Multiobjective optimisation model for the selection of critical suppliers integrating sustainability criteria

Abstract

Most companies are seeking their supplier base around the world. However, sourcing from a global supply base exposes buying companies to a notable set of risks and naturally increases transportation distance with the associated environmental consequences. In this study, we propose a multiobjective order allocation model for selecting primary and backup suppliers in a global supply chain setting. Our model explicitly minimises product costs, transportation costs and the cost of exceeding CO2 allowances within total procurement cost, while also minimising lead-time, sustainability risks and greenhouse gas (GHG) emissions. We present a case study where our model is applied to a global manufacturer of consumer goods and the current supply scenario is compared against an optimal scenario given by the proposed model. Even though total procurement cost is given the highest priority, the optimal scenario (which assigns orders to primary suppliers locally located) represents important advantages in relation to all the criteria evaluated.

Full text

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nt. J. Operational Research, Vol. 33, No. 2, 2018
Copyright © 2018 Inderscience Enterprises Ltd.
Multiobjective optimisation model for the selection of
critical suppliers integrating sustainability criteria
Aineth Torres-Ruiz* and A. Ravindran
Industrial Engineering Department,
The Pennsylvania State University,
State College, PA, USA
Email: azt113@gmail.com
Email: axr32@engr.psu.edu
*Corresponding author
Abstract: Most companies are seeking their supplier base around the
world. However, sourcing from a global supply base exposes buying
companies to a notable set of risks and naturally increases transportation
distance with the associated environmental consequences. In this study, we
propose a multiobjective order allocation model for selecting primary and
backup suppliers in a global supply chain setting. Our model explicitly
minimises product costs, transportation costs and the cost of exceeding CO2
allowances within total procurement cost, while also minimising lead-time,
sustainability risks and greenhouse gas (GHG) emissions. We present a case
study where our model is applied to a global manufacturer of consumer goods
and the current supply scenario is compared against an optimal scenario given
by the proposed model. Even though total procurement cost is given the highest
priority, the optimal scenario (which assigns orders to primary suppliers locally
located) represents important advantages in relation to all the criteria evaluated.
Keywords: supplier selection; supply risk; green procurement; multiobjective
optimisation; goal programming; sustainable procurement; global supply chain;
GHG emissions.
Reference to this paper should be made as follows: Torres-Ruiz, A. and
Ravindran, A. (2018) ‘Multiobjective optimisation model for the selection
of critical suppliers integrating sustainability criteria’, Int. J. Operational
Research, Vol. 33, No. 2, pp.208–238.
Biographical notes: Aineth Torres-Ruiz received her Doctorate degree in
Industrial Engineering from The Pennsylvania State University in 2015. She
received her MS in Forest Resources and Operations Research and MEng in
Industrial Engineering from the same university. She has taught courses in
supply chain planning and lean manufacturing at the Instituto Tecnologico de
Monterrey (ITESM) in Mexico. Her research interests include the application
of operations research methods and data science to sustainable supply chain
optimisation and healthcare delivery systems. She is also a member of the
Institute of Industrial Engineers and of the Society of Women Engineers.
A. ‘Ravi’ Ravindran is a Professor and past Department Head of Industrial and
Manufacturing Engineering at the Pennsylvania State University. Formerly,
he was a faculty member in the School of Industrial Engineering at Purdue
University for 13 years (1969–1982) and at the University of Oklahoma for
15 years (1982–1997). He received his BS in Electrical Engineering with
honours from India. His graduate degrees are from the University of California,
Berkeley, where he received his MS and PhD in Industrial Engineering and

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ultiobjective optimisation model for the selection of critical suppliers 209
Operations Research. His area of specialisation is operations research with
research interests in multiple criteria decision-making, financial engineering,
healthcare delivery systems and supply chain optimisation. He has published
six books and over 100 journal articles in operations research. His latest book
on supply chain engineering has won the Book-of-the-Year Award in 2013
from the Institute of Industrial Engineers.
1 Introduction
Critical items are those that have low cost but a high supply risk. Therefore, for critical
items, the primary objective is to reduce total risk even if that comes at a higher price
(Kraljic, 1983; Bensaou, 1999). Although these items represent a small portion of the
total cost of procurement, they show a very high level of service disruption. Moreover,
because there may be very few suppliers who could supply critical items, companies
often look at global sourcing. Corporations buy from foreign suppliers for many reasons,
including to establish a presence in foreign markets, to increase their potential suppliers,
to react to competitors by lowering prices or to access unique supplies/capabilities
(Ravindran and Warsing, 2013). Global sourcing has grown steadily over the past few
decades and it is expected to continue growing in response to increased specialisation by
country and region (Shaw et al., 2013).
Supplier pre-qualification refers to the value assessment of suppliers according to key
sourcing requirements of the company. Supplier selection, or final choice, includes the
actual identification of the best suppliers. Here, the key problem is the allocation of
orders and quantities (frequency and volume) that are optimal. The selection of criteria
for supplier evaluation is usually impacted by the company’s objectives and the industry
sector where the company operates as well as by the product type (Vokurka et al. 1996).
However, there are certain shifts in the way the world operates that can bring
company-wide changes across sectors. For instance, the advent of the just-in-time
philosophy assigned greater priority to criteria related to on-time delivery (Agarwal et al.,
2011). Later, when outsourcing appeared as a key strategy for firms, geographic location
became a top criterion. Today, sustainable procurement is considered a critical priority by
90% of European CPOs (Van Hoek, 2012). Sustainable procurement means “making sure
that the products and services an organisation buys achieve value for money and generate
benefits not only for the organisation, but also for the planet” (ICLEI-Europe, 2015).
However, transportation and other supply chain (SC) activities inherently related to
global sourcing are major contributors to greenhouse gases (GHGs) which include
emissions of carbon dioxide (CO2), methane and other hydrocarbons, as well as nitrous
oxide (N2O). Around 19% of the energy consumption and almost a quarter of the
energy-related CO2 emissions worldwide result from logistics and transportation
activities (International Energy Agency, 2010). The US Environmental Protection
Agency (EPA) estimates that during the period from 1990 to 2010, transportation-related
emissions rose by 18% (Environmental Protection Agency, 2012). Figure 1 shows how
the overall GHG emitted by truck transportation in the USA consistently increased
between 1990 and 2006 while the emissions of other transportations modes remained
stable. As transportation and logistics systems continue to integrate, their impacts on the
physical environment will become more complex. Considering current worldwide trends

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in transportation mode usage, transportation demand is expected to increase by 80% by
2050. As a consequence, worldwide transportation related emissions are projected to
nearly double in 2050 (International Energy Agency, 2010). Even an improvement in
energy efficiency will not be sufficient to counter balance this increase in global
emissions of GHGs (Hoen et al., 2014). Unless transportation-related emissions are
reduced significantly, it will be very difficult to achieve the target set by the
Intergovernmental Panel on Climate Change (IPPC) of a 50% reduction in total carbon
emissions by 2050 (Edenhofer et al., 2014).
Figure 1 GHG emissions from US freight sources
Recognising this threat, governmental regulatory frameworks to reduce GHGs emissions
are currently being implemented around the globe (Hoen et al., 2013, 2014). As a
consequence, companies are facing new realities that need to consider the existing
mechanisms to meet new legal obligations and reduce their carbon footprint (Chaabane
et al., 2011).
However, while most companies’ initiatives have focused on reducing emissions
related to physical processes (e.g., replacing energy inefficient equipment and facilities,
finding less polluting sources of energy, or instituting energy savings programs), they
tend to overlook business practices and operational policies as potentially significant
sources of emissions (Benjaafar et al., 2013). For instance, to minimise financial risk in
the face of uncertain demand, companies keep less inventory, which requires them to
make smaller but more frequent shipments to support reduced lead-times. While these
‘lean’ practices may minimise manufacturing waste, they rarely consider the GHG impact
associated with more frequent transportation, which can be high. Moreover, many
companies are accelerating their spending on faster kinds of transportation
(i.e., motor-trucks and other vehicles- and air). These transportation modes have the most
unfavourable environmental impact per ton mile. Motor transportation is four times less
fuel-efficient per ton mile than rail (Facanha and Horvath, 2007), and emissions from
airfreight can be 600 times higher than those from rail or ocean shipping and nearly
90 times higher than those from motor transportation (Golicic et al., 2010).
The most likely regulations that may affect transportation in the near future include
the following (Hoen et al., 2014; Palak et al., 2014):

