An integrated approach for sustainable supply chain planning

Author's Accepted Manuscript

An Integrated Approach for Sustainable Sup-ply Chain Planning

Tasseda Boukherroub, Angel Ruiz, Alain Guinet,Julien Fondrevelle

PII: S0305-0548(14)00236-6DOI: http://dx.doi.org/10.1016/j.cor.2014.09.002Reference: CAOR3652

To appear in: Computers & Operations Research

Cite this article as: Tasseda Boukherroub, Angel Ruiz, Alain Guinet, JulienFondrevelle, An Integrated Approach for Sustainable Supply Chain Planning,Computers & Operations Research, http://dx.doi.org/10.1016/j.cor.2014.09.002

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http://dx.doi.org/10.1016/j.cor.2014.09.002






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An Integrated Approach for Sustainable Supply Chain Planning

Tasseda Boukherroub1,2

, Angel Ruiz1,3

*, Alain Guinet4, Julien Fondrevelle

4

1Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT)

2Faculté de Foresterie de Géographie et de Géomatique 3Faculté des Sciences de l’Administration

Laval University, 2325, rue de la Terrasse, Québec (Québec) G1V 0A6 – Canada 4Université de Lyon, INSA-Lyon, DISP EA4570, 69621 VILLEURBANNE, France

*Corresponding author: Tel: 418 656 8230; Fax: 418 656 2131; E-mail address:

[email protected]

Abstract

This paper proposes an integrated approach for transposing sustainable development

principles to supply chain planning models. Inspired by research on performance

measurement, we designed a method that links sustainability performance to supply chain

decisions, and allows setting coherent performance measures. By transposing this method to a

multi-objective mathematical programming, the supply chain planning is optimized while the

economic, environmental and social performances are all coherently integrated into the

model. To illustrate our approach, we applied it to a Canadian lumber industry case. We

solved the mathematical model by using the weighted goal programming technique, which

results in a set of “compromise” solutions allowing the decision maker to choose the

alternative that reflects the balance he/she wishes to make regarding the three dimensions of

sustainability.

Keywords: supply chain planning, sustainable development, performance measurement,

multi-objective mathematical programming, weighted goal programming.

1. Introduction

The growing public concern about environmental issues in our contemporary era goes hand in

hand with an emerging distrust of a certain pattern of economic development that causes

damages to nature, hazards to human health and leads, furthermore, to an unfathomable social

inequality. As a consequence, there had been and still is a strong demand for product

traceability (carbon footprint, product composition and disposal, working conditions in

supplier countries, etc.) and a tightening of government regulations (European WEEE

directive, carbon tax, etc.). In order to meet these requirements, companies have begun to

incorporate sustainability concerns in the management of their operations in line with

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corporate social responsibility (CSR). CSR is “a concept whereby companies integrate social

and environmental concerns in their business operations and in their interaction with their

stakeholders on a voluntary basis” [1]. Recent studies suggest that a strategy based on CSR is

a differentiating factor [2] [3], and its implementation would improve the relationships of a

given company with its stakeholders while improving its profitability at the same time [4].

Yet, mathematical models allowing the effective transposition of sustainable development

principles to the SC operations in an integrated way (i.e. taking into account the economic,

environmental and social dimensions) are quite rare in the literature.

Our research aims at contributing to the improvement of the afore-mentioned situation. We

address the problem of transposing sustainable development principles to SC planning

models. Inspired by research on performance measurement, we propose a method that allows

to: first, specify sustainability performance criteria to be measured; second, link these criteria

to the SC decisions by relying on consistency analysis (how the SC decisions affect each

performance criterion); and finally, set coherent measures following the economic,

environmental, and social dimensions. This generic method is linked to a multi-objective

mathematical programming (MOP) model that “optimizes” the operations of the SC and

assesses its sustainability performance, using coherent indicators. We illustrate our approach

by applying it to a decision-making problem inspired by the Canadian lumber industry. The

MOP is solved by using the weighted goal programming technique, which leads to a set of

solutions (Pareto solutions) allowing the decision maker to choose the one reflecting best

his/her preferences regarding the economic, environmental, and social performances.

The remainder of the paper is organized as follows. Section 2 introduces the concept of

sustainable SC planning, presents a brief literature review on sustainable SC planning models,

and finally, gives an overview on the most important performance measurement methods. In

Section 3, we present our integrated approach. Section 4 introduces the case study, followed

by the application of our approach to it, and the according mathematical formulation. Section

5 presents our experiments and preliminary results. Finally, we draw some conclusions and

give insights on our future work in section 6.

2. Literature review

The aim of this section is threefold. First, it provides a brief introduction to SC planning and

sustainability in order to describe the concept of “sustainable SC planning”. Secondly, it

presents a literature review on sustainable SC planning models with the purpose of analyzing

the level to which sustainability concerns have been transposed to OR models. Finally, it

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provides an overview on the most popular performance measurement methods in an attempt

to analyze their potential contribution to sustainable SC planning models.

2.1 Sustainable supply chain planning

SC planning is an important function of the SC management. It is concerned with the

determination of a set of decisions that govern the operations of the SC. Three decision levels

could be distinguished, on the basis of time horizon, namely: strategic, tactical, and

operational [5] [6]. Traditionally, the focus of SC planning models was mainly drawn on cost

minimization [7]. However, with the consumers’ increasing awareness about environmental

and social issues, and due to the tightening of legislation in this regard, researchers and

practitioners are more and more interested in developing decision making models in an

attempt to incorporate sustainability concerns. Sustainable development is “a development

that meets the needs of the present without compromising the ability of future generations to

meet their own needs” [8]. The emphasis is drawn on the economic development duration, the

respect of natural systems, and social equity, forming what is generally known as 3P, “the

three pillars” of sustainability (3P: Profit, Planet, and People). The transposition of the 3P to

industrial operations is reflected by the concept of CSR [1]. The three bottom line approach

(TBL) introduced in [9] enhances the CSR concept, by stressing the need to achieve a

minimum performance for the three dimensions of sustainability and balancing them.

Sustainable SC planning could be thus defined as the integration of sustainability concerns to

the decisions of the SC, in an attempt to improve and balance the economic, environmental,

and social performances.

When environmental and economic aspects are considered without incorporating the social

dimension, the SC refers to “green logistics” [7] [10] [11]. In our work we focus on forward

SCs. Indeed, even though reverse logistics and closed-loop SCs are largely considered as

being sustainable or green (since they may contribute to reduce wastes and save raw material

use), it is argued that adding reverse processes and closing the loop don’t make systematically

the SC “sustainable” or “green” [12] [13]. In this sense, Rubio et al. (2008) [13] analyzed 10

years of research (1995-2005) on reverse logistics, product recovery and closed-loop SCs, and

show that almost all the models have economic drivers as the main objective. On other hand,

it is claimed that cleaning processes may be polluting, and much transportation may be

needed to generate large enough volumes for recycling or remanufacturing [7]. Interested

reader can refer to [12] [14] [15] [16].

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2.2 Literature review on sustainable SC planning models

We analyzed several mathematical models that have been proposed to handle different SC

planning decisions (strategic, tactical, and operational) incorporating at least two of the three

dimensions of sustainable development, published between 1998 and 2013. As mentioned

above, we focused mainly on forward SCs.

While all the models take into account the economic and the environmental dimensions, we

found no model incorporating economic and social dimensions together or environmental and

social dimensions together. Regarding the economic aspects, financial performance criteria

such as cost, profit or Net Present Value (NPV) have been considered in all papers. Other

“economic” criteria such as responsiveness, quality, reliability, etc. have been integrated in

some works [17] [18] [19] [20]. Concerning environmental dimension, greenhouse gas

(GHG) emission is obviously the criterion most often considered in the literature [21] [22]

[23] [24], etc. For instance, Tao et al. (2010) [25], Bonney and Jaber (2011) [26], Hua et al.

(2011) [27], Bouchery et al. (2012) [28], Veen and Venugopal (2013) [29] have all extended

the classical economic order quantity (EOQ) model to incorporate carbon emissions. Other

criteria such as pollution, resource use (energy, raw material, etc.) received less, but

significant interest [17] [18] [19] [30], etc. Furthermore, it is worth noting that studies

considering environmental criteria are often related to the legislation, on GHG (carbon taxes,

cap-and-trade mechanism, etc.), recycling (products take-back schemes, etc.), pollution [31]

[32] [33] [34], etc. Regarding social criteria, almost only potential long-term damages to

human health (end-point impact caused by climate change, ozone layer depletion, etc.) are

taken into account in some studies based on life cycle assessment approach (LCA)1. Apart

from these works, we identified only three models considering other social criteria. You et al.

