,for each cooker and for each period on the planning horizon (1) the varianceof the basic density in a cooker is minimized and (2) the dierence betweenthe average basic density and the target one (i.e. the one for which thecooking parameters have been set) is also minimized.

    This paper contributes a two-phase solving approach to this dicult prob-lem. In the rst phase, two simple heuristics cooperate to build a restrictedsearch space. This search space is then explored during the second phase.The remainder of this paper is organized as follows. The following sectionpositions this work with respect to previous operations research applications

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  • made in the forestry eld. It also reviews some relevant papers allowing theinterested reader to survey hybrid algorithms or hybrid solving approaches.Section 3 will introduce the two mathematical models used in this work. Sec-tion 4 will describe the overall structure of the proposed hybrid algorithm.Computational results will be presented and analyzed in Section 5. Finally,Section 6 concludes the paper.

    2. Positioning of the paper in the literature

    Since this work presents the development of a new search algorithm for avery specic industrial context, this section is divided into two distinct parts.The rst part focuses on the pulp and paper industry. More specically, itreports some of the most recent and relevant works regarding operations re-search application to solve production planning and transportation problemsin this industry. The second part introduces the reader to the eld of hybridalgorithms, an emergent and promising approach in the operations researcheld to solve combinatorial problems. In both cases, reporting an exhaustiveliterature review would be far beyond the scope and the needs of this work.Nonetheless, the objective of this section is to allow the reader to positionthis contribution within the two mentioned research streams.

    In the last years, the number of operations research contributions madeto the forestry supply chain, particularly to the pulp and pa