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ultiobjective optimisation model for the selection of critical suppliers 211
1 Setting a carbon cap on the amount of GHG emissions: Under this regulation firms
are limited to generate a certain quantity of emissions based on parameters as
location, type of process and company size. As a result, the total carbon emitted over
a finite horizon cannot surpass this cap.
2 Establishing a carbon (or diesel) tax: An alternative to strict caps on emissions is not
to restrict emissions but instead penalise emissions using a carbon tax. A carbon tax
can take on a variety of forms. In its simplest form, the tax is a financial penalty
linear in the number of carbon units emitted.
3 Inclusion in or creation of a separate emission trading schemes (ETS): Here firms
are allowed to emit more than their prescribed caps but are penalised to buy an
amount of carbon credits equivalent to the amount of emissions that exceed the cap.
Firms are also rewarded for emitting less than their caps by receiving tradable credits
equivalent to the difference between their caps and their actual emissions.
In response to the observed increase in environmental and social (E&S) awareness within
SCs, several papers related to sustainable SC management have been published recently.
However, most of the academic papers on the topic have focused on the management
(qualitative) side with almost an insignificant number of studies proposing quantitative
models. In Seuring’s (2013) study, only 36 out of 309 surveyed articles included a
quantitative approach to sustainability in the purchasing function. A different study
carried out by Genovese et al. (2013), which reviewed only papers on green supplier
selection, found no more than 25 articles during the period 2007–2010. In this paper, we
propose the implementation of a two phase methodology that jointly addresses global
supplier selection and the minimisation of GHG emissions, while considering ETS and
the exposure to sustainability risks. Our methodology integrates the works of Bilsel and
Ravindran (2011), Chaabane et al. (2011), Kungwalsong and Ravindran (2012) and
Kungwalsong (2013). In the first phase, a sustainability risk assessment of suppliers is
implemented. For this, we use the supplier sustainability risk assessment framework
developed in Torres-Ruiz (2015), which considers economic, E&S criteria in the
evaluation of short and long-term supplier risks. Then, in phase 2, a multi-objective
mixed integer linear program (MILP) is developed for order allocation among a primary
and a backup supplier. In addition to sustainability risk, the MILP model optimises
lead-time, GHG emissions and total purchase cost (which includes product and
transportation costs as well as costs resulting from exceeding the allowed cap of GHG
emissions). Our methodology represents a unique approach that provides a
comprehensive framework linking traditional decision making related to procurement
(i.e., optimisation of logistic costs and lead times) with the mitigation of sustainability
risk related to:
1 the minimisation of supplier sustainability risk
2 the minimisation of GHG emissions from production and transportation
3 the minimisation of costs in carbon trading.
Moreover, our approach provides a risk mitigation mechanism for supply disruptions by
allowing the selection of backup suppliers.

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In Section 2, we present a literature review of the mathematical models addressing
global sourcing and transportation, particularly those incorporating environmental
impacts and ETSs. Then, the proposed framework for the selection of critical suppliers
and the MILP model are introduced in Section 3. Section 4 presents the solution
methodology. Section 5 includes a case study applied to a multi-national manufacturer of
consumer goods. Case study results obtained are discussed in Section 6 and the
conclusions and further research are presented in Section 7.
2 Literature review
2.1 Quantitative models for supplier selection
The process of supplier pre-qualification involves reducing the initial pool of suppliers,
through a pre-screening process, where minimum acceptance specifications are required.
Suppliers are evaluated using multiple criteria ranking methods to select a portion of the
suppliers. The criteria considered may be quantitative and/or qualitative. Several ranking
methods have been used in the multicriteria decision making literature (Masud and
Ravindran, 2008). Ravindran and Wadhwa (2009) and Ravindran and Warsing (2013)
provide a good discussion of these methods in the supplier pre-qualification context. Ho
et al. (2010) presented a review of multiple criteria approaches mentioned in 78 articles
appearing in international journals between 2000 and 2008. Agarwal et al. (2011) offered
a different review based on 68 articles published between 2000 and 2011 related to
supplier evaluation and selection. According to these studies, the most common multiple
criteria ranking methods for supplier pre-qualification include Lp metric, linear weighting
methods (rating, borda count, analytical hierarchy process), multi-attribute utility theory,
cluster analysis and data envelopment analysis.
During the final choice phase, or the supplier selection phase, the short listed
suppliers are evaluated more extensively. The problem here is the allocation of orders and
quantities (frequency and volume) that are optimal. While the identification of suppliers
is more strategic in nature, the allocation issues are regarded as tactical decisions. Here,
linear weighting methods (appropriate for the phase of pre-qualification) and total cost of
ownership methods are generally used in single sourcing strategies, where the entire order
is assigned to one supplier. Mathematical programming models are generally
recommended for multiple sourcing situations. These models allow the inclusion of
constraints related to capacity, delivery time, quality, and others, where suppliers are
selected along with their order allocations. One of the disadvantages of the mathematical
programming method is its failure to account for qualitative factors that may affect a
supplier’s performance. This is addressed by some authors through the development of
hybrid approaches that use AHP or MAUT in the pre-qualification phase and for the
determination of weights of objectives. The articles on multiple sourcing are broadly
classified in two categories:
a single objective
b multiple objectives.
Multiple objective models deal with optimisation problems involving two or more
conflicting criteria. A common method for solving multiple objective models is goal

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programming (GP). In GP, all the objectives are assigned target levels for achievement as
well as a relative priority/weight on achieving these levels. Targets are goals to aspire for
and not absolute constraints. The objective function of the GP model is to minimise the
prioritised/weighted deviations of the objectives from their target levels (Ravindran and
Warsing, 2013).
Most approaches to supplier selection in the literature that consider order allocation
assume that the transportation costs are either managed by suppliers and, therefore,
considered to be a part of the unit price; or that transportation costs are managed by the
buyer and, therefore, considered to be a part of the setup/ordering cost (Warsing, 2008).
However, these assumptions avoid addressing the impact that specific transportation
costs may have in the planning and allocation of resources (i.e., focusing efforts in
improving costs due to transportation inefficiencies rather than in overall procurement
costs). Some of the studies that specifically address transportation costs during supplier
selection through mathematical programming include: Kasilingam and Lee (1996) who
developed a mixed linear integer model to select part vendors and determine order
quantities. Their model includes a chance constraint for the demand. The objective was to
minimise the sum of purchasing and transportation costs along with fixed costs for
establishing vendors, and the fixed and variable costs of low quality parts. Li et al. (2010)
introduced an integrated transportation-inventory model, where the transportation
process, transportation cost, transportation time and transportation capacity may vary
between the two adjacent nodes according to the transfer between the various
transportation modes. They minimise total cost, which consists of transportation cost,
inventory cost, stock-out cost and time cost using a normal distribution. Fang (2010) built
a 0-1 mixed integer program seeking to maximise profit of the SC related to sale price,
product manufacturing cost and the transportation cost subject to response time and flow
rate of equilibrium containers in an intermodal transportation environment. Kungwalsong
and Ravindran (2014) developed a multi-criteria mathematical programming model that
aids in the design of global SC networks. Transportation costs are estimated based on
fixed shipping costs when a particular link is selected. Bilsel and Ravindran (2011)
proposed a multiobjective chance constrained programming model for supplier selection,
which identified primary and backup suppliers under uncertainty. Transportation costs
were only considered implicitly within the variable costs in the objective function.
2.2 Quantitative models for sustainable supplier selection
Considering the need for analytical models that evaluate the environmental impact of
SCs, a number of studies have extended traditional SC management models to account
for carbon emissions due to production, inventory and/or transportation in the SC: Bayat
et al. (2011) showed a case study where the sustainable performance of a SC is analysed
considering two shift modes for six different types of raw material. Factors such as
weight, truck loads and miles are used to evaluate the carbon footprint due to
transportation. They found that rail transportation showed low operation cost and low
carbon footprint impact. However, truck shipments were predictable and cheaper to set
up. Jaegler and Burlat (2010) used discrete event simulation to benchmark SCs composed
of firms with various levels of efficiency, two types of products (depending on weight
and bulk) and four different locations (local, regional, continental and global). They
evaluate their resulting performances in terms of inventory levels, customer service, and

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CO2 emissions due to storage and transportation. Bauer et al. (2010) propose an integer
programming model to identify a transportation network design that minimises total
emissions due to transportation. Arikan et al. (2013) investigated the impacts of
transportation lead time variability on the SC costs and emissions.
Only a few authors have addressed the integration of ETSs within the operational and
SC decisions. Hua et al. (2011) investigated how firms manage carbon footprints in
inventory control management under carbon emission trading mechanisms. They derive
an optimal order quantity and compare it with that for the classical EOQ model by
examining the impacts of carbon cap and carbon price on order size, carbon emissions,
and total cost. Palak et al. (2014) considered the impacts of different carbon regulatory
mechanisms (carbon cap, carbon tax, carbon cap and trade, and carbon offset) on
transportation and inventory replenishment decisions in a biofuel SC. Depending on the
distance travelled and transportation mode accessibility, barge, rail, or truck was used to
replenish inventories. Their goal was to identify suppliers and a replenishment schedule
that minimises total replenishment (purchase plus transportation) and inventory holding
costs. Benjaafar et al. (2013) proposed modifications to various basic inventory models
considering four different regulatory policy settings which include
a mandatory carbon caps
b taxes on the amount of emissions
c ETS
d ETS with firms allowed to invest in carbon offsets.
Bing et al. (2015) present a model for a global reverse SC network requiring waste
reprocessing. They incorporate a sensitivity analysis of various carbon trading scenarios,
where carbon price and emission cap were varied. Finally, Chaabane et al. (2011, 2012)
proposed mixed-integer linear programming models for SC designs that are sensitive to
the carbon market, where carbon emissions and total logistics costs are integrated in the
design of the SC. In Chaabane et al. (2011), carbon trading is integrated within a forward
SC network design through a multiobjective optimisation model. The solution
methodology uses GP and provides decision makers with the ability to understand the
trade-offs between total logistics costs and GHGs reduction. In Chaabane et al. (2012),
the authors consider life cycle assessment (LCA) principles, in addition to the traditional
material balance constraints at each node in the SC. They analyse the impact of carbon
price variations on the SC configuration, the impact of recycling strategies on SC
planning decisions and the final impact of limit on emissions.
2.3 Quantitative models for sustainable supply risk management
Global competition has allowed companies to offer increased product variety and
outsourcing of core operational activities such as manufacturing. These initiatives make
SCs more vulnerable to disruptions caused by multiple factors. In addition, SCs are more
exposed to stakeholder scrutiny, which creates vulnerability to reputation damage, access
to capital and to regulatory compliance. Risk is the probability and severity of adverse
effects (Ravindran et al., 2010). SC risk management can be defined as “the identification
and management of risks within the SC and risks external to it through a coordinated
approach amongst SC members to reduce SC vulnerability as a whole” (University of