(2011) [36] designed a bio-fuel SC and considered the maximization of local employment by

using JEDI tool (Jobs and Economic Development Impact model) that allows estimating the

number of direct and indirect local jobs created for each unit expenditure related to facility

construction or operating. Pérez-Fortes et al. (2012) [37] maximized the distribution of jobs to

be created, by dispersing as wide as possible the location of the production technologies.

Pishvaee et al. (2012) [38] maximized the “SC corporate social responsibility” by

1 The LCA method quantifies energy, and globally used inputs and released waste at every stage in the product

life cycle. The information is then translated into a set of socio-environmental impacts categories such as climate change, resource depletion, etc. and an indicator is set to each impact category [35]. The indicators could further be aggregated into one single index that captures the global socio-environmental impact such as Eco-indicator 99, IMPACT 2002+, etc.

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introducing a weighted sum of four indicators measuring one environmental criterion (wastes

generated during manufacturing), and three social criteria: the total number of jobs created,

the total share of hazardous materials contained in the products and the total number of days

lost due to accidents at work.

Globally, three main observations can be made. First, there is an obvious lack of models

integrating all the three dimensions of sustainable development, as social criteria are

marginalized. Second, in several models, SC performance is “economic-driven” since the

environmental criteria are incorporated in the economic objective function (for instance, by

using a penalty cost (carbon tax)) or integrated as constraints (for instance, by fixing an upper

cap, limiting the emissions of CO2), leading to mono-objective mathematical models.

Therefore, the environmental performance could not be optimized, and no real balance could

be achieved between the environmental and the economic performances. Finally, bi-objective

models considering socio-environmental criteria measure them by using an aggregated index

(for instance Eco-indicator 99, IMPACT 2002+, “SC corporate social responsibility”), so

balancing the three sustainability performances is not allowed (for instance profit, damage to

human health and damage to the ecosystem in models considering Eco-indicator 99).

To the best of our knowledge, only You et al. (2011) [36] analyzed the Pareto frontier

regarding the three sustainability dimensions. Therefore, we could conclude that there is an

acute lack of integrated approaches allowing the effective implementation of the three

dimensions of sustainability in OR literature, in line with the TBL approach. This conclusion

led us to examine the most popular performance measurement methods in an attempt to

analyze how they could be adapted to enhance OR models on sustainable SC planning that we

present in the next section.

2.3. An overview of performance measurement methods

As sustainability performance encompasses multiple dimensions, we focused on performance

measurement methods considering multiple criteria. The early contributions were proposed in

the 1980s. For instance, Globerson (1985) [39] proposed an approach based on four steps: (1)

identification of the critical performance criteria (2) establishment of performance indicators,

(3) definition of targets to be achieved for each criterion using benchmarking, and (4) design

of a control loop to correct the deviations from the targets. Since then, many contributions

appeared in the literature. We report here on the most significant contributions in the

literature. Interested reader can refer to Clivillé (2004) [40] for a deeper literature review.

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Based on the business activities/processes, ABC/ABM methods (Activity-Based Costing and

Activity-Based Management, respectively) [41] introduced the concept of “performance

inducers” aiming at identifying the factors that could improve the performance of the business

activities/processes. ECOGRAI method [42] aims at designing and implementing a coherent

performance indicator system. It is based on the triplet (objective, decision variable, indicator)

where decision variables are the variables on which the decision maker could act in order to

achieve the objectives. The balanced scorecard (BSC) [43] attempts to balance the

performance following four aspects (financial, customers, internal business, and learning &

growth). It considers within each aspect the objectives to be achieved, measures (performance

indicators), targets, and initiatives. Later, several works proposed including sustainability

criteria to the BSC such as [44], [45], etc. For instance, Bieker [45] suggested adding a fifth

aspect: society. He proposed within this aspect, a set of indicators such as expense amounts in

collaborative campaigns, lobbying and technology transfer, etc.

The Quantitative Model for the Performance Measurement System (QMPMS) developed by

Bititci (1995) [46] is based on the identification of action variables that would impact

performance. These impacts are then quantified using the AHP method (Analytical Hierarchy

Process) [47], and finally aggregated by operating a weighted sum. The Supply Chain

Operations Reference Model (SCOR) aims at evaluating and improving SC performance

based on the best practices and five generic metrics (reliability, responsiveness, agility, costs,

and assets). The best practices are expected to contribute in heightening the performance of

the business processes. The latest version of SCOR [48] introduced the reference model

GreenSCOR. This latter highlights a number environmentally friendly best practices

(environmental management system implementation, recyclable material identification, load

maximization, etc.) as well as a set of environmental indicators such as GHG emission,

percentage of waste recycled, liquid waste generated, etc.

The main conclusion that could be made regarding the approaches proposed in the literature

on performance measurement is that they are all based on three invariants forming a triplet:

(objectives, variables, measures).

- The objectives are related to the performance criteria to be evaluated.

- The variables are the set of factors (performance inducers, action variables, best practices,

etc.) that impact the performance.

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- And finally, the measures are the indicators that asses the achievement level of each

performance criterion.

3. An integrated approach for sustainable supply chain planning

Given the lack of sustainable SC planning models in OR literature, we propose an integrated

approach allowing the effective and coherent integration of the three sustainability

dimensions into mathematical optimization models (figure 1). In simple words, our approach

seeks to ensure that the solutions produced by the mathematical model really optimize the SC

performance in terms of the 3P perspectives.

Figure 1: A framework for transposing sustainability principles to SC planning models

When applied to a sustainable SC planning problem, the “Objectives” of the triplet

(objectives, variables, measures) will correspond to the criteria of sustainability performance

we are aiming at evaluating. “Variables” will correspond to the decisions of the SC that

should be made (strategic, tactical, or operational). And finally, “Measures” will correspond

to the performance indicators of the SC that measure the achievement of each sustainability

performance criterion. These indicators should be coherently designed and should effectively

measure all the three sustainability performances. This could be achieved by performing a

consistency analysis that allows identifying which SC decisions impact the sustainability

criteria. The idea behind this consistency analysis is that a better knowledge of the SC

decision potential impact on the SC performance would improve the quality and effectiveness

of the indicators, and further facilitates the mathematical formulation of these indicators. For

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example, at the tactical level, decisions related to sourcing would affect the costs, the amount

of GHG released due to transport distances, and even local employment (e.g. local sourcing

versus foreign sourcing). Note that the SC decisions should not be confused with the decision

variables used within the multi-objective mathematical programming (MOP), which is

considered in our approach as an implementing tool (Figure 1). Indeed, the decision variables

are only an abstraction of the SC decisions. However, the consistency analysis will remain

valid, and will enhance the design of coherent and effective sustainability indicators, which

are modelled within the MOP by objective functions.

The next paragraphs discuss in details the sustainability performance criteria, the consistency

analysis, and the performance indicators.

3.1 Sustainability performance criteria

We aim at specifying the economic, environmental and social performance criteria that could

be considered for a given SC planning problem. Traditionally, the common attributes

considered for the performance measurement of the SC are related to financial aspects (cost,

return on investment, etc.), flexibility (flexibility of production, distribution, etc.),

responsiveness (lead time, cycle time, etc.), reliability (reliability of forecasts, delivery service

level, etc.), and quality (quality of production, service quality, etc.) [49]. There is no

consensus on what should be the environmental and social performances as it depends on the

industrial sector, the region or country where the operations are located, etc. However, several

international standards such as SCOR reference model, OECD guidelines [50], GRI [51], ISO

26000 [52], etc. and scientific works propose criteria more or less generic that could be

adapted. In this sense, Baumann (2011) [53] conducted a depth literature review and

categorized SC sustainability performance. Inspired by her work; we suggest considering 12

criteria to cover the three dimensions of sustainability (Table 1): five are related to the

economic dimension, four to the environmental dimension, and three to the social dimension.

