GLENN WEIGEL
A STRATEGIC PLANNING MODEL FOR MAXIMIZING VALUE CREATION IN PULP AND
PAPER MILLS
Mémoire présentée à la Faculté des études supérieures de l’Université Laval
dans le cadre du programme de Maîtrise en génie mécanique pour l’obtention du grade de Maître ès sciences (M.Sc.)
DÉPARTEMENT DE GÉNIE MÉCANIQUE FACULTÉ DES SCIENCES ET DE GÉNIE
UNIVERSITÉ LAVAL QUÉBEC
2005 © Glenn Weigel, 2005
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Résumé L’industrie canadienne des pâtes et papiers fait face à plusieurs défis importants. Un de ces
défis consiste à trouver de nouveaux moyens d’améliorer la création de valeur à travers la
chaîne logistique, en fabriquant des produits de haute qualité à partir de matières premières
de qualités variables. Généralement, deux stratégies parallèles sont envisagées pour relever
ce défi. La première stratégie implique de gérer les flux des matériaux à travers la chaîne
logistique de telle manière que les divers types de fibres soient utilisés au mieux par une
sélection adaptée des processus à utiliser et des produits à fabriquer. La deuxième stratégie
implique de définir la gamme de produits de telle manière qu’elle permette de profiter au
mieux des opportunités d’affaires et des propriétés des fibres existantes. La première
stratégie est basée sur la ressource tandis que la deuxième stratégie est basée sur les
marchés.
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Abstract The Canadian pulp and paper industry is facing several important challenges. One of these
challenges is to find new ways of improving value creation throughout the value chain
while manufacturing high quality products from raw materials with inherently variable
properties. This challenge can be addressed using two parallel strategies. The first of these
involves managing the flow of materials through the value chain in such a way that fibre
grades are directed to the processes and end-products to which they are best suited. The
second involves tailoring the end-product range to take maximum advantage of existing
market conditions and fibre resource properties. Operating simultaneously, these strategies
ensure the profits generated from the available fibre resources are maximized.
This thesis presents a strategic planning model which provides a mathematical framework
for developing these strategies. The model uses customer demand and market value to
determine how strongly each end-product is pulled through the value chain, and raw
material availability and cost, together with established relationships between fibre
properties and pulp and paper properties, to determine how various fibre grades are utilized.
The model itself is a large mixed-integer program which was implemented using ILOG
OPL Studio 3.7 with ILOG CPLEX 9.0 as solver. A test case was developed based on a
realistic integrated pulp and paper mill, and the model was validated using a series of
example scenarios. The results show that the model is valid, that it can be used to identify
strategies for significantly improving value creation, and that it can be solved quickly
enough to allow its expansion to a production network environment.
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Acknowledgements Many thanks to Sophie D’Amours, Alain Martel, Paul Watson, Robert Beauregard, Rita
Penco, Judy Mackenzie, Wai Gee, Surjit Johal, Ashif Hussein, Bernard Yeun, Val
Lawrence, the Pulp and Paper Research Institute of Canada (Paprican), and the Forac
Research Consortium.
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Table of contents Résumé.....................................................................................................................................i Abstract.................................................................................................................................. ii Acknowledgements............................................................................................................... iii 1 Introduction.....................................................................................................................1
1.1 Wood fibre ..............................................................................................................1 1.2 Pulp production.......................................................................................................3 1.3 Paper production .....................................................................................................5 1.4 The Canadian pulp and paper industry ...................................................................7
2 Literature review...........................................................................................................10 2.1 Value chain modeling ...........................................................................................10 2.2 Pulp and paper industry-specific value chain models...........................................13 2.3 Relationships between macro-level wood properties and pulp and paper
properties ..............................................................................................................15 2.4 Relationships between fundamental fibre properties and pulp and paper properties ..............................................................................................................................17 2.5 Effects of furnish mixtures on pulp and paper properties.....................................17 2.6 Improving value creation through wood flow management .................................18 2.7 Incorporating fibre property effects into a pulp and paper industry-specific value
chain model...........................................................................................................20 3 Problem formulation .....................................................................................................22
3.1 The pulp and paper industry value chain ..............................................................22 3.2 Production stages and material flows ...................................................................24 3.3 Definition of key concepts....................................................................................26
3.3.1 Products and product groups.........................................................................26 3.3.2 Supply sources ..............................................................................................26 3.3.3 Sorting options..............................................................................................27 3.3.4 Chipping systems..........................................................................................28 3.3.5 Chip handling systems ..................................................................................28 3.3.6 Production recipes.........................................................................................29 3.3.7 Pulp and paper production systems ..............................................................29 3.3.8 Paper conversion systems .............................................................................32 3.3.9 External paper converters .............................................................................33 3.3.10 Customers .....................................................................................................33
4 Model formulation ........................................................................................................34 4.1 Definition of indexes ............................................................................................34 4.2 Definition of sets and subsets ...............................................................................34 4.3 Definition of input parameters ..............................................................................37 4.4 Definition of decision variables............................................................................40 4.5 Mixed-integer programming model......................................................................42 4.6 Discussion of the objective function.....................................................................46 4.7 Discussion of the constraints ................................................................................47
5 Using the model ............................................................................................................51 5.1 Defining the system structure ...............................................................................51 5.2 Defining input parameter values...........................................................................56
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5.3 Optimizing the system ..........................................................................................60 5.4 Interpreting optimized decision variable values ...................................................60
6 Example ........................................................................................................................62 6.1 System structure....................................................................................................62 6.2 Input parameter values..........................................................................................68 6.3 Scenario 1: Base case............................................................................................73 6.4 Scenario 2: Fibre resource allocation....................................................................76 6.5 Scenario 3: Product range selection......................................................................79
7 Discussion.....................................................................................................................81 7.1 Assumptions and limitations.................................................................................81 7.2 Scope and other considerations.............................................................................85 7.3 Expanding the model ............................................................................................86
Conclusions...........................................................................................................................89 References.............................................................................................................................91 Appendix A: ILOG OPL code ..............................................................................................95 Appendix B: Microsoft Access database relationships.......................................................124 Appendix C: Input parameter values used in scenario 1 ....................................................126
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List of tables Table 1 Selected chemical and mechanical pulping properties of some common
Canadian wood species.....................................................................................16 Table 2 Potential sorting options for a log supply made up of eastern spruce, balsam fir,
and a mixture of other less utilized species ......................................................27 Table 3 Potential flexible pulp production system options............................................30 Table 4 Pulp production capabilities associated with the production system options
presented in Table 3..........................................................................................31 Table 5 Pulp and paper properties of the fibre grades used in the example ..................63 Table 6 Definition of product groups used in the example............................................74 Table C 1 Units used for parameters in example scenario 1 ...........................................126 Table C 2 Upper and lower production limit (bj and bj) parameter values for external
paper converters used in example scenario 1..................................................127 Table C 3 Capacity requirement (ae,r) parameter values for pulp and paper grades use in
example scenario 1..........................................................................................128 Table C 4 Capacity availability (ke,m) parameter values for pulp and paper production
systems used in example scenario 1 ...............................................................130 Table C 5 Market demand (dg,c) parameter values used in example scenario 1..............131 Table C 6 Upper production limit (bp) parameter values for chip and internally processed
converted paper grades used in example scenario 1 .......................................132 Table C 7 Fixed and variable production cost (cp,j
fix and cp,jvar) parameter values for
externally processed converted paper grades used in example scenario 1 .....133 Table C 8 Sales revenue (rp,c) parameter values used in example scenario 1 .................134 Table C 9 Transport cost (cp,c) parameter values for pulp and paper grades used in
example scenario 1..........................................................................................135 Table C 10 Transport cost (cp,c,j) parameter values for externally processed converted
paper grades used in example scenario 1........................................................136 Table C 11 Transport cost (cp,c,s) parameter values for log and chip grades used in example
scenario 1 ........................................................................................................137 Table C 12 Input requirement (gp,p’,j) parameter values for externally processed converted
paper grades used in example scenario 1........................................................138 Table C 13 Input requirement (gp,p’,m) parameter values for chip and internally processed
converted paper grades used in example scenario 1 .......................................139 Table C 14 Input requirement (gp,r) parameter values for pulp and paper grades used in
example scenario 1..........................................................................................140 Table C 15 Procurement cost (cp,s) and upper and lower procurement limit (bp,s and bp,s)
parameter values for external supply sources used in example scenario 1.....143 Table C 16 Procurement cost (cp,s,i) and content ratio (hp,s,i) parameter values for internal
supply sources used in example scenario 1 ....................................................144 Table C 17 Fixed and variable production cost (cp,m
fix and cp,mvar) and capacity requirement
(ap,m) parameter values for chip and internally processed converted paper grades used in example scenario 1..................................................................145
Table C 18 Fixed and variable production cost (crfix and cr
var) and upper production limit (br) parameter values for pulp and paper grades used in example scenario 1 146
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Table C 19 Upper and lower procurement limit (bs,i and bs,i) parameter values for internal supply sources used in example scenario 1 ....................................................148
Table C 20 System implementation cost (cm) parameter values used in example scenario 1 . ....................................................................................................................149
Table C 21 Capacity availability (km) parameter values for chipping and paper conversion systems used in example scenario 1 ...............................................................150
Table C 22 Capacity availability (nm) parameter values for chip handling systems used in example scenario 1..........................................................................................151
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List of figures Figure 1 Scanning electron micrograph of the corner of a block of lodgepole pine wood
............................................................................................................................2 Figure 2 Scanning electron micrograph of a segment of a single tracheid cell showing
exposed cellulose microfibrils ............................................................................3 Figure 3 Light micrographs of (A) black spruce kraft pulp, and (B) black spruce
thermomechanical pulp.......................................................................................4 Figure 4 Scanning electron micrograph of the corner of a laboratory-made black spruce
kraft pulp handsheet............................................................................................5 Figure 5 Scanning electron micrographs of the surfaces of laboratory-made (A) black
spruce, (B) Douglas fir, and (C) trembling aspen kraft pulp handsheets............7 Figure 6 2003 Canadian pulp and paper production by grade ..........................................8 Figure 7 Planning decisions in the pulp and paper industry ...........................................14 Figure 8 Log sorting strategy developed for mixed Norway spruce and Scots pine stands
in Sweden..........................................................................................................19 Figure 9 Wood flow management strategy developed for Tasman Pulp and Paper .......20 Figure 10 The pulp and paper industry value chain ..........................................................22 Figure 11 Material flows within a single integrated pulp and paper mill .........................24 Figure 12 Potential equipment components in a flexible pulp production system ...........30 Figure 13 Material flows and key decision variables........................................................50 Figure 14 Dependence of length-weighted fibre length (LWFL) on tree age for a
population of subalpine fir and lodgepole pine trees sampled from a single growth site.........................................................................................................52
Figure 15 Dependence of length-weighted fibre length (LWFL) on tree age for two populations of lodgepole pine trees sampled from two different growth sites with different site indexes.................................................................................53
Figure 16 Dependence of wet-web strength on average fibre length for an unbleached softwood kraft pulp at 30% solids content........................................................53
Figure 17 Dependence of kraft pulp yield at constant cooking conditions on species content in western SPF chip mixtures...............................................................54
Figure 18 Dependence of kraft pulp Kappa number (residual lignin content) at constant cooking conditions on species content in western SPF chip mixtures .............54
Figure 19 Dependence of thermomechanical pulp energy consumption at constant pulp freeness on species content in western SPF chip mixtures...............................55
Figure 20 Dependence of kraft pulp tensile strength on species content in western SPF chip mixtures.....................................................................................................55
Figure 21 Structure of the theoretical integrated pulp and paper mill used in the example.. ..........................................................................................................................62
Figure 22 Structure of the log supply used in the example...............................................64 Figure 23 Structure of the chip supply used in the example .............................................65 Figure 24 Structure of the pulp production operation used in the example ......................67 Figure 25 Structure of the paper production operation used in the example ....................68 Figure 26 Structure of the optimized production scheme for scenario 1 ..........................76 Figure 27 Structure of the optimized production scheme for scenario 2 ..........................78 Figure 28 Structure of the optimized production scheme for scenario 3 ..........................80
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Figure 29 Arcs added to accommodate log and chip trading............................................81 Figure 30 Linearization by piecewise linear approximations ...........................................83 Figure 31 Linearization by successive linear approximations ..........................................83 Figure 32 Linearization by successive gradient approximations ......................................84 Figure 33 Effect of lot size on inventory and fixed production costs ...............................85 Figure 34 Arcs added to accommodate the flow of materials between mills ...................87 Figure B 1 Input database relationships............................................................................124 Figure B 2 Output database relationships .........................................................................125
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1 Introduction This thesis presents a mixed-integer programming model for maximizing value creation in
pulp and paper mills. The model functions at the strategic planning level, and combines the
optimization of fibre resource allocation, technology implementation, and end-product
range selection decisions within a single integrated pulp and paper mill.