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ultiobjective optimisation model for the selection of critical suppliers 215
Cranfield-School of Management, 2002). Multiple authors have considered the
evaluation of environmental performance within supplier selection (Lee et al., 2009;
Büyüközkan and Çifçi, 2012; Tsai and Hung, 2009; Tuzkaya et al., 2009; Bai et al., 2010;
Bai and Sarkis, 2014; Humphreys, 2003; Shalk and Walld, 2011) but not from a risk
perspective. Hoti et al. (2007) indicate that the scientific community has attempted to
measure E&S risk through the form of indexes. Examples of indexes used include the
environmental sustainability index (ESI), the environmental performance index (EPI), the
Dow Jones sustainability indexes (DJSI) and the well being index (WBI). However, the
scholarly literature has overlooked the identification of the type of risks caused
by not addressing E&S risks adequately. Examples of E&S hazards, which are
directly-controllable by SCs include: type of fuel in manufacturing and transportation,
wastewater intensity and unfair labour wages. Non-directly controllable E&S risks
include natural disasters (tornados, droughts, etc.), political unrest, famine, war, etc.
Natural disasters have received more attention in the academic literature (see, for
example: Yang, 2007; Ayyub et al., 2009; Bilsel and Ravindran, 2012; Vazquez-Brust et
al., 2012; Kungwalsong and Ravindran, 2012, 2014) as they have been included in the list
of disruptive risks, which occur infrequently but which can bring considerable damages
to the SC. Risks stemming from supplier irresponsibility in terms of violation of ethical
and environmental standards have only recently become a prominent topic within the
field of supply management and global sourcing.
3 Proposed approach
When selecting suppliers for global sourcing, in addition to cost and strategic
environmental trading schemes, lead time is a factor that needs to be evaluated to ensure
on-time delivery of products. Moreover, given the disruptions faced globally by various
types of threats, internal and external to a supplier operations, it becomes crucial for firms
to be able to assess sustainability risk levels related to each potential supplier. In order to
advance research in this direction, we present the following two phase approach:
x phase 1: perform a supplier sustainability risk assessment
x phase 2: apply mixed integer linear programming (MILP) model to optimise total
logistics cost, lead-time, supply risk and GHG emissions in order allocation.
Specific details about each step are provided in the following sub-sections.
3.1 Phase 1: sustainability risk assessment of critical suppliers
In this step, a risk assessment is performed on potential suppliers of critical items. The
result of this step is a supplier sustainability risk score (SSRS), which will be used in
phase 2. Figure 2 represents the hierarchies used for this assessment. Risk is evaluated
with respect to two main sources of hazards: supplier country hazards and supplier risks.
A hazard is any source of potential damage, harm or adverse effects on something or
someone under certain conditions (Vazquez-Brust et al., 2012). Economic, E&S hazards
are considered at the country and at the supplier level. In addition, risk depends on the
type of risk management practices, which include risk monitoring and risk mitigation
practices. Risk monitoring activities can include asking the suppliers to respond to

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periodic questionnaires, the actual certification of working systems and the
implementation of audits to corroborate the practices implemented by the suppliers.
Strategies for mitigating sustainability risks include the implementation of adequate
collaborative and development practices with the suppliers (practices that promote the
transfer of know-how, joint development of products, etc.). Once data are collected for all
the risk indicators, a combination of AHP and three-point rating methods is used to
obtain a numerical assessment (i.e., the SSRS) for each supplier. A unique contribution of
this framework is that it integrates the opinion of multiple stakeholders and also
takes into consideration factors affecting short and long term sustainability of the
supplier-buyer relationship as well as directly and indirectly controllable risks. For more
details on how to obtain the SSRS refer to Torres-Ruiz (2015).
Figure 2 Decision hierarchy for sustainability risk assessment of individual suppliers
3.2 Phase 2: MILP multiobjective model to minimise logistic objectives and
sustainable procurement risks for global sourcing under a carbon
emissions trading scheme
In phase 2, supplier risk is optimised along with logistic costs, lead-time and GHG
emissions taking into consideration ETS. In addition, the proposed mathematical model
allows the identification of backup suppliers, who will supply products in the case of
unexpected SC disruptions.
Under an ETS CO
2 is tradable. This system is based on the allocation of
units to a company for exceeding its intensity-based GHG emissions reduction targets
[One carbon credit equals the right to emit one metric ton of carbon dioxide equivalent

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ultiobjective optimisation model for the selection of critical suppliers 217
(CO2e), which is a broadly accepted measure for global warming. A GHG global
warming potential (GWP) measures its ability to trap heat in the atmosphere in relation to
the warming potential of CO2, which is set at a value of 1. For example, the GWP value
of methane is 21, which means that a metric ton of methane is approximately 21 times as
effective at warming the atmosphere compared to a metric ton of CO2. Thus, in terms of
CO2 equivalents, a metric ton of methane is the same as 21 metric tons of CO2.]. At the
end of each compliance period, the emissions of the company are verified. Each emitter
must then offset its GHG emissions against its intensity-based GHG emissions reduction
target established by the government. The discrepancy between the imposed target and
the actual emissions may be offset by, among other things, the purchase of units on the
domestic market. In addition to internal reductions, large emitters will be able to buy
units from the carbon market in order to ensure compliance with their GHG emissions
reduction obligations. On the other hand, those companies with emissions less than the
cap will have the possibility to sell credits in the carbon market and generate revenue.
Thus, ‘‘carbon management’’ consists of taking the decision on the most cost-effective
strategy to be in compliance either with environmental regulation or with voluntary
targets.
For our research, we combine the works of Bilsel and Ravindran (2011) and
Chaabane et al. (2011) and introduce a mathematical model for managing global sourcing
using a portfolio of primary and backup suppliers that meets logistic cost, lead-time,
supply risk and environmental emissions objectives. The total logistic cost objective
includes fixed and variable costs. Variable costs include raw material acquisition costs,
transportation costs and GHG emissions costs. Transportation cost is based on the cost
per unit incurred by the use of different transportation modes. Within the logistic costs,
we also include costs resulting from exceeding the GHG carbon cap allocated to direct
sourcing. By factoring transportation costs and the cost of environmental emissions in the
objective, companies can motivate their suppliers to implement more efficient ways of
transportation in terms of both operational and environmental costs. A second objective is
lead-time and a third objective is sustainability supply risk. The third objective
incorporates the supplier risk scores (SSRS) calculated in phase 1. Finally, a fourth
objective seeks to optimise GHG emissions levels to facilitate the analysis of tradeoffs or
win-win situations between sustainability goals and the other company goals. GHG
emissions are measured in terms of CO2e.
The notations to be used in the optimisation model are the following:
Sets
i products (i = 1, 2, 3, …, I)
j suppliers (j = 1, 2, 3, …, J)
r supply levels.
Note: primary suppliers are assigned to level 1, i.e., r = 1. Levels 2, 3, … represent
backup suppliers who will be used in order, when a primary supplier has a supply
disruption.

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Parameters
Capij capacity of product i for supplier j
Fjr fixed ordering cost of supplier j at supply level r
Pijr price of product i from supplier j at supply level r (note: price varies depending
on whether a supplier is primary or backup)
Lijr lead-time of product i by supplier j at supply level r (in days)
Di mean demand of product i (in tons)
SRSj sustainability risk score of supplier j
TCij cost of transporting product i by supplier j
GC cost per ton of CO2 equivalent units
GTEFj GHG CO
2 emission factor related to the transportation of goods coming from
supplier j
GPEFj GHG CO
2 Emission Factor related to production of products coming from
supplier j
DISj distance travelled from supplier j
Ej energy conversion factor related to supplier j
Lim GHG emissions allowances (the cap fixed by government regulations or
corporate strategy)
p max number of primary suppliers that can be chosen.
Continuous decision variables
Z objective function (Z1, Z2, Z3, Z4)
xij1 quantity in tons of product i ordered from supplier j at supply level 1
(primary supplier); xijr = 0 for r > 1.
Discrete decision variable
zijr binary variable is 1 if supplier j is used at supply level r for product i and 0,
otherwise.
Objectives
The conflicting objectives used in the model are minimisation of total logistic costs,
lead-time, supply risk and GHG emissions. The mathematical expressions for these
objectives are as follows:
Total logistics cost (Z1) includes three components: purchasing cost, transportation cost
and GHG emissions costs. Primary suppliers are those who meet regular demand, while
backup suppliers meet demand in case of disruptions or when demand variability cannot
be covered by the primary suppliers. Primary suppliers are assigned to supply level one

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ultiobjective optimisation model for the selection of critical suppliers 219
while other suppliers are sequentially assigned to levels from two to ,
c
r ,
c
drJ
where J
is the number of suppliers and
c
r is the maximum number of primary and backup
suppliers. The model is designed to assign suppliers at consecutive supply levels to
provide a plan for risk mitigation when there is supply disruption. This assumes that a
backup supplier will be used only when a disruption occurs. The backup supplier will be
on short notice and will not have readily available shipments to be able to provide a high
level of service. Therefore, a backup supplier at level r is assumed to demand a higher
price and have a longer lead-time than a supplier assigned to level r – 1. Overall, the
buyer is willing to accept the decreased performance in service in order to minimise the
amount of lost sales or backorders.
Z1.1: Purchasing cost is given by:
11
11
11
cc
 