Table 1: Sustainability performance criteria (inspired by [53])

Dimension Economy (Eco) Environment (Env) Society (Soc)

Criterion Financial performance

Responsiveness

Flexibility

Reliability

Quality

Resources consumption

Climate change

Pollution

Hazardous materials

Health and safety

Job creation and wealth

Work conditions

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3.2 Consistency analysis and performance indicators

Consistency analysis consists in evaluating qualitatively the potential impact of each decision

involved in the SC planning problem (i.e. decisions related to procurement, manufacturing,

transport, etc. involved at the decision level considered within the problem) on the

performance criteria targeted by the decision maker (for example, those specified in Table 1).

Once the SC decisions are modelled as decision variables within the MOP, the consistency

analysis results could be refined, by considering directly the impact of each decision variable

on each performance criterion.

The performance indicators are thus logically derived from the consistency analysis. We

model them within the MOP by using objective functions. This could be done by linking the

decision variables that have an impact on a given performance criterion by using some

coefficients and factors. For example, if we consider the environmental criterion “climate

change”, some factors tied to GHG emissions released due to transportation, manufacturing,

etc. could be simply multiplied by the amounts of products transported or manufactured. The

resulting weighted sum would be modelled as an objective function measuring the total GHG

emissions released by the operations of the SC. Note that, the MOP not only allows setting

performance indicators, but also optimizes the performance.

To show the relevance of our approach, we present in the next section how we applied it to a

wood SC tactical planning problem inspired by the Canadian lumber industry.

4. Application: a sustainable wood SC tactical planning

This section is divided into three parts. The first one presents the case study. In the second

part, we show how we applied our integrated approach to the case study, and formulate the

objective functions. The third part presents the integral mathematical formulation.

4.1 Case study: lumber industry in Quebec

We study the lumber industry case proposed in Vila et al. (2006) [54]. It considers a typical

Canadian company operating in the region of Quebec: Virtu@l Lumber [54]. The company

manufactures lumber and chips. Figure 2 presents the manufacturing processes. The main

activities are now described.

• Supply Market:

The wood is mainly supplied from public forests (90% of the forests are owned by the State in

Canada). Three species of wood are available: spruce, pine, and fir. These ones are

representative of the species used to manufacture lumber in the province of Qu

Depending on the diameter and length, various types of stems could be obtained after

harvesting.

• Bucking

Once harvested, the stems of different species and sizes

forest, if the technology is available

“divergent” because from one common stem, logs of various lengths could be obtained

(Figure 3). In addition, multiple bucking patterns (recipes) could be applied depending on the

characteristics of the stems (diameter and length) and the bucking technologies available.

Figure 2. Lumber industry manufacturing processes [54]

• Sawing

After bucking, the logs are sawn into green lumber

process and several sawing patterns could be applied as well, depending on the technologies

available and the characteristics of the logs.

2 http://shop.csa.ca/

representative of the species used to manufacture lumber in the province of Qu


of different species and sizes can be bucked into logs directly in the

if the technology is available, or bucked later in sawmills. Such a process is

from one common stem, logs of various lengths could be obtained


(diameter and length) and the bucking technologies available.

Lumber industry manufacturing processes [54]

After bucking, the logs are sawn into green lumber and rough lumber. This is also a divergent


available and the characteristics of the logs. Choosing a cutting pattern for bucking or sawing

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representative of the species used to manufacture lumber in the province of Quebec2.


be bucked into logs directly in the

Such a process is

from one common stem, logs of various lengths could be obtained


(diameter and length) and the bucking technologies available.

This is also a divergent


for bucking or sawing

is crucial as it determines (1) the dimensi

also (2) the efficiency of the process

Two bucking patterns

Figure 3. Examples of cutting patterns for bucking and sawing activities

• Drying

The lumber is then dried in larges dryers. In Quebec, it is common in summer to dry first the

lumber in open air before using the dryers.

• Chipping

The rejects generated during bucking and sawing

types are produced depending on the

• Planing/Grading

Planing/Grading process aims at removing extra

the external aspect of the lumber.

products (MSR, Premium, Dimension lumber

or mechanically. Typically MSR lumber (Machine Stress Rated) is obtained if the lumber is

enough resistant to a certain mechanical pressure.

• Sales market

Three main market segments are usually distinguished

large retailers and industrial customers

value is sold to industrial customers

higher value than dimension lumber, which is

are sold to pulp and paper mills. The usual customers of the Canadian lumber and chips are

located in the USA and Canada [54]

the dimensions of the output products and their quantities, and

(2) the efficiency of the process (i.e. quantity of rejects).

Two bucking patterns Two sawing patterns

Figure 3. Examples of cutting patterns for bucking and sawing activities


lumber in open air before using the dryers.

generated during bucking and sawing are transformed into chips. Three

types are produced depending on the tree species.

process aims at removing extra-lengths, correcting the shape and improving

the external aspect of the lumber. The lumber is then categorized into various finished

imension lumber) depending on its quality. This is don


enough resistant to a certain mechanical pressure.

hree main market segments are usually distinguished in lumber industry: the spot market,

large retailers and industrial customers. MSR lumber that presents the highest

industrial customers. Premium lumber is sold to retailers. This product is

lumber, which is sold to the spot market. Chips on the other side


[54].

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quantities, and

Figure 3. Examples of cutting patterns for bucking and sawing activities [54].


. Three quality

lengths, correcting the shape and improving

into various finished

ing on its quality. This is done visually


: the spot market,

MSR lumber that presents the highest quality and

. This product is of

. Chips on the other side


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Virtu@l lumber company case owns three sawmills located in the regions of Chicoutimi,

Maniwaki, and Scott in the province of Quebec. The three sawmills can harvest wood from

three different forests, located in Chicoutimi, Maniwaki, and Scott (respectively). The mix of

species available in the three forests is presented in table 2. The three sawmills have different

technologies that could be used to process the wood and also different capacities. A single

technology is considered for each activity except for sawing, which can use eight foot (8’)

and/or random length (RL) technologies, planning/grading which can use classic and/or MSR

technologies, and for drying, which could be done in the open air or inside dryers. The

bucking technology offers three different cutting patterns, whereas the two sawing

technologies, five and four respectively. Bucking is done completely in Scott forest, partially

in Maniwaki forest, and no bucking is available in the forest of Chicoutimi. Bucking could be

also performed in the sawmills of Maniwaki and Chicoutimi, but not in Scott. The two sawing

technologies and the chipping technology are all available in the three sawmills. However, the

two drying technologies and the two planing/grading ones are available only in Chicoutimi

and Scott. In Maniwaki, only drying inside dryers and classic planing/grading technology are

possible.

Chips are sold to one Canadian paper mill located in Quebec and lumber is sold to three

industrial customers (Rivière-de-Loup, Canada, Boston and Bangor, USA), two retailers

(Montreal and Bangor) and to one spot market (Toronto).

In the Virtu@l lumber case, transportation by truck is the only mode used. However, the train

is also usually used to transport forest products. Therefore we consider both alternatives. We

also assume that harvesting and bucking could be outsourced to two alternative forest

contractors. Indeed, outsourcing such activities is very common in Quebec. Finally, we assign

to each forest and sawmill three regions where employees could be hired.

Table 2: Mix of species in the three forests

Species Spruce Pine Fir

Forests

Chicoutimi 75% - 25%

Maniwaki 75% 15% 10%

Scott 40% - 60%

In this work we use the case Virtu@l Lumber to illustrate our approach on the tactical

planning of the SC. The problem is formulated as follows: Given the customer’s demand and

the available resources (forest resource, machines, labor, storage capacities, etc.), how

sustainability concerns could be integrated into the tactical planning with regard to

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procurement, manufacturing, inventory, transportation, and employment in order to meet the

demand without exceeding the available capacities? In particular, the following SC decisions

are considered:

Procurement The volume of wood to harvest in the forests and the volume of wood to source from forest contractors (outsourced).

Manufacturing Volumes of products to manufacture, using the right cutting patterns.

Inventory The inventory of different products to keep in sawmills

Transportation The volume of the products to transport between the business units (forests, forest contractors, sawmills, customers) using the right transportation modes.

Employment The number of employees needed in the forests, and in sawmills.

The following hypotheses are assumed:

→ The planning horizon is divided into multiple season periods. Our aim is to take into

account the seasonal behaviour of demand and wood procurement. Demand for each

product and period need to be fulfilled.

→ The SC operations are managed according to MTS (Make-to-Stock) policy and we

consider a stock for each product.

→ Harvesting could be performed by forest contractors, who are the usual partners of the

company. Therefore, we do not consider fixed costs related to forest contractor selection.