The Introduction section presents a general description of the wood fibre resource, an
overview of the pulp and paper production processes, and a summary of the key challenges
facing the Canadian pulp and paper industry. The Literature review section summarizes the
current state of knowledge in the areas of value chain modeling and fibre property
relationships and presents a vision for integrating this knowledge into a comprehensive,
industry-specific value chain model. The Problem formulation section presents an overview
of the pulp and paper industry value chain and a summary of the key concepts used in the
model. The Model formulation section presents the model itself and provides a detailed
description of the objective function and constraints. The Using the model section offers
guidelines for the definition of system structure, the establishment of input parameter
values, and the interpretation of decision variable values. The Example section presents a
series of three test case scenarios illustrating how the model can be used to optimize value
creation within a theoretical integrated pulp and paper mill. The Discussion section reviews
the assumptions and limitations inherent to the model, and offers suggestions for expanding
the model to a production network environment. The Conclusions section provides a
summary of the work and its implications.
1.1 Wood fibre Wood fibre constitutes the largest component of most pulp and paper products. The term
wood fibre itself commonly refers to the tracheid cells which make up the bulk of the
woody tissue in trees. These cells, or fibres, are roughly tubular in shape, and are oriented
parallel to the tree stem as shown in Figure 1. Their dimensions are quite variable, but
softwood fibres typically range from 3 to 4 millimetres in length, 30 to 50 microns in
diameter, and 2 to 5 microns in wall thickness. Hardwood fibres tend to be much shorter 55
2
and finer, typically ranging from 1 to 2 millimetres in length, 10 to 40 microns in diameter,
and 1 to 4 microns in wall thickness [1].
Figure 1 Scanning electron micrograph of the corner of a block of lodgepole pine wood (the tracheid cells are oriented parallel to the tree stem)
Wood fibres are made up of three primary constituents: cellulose, lignin and hemicellulose
[2]. Cellulose is a crystalline compound which is organized into strands called microfibrils.
These microfibrils, which serve as the main structural elements of fibres, are wound in a
helix around the fibre axis as shown in Figure 2. The angle of this helix with respect to the
fibre axis is called the microfibril angle. Lignin, on the other hand, is an amorphous
compound. It serves as a matrix to hold the cellulose microfibrils in place and to bond
fibres to one another in woody tissue. Hemicellulose is a semi-crystalline compound which
serves as an interface between cellulose and lignin.
Fibre dimensions, microfibril angle and chemical composition all play important roles in
determining pulp and paper properties. Each of these fibre properties can vary significantly
between tree species, between growth sites, between individual trees, and even within
single trees.
Tracheid cells
Ray cells
Resin canal
50µm
3
Figure 2 Scanning electron micrograph of a segment of a single tracheid cell showing exposed cellulose microfibrils
1.2 Pulp production In Canada, most of the wood harvested is used to produce lumber. The residues of lumber
production, together with logs harvested specifically for pulp production, are debarked and
usually cut into thin chips before pulping. The chips are then screened to remove
undersized and oversized fractions, and pulped to break the woody tissue down into
individual fibres. This can be done either chemically or mechanically.
Chemical pulping involves using chemicals to dissolve the lignin that binds the fibres
together. This is achieved by pre-steaming and then cooking wood chips in large vessels
called digesters using chemical liquors and elevated temperatures. The most commonly
used chemical pulping process is the sulfide or kraft process, in which hydroxide and
hydrogen sulfide ions are the main active components [3].
Chemical pulping processes cause relatively little damage to fibre structure. They also
remove most of the lignin present, leaving chemical pulp fibres flexible and relatively easy
to bleach. Chemical pulp yields can vary significantly depending on the chemical
composition of the wood chips and the processing conditions used, but are typically on the
order of 50% for bleachable grade pulps [3]. These factors make chemical pulps suitable
Cellulose microfibrils
2µm
4
for longer life-cycle products where strength, durability and brightness are important
considerations.
Mechanical pulping involves using mechanical force to pull fibres apart. This is achieved
by refining wood chips between ribbed refiner discs, or grinding pulp logs against abrasive
pulpstones. Water, elevated temperatures and elevated pressures are usually used to soften
the furnish during refining or grinding. Thermomechanical pulping, in which pre-steamed
wood chips are refined between counter-rotating refiner discs at elevated temperature and
pressure, is the most commonly used mechanical pulping process [4].
Mechanical pulping processes tend to cause significant damage to fibre structure. They
break down a significant proportion of fibres into short fragments called fines and leave
most of the lignin in place. This leaves mechanical pulp fibres relatively stiff and more
difficult to bleach. Mechanical pulp yields are typically on the order of 98% [4]. These
factors make mechanical pulps suitable for shorter life-cycle products where cost and basis
weight are important considerations. Figure 3 illustrates some typical physical differences
between chemical and mechanical pulps.
Figure 3 Light micrographs of (A) black spruce kraft pulp, and (B) black spruce thermomechanical pulp
After chemical or mechanical processing, pulps are passed through a series of washing and
screening steps to remove knots and shives (fibre bundles not completely separated by
processing) and other contaminants. The knots and shives are then usually reprocessed and
added back into the pulp stream. In the case of chemical pulps, spent cooking liquors are
B A 150µm 150µm
5
also extracted and passed through a chemical recovery system in which organic compounds
are burned off and sodium sulfide and sodium hydroxide are recovered for reuse.
Depending on the properties and intended end-uses, pulps may also be bleached using a
sequence of different chemical reactions or stages. These often include some combination
of oxygen delignification, alkaline extraction, acid hydrolysis, and chlorine dioxide, ozone,
peroxide and sodium hydrosulfite bleaching [3, 4]. Pulps destined for sale as market pulps
are then typically formed into pads and dried before transport to customers. Those destined
for in-mill paper production are usually concentrated and stored in large tanks. Before use
in paper production, most chemical pulps and some mechanical pulps are beaten or post
refined in order to develop specific fibre properties such as bondability.
1.3 Paper production Paper production involves reforming the separated pulp fibres into sheets. During this
process, the fibres are compressed and bonded to one another as shown in Figure 4.
Figure 4 Scanning electron micrograph of the corner of a laboratory-made black spruce kraft pulp handsheet
Papermaking processes vary somewhat depending on the nature of the end-product, but
they can generally be broken down into four stages: formation, wet pressing, drying and
finishing. A thorough explanation of these stages can be found in Papermaking Science and
Technology [5, 6, 7]. In the formation stage, a dilute pulp stock (usually less than 1% fibre
by weight) is deposited onto a moving fabric or wire [5]. Water is drained, usually under
vacuum, through the wire to form a loose sheet called a wet web. In the wet pressing stage,
100µm
6
the wet web is compressed by passing it through the nip formed by two rolls or, in some
cases, a roll and a press shoe. The mechanical pressure generated in the press acts to
transfer water from the wet web to a press felt. In the drying stage, the web is dried to
between 5% and 9% moisture content through thermal evaporation [6]. The most common
drying method involves passing the web over a series of steam-heated cylinders. The
processes used in the finishing stage vary considerably depending on the nature of the end-
product. The web may be calendared, for example, by passing it through a series of press
rolls to develop certain surface properties and produce specific sheet thicknesses. The
reeling, winding and sheet finishing or converting processes can also be thought of as part
of the finishing stage [7].
Fibre dimensions, microfibril angle and chemical composition all have important effects on
sheet properties. Fibre length, for example, affects inter-fibre bonding and therefore paper
strength. Fibre transverse dimensions and microfibril angle affect fibre compressibility and
therefore paper strength, bulk, smoothness and opacity. Figure 5 illustrates some typical
physical differences between papers made with different kraft pulp fibre types. Other
factors such as the proportion of fines present, the quality of sheet formation, the types and
amounts of fillers and coatings used, and the type of finishing treatment applied also play
important roles in determining paper properties. Paper producers can adjust the types of
pulps used, the amounts of fillers and coatings added, and the processing parameters used
in order to achieve the quality requirements of specific end-products.
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Figure 5 Scanning electron micrographs of the surfaces of laboratory-made (A) black spruce, (B) Douglas fir, and (C) trembling aspen kraft pulp handsheets
1.4 The Canadian pulp and paper industry The pulp and paper industry is a major contributor to the Canadian economy. In 2003, the
industry produced 45.9 million metric tonnes of products which had a combined value of
33.2 billion dollars [8, 9]. This represented approximately 6% of the value of all products
manufactured in Canada in 2003 [9]. Nearly two thirds of Canada’s annual pulp and paper
production is exported, and Canada is currently the world’s leading exporter of market pulp
and newsprint [9, 10]. Canadian pulp and paper production volumes for 2003 are shown in
Figure 6.
The industry is, however, facing several significant challenges. Market globalization,
advances in electronic media technologies, volatile commodity prices, and chronic supply
and demand cyclicality are all having major impacts on the business environment. At the
same time, customer demands and the trend towards product specialization are increasing
the importance of product quality and consistency, and cost factors and environmental
B
C
A
100µm
100µm 100µm
8
pressures are placing ever tighter constraints on raw material supplies. Together, these
factors are making it increasingly critical that Canadian producers find ways to maximize
the value created from available fibre resources.