¦¦¦ ¦¦ ¦¦¦
IJrp IJ IJrp
j
r ijr ij ij ijr ijr
ijr ij ijr
F
zPx Pz (1.a)
Since the buyer will not order from a backup supplier until necessary, we assume that the
fixed costs of backup suppliers would be smaller than those of primary suppliers. Also,
fixed costs are assumed to be smaller for suppliers at level r – 1 than for suppliers at level
r. However, the buyer would still need to cover fixed costs for backups as he/she may
still have to sign a contract with the backup suppliers to be able to use them when needed.
Therefore, the fixed cost term 1
1
()
c
¦¦¦
IJrp
ijr ijr
ijr Pz covers all assignment levels to
account for both primary and backup suppliers. Variable costs for raw materials
acquisition are represented by two terms:
1 11
¦¦
IJ
ij ij
ij
Px
2 1
2.
c
¦¦¦
IJrp
ijr ijr
ijr Pz
The first term corresponds to the product price given by primary suppliers. The second
term covers r from 2 to 1
crp and can be considered as the opportunity cost related to
backup suppliers. This term involves the binary variable zijr since no shipments are
received from backup suppliers. Opportunity costs are considered in the objective in
order to reduce the ‘cost’ incurred by the next best options. In other words, to ensure the
best choice among the potential backup suppliers.
Z1.2: Transportation costs given by equation (1.b) are based on total transportation cost
per ton of product delivered from supplier j. Each supplier is assumed to use a particular
choice of transportation mode and the same mode is used irrespective of the supply level.
Therefore, transportation costs will be constant irrespective of the supply level assigned.
1
12
c

¦¦ ¦¦¦
IJ IJrp
ij ij ij ijr
ij ijr
TC x TC z (1.b)
Although transportation cost is also a variable cost we separate it from purchase price in
order to provide incentives to improve the efficiency of transportation. The expression for
the transportation cost is also broken into primary and backup suppliers similar to the
purchase cost.

220
A
. Torres-Ruiz and A. Ravindran
Z1.3: Costs of GHGs given by equation (1.c) include the costs per ton of CO2 equivalent
units emitted into the atmosphere (GC) and the GHG amount emitted through both the
transportation and the production processes. The GHG emissions related to transportation
take into account the following:
a A GHG emission factor (GTEFm) that depends on the type of fuel related to the
transportation mode used by the supplier. Table 1 lists the emission factors estimated
for fuels used by various modes of transportation according to the Standard
EN16258: “Methodology for calculation and declaration of energy consumption and
GHG emissions of transport services” developed by the European Association for
Forwarding, Transport, Logistics and Customs Services (CLECAT) (Shmied and
Knörr, 2012). These factors refer to the direct and indirect emissions attributed to
vehicle operation and energy production processes1.
b Distance travelled (DISj) by the product delivered by the supplier
c An energy conversion factor (Ej), which is used to estimate the amount of energy
consumption, based on the characteristics of the transportation mode used by a
supplier. Table 2 lists the energy conversion factors estimated by the CECLAT for
standard vehicles used in various transportation modes to transport volume and bulk
products.
d The weight of the order placed with the supplier (xijr)
The GHG emissions from production result from multiplying the production GHG
emission factor (GPEFj) of a given product by the total weight of the quantity ordered
(xijr). The amount of GHG CO
2 emissions per ton of product for different types of
industrial processes can be obtained from the database on GHG emission factors
developed by IPCC (2012).
Table 1 GHG emission factors for fuel types
Fuel type CO2 emissions
kgCO2e/kg kgCO2e/l
Diesel 3.9 3.24
Jet kerosene 3.88 3.1
Heavy fuel oil (HFO) 3.41 3.31
Table 2 Energy conversion factors for standard vehicles used in various transportation modes
to transport volume and bulk products
Mode Fuel type
Energy consumption
Volume goods Bulk goods
Truck (24t–40t) Diesel (litre/tkm) 0.033 0.016
Rail 1,500 (long train) Diesel (litre/tkm) 0.009 0.006
Ship intracontinental Heavy fuel oil (kg/tkm) 0.0123 0.0051
Air (long distance) Jet kerosene (kg/tkm) 0.267 0.267a
Note: aDue to lack of approximate estimations for bulk goods, this value is assumed to be
equal to that for volume goods.

M
ultiobjective optimisation model for the selection of critical suppliers 221
The allowable carbon cap is subtracted from the sum of the GHGs emitted through both
transportation and production [see equation (1.c)]. The cap limit is assumed to be known.
A positive value from this difference implies that the buying company is exceeding its
allowance limit and, therefore, by law will need to pay for new allowances. A negative
value implies that the company emitted less than the allowable limit and, therefore, has
allowances available to sell or trade which will represent an additional source of income
to the company. The binary variable zijr is assigned to backup suppliers in order to reduce
the cost incurred by the next best option.


1
1
2
c
ª

«
«
¬
º

»
¼
¦¦
¦¦¦
IJ
ij j j j j
ij
IJrp
ijr j j j j
ijr
GC x GTEF DIS E GPEF
zGTEFDISE GPEF Lim
(1.c)
The complete expression for the total logistic cost (Z1) objective is given in equation (1)
by combining equations (1.a), (1.b) and (1.c):


11
12
1
12
1
1
2
1
cc
 
c
c


ª
  
«
«
¬
º

»
¼
¦¦ ¦ ¦¦ ¦¦ ¦
¦¦ ¦¦¦
¦¦
¦¦¦
rp rp
IJ IJ IJ
jr ijr ijr ijr ijr ijr
ijr ij ijr
IJ IJrp
ij ij ij ijr
ij ijr
IJ
ij j j j j
ij
IJrp
ijr j j j j
ijr
ZFzPzPz
TC x TC z
GC x GTEF DIS E GPEF
zGTEFDISE GPEF Lim
(1)
Lead-time (Z2) consists of the summation of the product of lead-time of each product and
the quantity supplied over all the products, suppliers and supplier levels. The second term
represents the lead-time opportunity cost of back up suppliers.
1
11 2
2c

¦¦ ¦¦¦
IJ IJrp
ij ij ijr ijr
ij ijr
Z
Lx Lz (2)
Supplier risk (Z3) considers the product of the sustainability risk scores obtained in Step
1 by the quantity supplied over all the products, suppliers and supplier levels. This
represents a weighted average risk score and also considers opportunity costs of backup
suppliers.
1
12
3c

¦¦ ¦¦¦
IJ IJrp
j
ij j ijr
ij ijr
Z
SRS x SRS z (3)
GHG emissions (Z4) are obtained from the sum of GHG emissions (in kilograms of
CO2e) from production and transportation of products from primary suppliers as
indicated in the cost objective (Z1). The terms in these two equations representing backup
suppliers can be interpreted as opportunity costs since these suppliers do not supply
products on a regular basis.

222
A
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

1
1
2
4
c


¦¦
¦¦¦
IJ
ij j j j j
ij
IJrp
ijr j j j j
ijr
Z x GTEF DIS E GPEF
zGTEFDISE GPEF
(4)
The constraints in the model are as follows:
1 Demand constraints: The buyer demand for product i is satisfied entirely by the
primary suppliers.
1 
¦J
ij i
j
x
Di (5)
2 Capacity constraints: Each primary supplier j has a maximum capacity for product i,
given by Capij. Total order placed with this supplier is limited by its capacity which
is also based on product weight.
11
,d
ij ij ij
x
Cap z i j (6)
3 Maximum number of primary suppliers: Limits the total number of primary suppliers
for any one product to p where .
c
d
dpr J The value of p is determined
exogenously by the buyer based on its outsourcing strategy. When p = 1 the model
represents a single sourcing strategy.
1 d
¦J
ij
jzpi (7)
4 Maximum number of backup suppliers: Ensures that, after determining up to p
primary suppliers, the remaining suppliers are assigned as backups. Note that once
the p primary suppliers are determined, there remains ()
c

rp backup suppliers and,
therefore, suppliers can be assigned up to level 1.
c

rp
1 , 2,..., 1.
c
 
¦J
ijr
jzirrp (8)
5 Supplier level constraint: Any given supplier is assigned to only one supply level for
the same product. In other words, a supplier can be primary or backup for a given
product, but not both. However, a supplier can be a backup for more than one
product.
1
11 ,
c

¦rp
ijr
rzij (9)
6 Binary variables: zijr is used to quantify fixed costs for primary suppliers and
opportunity costs for secondary suppliers in the objective.
(0,1) , ,
ijr
zijr (10)
7 Product quantity constraint:
10 ,t
ij
x
ij (11)
for 2, 0 ,t 
ijr
rx ij (12)

