value chain analysis

Applied Mathematical Modelling 40 (2016) 10153–10166

Contents lists available at ScienceDirect

Applied Mathematical Modelling
journal homepage: www.elsevier.com/locate/apm

A comprehensive multidimensional framework for assessing
the performance of sustainable supply chains
Payman Ahi∗, Mohamad Y. Jaber, Cory Searcy
Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada

a r t i c l e

i n f o

Article history:
Received 2 October 2015
Revised 30 June 2016
Accepted 1 July 2016
Available online 12 July 2016
Keywords:
Sustainable supply chain management
(SSCM)
Performance assessment
Stochastic approach
Multidimensional
SSCM characteristics
Integrative framework

a b s t r a c t

Managing sustainable supply chains is an area of growing interest in both academia and
practice. The successful implementation of sustainable supply chain management (SSCM)
practices is now recognized as a critical component of overall business sustainability. However, there is a dearth of established theories, models, and frameworks for assessing sustainable supply chain (SSC) performance. To help address this issue, this paper proposes
an integrative multidimensional framework for a comprehensive evaluation of SSC performance. The framework is an extension of the sustainability model developed in an earlier study by Ahi and Searcy [4]. The key contribution of the current research is that the
proposed stochastic framework is capable of accommodating any number of performance
characteristics associated with SSCM. The framework is not restricted to the three traditional areas of the triple bottom line, namely economic, environmental, and social issues.
This is important given the wide range of challenges and opportunities present in different supply chains. It is recognized that a key challenge in applying the framework is data
availability and quality. The implications of the proposed framework are discussed and recommendations for future research are provided.
© 2016 Elsevier Inc. All rights reserved.

1. Introduction
Sustainability and supply chain management (SCM) have each been the subject of considerable research over the last
several decades. Both of these concepts have been defined in a multitude of different ways. Sustainability is commonly defined as using resources to “meet the needs of the present in a way that the future generations’ ability to meet their own
needs will not be compromised” [1]. However, such an all-encompassing definition can present challenges when the aim is
to operationalize sustainability. As a result, there is no collective consensus on what key characteristics can be used to comprehensively portray the sustainability concept in a business context [2]. Similarly, there have been numerous definitions
of SCM published in the literature. As a representative example, Stock and Boyer [3, p. 706] defined SCM as “the management of a network of relationships within a firm and between interdependent organizations and business units consisting of
material suppliers, purchasing, production facilities, logistics, marketing, and related systems that facilitate the forward and
reverse flow of materials, services, finances and information from the original producer to final customer with the benefits
of adding value, maximizing profitability through efficiencies, and achieving customer satisfaction.” A number of key characteristics may be extracted from that definition, such as the focus on coordination, relationships, value, and efficiency [4].

∗

Corresponding author. Fax: +1 416 979 5265.
E-mail address: (P. Ahi).

/>0307-904X/© 2016 Elsevier Inc. All rights reserved.


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P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

Table 1
Quantitative analytical modeling approaches for assessing sustainability issues in the supply chain.
Modeling approaches

Description

Typical approach/components addressed

Life-cycle assessment (LCA)
based models

Systematic methods for investigating the potential
environmental impacts associated with a product,
process, or activity, by identifying and quantifying
materials used, energy consumed, and wastes
discharged to the environment [21,22].
A structured technique for simplifying, organizing,
and analyzing complex and multi objective
decisions [29,30].
Standard and well established methodologies on
evaluating and assessing sustainability issues in
supply chains [18].
Disciplines that explicitly deliberate multiple
conflicting criteria, which require to be evaluated
in decision-making processes.
Techniques in which relationships between outputs
of some performance measures and the supply
chain’s input parameters alongside their related

decision factors can be analyzed.

Evaluating environmental issues and
attempting to minimize their impacts along a
supply chain.

[23–28]

Evaluating complex decision situations where
environmental and economic goals are
assessed simultaneously.
Balancing of environmental and economic
issues by utilizing relevant equilibrium or
optimum solution(s)
Optimizing environmental and economic
criteria by balancing trade-offs or proposing
optimal solutions
Evaluating outputs of environmental capital
(e.g., renewable and non-renewable ecological
goods, material use, and impact of emissions
on human health) and economic goals (i.e.,
lowering costs and/or maximizing profits)
along supply chain networks.
Policy prioritization, decision-making, and
communication with respect to various levels
of system performance.

[31–34]

Applications of the analytic

hierarchy process (AHP)
Equilibrium models

Multi-criteria decision making
(MCDM) models
Input–output analysis (IOA)
based models

Composite metrics

Practical tools in focusing attention through their
abilities to summarize complex and multifaceted
problems into single metrics [48].

Example
articles

[35–38]

[39–42]

[43–47]

[17,49–51]

Adopted from Ahi and Searcy 2015 [15].