13.4
12.00.6
8.5
6.5
1.22.8 1.0
chemical pulp
mechanical pulp
chemimechanical pulp
newsprint
other printing + writing papers
tissue + specialty papers
containerboard
boxboard
Figure 6 2003 Canadian pulp and paper production by grade (values in million metric tonnes) [8]
Pulp and paper production itself poses a parallel challenge. As explained above, pulp and
paper product quality is governed by processing conditions on one hand, and fibre quality
attributes on the other. Natural variations in fibre quality attributes leave pulp and paper
producers with the considerable task of producing products of consistent quality from raw
materials of highly variable quality. Managing the flow of materials through the value
chain in such a way that fibre grades are directed to the processes and end-products to
which they are best suited will be key to resolving these issues.
This thesis presents a pulp and paper industry-specific strategic planning model whose
objective is to provide a means of addressing these challenges. The model is a mixed-
integer program which provides a mathematical framework for optimizing material flows
within a single integrated pulp and paper mill. Operation-specific data are entered into the
model, and the model then allocates raw materials to processes and end-products in such a
way that value creation is maximized.
The strategy behind the model is to divide the aggregate fibre supply into distinct fibre
classes or grades, and allow known relationships between fibre properties and pulp and
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paper properties to determine how each fibre grade is utilized. Customer demand and
market value data are used to determine how strongly each end-product is pulled through
the value chain, and established relationships between fibre properties and pulp and paper
properties are used to match fibre grades with the processes and end-products to which they
are best suited.
This model can be used as a tool for maximizing value creation through two parallel
strategies. The first strategy involves managing the flow of materials through the value
chain in such a way that fibre grades are allocated to the processes and end-products in
which they create the greatest value. The second involves tailoring the end-product range to
include the products which create the greatest value from the existing fibre resource
properties and market conditions. The model can also be used as a tool for assessing the
economic potential of new processes and end-products, and developing improved chip
quality measures based on process requirements and end-product quality.
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2 Literature review Developing an effective mathematical model for optimizing value creation in the pulp and
paper industry will involve integrating several key pieces of knowledge. This includes
knowledge of value chain modeling methodologies, knowledge of the features specific to
the pulp and paper industry value chain, knowledge of the relationships between fibre
properties and pulp and paper properties, and familiarity with the implementation of wood
flow management strategies. The current state of understanding in each of these areas is
discussed below.
2.1 Value chain modeling At the most global level, value chain modeling can incorporate all of the aspects of supply
chain design. It can include modeling the selection of locations, missions, technologies and
capacities for production-distribution centres, the allocation of suppliers and customers to
those centres, the selection of transportation modes and routes, and the management of
product flows. In order to function, value chain models must adopt some mathematical
conceptualization of the business process. Lakhal et al. [11] discuss two main alternatives
for the manufacturing industry: the activity-based approach and the resource-based
approach.
Lakhal et al. [12] present a general model following the activity-based approach. This
approach associates each manufacturing activity with a number of processes describing the
use of technologies to transform input products into output products. Each process has an
associated cost, and each technology has an associated capacity. The objective of the model
amounts to maximizing the value created by all activities.
Martel [13] presents a general model following the resource-based approach. This approach
associates each product with a number of bills-of-material describing the technologies and
input products used in its manufacture. Each bill-of-material has an associated cost, and
each technology has an associated capacity. The objective of the model amounts to
maximizing the value created by all products manufactured.
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Either of these approaches could be used to model the pulp and paper industry value chain.
However, it is common to use the activity-based approach in manufacturing applications
such as those found in the food, petrochemical and pharmaceutical industries [13].
Any number of papers could be cited to illustrate the key features of value chain modelling
mathematics. The work of Geoffrion and Graves [14], and Santoso et al. [15] will be used
as examples in the following discussion.
The model presented by Geoffrion and Graves [14] focuses on the optimization of the
distribution network component of multi-commodity production-distribution networks.
This includes the selection of sites and capacities for distribution centres, the assignment of
distribution centres to demand zones, and the establishment of transportation flows for
commodities. The model itself is a single-period mixed-integer program whose objective is
the minimization of costs under supply, capacity and demand constraints. It uses a chain-
based formulation in which each possible path from production centre through distribution
centre to demand zone is defined explicitly as a continuous chain. Each of these chains is
assigned a unique transportation cost parameter, and the total transportation cost is
expressed as the product of this parameter and a continuous variable representing
commodity flow along the chain. Each distribution centre is also assigned unique fixed and
variable operating cost parameters. Total fixed operating cost is then expressed as the
product of the fixed cost parameter and a binary variable representing the status (active or
inactive) of the distribution centre, and total variable operating cost is expressed as the
product of the variable cost parameter, a demand parameter tied to commodity flow, and a
binary variable representing the status (allocated or not allocated to a specific demand
zone) of the distribution centre.
This formulation is well suited to applications where commodities are not altered between
the source and destination ends of the supply chain, and where commodity flows from
distribution centres to demand zones are tied directly to demand parameters through
equality constraints. These conditions do not generally apply to the pulp and paper industry.
The model presented by Santoso et al. [15] focuses on the global optimization of multi-
commodity production-distribution networks. This includes the selection of sites, capacities
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and technologies for production and distribution centres, the assignment of suppliers and
commodities to production centres, the assignment of commodities and demand zones to
distribution centres, and the establishment of transportation flows for commodities. The
model itself is a single-period mixed-integer program whose objective is the minimization
of costs under supply, capacity and demand constraints. It uses an arc-based formulation in
which suppliers, production centres, distribution centres and demand zones are defined as
nodes, and the transportation links between them are defined as arcs. Each node is assigned
a unique fixed operating cost parameter, and the total fixed operating cost is expressed as
the product of this parameter and a binary variable representing the status (active or
inactive) of the node. Each arc is assigned a unique variable cost parameter which
represents the total cost of processing a commodity at the source node and transporting it to
the destination node. Total processing and transportation costs are then expressed as the
product of this parameter and a continuous variable representing commodity flow along the
arc.
This formulation uses a series of flow conservation constraints to ensure that the flow of
commodities into each node is balanced by the flow of commodities out of that node.
Production recipe parameters are used to represent bills-of-material for alterations to
commodities at production centre nodes.
The selection of manufacturing technologies is also of particular interest in the context of
the model presented in this thesis. Paquet et al. [16] present a manufacturing network
design model which includes the optimization of technology selection decisions. The model
defines a capacity option as a number of units of capacity of a specific manufacturing
technology, each with its own unique fixed and variable implementation costs and floor
space requirements. A series of capacity options are available to each manufacturing node
in the network, and the objective of the model amounts to selecting the options which fulfill
customer demand at minimum cost. Binary variables are used to represent the status
(implemented or not implemented) of each capacity option, and continuous variables are
used to represent the production volume associated with each capacity option. Specific
constraints are used to ensure that the total capacity required by all products manufactured
does not exceed the capacity provided by the capacity options implemented, and that the
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total floor space required by all capacity options implemented does not exceed the floor
space available at each production-distribution centre.
2.2 Pulp and paper industry-specific value chain models Although value chain modeling is relatively new to the pulp and paper industry, a number
of models have been developed which focus on the optimization of various components of
the value chain. Rönnqvist [17] presents a comprehensive review of mathematical
modeling applications in the forest products industry as a whole. These applications range
from forest management and harvesting [18, 19] to production planning and process control
[20, 21], transportation planning and routing [22, 23], and capital investment planning [24,
25].
Martel et al. [26] present an overview of the various planning decisions specific to the pulp
and paper industry. These planning decisions are summarized in Figure 7. At the strategic
planning level, decisions relate to the definition of a structure for the supply chain network.
This includes the definition of location, mission, capacity and technology for each
procurement, production and distribution centre, and the selection of transportation modes.
These decisions are generally considered over a planning horizon of at least five years. This
provides a framework for the tactical planning level, where decisions relate to the
establishment of a set of rules under which the supply chain network must operate. This
includes the establishment of customer service levels and inventory policies, the
assignment of products to machines, the establishment of production sequences, and the
assignment of customers to production and distribution centres. These decisions are
generally considered over a planning horizon of one year divided into seasonal periods.
This provides a framework for the operational planning level, where decisions relate to the
synchronization of activities and lot sizing. This includes the establishment of daily
procurement, production and distribution plans. These decisions are generally considered
over a planning horizon of a few months divided into daily periods.
14
Figure 7 Planning decisions in the pulp and paper industry [26]
Philpott and Everett [27] and Bredström et al. [28] present pulp and paper industry-specific
value chain models which combine the optimization of raw material procurement,
production and distribution decisions.
The model presented by Philpott and Everett [27] was developed for Fletcher Challenge
Paper Australasia. It focuses on the allocation of raw material suppliers to mills, products to
paper machines, and paper machines to customers. The model operates at the tactical
planning level, and is built around the concept of product clusters, or groups of products
that can be produced on a single paper machine over the course of the planning period.
Each product cluster has a unique set of capital investment costs, fixed and variable
production costs, product changeover costs, and production capacities associated with each
paper machine. The costs associated with procuring raw materials and delivering finished
Procurement Production Distribution Sales
Strategic planning
Raw material procurement decisions, production-distribution centre location, mission, technology, and capacity decisions, product and market selection decisions, transportation network decisions
Procurement-production-distribution network design
Aggregate planning
Product assignment to production-distribution centres, and procurement, production, inventory, and transportation policies
Long-term forecasts
Mid-term forecasts Demand planning
Demand forecasts, market and customer allocation, ordering policies
Daily forecasts
Production plans
Production capacities and policies, product assignments Supply information
Production-distribution planning
Production, inventory and transport planning
Material procurement
planning
Deliveries Demand
fulfillment
Procurement quantities
Supply delivery scheduling
Production plans Deliveries Availability
Orders
Product delivery scheduling
Production scheduling
15
products to customers are also dependent on the assignment of product clusters to specific
paper machines. The objective of the model amounts to assigning product clusters to paper
machines in such a way that total profit is maximized.
The two models presented by Bredström et al. [28] were developed for Södra Cell AB in
Scandinavia. Both focus on the allocation of production schemes to mills. The first of these
models functions at the operational planning level, and is built around the concept of
production plans, or combinations and sequences of production recipes that can be used at
a single mill to produce a certain group of products over the course of the planning period.
Each production plan has a unique set of capital investment costs, fixed and variable
production costs, product changeover costs, and production capacities associated with each
mill. The costs associated with procuring and storing raw materials at the mill and storing
and delivering finished products through the distribution network are also dependent on the
assignment of production plans to specific mills. The objective of the model amounts to
assigning production plans to mills in such a way that total cost is minimized. The second
model also functions at the operational level, but defines daily production decisions
explicitly rather than using the concept of production plans.
2.3 Relationships between macro-level wood properties and pulp and paper properties
Incorporating wood flow management strategies into a pulp and paper industry-specific
value chain model similar to those described above requires an understanding of the
relationships between fibre properties and pulp and paper properties.
A significant amount of work has been done to describe the effects of tree species and
juvenile and mature wood contents on pulp and paper properties. The properties studied
generally include processing requirements such as alkali and energy consumption,
processing responses such as pulp yield and freeness, and end-product properties such as
tear and tensile strengths. MacLeod [29] presents a comprehensive summary of the kraft
pulping properties of the most common Canadian hardwood and softwood species. Hatton
[30] and Hatton and Johal [31], among others, present summaries of the mechanical
16
pulping properties of various Canadian hardwood and softwood species. Selected properties
of some of the more common Canadian species are summarized in Table 1.