→ Different alternative technologies are available for the various manufacturing processes.

Several alternative recipes (bucking and sawing patterns) are possible as well.

→ Transport is performed by third-party logistics providers (3PL). The potential carriers are

known and selected before the beginning of the planning horizon. Fixed costs of transport

related to carrier selection are thus not considered. In addition, transportation is assumed to

be done on truckload basis, so the costs are considered proportional to the volume

transported. Finally, different transportation modes are available (e.g. truck and train).

→ In the Canadian forest industry, it is common that forest workers move from one forest to

another as skilled employees are very scarce. We generalize this practice to sawmills, as it

could bring benefits for workers and managers with regard to employment opportunities.

For instance, employees could be transferred to another production site if the workload

requires it. Employee transfer from one site to another (forest or sawmill) is allowed only if

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the distance between the employee’s residence region and the destination site does not

exceed a given limit.

→ Additional employees could be hired at the beginning of a season, and some employees

could also be laid-off. Note that, in Quebec, hiring and laying-off policies are relatively

flexible and costless. In this regard, the labor unions in the forest industry sector are not

powerful.

→ Employees are supposed to have flexible skills. Therefore, they could perform any

production activity within the sites of the SC.

4.2 Application of our integrated approach to Virtu@l Lumber case

Before presenting our application, we first describe the modelling approach we adopted to

take into account the divergent aspect characterizing the processes of bucking and sawing. A

comprehensive description of divergent system modelling is not the goal of this paper, but we

think that some basic notions are required to better understand the mathematical formulation.

Then, we introduce the decision variables of the mathematical model. Finally, we present the

application of our approach.

• Modelling approach (divergent processes)

Traditionally, 2 main approaches are adopted in the OR literature to describe a manufacturing

system: the material balance approach (for example [55] [56]) and the activity-based approach

(for example [54] [57]). Within the former, the consumption of raw materials and

intermediate products is calculated without taking into account the specificities of the

processes that transform them. However, the production processes could have a major impact

on the output products (the type, the quantity, the percentage of rejects, etc.). It is the case in

the lumber industry context (section 4.1). Therefore, we adopt the second approach, which is

more appropriate. This approach considers that an activity consumes several resources such as

labor, energy, water, etc., in order to transform input products to output products using a

particular technology that specifies how the inputs are transformed into outputs ([54] [57]

[58] [59]), for instance by using a specific bucking or sawing pattern in divergent processes.

In addition, the generation of undesirable outputs such as waste, pollution, etc. could be easily

considered. Figure 4 shows how we modelled a divergent process relying on the activity-

based approach.

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Figure 4. The modelling approach adopted for divergent processes

We assigned to each available technology a distinct activity as in [57]. Then, for each activity,

we defined a set of recipes that could be applied to the input products to obtain the output

products as in [54]. The recipes correspond to cutting patterns for bucking and sawing (see

Figure 3). Concerning the other activities, only one recipe is available. For instance, chipping

1m3 of wood rejects yields xm3 chips, which corresponds to one recipe. One consequence of

adopting such a modelling approach is related to the manufacturing decision variable: the

focus is drawn on the volume of the input products to be consumed by the activities rather

than the volume of outputs products, as it is usually considered in mathematical models

handling “convergent” processes (assembly or mixing products). Indeed, as in divergent

processes multiple output products are obtained at once from one common product, they

depend on each other making it hard to track-back the use of the input product, from the raw

materials up to the finished products (see for example [54]). This is taken into account in the

flow conservation constraints (section 4.3). The set of indexes is now introduced before

describing the decision variables of our mathematical formulation.

- Periods.

� = {1, 2, … , �} set of the periods of the planning horizon (i.e. seasons).

- Business units.

set of the forests where the wood could be harvested. The sawmills pay a certain

prices for each m3 of wood procured in a given forest.

� set of potential forest contractors procuring stems and logs.

� set of all regions where employees live.

16

set of sawmills and harvesting areas. Although harvesting is done in the forests, we

consider in our model the harvesting areas as sites sourcing raw materials (i.e.

wood) from the forests.

� (�) sub-set of regions where harvesting area or sawmill i could hire its employees.

�(�) sub-set of sites (harvesting areas and sawmills) that could hire in the regionj. � set of customers.

- Transportation modes.

� set of transportation modes.

� = �� ∪ � ∪ � �. �� is the set of transportation modes from the forest contractors

to the sawmills, � the set of transportation modes between the harvesting areas and the

sawmills, and between the sawmills, and � � is the set of transportation modes from the

sawmills to the customers.

- Activities, recipes, and products.

� set of all activities (i.e. all technologies available in the harvesting areas and in

the sawmills).

��(�) sub-set of A, corresponding to the technologies implemented insite i (a sawmill

or a harvesting area).

�� set of all recipes.

��(�) sub-set of recipes that could be used by activity (i.e. technology)a.

��(�) sub-set of activities using recipe r.

� set of all input and output products (i.e. trees, stems, logs, green lumber, rejects,

chips, dried lumber).

�� !(") set of input products from which output product p could be obtained.

�� !(�) set of input products on which recipe rcould be applied

��(") sub-set of recipes applicable to input product p (trees, stems, logs, wood rejects,

and green lumber).

��$%&(") set of recipes that could be used to obtain output product p (stems, logs, rejects,

chips, green lumber, and dried lumber).

Note that � = �� ∪ ��, where �� is the set of raw materials (trees),and�� is the set of

manufactured products. Moreover�� = ��)* ∪ ��* with ��)*is the set of intermediate

products (stems, logs, green lumber, and rejects) and ��*, the set of finished products (dried

lumber and chips). +��)* (∁ ��)*) is the set of outsourced products (logs and stems).

17

• Decision variables

- Procurement.

-.* / volume3 of product " (trees) to procure from forest 0 (i.e. to buy from the State) for

harvesting in area � at period &.

-�.) / volume of product " (stems and logs) sourced from forest contractor � by sawmill � at period &.

- Manufacturing.

1.23 / volume of input product p to be consumed (transformed into output products) by

activity a using recipe r in the harvesting area or sawmill i at period t.

As mentioned before, we focus on the input products to be transformed. This approach has also

been adopted in [54].

- Inventory.

4. / inventory of product p in harvesting area (i.e. the part of the wood volume bought

from the State to be harvested in the next period) or sawmill i at the end of period &.

- Transportation.

6� .) /7 volume of product" (stems or logs) carried from forest contractor � to sawmill �

using transportation mode 8 at period &.

6 . 9/7 volume of product " (stems, rejects, or logs) carried from harvesting area or

sawmill � to sawmill �9using transportation mode 8 at period &.

6 �. :/7 volume of product " (lumber or chips) carried from sawmill � to customer ; using

transportation mode 8 at period &.

- Employment.

<�=> / number of employees living in region � and working in site � (harvesting area or

sawmill) at period &.

<?> / number of employees living in region � hired by site � at period &.

<> / number of employees living in region � laid-off by site � at period &.

<�> 9/ number of employees living in region � transferred from site �to site �′ at period &.

We now present how we applied our approach and formulated the objective functions of our

mathematical model.

3 The quantities are expressed in terms of volume (m3 for trees, stems, logs, and rejects, board foot for green lumber and lumber, and metric ton for flakes).

18

4.2.1 Selection of sustainability performance criteria

The government of Quebec not only tresses the need that forest companies operate their

activities with more efficiency, from the forests up to the end customers, but it also

emphasizes on the necessity that forest industry creates job opportunities and promotes

regional employment, attractive work conditions, and contributes, as one of the most

important industries in Canada in its effort to offset climate change. Therefore, we consider

financial performance (Eco.1), climate change (Env.2), and job creation and wealth (Soc.2)

(table 1) as the sustainability performance criteria to be integrated in the wood SC planning

problem under study. Within the social dimension, we take into account two sub-criteria;

local job creation (Soc.2.a), and employment stability (Soc.2.b) as the social concerns are

marginalized in the literature. They are also the top priority of the government in Quebec.

4.2.2 Consistency analysis and performance indicators

The consistency analysis results are presented in Table 3, where an “X” indicates that a given

decision and each of the associated decision variables have an impact on each performance

criterion. Note that our analysis is qualitative and not exhaustive. Our aim is to illustrate how

such analysis could be performed.