However, much like sustainability, there is a lack of consensus on what key characteristics can completely represent SCM
[3].
Increasingly, the previously independent bodies of literature on sustainability and SCM have been converging [5,6]. A

growing number of organizations are also considering sustainability as a part of their SCM practices [7]. The integration of
these two concepts has created various terms and expressions in the literature and in practice [8]. Examples include green
supply chain management, sustainable supply chain management, and green logistics, among many others [8]. Sustainable
supply chain management (SSCM) (i.e., arguably an extension of green supply chain management) is the term that best
captures the integration of sustainability and SCM issues [4,9].
There have been many different definitions suggested to describe SSCM [e.g., 10,11]. Based on a review of previously
published definitions, Ahi and Searcy [4, p. 339] provided a comprehensive definition of SSCM: “The creation of coordinated supply chains through the voluntary integration of economic, environmental, and social considerations with key interorganizational business systems designed to efficiently and effectively manage the material, information, and capital flows
associated with the procurement, production, and distribution of products or services in order to meet stakeholder requirements and improve the profitability, competitiveness, and resilience of the organization over the short- and long-term.”
The definition was explicitly written to capture the key characteristics of both business sustainability (i.e., economic, environmental, social, stakeholder, volunteer, resilience, and long-term focuses) and SCM (i.e., flow, coordination, stakeholder,
relationship, value, efficiency, and performance focuses). The definition of SSCM provided by Ahi and Searcy [4] will be used
in this paper.
Building on the definition above, one of the underlying foundations of SSCM is that it assumes that the concept of sustainability cannot be confined within the limits of any one firm, as its implications extend well beyond those boundaries
[12]. The many players in a supply chain (e.g., suppliers, focal firm, distributors, customers, etc.) greatly increase the complexity of incorporating sustainability into SCM. This is, in part, due to the large number of potential interactions between
the players in the supply chain [13,14]. This complexity is also due to the inherently multidimensional nature of sustainability, which encompasses the “triple bottom line” of economic, environmental, and social aspects as a minimum. Moreover,
the fact that these issues and interactions must be considered over time adds further complexity to the subject. These challenges highlight the fact that it is difficult to determine if a sustainable state has been reached. Measuring progress toward,
or away, from sustainability is often the best that can be achieved. Thus, one of the difficulties of measuring SSCM performance is that supply chains can simultaneously move away from sustainable conditions in some aspects and move toward
sustainable conditions in others. Supply chains can, therefore, move further away from an ideal sustainable state even if
most performance indicators are exhibiting improvements. To better understand these interactions, more research on the
potential conflicts and trade-offs between sustainability goals, objectives, and indicators in SSCM is needed [15,16].
Drawing on the recent research by Hassini et al. [17], Seuring [18], Brandenburg et al. [19], Brandenburg and Rebs [13],
and Beske-Janssen et al. [20], quantitative analytical modeling approaches suggested for assessing sustainability issues in
the supply chain may be categorized as summarized in Table 1. As highlighted in the table, these categories include life


P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

10155

cycle assessment (LCA) based models, applications of the analytic hierarchy process (AHP), equilibrium models, multi-criteria
decision-making (MCDM) models, models based on input-output (IO) analysis, and composite metrics.

The existing research highlights that relatively little work has been done to date on probabilistic approaches to SSCM
performance measurement. This is important as the factors that affect SSCM performance are dynamic in nature and vary
over time. The existing modeling approaches demonstrate either a strong dominance on explicitly addressing environmental
issues, such as material use, emissions impacts, non-renewable and renewable ecological goods, and ecosystem services [e.g.,
22,23,25,26,28,52–56], or a combination of environmental and economic considerations, such as maximizing profits and/or
reducing costs [e.g., 21,43–47,57–61]. As highlighted by a number of authors [e.g., 27,62–65], there have been few attempts
made to explicitly address social issues in SSCM [11,13,18,19,66–70]. Accordingly, integrated multidimensional sustainability frameworks are strongly required to meaningfully analyze the interactions and trade-offs among potentially conflicting
objectives in sustainable supply chains [13,14,17,19,71].
It is important to recognize that not all the entailed interactions in a sustainable supply chain (SSC) will have the same
relevance, magnitude, and significance in all contexts. Moreover, different factors may be specified with different units of
measurement or even stipulated in qualitative terms. Therefore, it is argued that the supportive and hindering factors involved in SSCs are all fundamentally context-dependent entities [15]. The need to address such context-dependent factors,
while simultaneously facing the difficulties of distinguishing the transition between states of sustainability and unsustainability in supply chains, indicate that a nondeterministic, variable characterization of SSC functions is needed to provide a
realistic and convincing analytical modeling approach for assessing the performance of SSCs. This need may be met through
the development of probabilistic-based models and/or frameworks. The need for probabilistic-based approaches has also
been highlighted in the recent literature [i.e., 13,15,19]. To respond to this need, a comprehensive stochastic framework for
measuring SSC performance is proposed in this paper. The proposed framework is an extension of the (sustainability) model
developed in an earlier study by Ahi and Searcy [15]. Accordingly, some of the assumptions made in the earlier study are
relaxed. In particular, the framework proposed in this paper is capable of accommodating n sustainability characteristics,
as opposed to the earlier study which accommodated only three. The framework in this paper thus generalizes the model
presented by Ahi and Searcy [15]. This adds substantial complexity to the model, but is critical given the large number of
potential sustainability factors that must be considered in anyone supply chain and the fact that these factors can change
between chains.
This paper makes several contributions to the literature. It provides one of the first comprehensive multidimensional
frameworks for assessing performance in SSCM. The developed framework is based on context-dependent sustainability factors (i.e., enablers and inhibiters) that may be dynamically functioning in a SSC. The framework thus provides an integrated,
multidimensional ability to stochastically address any number of characteristics that may be involved in managing SSCs.
Accordingly, given the requirement and importance of considering and employing nondeterministic characterization of SSC
functions (i.e., discussed earlier), the proposed framework significantly extends the existing literature in that it is the first
probabilistic framework capable of accommodating n sustainability characteristics. It, therefore, proposes an approach that
is more realistic in assessing performance in SSCM.
The remainder of the paper is organized as follows. The basic principles underlying the proposed framework, along with