Table 1 Selected chemical and mechanical pulping properties of some common Canadian wood species (chemical pulp properties were measured at constant cooking conditions and pulp freeness; mechanical pulp properties were measured at constant pulp freeness) [29, 30]
Chemical pulps Mechanical pulps
Pulp yield
(%) [29]
Tensile index (N.m/g)
[29]
Refining energy (MJ/kg) [30, 31]
Tensile index (N.m/g) [30, 31]
Douglas fir 47.5 91 11.8 33
Western hemlock 44.3 114 - -
Western redcedar 45.9 148 - -
Amabilis fir 46.9 129 - -
Lodgepole pine 47.4 126 13.4 35
Jack pine 47.3 120 12.6 38
Black spruce 49.9 132 12.8 42
Hybrid poplar 55.7 100 - -
White birch 53.4 118 - -
Other macro-level properties such as tree age and growth site conditions are also known to
affect wood and pulp and paper properties. Wilhelmsson et al. [32] describe the effects of
tree diameter, tree age and site conditions on wood density, latewood content and juvenile
wood content in Norway spruce and Scots pine. Pitts et al. [33] and Pitts and Watson [34]
describe the effects of tree age, biogeoclimatic zone and site index on wood density, fibre
length and fibre coarseness in western SPF (white spruce, lodgepole pine, and subalpine fir)
and eastern spruce-balsam fir mixtures. Although these effects do not constitute direct links
between macro-level properties and pulp and paper properties, such links could be
established by incorporating relationships between wood and fibre properties and pulp and
paper properties.
17
2.4 Relationships between fundamental fibre properties and pulp and paper properties
Although the types of relationships described above can be very useful at the global level,
they can be confounded by other effects such as silvicultural intervention and genetic
variability. A slightly different approach is to establish relationships between fundamental
fibre properties (such as fibre transverse dimensions and microfibril angle) and pulp and
paper properties. Once these relationships are established, the fundamental properties of the
fibre supply can be measured and used to predict pulp and paper properties.
A significant amount of work has been done to describe the effects of certain fundamental
fibre properties on pulp and paper properties. Seth [35] and Seth et al. [36] summarize the
effects of fibre length and transverse dimensions on various pulp and paper properties. Jang
et al. [37] describe the effects of microfibril angle on fibre compressibility, and discuss the
implications for pulp and paper properties. These and other studies have shown that, in
general, increasing fibre length improves paper tensile strength, and decreasing fibre wall
thickness and microfibril angle improves fibre compressibility.
One of the challenges to using fibre properties to predict pulp and paper properties is that
the high degree of covariance between many properties makes it difficult to establish direct
causal relationships. Wimmer et al. [38] describe a method for establishing causal
relationships using path analysis and regression weights. This method is used to describe
the effects of wood density, fibre length and microfibril angle on several important pulp
and paper properties in juvenile eucalyptus globulus.
2.5 Effects of furnish mixtures on pulp and paper properties At the industrial level, many pulps and most paper grades are made from furnish mixtures.
Many pulps are made using species groups such as western SPF which are grown,
harvested and processed together. Many fine paper grades are made using mixtures of
hardwood and softwood pulps. This necessitates an understanding of the effects of mixing
raw materials with different properties on end-product properties.
18
The problem remains relatively simple when processing responses and end-product
properties are linear functions of the relative amounts of the various raw materials in the
furnish. Rao et al. [39], for example, present a simple linear programming model for
finding the least-cost blends of various hardwood and non-wood fibre furnishes which
satisfy certain minimum density, strength, smoothness and opacity requirements. In most
cases, simple linear functions were found to provide sufficient predictive accuracy. The
problem becomes considerably more complex when the functions are non-linear. Hussein
et al. [40, 41, 42] and Johal et al. [43, 43] present linear, quadratic and cubic regression
models for predicting the kraft and mechanical pulp properties of three common Canadian
softwood chip mixtures. In many cases, simple linear functions were found to provide
sufficient predictive accuracy.
2.6 Improving value creation through wood flow management A significant amount of work has gone into developing wood flow management strategies
for improving pulp and paper process stability and end-product quality. Although these
strategies are not based on modeling and optimization, most involve some form of sorting
combined with a targeted processing strategy. Sweden is one of the world leaders in this
area. Swedish wood supplies are routinely sorted based on species, and several new sorting
strategies are under rapid development. Many of these strategies extend their focus beyond
simple wood processing to include a larger component of the forest products value chain.
Duchesne et al. [45] describes a log sorting strategy developed for mixed Norway spruce
and Scots pine stands in Sweden. This strategy, summarized in Figure 8, is based on a
combination of tree species, tree height (or dominance level) and log type. Differences
between log types were found to be of greatest significance, and the authors suggest that
significant improvements in process stability and end-product quality could be achieved by
managing top log, and butt and middle log classes separately. Williams [46] describes a
wood flow management strategy developed for Tasman Pulp and Paper in New Zealand.
This strategy, summarized in Figure 9, is based largely on wood density. Implementing the
strategy enabled Tasman to stabilize the quality of its existing products and begin the
production of new specialty-grade products.
19
Figure 8 Log sorting strategy developed for mixed Norway spruce and Scots pine stands in Sweden [45]
Mixed stand
Norway spruce
Scots pine
Suppressed trees
Co-dominant trees
Suppressed trees
Co-dominant trees
Top logs
Butt + middle logs
Top logs
Butt + middle logs
20
Figure 9 Wood flow management strategy developed for Tasman Pulp and Paper [46]
2.7 Incorporating fibre property effects into a pulp and paper industry-specific value chain model
Using relationships between fibre properties and pulp and paper properties to develop wood
flow management strategies for optimizing value creation within the context of a
comprehensive, industry-specific value chain model requires bringing together the various
pieces of knowledge discussed above. The model presented in this thesis attempts to
accomplish this by breaking the pulp and paper manufacturing process down into its
fundamental processes, and providing a mathematical framework for describing the flow of
materials between those processes. The model considers options for dividing fibre supplies
Log supply
Low density pine
Mixed species
Very high density pine
High density pine
Low density pine
Sawmill chips
High density pine
Low density pine
Medium density pineMedium density pine
High density pine
Medium density pine
Mechanical pulps
Chip supply
Chemical pulps
Newsprint
Customers
Customers
21
into individual classes or grades based on the distribution of fibre properties within those
supplies. It then uses known relationships between fibre properties and processing
requirements to associate specific costs and capacity requirements to the use of different
fibre grades in different production recipes. It also constrains production recipe options
through specific quality requirements imposed on end-products. Maximizing total profits in
this system forces the allocation of fibre grades to the processes and end-products to which
they are best suited.
This approach could be implemented within several different contexts. The multi-site multi-
period context involves the optimization of a network of production-distribution centres
over a series of discreet time periods in which resource availability and customer demand
may vary. The optimization of product inventory levels and the timing of technology
implementation decisions are often included in this type of problem. The model presented
in this thesis is implemented in the single-site single-period context, which involves the
optimization of a single production-distribution centre within a single time period. The
model operates at the strategic planning level, and it assumes that technology
implementation decisions are executed at the beginning of the planning period.
22
3 Problem formulation
3.1 The pulp and paper industry value chain An overview of the pulp and paper industry value chain is presented in Figure 10. This
chain begins with standing trees in the forest. The majority of Canada’s forests are natural
growth woodlands owned by the government. Forest products companies are granted
licenses to harvest specific volumes of wood from specific areas over the term of a tenure.
These harvest areas typically contain more than one tree species, and often include a range
of different tree age classes. They may also span more than one biogeoclimatic subzone.
These and other factors such as silvicultural intervention and genetic variability lead to
significant fibre property variations within the Canadian wood supply.
Figure 10 The pulp and paper industry value chain
A much smaller proportion of Canada’s forests are privately owned plantation woodlands.
Privately owned plantations very often contain a single tree species and age class, although
this is not always the case.
Lumber
Forest Logs Chips Pulp Paper Sheets
Harvesting Chipping Pulp production
Paper production
Conversion
Non-fibreproducts
Residues Non-fibre products
Sawmilling Chipping
Customers
Customers Customers Customers Customers Customers
23
More than 80% of the wood harvested in Canada is used in lumber production [47]. In
some cases, trees are sorted by species during harvesting and processed individually. In
most cases however, common species mixtures such as western SPF and eastern spruce-
balsam fir are managed as a single species class and processed together. The residues of
sawmilling are converted to chips for use in pulp production. Even in cases where species
were separated before sawmilling, they are often recombined after chipping. Also, because
of the complexity of the chip supply, other species can sometimes find their way into
common species classes. For example, interior Douglas fir chips are sometimes found in
western SPF mixtures, and jack pine chips are sometimes found in eastern spruce-balsam
fir mixtures. In Canada, sawmilling residues account for 55% of all fibre found in pulp and
paper products [48].
Less than 20% of the wood harvested in Canada is converted directly into chips and used in
pulp production [47]. These chips are more likely to contain a single tree species, but also
tend to constitute lower quality wood. In Canada, roundwood accounts for 21% of all fibre
found in pulp and paper products [48].
Wood chips are sometimes graded according to chip quality indexes established by
individual pulp and paper producers. These indexes are generally based on chip size
distributions and contaminant contents, and chip prices are linked to the indexes through
bonus and penalty systems.
One or several different chip types may be used to produce a single grade of pulp. Pulp
quality is dependent on fibre properties, chip quality and processing conditions. Pulp grades
are generally marketed as having specific brightness and strength properties, and failing to
meet these specifications can result in costly product downgrades and, in extreme cases,
returned shipments or customer losses.
Several different pulp grades are generally used to produce a single grade of paper.
Recycled fibre is sometimes added to reduce costs or conform to government regulations.
In Canada, recycled paper accounts for 24% of all fibre found in pulp and paper products
[48]. Paper quality is dependent on fibre quality and sheet formation and, as with pulp
grades, failing to meet specific brightness and strength specifications can result in costly
24
product downgrades, returned shipments and customer losses. Some paper grades such as
newsprint and lightweight mechanical papers are typically sold in the form of rolls. Other
grades such as fine papers are usually converted and sold in the form of sheets or cut-to-
size rolls.
3.2 Production stages and material flows The model presented in this paper focuses on material flows within a single integrated pulp
and paper mill as shown in Figure 11. This mill has access to a set of log grades which it
can purchase from internal sources such as affiliated forestry operations, or external
suppliers such as independent log vendors. The set of log grades available from internal
sources is dependent on the sorting options used to divide the aggregate supplies into
individual log grades. It is assumed that log grades purchased from internal sources may be
resold if they are not used in production, but those purchased from external suppliers may
not be resold. A chipping system is used to convert log grades into chip grades.
Figure 11 Material flows within a single integrated pulp and paper mill
Log customers
25
The mill also has access to a set of chip grades which it can purchase from internal sources
such as affiliated sawmills, or external suppliers such as independent chip vendors. The set
of chip grades available from internal sources is also dependent on the sorting options used
to divide the aggregate supplies into individual chip grades. It is assumed that chip grades
purchased from internal sources may be resold if they are not used in production, but those
purchased from external suppliers may not be resold. A chip handling system is used to
store and handle chips at the mill.
