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

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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