M
ultiobjective optimisation model for the selection of critical suppliers 223
The sustainable sourcing model described before has the objective to identify trade-offs
or win-win opportunities among supplier economics, delivery, risk and environmental
performance. The economic objective is evaluated by the total logistic cost. Delivery is
evaluated by lead-time. Risk by a sustainability supply risk score and the environmental
performance is evaluated by the total emissions of GHG.
4 Solution methodology
We solve the order allocation multi-objective problem using GP. In GP, all the objectives
are assigned target levels for achievement and a relative priority on achieving these
levels. GP treats these targets as goals to aspire for and not as absolute constraints. There
are two types of GP: preemptive and non-preemptive. In the preemptive case, goals at
higher priority must be satisfied before lower priority goals are even considered.
Therefore, the problem reduces to a sequence of single-objective optimisation problems.
In the non-preemptive case, different weights are assigned to each goal turning the
problem into a single-objective optimisation problem, consequently assuming a linear
utility function. Since the nature of the supplier selection problem suggests that the utility
function is nonlinear, implementing a non-preemptive GP model might not be very
realistic; therefore we propose a preemptive GP model to solve the multi-criteria
problem. Using GP represents several advantages:
1 firms can set planning goals related to the supplier selection criteria and policies
2 companies can also assign priorities on these goals, reflecting their relative
importance
3 setting goals allows a company to control the deviation from targets and achieve
tradeoffs for goals in conflict (Mendoza et al., 2008).
In order to formulate a goal program, we need to define goal constraints. A goal
constraint specifies a target value that realistically is the most desirable value for each
objective function. Also, goal constraints (Gi) require the indication of deviational
variables. Deviational variables serve to control the negative (d–) and positive deviation
(d+) from the specified target level. In addition, for preemptive goal programming
(P-GP), we need to indicate a priority ranking for each objective (P1, P2, Pn,).
The P-GP formulation for our global sourcing model, which considers the total
logistics cost goal [equation (14)], the lead-time goal [equation (15)], the risk goal
[equation (16)] and the GHG emissions goal [equation (17)], is the following:
Objective:
1234
1234



M
in Pd Pd Pd Pd (13)
Goal constraints:
x Goal 1: total logistics cost

224
A
. Torres-Ruiz and A. Ravindran


11
11
12
1
12
1
1
2
111
cc
 
c
c



ª
  
«
«
¬
º

»
¼

¦¦ ¦ ¦¦ ¦¦ ¦
¦¦ ¦¦¦
¦¦
¦¦¦
rp rp
IJ IJ IJ
jr ijr ij ij ijr ijr
ijr ij ijr
IJ IJrp
ij ij ij ijr
ij ijr
IJ
ij j j j j
ij
IJrp
ijr j j j j
ijr
Fz Px Pz
TC x TC z
GC x GTEF DIS E GPEF
zGTEFDISE GPEF Lim
dd G
(14)
x Goal 2: lead-time
1
11 2 2
22
c 

¦¦ ¦¦¦
IJ IJrp
ij ij ijr ijr
ij ijr
Lx Lz d d G (15)
x Goal 3: supply risk
1
13
3
23
c 

¦¦ ¦¦¦
IJ IJrp
jij jijr
ij ijr
SRS x SRS z d d G (16)
x Goal 4: GHG emissions


1
1
2
444
c


º

»
¼

¦¦
¦¦¦
IJ
ij j j j j
ij
IJrp
ijr j j j j
ijr
x GTEF DIS E GPEF
zGTEFDISEGPEF Lim
dd G
(17)
Real constraints [equations (5) to (12)]:
Where G1, G2, G3 and G4 are the goals set for logistics cost, lead-time, supplier risk and
GHG emissions, respectively. Since all the objectives are to be minimised, the GP model
will minimise the positive deviations 1234
(,,,)


dddd of the stated goals. The P1, P2, P3,
P4 symbols stand for preemptive priorities, determining the hierarchy of goals. Goals of
higher priority are to be satisfied first, before the lower priority goals are even
considered. In this illustration, total logistic cost is the most important criterion, followed
by lead-time, (sustainable) supplier risk and GHG emissions. P-GP involves solving a
sequence of optimisation problems. In this approach, P1 forces 1

d to be as low as
possible. Then P2 takes over and tries to minimise 2,

d while preserving 1

d equal to the
minimum value achieved under P1 (Masud and Ravindran, 2008). The model is also
subject to the real constraints indicated by equations (5) to (12).

M
ultiobjective optimisation model for the selection of critical suppliers 225
5 Case study
5.1 Data collection
To demonstrate the methodology proposed in Section 4, we used the data contributed by
a global manufacturer of consumer products located in central Mexico. The manufacturer
evaluated his exposure to sustainability risks through its supply base integrated by a total
of 38 different vendors supplying 857 items. A preliminary portfolio analysis showed that
13% of all suppliers could be categorised as critical suppliers. These five suppliers
provided 18 items. None of the suppliers have products in common. Table 3 lists the five
suppliers and their profiles.
Table 3 Profile of the critical suppliers for the case study
Critical
supplier ID
Country of
origin % Spend Number of
items supplied Items ID Type of
item
S01 Brazil 0.23% 7 515–521 Packaging
S02 USA 0.16% 8 555–562
S03 USA 0.03% 1 513
S04 Mexico 0.00% 1 853
S05 Brazil 0.00% 1 491 Ingredient
The company wants to mitigate its risk by assigning backup suppliers for each of the 18
items supplied within the critical segment. For this, they looked for additional potential
suppliers for each product among the existing pool of suppliers and the resulting supplier
list is given in Table 4. Note that suppliers 1 through 5 are the current critical suppliers
for the 18 products.
Table 4 Products and set of potential suppliers identified
Supplier
ID
Item ID
513
515
516
517
518
519
520
521
555
556
557
558
559
560
561
562
491
853
S01 x x x x x x x
S02 x x x x x x x x
S03 x
S04 x
S05 x
S06 x x x x x x x
S07 x x x x x x x x
S08 x
S09 x x x x x x x x
S10 x
S11 x x x x x x x
S12 x x x x x x x x
S13 x x x x x x x
S14 x

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Table 5 Working set of product families and suppliers for this study
Notes: FP1: family of products # 1; FP2: family of products # 2; FP3: family of products # 3
Item ID
FP1 FP2 FP3
Original
supplier
ID
New
supplier
ID
Country
of
origin
518
519
515
516
517
520
521
555
556
557
558
559
560
561
562
491
S01 S01 BR x x x x x x x
S06 S02 MX x x x x x x x
S11 S03 BR x x x x x x x
S13 S04 MX x x x x x x x
S02 S05 US x x x x x x x x
S07 S06 MX x x x x x x x x
S09 S07 US x x x x x x x x
S12 S08 MX x x x x x x x x
S05 S09 BR x
S08 S10 MX x
S14 S11 US x

M
ultiobjective optimisation model for the selection of critical suppliers 227
Given the time constraints of the case study, we include only those products for which the
potential suppliers are already part of the supplier pool and for which at least three
potential backup suppliers are available. Products 513 and 853 (Table 4), do not meet this
requirement. Therefore, they are excluded from further analysis. Based on this, Table 5
lists the 16 products and 11 suppliers that are left to illustrate our methodology with their
countries of origin. For clarification, we assigned new supplier identification numbers
based on the products supplied. Notice that local suppliers from Mexico (MX) are
included for each of the product categories. Also, upon agreement with the purchasing
team, it was decided to group the different items within product families. The reasons for
this are the following:
1 there is commonality among some of the products, which implies that a supplier for
one of the products can easily supply the products within the same product family
2 data on cost is globally estimated for each supplier by the weight of an aggregated
order, which implies that there is no distinction between the prices of individual
items.
Based on this, our problem is simplified to three different families of products and their
potential suppliers listed in Table 5.
5.2 Order allocation by GP
Once the supplier risk scores are obtained, the purchasing team can allocate the product
demand among the potential suppliers. Here, we demonstrate the implementation of the
MILP model proposed in Section 3.2 for the case when there are several potential
suppliers for each product.
5.2.1 Data description
Table 6 lists the product families and the total demand and supplier capacity resulting
from aggregating the individual demands and capacities of the products within each
product family. Note that for product family FP1, the potential suppliers are S01, S02,
S03 and S04. For FP2, the suppliers are S05, S06, S07 and S08. For FP3, there are only
three potential suppliers: S09, S10 and S11.
Table 6 Demand and capacity values corresponding to different product families (TONS)
Item ID Product
family ID
Total
demand Total supplier capacity
515–521 FP1 53.8 69.94 (S01) 62.30 (S02) 67.25 (S03) 62.43 (S04)
552–562 FP2 36.49 47.44 (S05) 40.14 (S06) 38.31 (S07) 42.84 (S08)
491 FP3 2.81 3.09 (S09) 3.65 (S10) 3.09 (S11)
Table 7 lists the fixed costs related to placing an order according to different supply
levels. The product price and transportation cost of each supplier at different supply
levels are listed in Tables 8 and 9 respectively. They are estimated in US dollars (USD)
per ton of product. In general, local suppliers pay the transportation costs, while the buyer
covers the delivery costs for global suppliers. So, transportation costs for local suppliers
equal zero.