The mill also has access to a set of non-fibre products which it can purchase from external
suppliers. A pulp production system is used to convert chip grades and certain non-fibre
products (chemicals) into pulp grades. These pulp grades may be sold as market pulps or
used in in-house paper production. Other pulp grades not produced at the mill may also be
purchased from external suppliers for use in in-house paper production. A paper production
system is used to convert these pulp grades and certain non-fibre products into bulk paper
grades. Bulk paper grades may be sold in the form of rolls or converted and sold in the
form of sheets. Conversion may be performed internally using a paper conversion system
or externally using an external paper converter.
The model uses a series of decision variables to represent the flow of each log, chip, pulp
and paper grade through the manufacturing process. Customer demand and market value
determine how strongly each end-product is pulled through the value chain, and the
availability and cost of each raw material, together with established relationships between
fibre properties and pulp and paper properties, determine how each fibre grade is utilized.
The implementation of sorting options at internal fibre sources and the selection of
chipping, chip handling, pulp and paper production, and paper conversion systems are all
tied to the demands imposed by material flows.
The objective of the model is to maximize profits under given supply and demand
conditions. Solving the model reveals which sorting options should be implemented, which
production systems should be deployed, and which fibre grades should be used to
manufacture specific end-products.
26
3.3 Definition of key concepts The model is built around a number of key concepts. The use of the concepts product,
product group, supply source, sorting option, production system, production recipe,
external paper converter, and customer is defined below.
3.3.1 Products and product groups The term product and the index p are used to define the materials used in the system. The
subsets PA, PB, PC, PD, PE and PN are used to define the sets of log grades (PA), chip
grades (PB), pulp grades (PC), bulk paper grades (PD), converted paper grades (PE), and
non-fibre products (PN) respectively. These products may be purchased from supply
sources, manufactured using various production systems, or sold to customers.
The term product group and the index g are used to define sets of products with similar
properties which constitute a single product for the purposes of sales and marketing. For
example, several different pulp grades manufactured using slightly different production
recipes might be grouped together into a product group called bleached softwood kraft
pulp. The subsets GC, GD, GE and GX are used to define the sets of pulp (GC), bulk paper
(GD), converted paper (GE), and log and chip (GX) product groups respectively. The
subset Pg is used to define the set of all products contained in product group g.
3.3.2 Supply sources The term supply source and the index s are used to define suppliers of specific products.
When the product is log or chip grades, the supply source may constitute a harvest area, a
sawmill, or a log or chip vendor. The term external supply source is used to define supply
sources (such as independent log and chip vendors) over which the pulp and paper mill has
no direct managerial control. The term internal supply source is used to define supply
sources (such as affiliated forestry and sawmill operations) over which the mill has some
direct managerial control. The subsets Spext and Sp
int are used to define the sets of external
and internal supply sources capable of providing product p. A single internal log or chip
supply source may provide one or several different log or chip grades, depending on how
the aggregate supply is sorted.
27
3.3.3 Sorting options The term sorting option and the index i are used to define the strategies available for
sorting aggregate log or chip supplies into distinct log or chip grades. These strategies
might be based on wood properties such as tree species, age, or growth site, and would be
designed to take advantage of the relationships between these properties and key pulp and
paper properties. Each internal log and chip supply source carries a unique set of potential
sorting options, and each sorting option provides a unique set of log or chip grades. An
example based on a log supply made up of eastern spruce, balsam fir, and a mixture of
other less utilized species is presented in Table 2.
Table 2 Potential sorting options for a log supply made up of eastern spruce, balsam fir, and a mixture of other less utilized species
Log grade
Grade 1 All species combined
Grade 2
Mixed spruce and balsam fir
Grade 3
Mixed less utilized species
Grade 4
Pure spruce
Grade 5
Pure balsam fir
Grade 6
Pure high density spruce
Grade 7
Pure low density spruce
1
2
3
Sort
ing
optio
n
4
In this example, the first sorting option corresponds to using the aggregate supply without
any sorting. This provides log grade 1 only. The second option corresponds to separating
the spruce and balsam fir from the mixed less utilized species. This provides log grades 2
and 3 only. The third option corresponds to further separating the spruce from the balsam
fir, and the fourth option corresponds to further separating high density spruce from low
density spruce. These options provide log grades 3, 4 and 5, and 3, 5, 6 and 7 respectively.
In practice, a set of viable sorting options would be established for each internal log and
chip supply source based on the distribution of fibre properties within each source, and the
potential for using those properties to influence key pulp and paper properties. The model
would then select the options which support the maximization of value creation. An
28
exclusivity constraint is used to ensure that only one sorting option is implemented at each
internal supply source.
The subset Is is used to define the set of sorting options available to supply source s, and the
binary variable Ys,isrt is used to indicate whether or not sorting option i is implemented at
supply source s. The parameter hp,s,i is used to define the proportion of log or chip grade p
in the aggregate supply from supply source s when using sorting option i. The procurement
cost for each log and chip grade purchased from an internal supply source (cp,s,i) is assumed
to be dependent on the supply source and sorting option selected.
3.3.4 Chipping systems The term chipping system and the index m are used to define the group of technologies used
to convert logs into chips. It is assumed that the chipping system requirement is a function
of the volume of chips produced, and that different systems may have different operating
costs and volume recovery efficiencies. In practice, a set of viable chipping system options
would be established based on projected needs, and the model would select the system
which supports the maximization of value creation. An exclusivity constraint is used to
ensure that no more than one chipping system is implemented.
The subsets Mp and Pm are used to define the set of chipping systems capable of producing
chip grade p and the set of chip grades that can be produced using chipping system m. The
binary variable Ymsys is used to indicate whether or not chipping system m is implemented.
The subset PPpout is used to define the set of chip grades which can be derived from log
grade p, and the parameter gp,p’,m is used to define the number of units of log grade p
required to produce a single unit of chip grade p’ when using chipping system m. Each
chipping system has its own unique implementation cost (cm).
3.3.5 Chip handling systems The term chip handling system and the index m are used to define the group of technologies
used to store and transport chips at the mill. It is assumed that the chip handling system
requirement is a function of the number of different chip grades used in production. In
practice, a set of viable chip handling system options would be established based on
29
projected needs, and the model would select the system which supports the maximization
of value creation. An exclusivity constraint is used to ensure that no more than one chip
handling system is implemented.
The binary variable Ymsys is used to indicate whether or not chip handling system m is
implemented. Each chip handling system also has its own unique implementation cost (cm).
3.3.6 Production recipes The term production recipe and the index r are used to define the set of inputs, the amount
of each input, and the production system used to produce a specific grade of pulp or paper.
Each pulp and paper product has a unique set of potential production recipes, and each
recipe is associated with a unique output product. In practice, a set of viable production
recipes would be established for each pulp and paper grade based on the fibre properties of
the inputs and the relationships between those properties and processing requirements.
These recipes would also be constrained by the quality requirements of the output product.
The model would then select the recipes which support the maximization of value creation.
The subset Rpin is used to define the set of recipes which use product p as an input, and the
subset Rpout is used to define the set of recipes which yield product p as an output. The
binary variable Yrrec is used to indicate whether or not recipe r is used in production, and
the parameter gp,r is used to define the number of units of input product p required to
produce a single unit of output product using recipe r. Each recipe has its own unique fixed
and variable production costs (crfix and cr
var).
3.3.7 Pulp and paper production systems The terms pulp production system and paper production system and the index m are used to
define the group of technologies used to produce pulp and paper. Each production system
option is comprised of a unique combination of aggregated equipment components which
carry the index e. An example based on a flexible pulp production system is presented in
Table 3 and Figure 12.
30
Table 3 Potential flexible pulp production system options
Equipment component
Comp. 1
Impregnation
Comp. 2
Refining Washing Screening Storage
Comp. 3
Bleaching 1
Comp. 4
Bleaching 2
Comp. 5
Impregnation Digestion Washing Screening Storage
Comp. 6
Bleaching 3
1
2
3
4
5
6
7
8
Prod
uctio
n sy
stem
opt
ion
9
Figure 12 Potential equipment components in a flexible pulp production system
Impregnation Refining, washing, screening and storage Bleaching Bleaching
Component 1 Component 2 Component 3 Component 4
Mechanical pulp line
Impregnation, digestion, washing, screening and storage Bleaching
Chemical pulp line
Component 5 Component 6
31
In this example, the first system option includes basic thermomechanical pulp (TMP)
production equipment components. The second and third options include additional
mechanical pulp bleaching components. The fourth option includes basic
chemithermomechanical pulp (CTMP) production equipment components, and the fifth and
sixth options again include additional mechanical pulp bleaching components. The seventh
option includes basic kraft pulp production equipment components, and the eighth option
includes an additional chemical pulp bleaching component. The ninth option includes all
TMP, CTMP and kraft pulp production and bleaching equipment components.
The inclusion or exclusion of various equipment components determines the set of products
each system is capable of producing. An example based on the pulp production systems
described above is presented in Table 4.
Table 4 Pulp production capabilities associated with the production system options presented in Table 3
Pulp grade
Grade 1
Unbleached TMP
Grade 2
Semi-bleached
TMP
Grade 3
Fully-bleached
TMP
Grade 4
Unbleached CTMP
Grade 5
Semi-bleached CTMP
Grade 6
Fully-bleached CTMP
Grade 7
Unbleached kraft
Grade 8
Fully-bleached
kraft
1
2
3
4
5
6
7
8
Prod
uctio
n sy
stem
opt
ion
9
In this example, the inclusion of a TMP production line (equipment component 2) in
production system 1 enables the production of unbleached TMP (grade 1). The addition of
mechanical pulp bleaching systems (equipment components 3 and 4) in production systems
2 and 3 enables the production of semi- and fully-bleached TMPs (grades 2 and 3). The
32
addition of a chemical impregnation vessel (equipment component 1) in production systems
4, 5 and 6 enables the production of CTMPs (grades 4, 5 and 6). The inclusion of a kraft
pulp production line (equipment component 5) in production system 7 enables the
production of unbleached kraft pulp (grade 7), and the addition of a chemical pulp
bleaching system (equipment component 6) in production system 8 enables the production
of bleached kraft pulp (grade 8). The inclusion of all equipment components in production
system 9 enables the production of all grades.
In practice, a set of viable pulp and paper production system options would be established
based on the equipment requirements of the potential product range. The size and capacity
of these systems would be constrained by the availability of space at the mill and the
projected demand for products. The model would then select the systems which support the
maximization of value creation. Exclusivity constraints are used to ensure that no more
than one pulp production system and one paper production system are implemented.
The subset Mr is used to define the set of production systems which enable the use of
production recipe r. The subsets Me and Re are used to define the set of production systems
which include equipment component e, and the set of production recipes which require the
use of equipment component e. The binary variable Ymsys is used to indicate whether or not
production system m is implemented. Each production system has its own unique
implementation cost (cm).
3.3.8 Paper conversion systems The term paper conversion system and the index m are used to define the group of
technologies used to convert paper rolls into sheets. It is assumed that the paper conversion
system requirement is a function of the type and volume of sheets produced, and that
different systems may have different operating costs and paper recovery efficiencies.