Table 3: Consistency between SC and Decision variables and Sustainability criteria

Sustainability criteria

SC decisions Decision

variables Eco.1 Env.2 Soc.2.a Soc.2.b

Procurement -.* / x -�.) / x x

Manufacturing 1.23 / x x x x

Inventory 4. / x x

Transportation

6� .) /7 x x

6 . 9/7 x x

6 �. :/7 x x

Employment

<�=> / x x x x <?> / x x x <> / x x x <�> 9/ x x

• Procurement

The volume of wood to harvest affects the financial performance as the company pays the

government for each volume unit harvested. The volume of wood to source from the forest

19

contractors also impacts the financial performance (acquisition cost, order cost, etc.). It could

indirectly affect local employment as the forest contractors may be local or foreign (for

instance they could be located outside the province of Quebec). Moreover, outsourcing may

reduce “in-house” workload (i.e. harvesting activity) resulting in fewer job opportunities.

• Manufacturing

The volume of products to manufacture affects all the performance criteria. Indeed, the use of

a particular technology impacts production costs. In addition, the application of a given

cutting pattern could generate more or less rejects that have low market value. Regarding the

environmental performance, the technologies may have different energy consumption levels,

and therefore may release unlike amounts of GHG impacting differently the climate change.

Drying process, for instance, when performed first in the open air and then in the dryers,

consumes much less energy than when it is performed in the dryers solely. Finally, depending

on the level of automation of the technologies and the workload, more or less labor could be

required. Therefore, manufacturing decisions impact job creation and employment stability,

respectively.

• Inventory

The inventory to keep in sawmills clearly affects the financial performance in terms of holding

and handling costs, among others. It may also affect work conditions through employment

stability for example, since inventory level is related to the volume of products to be

manufactured, impacting the workload from one season to another.

• Transportation

The volume of the products to be transported between the business units affects the financial

performance due to transportation costs. It also has a different environmental impact

depending on the selected transportation mode and the distances traveled between the sites of

origin and the sites of destination.

• Employment

The number of employees needed in the forests, and in sawmills impacts the financial

performance in terms of salaries. Moreover, employees’ travels from their region of residence

to their workplace also generate carbon emissions, which depend on the distances and the

transportation mode used. Obviously, the number of employees needed, including the number

to hire, the number to lay-off, and the number to transfer between sites impacts job creation

and employment stability.

20

Following this consistency analysis, performance indicators are modelled as objective

functions within the MOP.

• Economic indicator

We propose to measure the financial performance by computing the total SC costs (in $). We

define the following cost parameters (in $):

��.3 / unit cost of using activity (i.e. technology) � to transform input product " in site

(harvesting area or sawmill) �, at period &.

�4. / unit handling cost of product " in site �, at period &.

��.*/ unit cost of acquiring raw material (i.e. trees) " from forest 0,at period &.

� .)/ unit cost of sourcing product " (logs and stems) from forest contractor �, at period

&.

��A.) /7 transportation cost of 1 unit of volume of product " (per kilometer travelled) from

forest contractor � to sawmill � using transportation mode 8 at period &.

��A. 9/7 transportation cost of 1 unit of volume of product " (per kilometer travelled)

between sawmill � and sawmill �′ using transportation mode 8 at period &.

��A. :/7 transportation cost of 1 unit of volume of finished product " (volume per kilometer

travelled) from sawmill � to customer ; using transportation mode 8 at period &.

�</ unit labor cost at period & (i.e. the salary of 1 employee during 1 season).

Note that, as stated in the hypotheses, costs related to employee hiring or laying-off are

neglected, as well as fixed cost associated to forest contractor and transportation mode

selection (see the hypotheses in Section 4.1). Our financial performance indicator is modelled

by the objective function(B:C.D) to be minimized:

EFGH.I = ∑ ∑ K∑ ∑ ∑ ��"��&. 1"��& + �<& ∑ <�=��&�∈� (�) +"∈��(�)�∈��(�)�∈��(�)�∈ &

∑ �4"�&"∈� . 4"�& + ∑ ∑ ��"0&."∈��0∈ -"0�& + ∑ ∑ � "�&."∈+��0�∈� -�"��& +

∑ ∑ N��8 ∑ ��A"��&

8"∈+��0�∈� . 6� "��&

88∈�� + ∑ ∑ N��′

8 ∑ ��A"��′&8 ."∈��0�′∈ ,�′≠�8∈� 6 "��′&

8 +

∑ ∑ N�;8 ∑ ��A"�;&

8"∈��0 .;∈� 6 �"�;&

88∈� � P

Where:

N) 7 distance between forest contractor � and sawmill � using transportation mode 8.

N Q7 distance between sawmill � and sawmill �′ using transportation mode 8.

N :7 distance between sawmill � and customer ; using transportation mode 8.

21

• Environmental indicator

We measure the environmental performance “climate chage” by computing the total GHG

emission of the SC. We define the following CO2 emission coefficients that are related to the

decision variables having an impact on CO2 emissions:

R3. GHG emission factor of activity�per 1 unit of volume of input product " (CO2

equivalent/m³).

μ7. GHG emission factor of transportation mode 8 per 1 unit of volume of product

"transported and per 1 kilometer travelled (CO2 equivalent/m3.km).

T GHG emission factor per 1 employee per 1 kilometer travelled (CO2 equivalent

/km).

We model the environmental indicator by using the objective function(B!U.V) to be

minimized:

EFWX.Y =∑ ∑ K∑ ∑ ∑ R3..∈Z2[\(2) . 1.23 /2∈]Z3(3)3∈^)( ) + T ∑ N� > <�=> />∈_`( ) + ∈`/

∑ 7∈ab]` ∑ N) 7

)∈b] ∑ μ7..∈cdZef . 6� .) /7 + ∑ ∑ N Q

7 Q∈`, g Q7∈a`` ∑ μ7..∈dZef . 6 . Q/

7 +

∑ ∑ N :7

:∈]7∈a`] ∑ μ7..∈dZf . 6 �. :/7 P

Where N� > is the distance between residence region � and site �.

• Social indicators

1. Local employment (Soc.2.a)

The proximity of employees to production sites promotes local employment as well as

employee well-being (for example by reducing the time spent in either public or private

transport). We therefore propose minimizing the objective function ( C:.V.3) to maximize

these social benefits. C:.V.3 computes the total travelled distance multiplied by the total flow

of employees.

EhHG.Y.i = ∑ ∑ ∑ N� > <�=> />∈_`( ) ∈b/

Note that as we have integrated the minimization of the GHG emissions generated by

employees (which is proportional to the distance travelled) in (B!U.V)

(T ∑ ∑ ∑ N� > <�=> /),>∈_`( ) ∈b/ minimizing (B!U.V) tends to minimize ( C:.V). Therefore,

minimizing ( C:.V)is not required further.

2. Employment stability (Soc.2.b)

22

We evaluate employment stability by the objective function ( C:.V.j), which computes the

total number of hires and lay-offs. Minimizing C:.V.j contributes to favor the transfer of

employees between production sites instead of laying them off. Indeed, employee transfer

might be preferred by both workers (they avoid the loss of their job) and the company (it

reduces hiring and lay-off burdens). Moreover, employee transfer may enhance the

trustworthy relationship between the company and its employees, who may feel more

protected.

EhHG.Y.k = ∑ ∑ ∑ (<?> / + <> /)>∈_`( ) ∈b/

The next subsection presents the overall sustainable SC planning model.

4.3 Mathematical modelling

Once the sets of indexes and the decision variables have been introduced, we present all the

parameters of the mathematical model, the objective functions, and the model constraints. The

resulting model is a multi-objective linear programming integrating all the three sustainability

dimensions.

4.3.1 Model parameters

l.:/ demand of customer ; for finished product " (chips and lumber) at period &.

��"3 / capacity of activity � implemented in site � at period & (in terms of hours).

4��" / storage capacity of sawmill �at period & (in terms of volume).

4. /m ! minimum inventory of product " in site � in the end of period &.

4. ! / initial inventory of product " in site �.

��".*/ capacity of forest 0 for raw material " (i.e. volume of wood assigned by the

government) at period &.

��".)/ capacity of forest contractor � for product " (stems or logs) at period & (in volume).

<A��"/ capacity of an employee during period t (number of hours).

n.23 ! capacity of activity � required to transform 1 unit of volume of input product " using

recipe � (in hours).

o23.9. volume of output product" manufactured by activity � using recipe � from 1 unit of

23

volume of input product "9.