228
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indran
Table 7 Fixed ordering cost
Supplier S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11
Supply
level
1 900 550 700 550 900 550 700 700 700 550 550
2 810 495 630 495 810 495 630 630 630 495 495
3 689 421 536 421 689 421 536 536 536 421 421
4 551 337 428 337 551 337 428 428
Table 8 Product prices (USD/ton) offered by different suppliers at various supply levels
Supplier S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11
Supply
level
1 8,045 10,814 13,240 10,417 6,889 7,632 12,323 8,111 352 562 598
2 8,850 11,895 14,564 11,459 7,578 8,395 13,556 8,922 388 618 658
3 9,735 13,084 16,021 12,605 8,335 9,235 14,911 9,814 426 680 724
4 10,708 14,393 17,623 13,865 9,169 10,158 16,402 10,796
Table 9 Transportation cost (USD/Ton)
Supplier S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11
Transportation
cost (USD/ton)
441 0 1,059 0 481 0 919 0 21 0 0
Lead-times are listed in Table 10. Here, it is assumed that, when a backup supplier is
used, deliveries take longer.
Table 10 Lead-times (days) of suppliers at various supply levels
Supplier S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11
Supply
level
1 30 6 12 8 12 6 12 8 30 8 12
2 33 7 13 9 13 7 13 9 33 9 13
3 36 7 15 10 15 7 15 10 36 10 15
4 40 8 16 11 16 8 16 11
The supplier risk scores obtained in phase 1 are listed in Table 11 for the eleven
suppliers. Table 12 lists the parameters necessary to estimate total GHG emissions. The
last column indicates the transportation mode utilised by the supplier. American and
Mexican suppliers use road transportation, while suppliers located in Brazil use either sea
or air transportation depending on the product type. The usual shipping ports are the
Fortaleza terminal in Brazil and Laredo, Texas in the USA.
The GHG emission factors related to production (GPEF) for foil-based and
plastic-based products were obtained from the database on GHG emission factors
developed by IPCC (2012).
Table 11 Supplier risk scores
Supplier S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11
SRS 4.6 3.56 4.16 2.6 3.9 4.2 3.65 4.02 4.27 4.13 4.23

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ultiobjective optimisation model for the selection of critical suppliers 229
Table 12 Supplier distance, energy and GHG emission factors for transportation and
production related to specific suppliers
Supplier GTEF
Distance
(km)
Energy conversion
factor
GPEF
(CO2/ton)
Transportation
mode
S01 3.41 10,140 0.0123 1.7 Sea
S02 3.24 150 0.033 1.6 Truck
S03 3.41 10,140 0.0123 1.7 Sea
S04 3.24 360 0.033 1.6 Truck
S05 3.1 1,250 0.033 0.34 Truck
S06 3.24 230 0.033 0.34 Truck
S07 3.24 1,250 0.033 0.35 Truck
S08 3.24 1,100 0.033 0.35 Truck
S09 3.1 10,100 0.267 0.015 Air
S10 3.24 400 0.016 0.015 Truck
S11 3.24 1,250 0.016 0.015 Truck
To estimate the GHG emissions related to transportation, we use the following formula:
GHG emissions related to transportation
GHG emission factor ( ) Supplier distance ( )
Energy conversion factor ( ) Weight of quantity transported ( )


GTEF DIS
Ex
The amount of fuel consumed in transportation is derived through the energy conversion
factor. The value of this factor varies depending on the type of good being transported
and the transportation mode used. All the products considered in this study are volume
goods with the exception of FP3 which is a bulk product. Different transportation modes
use different fuel types. For example, if we want to estimate how much GHG emissions
are generated for transporting 50 tons of goods delivered by supplier 1, we need to
consider the energy conversion factor for heavy fuel oil (HFO), as this is the typical fuel
used in sea transportation. The GHG emission factor for transportation should also
correspond to this type of fuel. By using the values in Tables 1 and 2 for HFO we obtain:
2 2
3.41 CO e/kg 10,140 km 0.0123 kg/tkm 50 ton 21, 265.10 CO e 
For emissions trading, where GHGs are regulated, one emission permit or allowance is
considered equivalent to one metric ton of CO2 emissions. According to The European
Energy Exchange (EEX, 2014), at the end of September 2014, the cost of one emission
permit (GC) was at 6.19 € or 8.85 USD. The company in our case study has partially
identified its sources of GHG. According to their analysis, agricultural raw materials have
been identified as the main source of CO2 scope 3 (value chain) emissions, with
packaging production contributing an important, but clearly secondary, source of
emissions. The company uses third-party transportation companies (common carriers) to
transport raw materials to manufacturing facilities. The primary GHG emission source
from common carriers is CO2 from diesel fuel combustion. In the past, the level of
allowances allocated to the company, within its western European operations, covered
about 70% of the GHG emissions generated by its manufacturing sites. We consider that

230
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. Torres-Ruiz and A. Ra
v
indran
a regulatory agency will be interested in setting allowance limits taking as reference the
ideal scenario. Since GHG trading has not yet been implemented for operations in the
USA, in our study we assumed an allowance limit for our model based on a 30%
deviation from the ideal amount of GHG emissions.
5.2.2 P-GP solution
We now solve the order allocation model to identify one primary supplier and one backup
supplier for each of the three product families and compare the results obtained under the
current scenario, where the primary supplier is known, versus an optimal scenario, which
minimises the four objectives previously stated: total logistic costs, lead-time, supplier
risk and GHG emissions. First, we determine the ideal values that will serve as reference
to set targets for each objective. Table 13 lists the ideal values obtained considering the
allocation for the three families of products. Ideal values are the best values (minimum)
for each criterion obtained by optimising each criterion independently ignoring other
criteria.
Table 13 Ideal values
Objective Ideal value
Z1:logistic cost $921,813
Z2: lead time 595
Z3: supplier risk 296
Z4: GHG emissions 2,140
The selection of primary and backup suppliers that optimise each objective in the ideal
solution is shown in Table 14. Here it is interesting to note that, for FP1, suppliers 4
and 2 are ideal primary and backup suppliers when Z1 and Z3 are optimised
independently, while the order reverses when we optimise Z2 and Z4. For FP2, supplier 6
is the primary supplier except when optimising Z3 while supplier 5 is the backup when
Z1 and Z3 are optimised separately and 8 is the backup for Z2 and Z4. Finally, for FP3,
the ideal primary and backup suppliers are the same irrespective of the objective that we
are optimising.
Table 14 Primary and backup suppliers corresponding to the ideal solutions of each objective
and each product family
Product family FP1 FP1 FP1 FP1 FP2 FP2 FP2 FP2 FP3 FP3 FP3 FP3
Objective Z1 Z2 Z3 Z4 Z1 Z2 Z3 Z4 Z1 Z2 Z3 Z4
Primary supplier 4 2 4 2 6 6 7 6 10 10 10 10
Backup supplier 2 4 2 4 5 8 5 8 11 11 11 11
In the P-GP model we determine the optimal solution by assigning a priority of 1 to
logistic cost, a priority of 2 to lead-time, a priority of 3 to supplier risk and a priority of 4
to GHG emissions. The solution target is set at 10% above the ideal value for Z1, Z2 and
Z3 and at 30% above for Z4. Table 15 shows the results obtained. Table 16 lists the
primary and backup suppliers for the optimal solution to the P-GP model.

M
ultiobjective optimisation model for the selection of critical suppliers 231
Table 15 Optimal solution for P-GP
Objective Ideal value Target Value
achieved
Goal
achieved?
Deviation
from ideal
(Ideal + 10%)
Z1 $897,081 $986,789 $907,464 Yes –1%
Z2 595 655 595 Yes 0%
Z3 296 326 367 No –24%
Z4 2,140 2,782b 2140 Yes 0%
Note: bIdeal+30%
Table 16 Primary and backup suppliers for each product family according to P-GP
Product family Primary Backup
FP1 Supplier 2 Supplier 4
FP2 Supplier 6 Supplier 8
FP3 Supplier 10 Supplier 11
Notice that in the optimal scenario the target values were achieved for all objectives
except for Z3 (SSRS). Actually, the ideal values were achieved for Z2 (lead time) and Z4
(GHG emissions) but not for Z1 (logistic cost) and Z3. In the optimal scenario, most of
the primary and backup suppliers are located locally in Mexico, except supplier 11 that is
located in the USA. This implies that, by switching to the suppliers shown in Table 16,
the decision manager would obtain (nearly) ideal performance with respect to Z1, Z2 and
Z4 while additional efforts need to be implemented in order to decrease supplier
sustainability risk (Z3).
However, currently, the company uses suppliers 1, 5 and 9 as primary suppliers, with
no backup suppliers. Therefore, next, we apply the P-GP model for the identification of
the backup supplier for the current scenario by keeping the primary suppliers as the
current suppliers used by the company. Table 17 shows the optimal solution obtained and
Table 18 lists the current practice solution.
Table 17 P-GP solution when primary supplier is pre-established based on current practice
Objective Ideal value Target Value
achieved
Goal
achieved?
Deviation
from ideal
(Ideal + 10%)
Z1 $897,081 $986,789 $1,208,904 Yes –35%
Z2 595 655 2,160 Yes –263%
Z3 296 326 414 No –40%
Z4 2,140 35,844 51,206 Yes –2,293%
Table 18 Current primary suppliers and backup suppliers identified through P-GP for each
product family
Product family Primary Backup
FP1 Supplier 1 Supplier 2
FP2 Supplier 5 Supplier 6
FP3 Supplier 9 Supplier 10