Again, a set of viable paper conversion system options would be established based on
projected needs, and the model would select the system which supports the maximization
of value creation. An exclusivity constraint is used to ensure that no more than one paper
conversion system is implemented.
33
The subsets Mp and Pm are used to define the set of paper conversion systems capable of
producing converted paper grade p, and the set of converted paper grades that can be
produced using paper conversion system m. The binary variable Ymsys is used to indicate
whether or not paper conversion system m is implemented. The subset PPpout is used to
define the set of converted paper grades which can be derived from bulk paper grade p, and
the parameter gp,p’,m is used to define the number of units of bulk paper grade p required to
produce a single unit of converted paper grade p’ when using paper conversion system m.
Each paper conversion system has its own unique implementation cost (cm).
3.3.9 External paper converters The term external paper converter and the index j are used to define external providers of
paper conversion services. It is assumed that different external paper converters may have
different potential product ranges and different paper recovery efficiencies. The subset Jp is
used to define the set of external paper converters capable of producing converted paper
grade p, and the binary variable Yjext is used to indicate whether or not external paper
converter j is used. The parameter gp,p’,j is used to define the number of units of bulk paper
grade p required to produce a single unit of converted paper grade p’ when using external
paper converter j. Each external paper converter has its own unique fixed and variable
production costs (cp,jfix and cp,j
var).
3.3.10 Customers The term customer and the index c are used to define consumers of products. Customers
may constitute either individual clients or aggregated demand zones. The subset Cp is used
to define the set of customers of product p, and the subset Cg is used to define the set of
customers of product group g.
The model presented in this thesis integrates the key concepts detailed above into the
structure presented in Figure 11. The following section presents a detailed mathematical
formulation of the model.
34
4 Model formulation
4.1 Definition of indexes p products ( Pp ∈ )
g product groups ( Gg ∈ )
c customers or demand zones ( Cc ∈ )
s supply sources ( Ss ∈ )
i sorting options ( Ii ∈ )
m chipping, chip handling, pulp and paper production, and paper conversion system
options ( Mm ∈ )
e equipment components ( Ee ∈ )
r production recipes ( Rr ∈ )
j external paper converters ( Jj ∈ )
4.2 Definition of sets and subsets P set of all products
PN subset of non-fibre products ( PPN ⊂ )
PA subset of log grades ( PPA ⊂ )
PB subset of chip grades ( PPB ⊂ )
PC subset of pulp grades ( PPC ⊂ )
35
PD subset of bulk paper grades ( PPD ⊂ )
PE subset of converted paper grades ( PPE ⊂ )
PP subset of chip and converted paper grades ( PEPBPP ∪= )
outpPP subset of chip and converted paper grades which can be derived from log or bulk
paper grade p ( PPPPoutp ⊂ )
PX subset of log and chip grades ( PBPAPX ∪= )
PY subset of pulp and paper grades ( PEPDPCPY ∪∪= )
PZ subset of products available from external supply sources ( PCPBPAPNPZ ∪∪∪⊆ )
gP subset of products included in product group g ( PPg ⊂ )
mP subset of chip and converted paper grades which can be produced using chipping or
paper conversion system m ( PEPBPm ∪⊂ )
G set of all product groups
GA subset of log product groups ( GGA ⊂ )
GB subset of chip product groups ( GGB ⊂ )
GC subset of pulp product groups ( GGC ⊂ )
GD subset of bulk paper product groups ( GGD ⊂ )
GE subset of converted paper product groups ( GGE ⊂ )
36
C set of all customers
pC subset of customers of product p ( CCp ⊆ )
gC subset of customers of product group g ( CCg ⊆ )
S set of all supply sources
intS subset of internal supply sources ( SSint ⊂ )
intpS subset of internal supply sources of product p ( intint SS p ⊆ )
extS subset of external supply sources ( SS ext ⊆ )
extpS subset of external supply sources of product p ( extext
p SS ⊆ )
I set of all sorting options
sI subset of sorting options available to internal supply source s ( IIs ⊆ )
M set of all chipping, chip handling, pulp and paper production, and paper conversion
system options
MA subset of chipping system options ( MMA ⊂ )
MB subset of chip handling system options ( MMB ⊂ )
MC subset of pulp production system options ( MMC ⊂ )
MD subset of paper production system options ( MMD ⊂ )
ME subset of paper conversion system options ( MME ⊂ )
37
rM subset of pulp and paper production system options which enable the use of recipe r
( MDMCM r ∪⊂ )
eM subset of pulp and paper production system options which include equipment
component e ( MDMCMe ∪⊂ )
pM subset of chipping and paper conversion system options capable of producing chip
or converted paper grade p ( MEMBM p ∪⊂ )
E set of all equipment components
R set of all pulp and paper production recipes
outpR subset of recipes which output pulp or paper product p ( RRout
p ⊂ )
inpR subset of recipes which use product p as an input ( RRin
p ⊂ )
eR subset of recipes which use equipment component e ( RRe ⊂ )
J set of all external paper converters
pJ subset of external paper converters capable of producing converted paper grade p
( JJ p ⊆ )
4.3 Definition of input parameters c,pr revenue per unit of product p sold to customer c
fixc fixed overhead costs not directly associated with production
38
s,pc procurement cost per unit of product p purchased from external supply source s
i,s,pc procurement cost per unit of log or chip grade p purchased from internal supply
source s when using sorting option i
mc fixed cost of implementing chipping, chip handling, pulp or paper production, or
paper conversion system m
fixm,pc fixed production cost associated with producing chip or converted paper grade p
internally using chipping or paper conversion system m
varm,pc variable production cost associated with producing chip or converted paper grade p
internally using chipping or paper conversion system m
fixrc fixed cost associated with producing pulp or paper products using recipe r
varrc variable cost associated with producing pulp or paper products using recipe r
fixj,pc fixed production cost associated with producing converted paper grade p at external
paper converter j
varj,pc variable production cost associated with producing converted paper product family
p at external paper converter j
c,pc transport cost per unit of pulp or paper grade p delivered to customer c
39
s,c,pc transport cost per unit of log or chip grade p delivered to customer c from internal
supply source s
j,c,pc transport cost per unit of converted paper grade p delivered to customer c from
external paper converter j
c,gd demand for product group g from customer c
i,s,ph percentage of log or chip grade p contained in the aggregate supply of internal
supply source s when using sorting option i
m,'p,pg units of log or bulk paper grade p required to produce a single unit of chip or
converted paper grade p’ using chipping or paper conversion system m
r,pg units of product p required to produce a single unit of pulp or paper product using
recipe r
j,'p,pg units of bulk paper grade p required to produce a single unit of converted paper
grade p’ using external paper converter j
m,pa units of capacity required to produce a single unit of chip or converted paper grade p
using chipping or paper conversion system m
r,ea units of capacity of equipment component e required to produce a single unit of
pulp or paper product using recipe r
40
mk units of capacity provided by chipping or paper conversion system m
m,ek units of capacity of equipment component e provided by pulp or paper production
system m
mn maximum number of different chip grades handled by chip handling system m
rb upper limit on the production of pulp or paper products using recipe r
pb upper limit on the internal production of chip or converted paper grade p
s,pb upper limit on the purchase of product p from external supply source s
s,pb lower limit on the purchase of product p from external supply source s
i,sb upper limit on the purchase of log or chip grades from internal supply source s when
using sorting option i
i,sb lower limit on the purchase of log or chip grades from internal supply source s when
using sorting option i
jb upper limit on the production of converted paper grades at external paper converter j
jb lower limit on the production of converted paper grades at external paper converter j
4.4 Definition of decision variables c,pF units of pulp or paper product p sold to customer c
s,c,pF units of log or chip grade p sold to customer c from internal supply source s
j,c,pF units of converted paper grade p sold to customer c from external paper converter j
41
s,pF units of product p purchased from external supply source s
i,sF units of log or chip grades purchased from internal supply source s when using
sorting option i
m,pX units of chip or converted paper grade p produced internally using chipping or paper
conversion system m
rX units of pulp or paper product produced using recipe r
j,pX units of converted paper grade p produced at external paper converter j
srti,sY binary variable with value 1 if sorting option i is used at internal supply source s and
value 0 otherwise
sysmY binary variable with value 1 if chipping, chip handling, pulp or paper production, or
paper conversion system m is used and value 0 otherwise
recrY binary variable with value 1 if recipe r is used and value 0 otherwise
chippY binary variable with value 1 if chip grade p is used in production and value 0
otherwise
intm,pY binary variable with value 1 if chip or converted paper grade p is produced
internally using chipping or paper conversion system m and value 0 otherwise
extjY binary variable with value 1 if external paper converter j is used and value 0
otherwise
42
extj,pY binary variable with value 1 if converted paper grade p is produced at external paper
converter j is used and value 0 otherwise
4.5 Mixed-integer programming model Maximize:
Sales revenues −++ ∑ ∑ ∑∑ ∑∑ ∑ ∑
∈ ∈ ∈∈ ∈∈ ∈ ∈ PEp pCc pJjj,c,pc,p
PYp pCcc,pc,p
PXp pCc intpSs
s,c,pc,p FrFrFr
Fixed overhead, equipment implementation, and production costs
−−−−− ∑ ∑∑∑ ∑∑∈ ∈∈∈ ∈∈ PEp pJj
extj,p
fixj,p
Rr
recr
fixr
PPp pMm
intm,p
fixm,p
Mm
sysmm
fix YcYcYcYcc
Variable material procurement and production costs
−−−−− ∑ ∑∑∑ ∑∑ ∑∑ ∑ ∑∈ ∈∈∈ ∈∈ ∈∈ ∈ ∈ PEp pJj
j,pvar
j,pRr
rvarr
PPp pMmm,p
varm,p
PZp extpSs
s,ps,pPXp int
pSs sIii,si,s,pi,s,p XcXcXcFcFhc
Variable transport costs
∑ ∑ ∑∑ ∑∑ ∑ ∑∈ ∈ ∈∈ ∈∈ ∈ ∈
−−PEp Cc Jj
j,c,pj,c,pPYp Cc
c,pc,pPXp Cc Ss
s,c,ps,c,pp ppp
intp
FcFcFc
Subject to:
Market opportunity constraints for log and chip product groups
c,ggPp int
pSss,c,p dF ≤∑ ∑
∈ ∈
GBGAg ∪∈∀ gCc ∈∀ (1)
Market opportunity constraints for pulp and bulk paper product groups
c,ggPp
c,p dF ≤∑∈
GDGCg ∪∈∀ gCc ∈∀ (2)
43
Market opportunity constraints for converted paper product groups