<�=��"> number of workers available in region �at period &.

<�=> ! / initial number of employees living in region � and working in site �.

p&��"7 transport capacity of mode 8 in volume (m3).

�&��"7 transport capacity of mode 8 in weight (kg).

q. weight of one unit of volume of product " (in kg).

��.3 / unit cost of using activity (i.e. technology) � to transform input product " in site

(harvesting area or sawmill) �, at period &.

�4. / unit handling cost of product " in site � at period &.

��.*/ unit cost of acquiring raw material (i.e. trees) " from forest 0,at period &.

� .)/ unit cost of sourcing product " (logs and stems) from forest contractor �, at period &.

��A.) /7 transportation cost of 1 unit of volume of product " (per kilometer travelled) from

forest contractor � to sawmill � using transportation mode 8 at period &.

��A. 9/7 transportation cost of 1 unit of volume of product " (per kilometer travelled) between

sawmill � and sawmill �′ using transportation mode 8 at period &.

��A. :/7 transportation cost of 1 unit of volume of finished product " (volume per kilometer

travelled) from sawmill � to customer ; using transportation mode 8 at period &.

�</ unit labor cost at period & (i.e. the salary of 1 employee for 1 season).

R3. GHG emission factor of activity�per 1 unit of volume of input product " (CO2

equivalent/m³).

μ7. GHG emission factor of transportation mode 8 per 1 unit of volume of product

"transported and per 1 kilometer travelled (CO2 equivalent/m3.km).

T GHG emission factor per 1 employee per 1 kilometer travelled (CO2 equivalent/km).

<3 number of labor hours required for 1 operating hour of activity (i.e. technology) �.

N) 7 distance between forest contractor � and sawmill � when using transportation mode 8.

N Q7 distance between sawmill � and sawmill �′ when using transportation mode 8.

N :7 distance between sawmill � and customer ; when using transportation mode 8.

N� > distance between residence region � and site �.

24

4.3.2 Objective functions

Economic function

B:C.D = ∑ ∑ K∑ ∑ ∑ ��.3 / . 1.23 / + �</ ∑ <�=> />∈_`( ) +.∈Z2[\(2)2∈]Z3(3)3∈^)( ) ∈`/

∑ �4. /.∈Z . 4. / + ∑ ∑ ��.*/ ..∈_d*∈b -.* / + ∑ ∑ � .)/ ..∈cdZef)∈b] -�.) / +∑ ∑ N)

7 ∑ ��A.) /7

.∈cdZef)∈b] . 6� .) /7

7∈ab]b +

∑ ∑ N Q7 ∑ ��A. Q/

7 ..∈dZef Q∈`, Qg 7∈a`` 6 . Q/7 +

∑ ∑ N :7 ∑ ��A. :/

7.∈dZf .:∈] 6 �. :/

77∈a`] P

(1)

Environmental function

B!U.V = ∑ ∑ K∑ ∑ ∑ R3..∈Z2[\(2) . 1.23 /2∈]Z3(3)3∈^)( ) + T ∑ N� > <�=> />∈_`( ) + ∈`/

∑ 7∈ab]` ∑ N) 7

)∈b] ∑ μ7..∈cdZef . 6� .) /7 +

∑ ∑ N Q7

Q∈`, g Q7∈a`` ∑ μ7..∈dZef . 6 . Q/7 +

∑ ∑ N :7

:∈]7∈a`] ∑ μ7..∈dZf . 6 �. :/7 P

(2)

Social function

C:.V.j= ∑ ∑ ∑ (<?> / + <> /)>∈_`( ) ∈b/ (3)

4.3.1 Constraints

The capacity of any activity (i.e. technology) should not be exceeded.

∑ ∑ n.23 ! 1.23 /.∈Z2[\(2) ≤ ��"3 /2∈]Z3(3) ∀� ∈ , ∀� ∈ ��(�), ∀& ∈ � (4)

A product is processed in a site only if the activities consuming it are implemented in that site.

1.23 / = 0 ∀� ∈ , ∀� ∈ �\��(�), ∀� ∈ ��(�),∀" ∈ �� !(�),∀& ∈ � (5)

The storage capacity should not be exceeded.

∑ 4. /.∈Z ≤ 4��" / ∀� ∈ ,& ∈ � (6)

The inventory at the end of each period should be greater than the minimum required.

4. /m ! ≤ 4. / ∀" ∈ �,∀� ∈ ,∀& ∈ � (7)

The number of employees required during each period should cover the entire workload.

∑ <�=> />∈_`( ) = v∑ <33∈^)( ) ∑ ∑ n.23 ! . 1.23 /.∈Z2[\(2)2∈]Z3(3) P <A��"/⁄ ∀� ∈ , ∀& ∈ � (8)

A given site could hire employees only in the regions assigned to it.

∑ <�=> />∈_\_`( ) = 0 ∀� ∈ , ∀& ∈ � (9)

25

The number of employees working in a given site is given by:

<�=> D = <�=> ! / + <?> D + ∑ <�> Q D Q∈`_(>), Qg

−<> D −∑ <�> QD Q∈`_(>), Qg ∀� ∈ �, ∀� ∈ �(�) (10)

<�=> / = <�=> (/yD) + <?> / + ∑ <�> Q / Q∈`_(>), Qg

−<> / −∑ <�> Q/ Q∈`_(>), Qg ∀� ∈ �, ∀� ∈ �(�), ∀& ∈ �\1 (11)

The total number of employees laid-off or transferred from a given site during a period should not

exceed the number of employees working in that site in the previous period.

<> D +∑ <�> QD ≤ Q∈`_(>), Qg <�=> ! / ∀� ∈ �, ∀� ∈ �(�) (12)

<> / +∑ <�> Q/ ≤ Q∈`_(>), Qg <�=> (/yD) ∀� ∈ �, ∀� ∈ �(�), ∀& ∈ �\1 (13)

The number of employees hired from a given region should not exceed the total number of potential

employees available in that region.

∑ <�=> / ∈`_(>) ≤<�=��"> ∀� ∈ �, ∀& ∈ � (14)

The volume of products (stems or logs) sourced from the forest contractors by a given sawmill

should be equal to the total volume transported to that sawmill using all the transportation modes.

-� .) / =∑ 6� .) /7

7∈ab]` ∀" ∈ +��)* , ∀� ∈ �, ∀� ∈ , ∀& ∈ � (15)

The total volume of wood bought from the State during a period and the non-harvested volume part

bough in the previous period should be equal to the total volume harvested during that period and

the remaining volume at the end of the period (i.e. kept as inventory for the next period).

∑ -.* D*∈b +4. ! / = ∑ ∑ 1.23 D3∈^)( )∩^]Z(2)2∈]Z !(.) +4. D ∀" ∈ ��, ∀� ∈ (16)

∑ -.* /*∈b +4. (/yD) =∑ ∑ 1.23 /3∈^)( )∩^]Z(2)2∈]Z !(.) + 4. / ∀" ∈ ��, ∀� ∈ , ∀& ∈ �\1

(17)

The total volume of each product in a given site, either shipped from other sites, obtained by using

the activities implemented in that site (from the appropriate input products and cutting patterns), or

kept in stock in the precedent period should be equal to the total volume of the same product, either

consumed (i.e. transformed into output products) in that site, transported to other sites, or kept in

stock at the end of the period (constraints from 18 to 23).

∑ ∑ 6 . Q D7

Q∈`, Qg 7∈a`` + ∑ ∑ ∑ o23.Q.. 1.Q23 D.Q∈dZ[\(.)3∈^)( )∩^]Z(2)2∈]ZC{/(.) + 4. ! / =

∑ ∑ 1.23 D3∈^)( )∩^]Z(2)2∈]Z !(.) +∑ ∑ 6 . 9D

7 9g 7∈a`` +4. D ∀" ∈ ��)*\+��)* , ∀� ∈ (18)

26

∑ ∑ 6 . 9 /7

Q∈`, 9g 7∈a`` + ∑ ∑ ∑ o23.Q.. 1.Q23 /.Q∈dZ[\(.)3∈^)( )∩^]Z(2)2∈]ZC{/(.) +4. (/yD)

= ∑ ∑ 1.23 /3∈^)( )∩^]Z(2)2∈]Z !(.)