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The results shown in Tables 17 and 18 indicate that the current practice is very distant
from an ideal scenario with respect to all objectives. In the current scenario, primary
suppliers are located in Brazil and the USA, while the backup suppliers may be located in
Mexico. Therefore, the performance difference seems to originate in the distance of the
primary suppliers from the buyer’s location.
6 Discussion of results
The values achieved with respect to the four objectives for the current practice and the
optimal P-GP solution are summarised in Table 19. The current practice is not optimal
because long distance transportation has an important impact on our calculations for
logistic costs, lead-time, supplier risk and GHG emissions. Even though we assigned the
highest priority to Total Logistic Costs and the lowest priority to GHG emissions, the
optimal scenario indicates benefits obtained in all the objectives by switching to local
suppliers. The company would incur lower logistic costs (33%), lower procurement risk
(13%), lower lead time (263%) and lower GHG emissions (2293%).
Table 19 Comparison of current practice with the optimal P-GP solution
Objective Current practice
Optimal
P-GP solution
Improvement by
P-GP solution (%)
Z1: logistic cost $1,208,904 $907,464 33%
Z2: lead time 2,160 595 263%
Z3: supplier risk 414 367 13%
Z4: GHG emissions 51,206 2,140 2,293%
Figure 3 Disaggregation of total cost objective (in $USD) by evaluated scenario
Since minimising logistic costs has been defined as the top priority by the company, we
analysed the sources of logistics costs. In Figure 3 we disaggregated the total logistic cost
objective into the purchasing, transportation and GHGs costs for the current and the
optimal scenarios. In the optimal scenario, no transportation costs are incurred by the
company because local suppliers absorb these costs. Also, GHG emissions are negative
because the allowance limit is greater than the total emissions generated by local
suppliers. This reduces the overall logistic costs, if we assume that the company can sell
the allowances not used. In the Current scenario, purchase price is less, but transportation

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ultiobjective optimisation model for the selection of critical suppliers 233
and GHGs costs are incurred due to the long distance travelled by the items. Actually, if
the costs of GHG were not considered, the total logistic cost for the current scenario
would have been lower, even after accounting for transportation costs. This explains why
the current scenario is optimal for the company; because, at present, there is no regulation
mechanism that penalises the emission of GHGs.
To analyse further the source of logistic costs for the current practice, we compare the
GHG emissions per ton of product for each product family. As shown in Figure 4, we
obtain 427 tCO2e for FP1, 128 tCO2e for FP2 and 8,360 tCO2e for FP3! Under the
optimal scenario, all primary suppliers are located in Mexico and GHG emission levels
are not relevant. In the current scenario, FP1 and FP3 have primary suppliers located in
Brazil, while the primary supplier for FP2 is located in the USA. While suppliers 1 and 5
use either sea or ground transportation, supplier 9 uses air transport. This transportation
mode (used by the supplier of FP3) is generating about 94% of all emissions. Although
the demand for FP3 is very low, the energy emission factor for air is about sixteen times
larger than that for trucks (see Table 2 for bulk products). This is an interesting finding,
as it shows that by only changing the transportation mode of supplier 9 to truck or ship
for FP3, the company could reduce the cost for GHG emissions to a level that will make
the current primary supplier acceptable.
Figure 4 GHG emissions per ton of product in Current Practice for different families of products
We have demonstrated how an analysis of costs can help companies understand the
different sources of inefficiencies and better address each of them. In addition to the
logistic cost and GHG objectives, the purchasing team would need to consider the
disadvantages of global sourcing with respect to lead-time and supplier sustainability
risks as shown in Table 19 and make more informed decisions.
7 Conclusions and further research
In this study, we demonstrated the implementation of a two phase decision making
approach for the selection of critical suppliers. In phase 1, we applied the supplier
sustainability risk assessment methodology developed in Torres-Ruiz (2015). In phase 2,
we proposed an MILP order allocation model that incorporates general business and
environmental performance objectives to allocate orders for three different product

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families of a buyer located in central Mexico. Current and optimal scenarios were
compared with respect to their performance regarding each of the four objectives, using
P-GP. The current scenario set the primary suppliers as pre-established and identified
backup suppliers among a set of potential suppliers. The optimal scenario let the model
identify both primary and backup suppliers.
The results indicate that the current practice is far more expensive with respect to all
the objectives. Significant differences exist with respect to logistic costs, delivery time
and GHG emissions. The difference in performance is mainly related to the costs of
offshoring caused by global suppliers, who are the current primary suppliers. The use of
air transportation for one of the product families also increases greatly the costs related to
GHG emissions in the current scenario, which has the greatest impact in overall costs.
The optimal solution suggests an allocation of orders mainly among domestic suppliers.
Additionally, it demonstrates that an optimal solution, not only improves traditional
performance measures, such as cost and lead-time, but also those measures incorporating
environmental and sustainability risk factors, even when the primary objective is to
minimise total procurement cost. Finally, we analysed the sources of costs due to GHG
emissions and demonstrated that, in addition to distance, the choice of transportation
mode plays an important role in total procurement costs.
x Theoretical implications: As far as we know, there is no other study in the scientific
literature that integrates the assessment and management of various types of supply
risks in a comprehensive manner. In this study we assessed traditional risks along
with risks related to GHG emissions and E&S risks. In addition, by optimising these
risks and by identifying backup suppliers, we integrated a risk mitigation mechanism
in our methodology.
x Managerial implications: In a business as usual (BAU) scenario, a company may
find no cost benefits in shifting to local suppliers or to a different transportation
mode. However, new regulations are being implemented around the world. In the
case of Mexico, for example, since January 2015, all the organisations responsible
for emitting more than 25,000 tCO2e are required by law to report their emissions.
Moreover, since 2014, there exists a fuel tax of $3 per ton of CO2 emitted. These are
the first steps intended to bring more stringent regulations for GHG emissions. Under
scenarios like these, companies soon will start to feel the pressure of accounting for
the environmental cost of emitting GHGs because these costs will affect their
profitability. The proposed decision model can be used as a tool for predictive
analyses to prevent potential harms caused to SCs in terms of cost, lead-time, risk
and GHG emissions and possibly helping them look for alternative sourcing
strategies. Moreover, it helps them to be prepared for SC contingencies through the
identification of backup suppliers. The sooner the potential impact is understood, the
sooner and more capable companies will be able to face the coming challenges.
x Research limitations: Our study does not include a sensitivity analyses that could
help determine the impact of changes in carbon prices and carbon caps on the
supplier selection strategy. This would be interesting to analyse considering the
frequent change of carbon prices and the uncertainty in relation to GHG emission
levels. Also, the estimates for GHG conversion factors tend to make generalisations
that need to be carefully considered for each application. For instance, we did not
find a better estimate for the energy conversion factor of bulk products transported

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ultiobjective optimisation model for the selection of critical suppliers 235
by plane (Table 2) and our conclusions regarding emissions by air transport were
made under the assumption that the energy conversion factor for volume products is
the same as for bulk products.
x Future research directions: Our work can be extended in several directions. For
instance, the mathematical model can be used to compare the benefits of
implementing non-fossil fuels as well as other more fuel-efficient technologies for
transportation. Also, we did not consider inter-modal transportation and this could be
an important addition as global SCs usually involve the use of several transportation
modes in the delivery of products. Finally, we presented a strategic model for
supplier selection that calculates GHG emissions, using conversion factors that are
estimated based on general assumptions such as the use of full truckloads or
containers. It would be interesting to propose a model that considers specific
operational decisions of ordering materials from suppliers at different time periods
taking into account the prevailing GHG emissions rules.
Acknowledgements
The authors would like to express their sincere thanks to the referees for their valuable
suggestions and comments that significantly improved the presentation of this paper.
References
Agarwal, P. et al. (2011) ‘A review of multi-criteria decision making techniques for supplier
evaluation and selection’, International Journal of Industrial Engineering Computations,
Vol. 2, No. 4, pp.801–810.
Arikan, E., Fichtinger, J. and Ries, J.M. (2013) ‘Impact of transportation lead-time variability on
the economic and environmental performance of inventory systems’, International Journal of
Production Economics, November 2014, Vol. 157, pp.279–288.
Ayyub, B.M. et al. (2009) ‘Risk analysis of a protected hurricane-prone region II: computations and
illustrations’, Natural Hazards Review, Vol. 10, No. 2, pp.54–67.
Bai, C. and Sarkis, J. (2014) ‘Determining and applying sustainable supplier key performance
indicators’, Supply Chain Management: An International Journal, Vol. 19, No. 3, pp.275–291.
Bai, C., Sarkis, J. and Wei, X. (2010) ‘Addressing key sustainable supply chain management
issues using rough set methodology’, Management Research Review, Vol. 33, No. 12,
pp.1113–1127.
Bauer, J., Bektas, T. and Crainic, T.G. (2010) ‘Minimizing greenhouse gas emissions in intermodal
freight transport: an application to rail service design’, The Journal of the Operational
Research Society, Vol. 61, No. 3, pp.530–542.
Bayat, A. et al. (2011) ‘Sustainably driven supply chains’, IE Transactions, Vol. 43, No. 8,
pp.26–31.
Benjaafar, S., Li, Y. and Daskin, M. (2013) ‘Carbon footprint and the management of supply
chains: Insights from simple models’, IEEE Transactions on Automation Science and
Engineering, Vol. 10, No. 1, pp.99–116.
Bensaou, M. (1999) ‘Portfolios of buyer-supplier relationships’, Sloan Management Review,
Summer, 15 July, p.10.