c,ggPp pJj
j,c,pgPp
c,p dFF ≤+ ∑ ∑∑∈ ∈∈
GEg ∈∀ gCc ∈∀ (3)
Flow conservation constraints for non-fibre materials
∑∑∈∈
=inp
extp Rr
rr,pSs
s,p XgF PNp ∈∀ (4)
Flow conservation constraints for log grades
∑ ∑∑ ∑∑∑ ∑∈ ∈∈ ∈∈∈ ∈
+=+outp 'pp
intp
extp
intp s PP'p Mm
m,'pm,'p,pCc Ss
s,c,pSs
s,pSs Ii
i,si,s,p XgFFFh PAp ∈∀ (5)
Flow conservation constraints for chip grades
∑∑ ∑∑∑∑ ∑∈∈ ∈∈∈∈ ∈
+=++inpp
intp
extp
intp s Rr
rr,pCc Ss
s,c,pMAm
m,pSs
s,pSs Ii
i,si,s,p XgFXFFh PBp ∈∀ (6)
Flow conservation constraints for pulp grades
44
Sales constraints for log and chip grades
∑∑∈∈
≤sp Ii
i,si,s,pCc
s,c,p FhF PXp ∈∀ intpSs ∈∀ (11)
Procurement constraints for external supply sources
s,ps,ps,p bFb ≤≤ PZp ∈∀ extpSs ∈∀ (12)
Procurement constraints for internal supply sources srti,si,si,s
srti,si,s YbFYb ≤≤ intSs ∈∀ sIi ∈∀ (13)
First pulp and paper production constraints sys
mrecr YY ≤ Rr ∈∀ rMm∈∀ (14)
Second pulp and paper production constraints rec
rrr YbX ≤ Rr ∈∀ (15)
First internal chip production and paper conversion constraints sys
mint
m,p YY ≤ PPp ∈∀ pMm∈∀ (16)
Second internal chip production and paper conversion constraints int
m,ppm,p YbX ≤ PPp ∈∀ pMm∈∀ (17)
First external paper conversion constraints extj
extj,p YY ≤ PEp ∈∀ pJj ∈∀ (18)
Second external paper conversion constraints ext
j,pjj,p YbX ≤ PEp ∈∀ pJj ∈∀ (19)
Pulp and paper production system capacity constraints
∑∑∈∈
≤ee Mm
sysmm,e
Rrrr,e YkXa Ee∈∀ (20)
45
Chipping and paper conversion system capacity constraints
sysmm
Ppm,pm,p YkXa
m
≤∑∈
MEMAm ∪∈∀ (21)
External paper converter capacity constraints
extjj
PEpj,p
extjj YbXYb ≤≤ ∑
∈
Jj ∈∀ (22)
First chip handling system selection constraints
∑∈
≤inpRr
recr
chipp YY PBp ∈∀ (23)
Second chip handling system selection constraints
chipp
inpRr
rinpRr
rr,p YbXg⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡≤ ∑∑
∈∈
PBp ∈∀ (24)
Third chip handling system selection constraints
∑∑∈∈
=MBm
sysmm
PBp
chipp YnY (25)
Chipping, chip handling, pulp and paper production, and paper conversion system exclusivity constraints
1≤∑∈MAm
sysmY , 1≤∑
∈MBm
sysmY , 1≤∑
∈MCm
sysmY , 1≤∑
∈MDm
sysmY , 1≤∑
∈MEm
sysmY (26)
Sorting option exclusivity constraints
1=∑∈ sIi
i,sY intSs ∈∀ (27)
Binary and sign restrictions
0≥c,pF PYp ∈∀ pCc ∈∀ (28)
0≥s,c,pF PXp ∈∀ pCc ∈∀ intpSs ∈∀ (29)
46 0≥j,c,pF PEp ∈∀ pCc ∈∀ pJj ∈∀ (30)
0≥s,pF PZp ∈∀ extpSs ∈∀ (31)
0≥i,sF intSs ∈∀ sIi ∈∀ (32)
0≥m,pX PPp ∈∀ pMm∈∀ (33)
0≥rX Rr ∈∀ (34)
0≥j,pX PEp ∈∀ pJj ∈∀ (35)
{ }01,Y srti,s ∈ intSs ∈∀ sIi ∈∀ (36)
{ }01,Y sysm ∈ Mm∈∀ (37)
{ }01,Y recr ∈ Rr ∈∀ (38)
{ }01,Y chipp ∈ PBp ∈∀ (39)
{ }01,Y intm,p ∈ PPp ∈∀ pMm∈∀ (40)
{ }01,Y extj ∈ Jj ∈∀ (41)
{ }01,Y extj,p ∈ PEp ∈∀ pJj ∈∀ (42)
4.6 Discussion of the objective function The objective function is expressed as a maximization of sales revenues minus various
fixed and variable costs.
Sales revenues are divided into three terms corresponding to the sale of logs and chips from
internal supply sources, the sale of pulp and paper products from the mill, and the sale of
47
converted paper products from external paper converters. The unit sales revenue for each
product-customer pair is assumed to be independent of volume.
Fixed costs are divided into overhead costs, equipment implementation costs, and fixed
production costs. The equipment implementation cost term is expressed as the sum of costs
for all systems implemented. Fixed production costs are divided into three terms
corresponding to the production of chips and converted paper products at the mill, the
production of pulp and bulk paper products at the mill, the production of converted paper
products at external paper converters. These terms assume that a fixed cost is incurred for
each product produced and each recipe used during the planning period. A more detailed
description of the costs included in each fixed cost term is presented in the Using the model
section under the subheading Defining input parameter values.
Variable costs are divided into material procurement costs, variable production costs, and
transport costs. Material procurement costs are divided into two terms corresponding to the
procurement of logs and chips from internal supply sources, and the procurement of all
materials from external supply sources. Variable production costs are divided into three
terms corresponding to the production of chips and converted paper products at the mill, the
production of pulp and bulk paper products at the mill, and the production of converted
paper products at external paper converters. Transport costs are divided into three terms
corresponding to the transport of logs and chips from internal supply sources to customers,
the transport of pulp and paper products from the mill to customers, and the transport of
converted paper products from external paper converters to customers. All unit
procurement, production, and transport costs are assumed to be independent of volume. The
level of error introduced by this assumption should be relatively small since production
volumes in the pulp and paper industry are typically high enough to ensure that costs
already include significant economies of scale.
4.7 Discussion of the constraints Constraints (1) through (3) ensure that sales to customers do not exceed customer demand.
These constraints are expressed as less than or equal to relationships because the objective
of the model is to determine which demands are the most profitable to fulfill. When
48
contractual obligations exist, these constraints may be changed to equalities. Constraint (1)
assumes that only log and chip products originating from internal supply sources may be
sold to customers.
Constraints (4) through (10) ensure flow conservation for each product subset. Constraints
(4) through (8) use the parameter gp,r together with the subset Rpin, and the parameters gp,p’,m
and gp,p’,j together with the subset PPpout, to define quantities of products used in
downstream processes. Constraints (5) and (6) use the parameter-variable pair hp,s,i Fs,i to
ensure that log and chip products originating from internal supply sources are utilized in
accordance with their compositions in the aggregate supply.
Constraint (11) ensures that sales of log and chip products do not exceed the amounts
available from internal supply sources.
Constraints (12) and (13) ensure that purchases of all products from all supply sources fall
between the upper and lower limits established for each purchase from each supply source.
Constraint (13) uses the binary variable Ys,i to restrict the value of the procurement variable
Fp,s,i to 0 if the sorting option selected does not generate log or chip product p.
Constraints (14) and (15) set the values of the recipe use variable Yrrec and perform the
selection of the pulp and paper production systems. Constraint (14) uses the binary variable
Ymsys together with the subset Mr to restrict the value of Yr
rec to 0 if recipe r is not supported
by the production system selected. Constraint (15) uses the production variable Xr to force
the value of Yrrec to 1 if any amount of product is produced using recipe r. Constraints (16)
and (17) use similar logic to set the values of the internal chip production and paper
conversion variable Yp,mint using the variables Ym
sys and Xp,m and the subset Mp, and
constraints (18) and (19) use similar logic to set the values of the external paper conversion
variable Yp,jext using the variables Ym
sys and Xp,j and the subset Jp.
Constraints (20) and (21) ensure that production does not exceed the capacity of the
production systems selected. Constraint (20) uses the parameter-variable pair ke,m Ymsys to
define the number of units of capacity of equipment component e available during the
planning period and the parameter-variable pair ae,r Xr to define the number of units of that
49
capacity required during the planning period. Constraint (21) uses similar logic with the
parameter-variable pairs km Ymsys and ap,m Xp,m.
Constraint (22) ensures that external paper conversion does no exceed the capacity of the
external paper converters selected. This constraint uses the binary variable Yjext to restrict
the value of the paper conversion variable Xp,j to 0 if external paper converter j is not used.
Constraints (23) through (25) perform the selection of a chip handling system based on the
number of different chip grades used at the mill. Constraint (23) uses the binary variable
Yrrec and the subset Rp
in to restrict the value of the chip use variable Ypchip to 0 if chip grade
p is not used in production. Constraint (24) uses the parameter-variable pair gp,r Xr to force
the value of Ypchip to 1 if any amount of chip grade p is used in production. Constraint (25)
the forces the value of the system selection variable Ymsys to 1 when m is equal to the
number of chip grades used.
Constraint (26) ensures that no more than one chipping, chip handling, pulp production,
paper production, and paper conversion system are selected. These constraints are
expressed as a less than or equal to relationships because the objective of the model is to
determine which processes are the most profitable to maintain.
Constraint (27) ensures that a single sorting option is selected for each internal log and chip
supply source. Constraints (28) through (42) are binary and sign restrictions.
The material flows and key variables associated with this model are presented in Figure 13.
50
Figure 13 Material flows and key decision variables
p�PN �PC
Ymsys
Spint
Cp
Fp,s
Spext
gp,p’m Xp’m
gp,p’,j Xp’,j
gp,p’,m Xp’,m
p�PA
hp,s,iFs,i - Fp,c,s
p�PD p’�PE
Ymsys
gp,r Xr gp,r Xr
Ys,i Fp,c,s
Chipping Chip handling
Pulp produciton
Paper production
External conversion
Internal conversion
MC
Is Is
MA MB MD
ME
Cp
Cp Cp
Cp
Spint Sp
ext Spext Sp
ext
p�PB
p�PB p�PA p�PN p�PC p�PD
p�PE
p�PB p�PC p�PA p’�PB
Ys,i Fp,c,s
Fp,s hp,s,iFs,i - Fp,c,s
Ymsys Ym
sys
Fp,s Fp,c
Ymsys
Fp,s Fp,c
Fp,c,j
Fp,c
Process Decision Internal supply
External supply Customer
51
5 Using the model
5.1 Defining the system structure The first step in using the model entails defining the initial state of the system to be
optimized. This involves identifying the set of products included in the system, the set of
supply sources and customers associated with each product, the costs associated with the
procurement and transportation of products, and revenues associated with the sale of
products. It also involves defining product transformations in terms of production recipes
and establishing the costs and equipment requirements associated with each production
recipe.
Once the initial state is defined, a set of fibre resource allocation, equipment
implementation, and end-product range composition options can be established. This
involves defining a set of viable sorting options for each internal log and chip supply
source, a set of viable production recipes for each pulp and paper product, a set of viable
chipping, chip handling, pulp and paper production, and paper conversion system options,
and an expanded set of potential end-products and customers.