+∑ ∑ 6 . 9/7

9g 7∈a`` +4. / ∀" ∈ ��)*\+��)* , ∀� ∈ , ∀& ∈ �\1 (19)

∑ ∑ 6 . Q D7

Q∈`, Qg 7∈a`` + ∑ -�.) D)∈b]

+∑ ∑ ∑ o23.Q.. 1.Q23 D.Q∈dZ[\(.)3∈^)( )∩^]Z(2)2∈]ZC{/(.) + 4. ! / =

∑ ∑ 1.23 D3∈^)( )∩^]Z(2)2∈]Z !(.) + ∑ ∑ 6 . 9D7

9g 7∈a`` + 4. D ∀" ∈ +��)* , ∀� ∈ (20)

∑ ∑ 6 . Q /7

Q∈`, Qg 7∈a`` + ∑ -�.) /)∈b]

+∑ ∑ ∑ o23.Q.. 1.Q23 /.Q∈dZ[\(.)3∈^)( )∩^]Z(2)2∈]ZC{/(.) + 4. (/yD) =

∑ ∑ 1.23 /3∈^)( )∩^]Z(2)2∈]Z !(.) +∑ ∑ 6 . Q/7

Qg 7∈a`` + 4. / ∀" ∈ +��)* , ∀� ∈ , ∀& ∈ �\1 4

(21)

∑ ∑ ∑ o23.Q.. 1.Q23 D.Q∈dZ[\(.)3∈^)( )∩^]Z(2)2∈_]ZC{/(.) + 4. ! / =

∑ ∑ 6 �. :D7

:∈]7∈a`] + 4. D ∀" ∈ ��* , ∀� ∈ (22)

∑ ∑ ∑ o23.9.. 1.Q23 /.Q∈dZ[\(.)3∈^)( )∩^]Z(2)2∈]ZC{/(.) +4. (/yD) =

∑ ∑ 6 �. :/7

:∈]7∈a`] + 4. / ∀" ∈ ��* , ∀� ∈ , ∀& ∈ �\1 (23)

The volumes of a given finished product (lumber or chips) transported from all the sites to a given

customer, using all the transportation modes should be equal to the demand.

∑ ∑ 6 �. :/7

∈`7∈a`] = l.:/ ∀; ∈ �, ∀" ∈ ��* , ∀& ∈ � (24)

The volume of wood bought from the State should not exceed the allocated quantity.

∑ -.* / ∈` ≤ ��".*/ ∀" ∈ ��, ∀0 ∈ , ∀& ∈ � (25)

The volume of stems or logs supplied from the forest contractors should not exceed their production

capacity.

∑ -�.) / ∈` ≤ ��".)/ ∀" ∈ +��)* , ∀� ∈ �, ∀& ∈ � (26)

The transportation capacity should not be exceeded (in volume and weight, constraints 27 to 32).

∑ 6 �. :/7

. ≤ p&��"7 ∀� ∈ ,∀; ∈ �,∀8 ∈ � �, ∀& ∈ � (27)

∑ 6 . 9/7

. ≤ p&��"7 ∀� ∈ ,∀�9 ∈ , � ≠ �9, ∀8 ∈ � , ∀& ∈ � (28)

∑ 6� .) /7

. ≤ p&��"7 ∀� ∈ �,∀� ∈ ,∀8 ∈ �� , ∀& ∈ � (29)

∑ q.. 6 �. :/7

. ≤ �&��"7 ∀� ∈ ,∀; ∈ �,∀8 ∈ � �, , ∀& ∈ � (30)

∑ q.. 6 . 9/7

. ≤ �&��"7 ∀� ∈ ,∀�9 ∈ , � ≠ �9, ∀8 ∈ � , ∀& ∈ � (31)

∑ q.. 6� .) /7

. ≤ �&��"7 ∀� ∈ �,∀� ∈ ,∀8 ∈ �� , ∀& ∈ � (32)

All the decision variables are positive and continuous (we approximate the number of employees by

27

5. Experiments and numerical results

The goal of this section is to illustrate how the described approach could help the decision

maker understanding and making trade-offs with respect to the three sustainability dimensions

of the performance. We solved our mathematical model on the basis of the lumber industry

case presented in section 4.1. We considered various instances presenting different sizes and

parameter values. We first solved a simplified version of the problem to illustrate how our

model could be used by the decision maker as a decision support tool to assist her/him in

implementing the “right” CSR strategy. To this end we generated Pareto frontier that presents

different trade-offs between the economic, environmental, and social objectives. We then

solved four instances of the complete case where demand increases in order to analyze how

the trade-offs could be impacted. The mathematical model was implemented with IBM ILOG

CPLEX Optimization Studio 12.5 software. Experiments were run on an Intel(R) Core(TM)

i5 CPU PC with 2.53 GHz processor and 4 GB RAM for all instances.

• Simplified case

We consider a simplified version of Virtu@l Lumber (Section 4.1) by grouping the three

available wood species (spruce, pine, and fir) into one species family SPF4. Indeed, at the end

of the manufacturing process, all the lumber obtained is classified SPF and it is sold at the

same price within the same quality class (MSR, Premium, Dimension Lumber) regardless of

the spruce used to manufacture the end product. The characteristics of the simplified case are

presented in Table 4. Note that for this instance we consider all the manufacturing process

except planing/grading for the sake of simplification (this process will be integrated in the

second instance). Our aim here is to illustrate how our model could be used as a decision

support tool by the decision-maker.

Table 4: Characteristics of the simplified case.

# of forests: 3

# of operations: 5 + storage + transportation

4 https://www.cecobois.com

continuous variables).

1.23 / , 4. / , -.* / , -�.) / , 6� .) /7 , 6 . 9/

7 , 6 �. :/7 , <?> / , <�=> / , <�> 9/ ≥ 0 (33)

28

# of forest contractors: 2

# of technologies: 7

# of sawmills: 3

# of recipes: 16

# of transport modes: 2

# of product types: 30

# of hiring sites: 3

# of time periods: 6 (1 period = 3 months)

# of customers: 5

We first generated Pareto frontier to provide the decision makers with different solutions

presenting trade-offs between the three sustainability dimensions. To this end we assigned a

weight to each of the proposed objective functions and then we varied the weights. These

could be interpreted as the different possible preferences of the decision maker regarding the

tree sustainability dimensions. We did not aim at building the complete Pareto-frontier, but

our purpose was to illustrate how very different solutions could be obtained by applying

different preferences. By doing this, the manager could compare different solutions and select

the one that best reflects his/her preferences, and the balance he/she wants to make with

regards to the three sustainability dimensions.

We solved the mathematical model by using the weighted goal programming technique [60].

Each objective function was given a goal (or a target) and then the deviations from this set of

targets were minimized using a weighted deviation sum. To set the targets

B:C.D∗ , B!U.V

∗ , C:.V.j∗ for the objective functions B:C.D, B!U.V, C:.V.j, respectively, we

optimized each objective alone, without considering the rest. Therefore, each target represents

the best performance level for the economic, environmental, and social dimensions. In order

to harmonize the measurement scales and units, we have considered the relative deviations

NB:C, NB!U, N`C: , such that NB:C = b~��.�yb~��.�∗

b~��.�� yb~��.�

∗ , NB!U = b~\�.�yb~\�.�∗

b~\�.�� yb~\�.�

∗ , N`C: = b��.�.�yb��.�.�∗

b��.�.�� yb��.�.�

∗

with NB:C ≥ 0, NB!U ≥ 0, N`C: ≥ 0, and B:C.D`{. , B!U.V

`{. , C:.V.j`{. are upper bounds of the 3

objective functions (respectively).

These equalities and inequalities were added as new constraints to the mathematical

formulation and we minimized the new objective function = (�B:C. NB:C +�B!U . NB!U +�`C: . N`C:) × 100, where (�B:C, �B!U, �`C:) is a weight vector satisfying the conditions:

0 ≤ �B:C ≤ 1, 0 ≤ �B!U ≤ 1, 0 ≤ �`C: ≤ 1, and�B:C + �B!U +�`C: = 1.

In order to obtain Pareto solutions, we varied the values of the weights (�B:C, �B!U, �`C:)

between 0 and 1 with a step of 0.1 between each two successive values, while ensuring that

the sum of the three weights was equal to 1. Solving the model for one single set of weights

(e.g. 0.4, 0.3, 0.3) required around 20 seconds, and solving it for all the possible weight

29

combinations (66 in total) required 22 minutes and 31 seconds. Table 5 reports the best

possible value for each of the objectives when the other are not optimized as well as the

computational times and the number of variables and constraints.