236
A
. Torres-Ruiz and A. Ra
v
indran
Bilsel, R.U. and Ravindran, A. (2011) ‘A multiobjective chance constrained programming model
for supplier selection under uncertainty’, Transportation Research Part B: Methodological,
Vol. 45, No. 8, pp.1284–1300.
Bilsel, R.U. and Ravindran, A.R. (2012) ‘Modeling disruption supply chain risk management’,
International Journal of Operations Research and Information Systems, Vol. 3, No. 3,
pp.15–39.
Bing, X. et al. (2015) ‘Global reverse supply chain redesign for household plastic waste under the
emission trading scheme’, Journal of Cleaner Production, 15 September, Vol. 103, pp.28–39.
Büyüközkan, G. and Çifçi, G. (2012) ‘A novel hybrid MCDM approach based on fuzzy
DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers’, Expert Systems with
Applications, Vol. 39, No. 3, pp.3000–3011.
Chaabane, A. et al. (2011) ‘Trade-off model for carbon market sensitive green supply chain
network design’, International Journal of Operational Research, Vol. 10, No. 4, pp.416–440.
Chaabane, A., Ramudhin, A. and Paquet, M. (2012) ‘Design of sustainable supply chains under the
emission trading scheme’, International Journal of Production Economics, Vol. 135, No. 1,
pp.37–49.
Edenhofer, O. et al. (2014) Climate Change 2014, Mitigation of Climate Change, Contribution of
Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate
Change, Cambridge University, Cambridge, UK and New York, NY, USA, p.16.
Environmental Protection Agency (2012) Inventory of U.S. Greenhouse Gas Emissions and Sinks:
1990–2010 [online] http://www.epa.gov/climatechange/Downloads/ghgemissions/US-GHG-
Inventory-2012-Main-Text.pdf (accessed November 2014).
Facanha, C. and Horvath, A. (2007) ‘Evaluation of Life-cycle air emission factors of freight
transportation’, Environmental Science and Technology, Vol. 41, No. 20, pp.7138–7144.
Fang, Q. (2010) ‘Optimization model for intermodal transportation networks based on supply
chain’, in ICLEM: Logistics for Sustained Economic Development, pp.2698–2703.
Genovese, A. et al. (2013) ‘Greener supplier selection: state of the art and some empirical
evidence’, International Journal of Production Research, Vol. 51, No. 10, pp.2868–2886.
Golicic, S.L., Boerstler, C.N. and Ellram, L.M. (2010) ‘Greening transportation in the supply
chain’, MIT Sloan Management Review, Vol. 51, No. 2, pp.47–55.
Ho, W., Xu, X. and Dey, P.K. (2010) ‘Multi-criteria decision making approaches for supplier
evaluation and selection: a literature review’, European Journal of Operational Research,
Vol. 202, No. 1, pp.16–24.
Hoen, K.M.R. et al. (2013) ‘Switching transport modes to meet voluntary carbon emission targets’,
Transportation Science, Vol. 48, No. 4, pp.592–608 [online] http://dx.doi.org/10.1287/
trsc.2013.0481 (accessed November 2014).
Hoen, K.M.R. et al. (2014) ‘Effect of carbon emission regulations on transport mode selection
under stochastic demand’, Flexible Services and Manufacturing Journal, Vol. 26, Nos. 1–2,
pp.170–195.
Hoti, S., Pauwels, L.L. and McAleer, M. (2007) ‘Measuring environmental risk’, Journal of
Economic Surveys, Vol. 21, No. 5, pp.970–998.
Hua, G., Cheng, T.C.E. and Wang, S. (2011) ‘Managing carbon footprints in inventory
management’, International Journal of Production Economics, Vol. 132, No. 2, pp.178–185.
Humphreys, P. (2003) ‘Integrating environmental criteria into the supplier selection process’,
Journal of Materials Processing Technology, Vol. 138, No. 1-3, pp.349–356.
ICLEI-Europe (2015) Sustainable Economy and Procurement [online]
http://www.iclei-europe.org. International Energy Agency (2010) Transport Energy Efficiency
[online] http://www.iea.org/papers/2010/transport_energy_efficiency.pdf (accessed October
2015).
Jaegler, A. and Burlat, P. (2010) ‘Linking carbon performance and effectiveness of supply chains’,
in Collaborative Networks for a Sustainable World, Vol. 336 of the Series IFIP Advances in
Information and Communication Technology, pp.117–124.

M
ultiobjective optimisation model for the selection of critical suppliers 237
Kasilingam, R.G. and Lee, C.P. (1996) ‘Selection of vendors: a mixed-integer programming
approach’, in 19th International Conference on Computers and Industrial Engineering,
pp.347–350.
Kraljic, P. (1983) ‘Purchasing must become supply chain management’, Harvard Business Review,
Vol. 61, No. 5, pp.109–117.
Kungwalsong, K. (2013) Managing Disruption Risks in Global Supply Chains, PhD dissertation,
Department of Industrial Engineering, The Pennsylvania State University, University Park,
PA.
Kungwalsong, K. and Ravindran, A.R. (2012) ‘Modeling supply chain disruption risk
management’, IIE Annual Conference. Proceedings, pp.1–10.
Kungwalsong, K. and Ravindran, A.R. (2014) ‘Global supply chain network design incorporating
disruption risk’, International Journal of Business Analytics, Vol. 1, No. 3, pp.37–62.
Lee, A.H.I. et al. (2009) ‘A green supplier selection model for high-tech industry’, Expert Systems
with Applications, Vol. 36, No. 4, pp.7917–7927.
Li, Y., Su, Q. and Li, T. (2010) ‘The optimization and integration of the transportation and
inventory cost based on time in supply chain logistics system’, in International Conference on
Logistics Engineering and Intelligent Transportation Systems, pp.1–4.
Masud, A. and Ravindran, A. (2008) ‘Multiple criteria decision making’, in A.R. Ravindran (Ed.):
Operations Research and Management Science Handbook, CRC Press, Boca Raton, FL.
Mendoza, A., Santiago, E. and Ravindran, A.R. (2008) ‘A three-phase multicriteria method to the
supplier selection problem’, International Journal of Industrial Engineering, Vol. 15, No. 2,
pp.195–210.
Palak, G., Ekşioğlu, S.D. and Geunes, J. (2014) ‘Analyzing the impacts of carbon regulatory
mechanisms on supplier and mode selection decisions: an application to a biofuel supply
chain’, International Journal of Production Economics, Vol. 154, pp.198–216.
Ravindran, A.R. and Wadhwa, V. (2009) ‘Multi criteria optimization models for supplier
selection’, in A. Badiru and M. Thomas (Eds.): Handbook of Military Industrial Engineering,
CRC Press, Boca Raton, FL.
Ravindran, A.R. and Warsing, D.P. (2013) ‘Global supply chain management’, in Supply Chain
Engineering: Models and Applications, pp.449–487, CRC Press, Taylor and Francis Group,
Boca Raton, Florida.
Ravindran, A.R. et al. (2010) ‘Risk adjusted multicriteria supplier selection models with
applications’, International Journal of Production Research, Vol. 48, No. 2, pp.405–424.
Seuring, S. (2013) ‘A review of modeling approaches for sustainable supply chain management’,
Decision Support Systems, Vol. 54, No. 4, pp.1513–1520.
Shalk, M. and Walld, A-K. (2011) ‘Green supplier selection generic framework: a multi-attribute
utility theory approach’, International Journal of Sustainable Engineering, Vol. 4, No. 1,
pp.37–56.
Shaw, K., Shankar, R. and Yadav, S.S. (2013) ‘Global supplier selection considering sustainability
and carbon footprint issue: a HP multi-objective fuzzy linear programming approach’,
International Journal of Operational Research, Vol. 17, No. 2, pp.215–47.
Shmied, M. and Knörr, W. (2012) Calculating GHG Emissions for Freight Forwarding and
Logistics Services in Accordance with EN 16258 – Terms, Methods, Examples, European
Association for Forwarding, Transport, Logistics and Customs Services (CLECAT), Krefeld,
Germany, p.63.
The European Energy Exchange (EEX) (2014) Emissions Trading [online]
https://www.eex.com/en#/en (accessed 24 September 2014).
Torres-Ruiz, A. (2015) Multi-Objective Decision Support System For Sustainable Supplier
Management, PhD dissertation, Department of Industrial Engineering, The Pennsylvania State
University, University Park, PA.

238
A
. Torres-Ruiz and A. Ra
v
indran
Tsai, W-H. and Hung, S-J. (2009) ‘A fuzzy goal programming approach for green supply chain
optimisation under activity-based costing and performance evaluation with a value-chain
structure’, International Journal of Production Research, Vol. 47, No. 18, pp.4991–5017.
Tuzkaya, G. et al. (2009) ‘Environmental performance evaluation of suppliers: a hybrid fuzzy
multi-criteria decision approach’, International Journal of Environmental Science and
Technology, Vol. 6, No. 3, pp.477–490.
University of Cranfield-School of Management (2002) Supply Chain Vulnerability, Department of
Trade and Industry, Bedfordshire, UK, January, pp.1–8.
Van Hoek, R. (2012) From Backroom to Boardroom: Procurement Goes Strategic,
PwC [online] http://www.pwc.com/us/en/view/issue-16/strategic-procurement.jhtml
(accessed 30 January 2015).
Vazquez-Brust, D. et al. (2012) Evaluating the Firm’s Environmental Risk: A Conceptual
Framework. In Business and Environmental Risks: Spatial Interactions Between
Environmental Hazards and Social Vulnerabilities in Ibero-America, pp.15–33, Springer
Science+Business Media, London; New York.
Warsing, D.P. (2008) ‘Supply chain management’, in A.R. Ravindran (Ed.): Operations Research
and Management Science, CRC Press, Taylor and Francis Group, Boca Raton, FL.
Yang, T. (2007) Multi Objective Optimization Models for Managing Supply Risk in Supply Chains,
PhD dissertation, Department of Industrial Engineering, The Pennsylvania State University,
University Park, PA.
Notes
1 Named well-to-wheels emissions according to the EN16258.