The establishment of a set of viable sorting options for each internal log and chip supply
source should be based on the distribution of fibre properties within each supply, and the
relationships between those properties and processing and end-product quality
requirements. For example, a typical log supply in British Columbia might be made up of
white spruce, lodgepole pine and subalpine fir. This group of species is commonly
managed as a single species class called western SPF. Figure 14 shows the relationship
between tree age and length-weighted fibre length (an important determinant of paper
strength) for a population of subalpine fir and lodgepole pine trees sampled from a single
growth site in British Columbia. The data for white spruce has been left out of the figure
for clarity. Figure 15 shows the same relationship for two populations of lodgepole pine
trees sampled from two different growth sites with different site indexes (an important
determinant of a site’s productive potential). Figure 16 show the relationship between wet-
web tensile strength and average fibre length for an unbleached softwood kraft pulp. These
52
data suggest that, in applications where fibre length differences can be exploited, sorting
strategies could potentially be developed based on tree species, tree age, or growth site.
Similar relationships can be obtained for processing requirements such as energy and
chemical consumption, processing responses such as pulp yield, and end-product properties
such as tear and tensile strength. Examples are shown in Figures 17 through 20.
1.0
1.5
2.0
2.5
3.0
3.5
0 50 100 150 200
Age (years)
LWFL
(mm
)
Subalpine firLodgepole pine
Figure 14 Dependence of length-weighted fibre length (LWFL) on tree age for a population of subalpine fir and lodgepole pine trees sampled from a single growth site [33]
53
1.0
1.5
2.0
2.5
3.0
3.5
0 50 100 150 200
Age (years)
LWFL
(mm
)Site Index = 18Site Index = 24
Figure 15 Dependence of length-weighted fibre length (LWFL) on tree age for two populations of lodgepole pine trees sampled from two different growth sites with different site indexes [33]
0
50
100
150
0.0 1.0 2.0 3.0 4.0
Average fibre length (mm)
Wet
-web
tens
ile s
treng
th (m
)
Figure 16 Dependence of wet-web strength on average fibre length for an unbleached softwood kraft pulp at 30% solids content [49]
54
Figure 17 Dependence of kraft pulp yield at constant cooking conditions on species content in western SPF chip mixtures [41]
Figure 18 Dependence of kraft pulp Kappa number (residual lignin content) at constant cooking conditions on species content in western SPF chip mixtures [41]
Subalpine Fir
0.0
S p r u c e 0.0 0.51.0
L o d g e p o l e P i n e
4 8 . 4
Pulp yield ( % )
0 . 0
0 . 5
1 . 0S u b a l p i n e F i r
0 . 0
0 . 5
1 . 0
Spruce 0.0 0.5 1.0
Lodgepole Pine
3 5
Kappa number
55
Figure 19 Dependence of thermomechanical pulp energy consumption at constant pulp freeness on species content in western SPF chip mixtures [43]
Figure 20 Dependence of kraft pulp tensile strength on species content in western SPF chip mixtures [41]
The identification of a potential product range should be based on the strategic vision of the
producer, market demand and price projections, and the properties of the available fibre
0.0
0.5
1.0Subalpine Fir
0.0
0.5
1.0
Spruce 0.0 0.5 1.0
Lodgepole Pine
128 124 120 116 112
Tensile index (N*m/g)
1.0
Subalpine Fir
0.0
Spruce 0.0 0.5 1.0
Lodgepole Pine
0.01.0
0.50.5
11.0 10.8 10.6 10.4 10.2 10.0 9.8
Specific energy
(MJ/kg)
56
supply. Sorting aggregate fibre supplies into distinct fibre grades with more uniform
properties could potentially open up new opportunities for the production of specialty
product grades with very specific quality requirements.
The establishment of a set of viable production recipes for each pulp and paper product
should be based on the properties of the available fibre grades and the relationships
between those properties and end-product processing and quality requirements. For
example, it may be possible to achieve the brightness requirements of a bleached
mechanical pulp using either a naturally bright wood with a low chemical loading, or a
naturally dark wood with a high chemical loading. Similarly, it may be possible to achieve
the tensile strength requirements of a mechanical printing paper using either a high-strength
mechanical pulp alone, or a low-strength mechanical pulp and a reinforcement kraft pulp
together. The production costs associated with these different recipes could vary
significantly.
The establishment of a set of viable chipping, chip handling, pulp and paper production,
and paper conversion system options should be based on the processing requirements of the
potential product range and the space constraints imposed by the mill.
5.2 Defining input parameter values The second step in using the model involves defining the values of the input parameters.
The sales revenue parameters (rp,c) are assumed to be independent of volume, and should be
estimated based on market demand and price projections. In practice, sales revenues are
often dependent on volume, but including volume dependence would make the model non-
linear and more difficult to solve. A discussion of how volume dependence might be
incorporated into the model is presented in the Discussion section.
The fixed overhead cost parameter (cfix) should include all overhead and infrastructure costs
not directly associated with production. This parameter is included for completeness only.
Its sole purpose is to ensure the accuracy of the objective function value, and it has no
affect on the optimization.
57
The material procurement cost parameters (cp,s and cp,s,i) are assumed to be independent of
volume, and should be estimated based on market price projections. Both cp,s and cp,s,i
include inbound transport costs, and cp,s,i also includes any applicable sorting and handling
costs. These additional costs are also assumed to be independent of volume, but are
assumed to be dependent on the supply source and sorting option used. They should be
estimated based on labour and equipment requirements.
The equipment implementation cost parameters (cm) should include all costs associated
with deploying both new and existing equipment over the planning period. For existing
equipment, these costs should include the amortized value of the equipment plus the
opportunity cost associated with not reinvesting this value in capital markets. For new and
reconfigured equipment, these costs should also include the costs of setup and installation,
as well as the costs associated with any productivity losses expected. Because equipment
purchase costs tend to be very high, they are generally amortized over several years. The
proportion of these costs included in the value of cm should be aligned to the policies set
forth by management. Equipment implementation costs may be somewhat offset by
revenues generated through the sale of decommissioned equipment. If sales revenues
exceed implementation costs, cm will have a negative value.
The fixed production cost parameters (cp,mfix, cr
fix and cp,jfix) should include all costs
associated with equipment setup and productivity and product losses during product
changeover. These costs are assumed to be dependent on both the equipment used and the
products produced, and should be estimated based on labour requirements and product
values. In practice, fixed production costs are dependent on production scheduling policies.
A discussion of how this dependence might be handled is presented in the Discussion
section.
The variable production cost parameters (cp,mvar, cr
var and cp,jvar) should include all costs
associated with operating and maintaining equipment, storing and handling products, and
treating effluent streams. These costs are assumed to be dependent on both the equipment
used and the products produced, and should be estimated based on labour, energy and
equipment requirements. These parameters should also include costs associated with
productivity and product losses due to the production of reject products. The likelihood of
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producing reject products is assumed to be dependent on the inputs and equipment used and
the products produced, and the associated costs should be estimated based on product
values. The variable external paper conversion cost parameter (cp,jvar) also includes the cost
of transport between the mill and converter.
The outbound transport cost parameters (cp,c, cp,c,s and cp,c,j) are assumed to be independent
of volume, and should be estimated based on market price projections. Both cp,c,s and cp,c,j
assume that products are transported directly from internal supply sources and external
paper converters to customers.
The market demand parameters (dg,c) should be estimated based on market projections.
Demands associated with pulp and paper grades are, by definition, aggregated into bulk
grades which generally include several different potential production recipes. Demands
associated with log and chip grades may be aggregated into bulk grades or segregated by
individual grade.
The ratio parameters (hp,s,i) define the proportion of a specific fibre type within the
aggregate supply of an internal fibre supply source when using a specific sorting option.
The values should be calculated based on the composition of the supply source and the
nature of the sorting option.
The input requirement parameters (gp,p’,m, gp,r and gp,p’,j) define the number of units of each
input product required to produce a single unit of output product. Their values are assumed
to be dependent on the inputs and equipment used, and the products produced. The number
of units of logs required to produce a single unit of chips (gp,p’,m) should include wood
losses during debarking and chipping. It should also incorporate a conversion factor to
convert the units used to measure logs (usually cubic metres) into the units used to measure
chips (usually metric tonnes). The number of units of chips and chemicals required to
produce a single unit of pulp (gp,r) should incorporate the relationships between fibre
properties and processing requirements discussed above. For chemical pulps, gp,r should
reflect the pulp yield, chemical consumption, and reject product loss associated with each
fibre grade included in the recipe. gp,r should also reflect the chemical recovery efficiency
of the system. For mechanical pulps, gp,r should include the bleaching chemical
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consumption (if applicable) and reject product loss associated with each fibre grade
included in the recipe. The number of units of pulp and chemicals required to produce a
single unit of paper (gp,r) should also incorporate the relationships between fibre properties
and processing requirements discussed above, and should reflect the fibre recovery
efficiency of the system. The number of units of bulk paper required to produce a single
unit of converted paper (gp,p’,m and gp,p’,j) should incorporate trim losses. In practice, trim
losses are dependent on the number of parent roll size used and the sheet sizes produced.
The capacity requirement parameters (ap,m and ae,r) define the number of units of capacity
required to produce a single unit of output product. Their values are assumed to be
dependent on the system used, the products produced, and in the case of pulp and paper
production, the inputs used. The number of units of capacity required to produce a single
unit of pulp (ae,r) should incorporate the relationships between fibre properties and
processing requirements discussed above. The value of ae,r should reflect the wood density,
chip packing density, pulp yield, and reject product loss probabilities associated with each
fibre input in the recipe.
The capacity availability parameters (km and ke,m) define the number of units of capacity
provided by each production system option. These parameters should be expressed in terms
of units of output product over the length of the planning period.
The production limit parameters (br, bp, bj and bj) define the upper, and in the case of
external paper conversion, lower limits on the production of each product. The values of br
and bp should be estimated based on the production of a single product using the highest
capacity production system available. The only function of these parameters is to set the
values of the binary production and chip use variables Yrrec, Xp,m
int and Ypchip. It is therefore
safe to overestimate their values or assign them arbitrarily large values. The values of bj
and bj should be estimated based on the maximum and minimum order sizes accepted by
each external paper converter.
The procurement limit parameters (bp,s, bp,s, bs,i and bs,i) define the upper and lower limits
on the procurement of each product from each supply source. Their values should be
estimated based on the maximum and minimum order sizes accepted by each supply
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source. Where contractual obligations such as minimum harvest levels exist, the upper and
lower procurement limit parameters can be set equal.
5.3 Optimizing the system The model was coded using ILOG OPL Studio 3.7. Running an optimization requires that
the input parameters described above be entered into a structured Microsoft Access
database. Optimal decision variable values are written to a second structured Microsoft
Access database. The ILOG OPL code is presented in Appendix A, and the Microsoft
Access databases relationships are summarized in Appendix B.
5.4 Interpreting optimized decision variable values The values of the optimized material flow variables Fp,s and Fs,i indicate how many units of
each product should be purchased from each external and internal supply source. The
binary variables Ys,isrt and Ym
sys indicate which sorting option should be implemented at
each supply source and which chipping, chip handling, pulp and paper production, and
paper conversion systems should be implemented. The production variables Xp,m, Xr and Xp,j
indicate how many units of each product should be produced using each product