Table 5: Computing results for instance #1

Objective Weights

Best Obj.

Value Variables Constraints Time (sec.)

Eco ($) (1,0,0) 25 968 416 20

Env (Kg CO2 eq.) (0,1,0) 185 891 629 18 625 11 664 19

Soc (0,0,1) 15 21

Figure 5 shows the solutions obtained. Each point in Figure 5 represents one Pareto solution

and is defined by three values, each corresponding to a performance level with respect to the

three sustainability dimensions. Financial performance expressed in terms of total costs is

measured in $. Environmental performance expressed in terms of total GHG released is

measured in kg equivalent CO2. Finally, social performance (vertical axis) is expressed as the

number of employees hired and laid-off.

Figure 5. Pareto solutions

Based on these solutions, the decision maker can select the one matching best his/her CSR

strategy: societal oriented (employment stability promotion), environmental oriented

(sensitive reduction of the GHG emissions), etc. If he/she is aiming at minimizing economical

costs for example, solutions along the line “A” are the most interesting. If the decision maker

is mostly concerned by minimizing GHG emissions at any price, he/she should select the

solution within circle “B”. However, when comparing solution “B” with solutions in circle

GHG emissions x107 Eq.CO2

Hires + Layoffs

Costs x107 $

C A

B

“C”, one realizes that the price to pay in order to reach

GHG emissions (i.e. solution “B”)

preferred as they not only present a well

economical cost performance, but

The model also supports the decision maker with

provides the best performance that could be achieved for any

dimensions (by considering one single objective function

knowing the precise cost to pay in order to reach the desired environmental and social

performance levels. Finally, it allows

change under small variations of

shown in Figure 6. In particular,

exactly the minimal cost (NB:C =0.5% (NB:C ≤ 0,5%); and thirdly,

NB:C ≤ 3%). Therefore, Figure 6

verify the improvements that can be reached when

Figure 6. Environmental and social

• Complete case

The complete case considered the three species

process of planning/grading. T

considerably as the number of product types increases

variables and constraints increase significantly)

the final products into several products

various sections (2” x 3”, 2” x 4”,

“C”, one realizes that the price to pay in order to reach a slight improvement with regards to

GHG emissions (i.e. solution “B”) is very high. Thus, the solutions within “C”

present a well-balanced trade-off between GHG emission

but they also present good social performance.

supports the decision maker with other insightful information.

the best performance that could be achieved for any of the three

by considering one single objective function without the rest). Second,

the precise cost to pay in order to reach the desired environmental and social

it allows analyzing how environmental and social performan

of additional costs the decision maker is willing to pay

In particular, Figure 6 shows three set of solutions. First, solutions

= 0%); secondly, solutions having an additional cost

; and thirdly, solutions having an additional cost of up to 3%

Figure 6 offers various alternatives to the decision maker

verify the improvements that can be reached when he/she is willing to pay higher costs

Figure 6. Environmental and social performance changes obtained for additional cost

considered the three species (spruce, pine, and fir) and also integrated the

The complexity of the mathematical program

considerably as the number of product types increases from 30 up to 138 (the number of

variables and constraints increase significantly). The grading process for example,

the final products into several products ranging from MSR lumber to Dimension lumber with

”, 2” x 4”, 2”x 6”) and lengths (8’, Random Length), which was not

30

with regards to

e solutions within “C” might be

emissions, and

insightful information. First, it

of the three sustainability

Second, it allows

the precise cost to pay in order to reach the desired environmental and social

environmental and social performances

is willing to pay, as

solutions having

additional cost of up to

up to 3% (0,5% ≤to the decision maker, who can

higher costs.

obtained for additional costs

and also integrated the

mathematical program increases

(the number of

for example, classifies

ranging from MSR lumber to Dimension lumber with

, which was not

the case within the simplified version

order to appropriately model the demand in the market

Table 6

# of forests: 3

# of forest contractors: 2

# of sawmills: 3

# of transport modes: 2

# of hiring sites: 3

# of customers: 7

Here we generated Pareto solutions for various

good compromise solutions could still be guaranteed to the decision maker in case the

demand varied keeping the present capacity

of the objectives when the other are not optimized.

and 37 028 constraints, and it took around 40 seconds in average for solving each problem to

optimality.

Table 7: Computing results for the complete case

Weights

Basic demand

Best

Eco ($) (1,0,0) Env (kg CO2eq) (0,1,0) Soc (0,0,1)

We also generated approximated Pareto front

combinations of weights (as in the previous section)

required around 2640 seconds. Non

presented in figures 7 to 10.

the simplified version. We also considered seven customers instead of five in

order to appropriately model the demand in the market (Table 6).

Table 6: Instance #2 characteristics

# of operations: 6 + storage + transportation

# of technologies: 9

# of recipes: 18

# of product types: 138

# of time periods: 6 (1 period = 3 months)

generated Pareto solutions for various demand values. Our aim was


keeping the present capacity. Table 7 reports the best possible value for each

of the objectives when the other are not optimized. Each problem contained 63

constraints, and it took around 40 seconds in average for solving each problem to

the complete case for various demand scenarios

Basic demand

Best Obj.

Value

Demand +5%

Best Obj.

Value

Demand +10%

Best Obj.

Value

Demand +15%

4 767 231 5 054 404 5 341 680 13 204 461 13 204 461 13 204 461

~ 40 ~ 40 ~ 40

We also generated approximated Pareto frontiers for each demand scenario by solving 66

(as in the previous section). Solving the 66 combinations of weights

Non-dominated solutions for different demand scenarios are

31

instead of five in

+ storage + transportation

6 (1 period = 3 months)

was to analyse if


reports the best possible value for each

219 variables

constraints, and it took around 40 seconds in average for solving each problem to

and weights

Demand +15%

Best Obj.

Value

5 629 341 13 937 992

~ 40

by solving 66

Solving the 66 combinations of weights

olutions for different demand scenarios are

Figure 7. Pareto optimums for




We can observe from the results (

solutions with good compromises could still be guaranteed to the decision maker.

compromises are highlighted with the gray circles on

Pareto optimums for Basic Demand (66 combinations of weights).

Pareto optimums for Basic Demand +5% (66 combinations of weights).



lts (Figures 7 to 10) that even if the demand increases, Pareto

with good compromises could still be guaranteed to the decision maker.

compromises are highlighted with the gray circles on Figures 7 to 10. This finding

32

Basic Demand (66 combinations of weights).

Basic Demand +5% (66 combinations of weights).



emand increases, Pareto

with good compromises could still be guaranteed to the decision maker. The good

his finding stands for

33

all scenarios. This means that, in case of market opportunities, the SC could still remain

sustainable as good economic, environmental, and social performances are reached for

different demand scenarios.

6. Conclusion

We proposed in this paper an integrated approach for transposing sustainable development

principles to SC planning models. Despite the growing interest for the optimal planning of

sustainable SCs in OR, effective approaches allowing the implementation of the three pillars

(economy, environment, and society) are very scarce. Inspired by the literature on

performance measurement, we designed a method that links sustainability criteria to the SC

decisions, and allows setting coherent performance measures. By linking this method to

mathematical programming, the economic, environmental and social performances could all

be coherently integrated. Indeed, we formulated a MOP encompassing all the three

dimensions of sustainability. To illustrate our approach, we presented and solved the Virtu@l

Lumber case, a realistic case study [53] inspired by the Canadian lumber industry, by using

weighted goal programming. We showed though how the mathematical mode could be used

by the decision maker as a decision support tool to assist her/him in choosing the SC

operations plan that matches best her/his preferences in terms of economic, environmental,

and social performances. Furthermore, we showed through a sensitivity analysis that good

compromises could still be guaranteed for the decision maker for different demand values. In

our future work, we intend to deepen our research on OR decision-making tools integrating

sustainability concerns for the Canadian forest industry, where sustainable development is of

paramount importance in the sector.

Acknowledgments

Funding for this project was provided by la Région Rhône-Alpes and the consortium of

research FOR@C. We address our special thanks to M. Philippe Marier and M. Aziz Belaid.

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We focus in the optimization of the sustainable performance of a supply chain.

We propose an integrated approach linking performance measurement to multi-criteria optimization.

An accurate mathematical formulation for divergent processes is presented.

We apply our approach to an academic case inspired by an industrial application.

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An integrated approach for sustainable supply chain planning