its structure, will be presented in the next section. An illustrative application of the framework is provided and discussed
in Section 3. A thorough discussion highlighting the implications of the proposed framework is provided in Section 4. The
conclusions and recommendations for future research are provided in Section 5.
2. Formulating the framework
The underlying assumption in the development of the framework is that there are factors that both enable and inhibit
progress toward sustainability. This assumption emphasizes the need to include all relevant sustainability indicators in the
assessment of sustainability performance and is consistent with Ahi and Searcy [15]. In line with that assumption, it has
been conceptualized that any supply chain, and the respective players within it, will have some capacity, as determined
through the application of the framework, to overcome the sustainability challenges it faces. In this light, the enabler factors
increase the capacity of the supply chain to move toward sustainability and to overcome its key sustainability challenges.
The inhibitor factors, on the other hand, represent challenges to the supply chain and/or reduce the capacity of the chain to
endure and overcome such challenges. The framework is based on the principle that if the supply chain’s capacity exceeds
the challenges posed by the inhibitors, it will be making progress toward sustainability. Otherwise, its sustainability position
will regress.
Drawing on the above, Fig. 1 illustrates the structure of the proposed comprehensive framework. The figure shows that
indicators are needed to address the key characteristics of SSCM. The framework is capable of addressing any number of
characteristics. These indicators must also address the key players across the entire supply chain, such as suppliers, distributors, and customers. This emphasis on the entire supply chain is needed to ensure that no key impacts are missed.
Building on the SSCM characteristics, supply chain players, and indicators, the model proposed in this paper provides a basis for measuring SSC performance. This can, in turn, feed into an organization’s broader performance measurement system
and provide a basis for education, communication, and decision-making around SSC performance. Several examples of possible enablers and inhibitors that can be addressed by the selected indicators and vary from supply chain to supply chain
are presented in Ahi and Searcy [15]. The implications of the framework are discussed further later on in the paper.


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P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

Fig. 1. Structure of the proposed framework for measuring SSC performance.

The foundation of the framework is that the success, or failure, of the supply chain in moving toward sustainability is
conceptualized as a probability. Specifically, the probability that the SSC is positioned to progress toward sustainability is

equal to the probability that the SSC’s capacity is more than the imposed challenges. Therefore:

SSCP = Pr (CSSC > GSSC ) = Pr (CSSC − GSSC > 0 ),

(1)

where:
SSCP = Sustainable supply chain performance
CSSC = Capacity of the SSC
GSSC = Challenge imposed on the SSC.
If the probability density functions (PDF) for the capacity CSSC and challenge GSSC can be denoted by fc (c) and fg (g),
respectively, then the corresponding Cumulative Distribution Functions (CDF) for the capacity and challenge may be defined
as:

Fc cˆ =
Fg gˆ =

cˆ
0
gˆ
0

fc (c )dc

(2)

fg (g)dg ,

(3)

where:
cˆ = Maximum available capacity
gˆ = Maximum imposed challenges.
Again, the SSC’s successful performance is the probability that the capacity exceeds the challenge. Under these conditions,
the assumption is that progress toward sustainability is being made. Therefore: [72]

SSC p = Pr (CSSC > GSSC ) =

+∞
−∞

f c (c )

c
−∞

fg (g)dg dc ,

(4)

where:
c = Random variable representing capacity of the SSC
g = Random variable representing challenge to the SSC.
For the purposes of this study, all computations are carried out while assuming log-normal distributions for both capacity
and challenge parameters. The employment of log-normal distributions is particularly useful when the uncertainties about
the capacity, challenge, or both types of parameters, are relatively large [73].
It should be noted that the model developed earlier by Ahi and Searcy [15] assumed normal distributions for all the
involved factors. While the employment of normal distributions can be an acceptable approach in practice, it does not

P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

10157

account for potential negative values for the capacity and challenge variables. Negative values were therefore not considered
by Ahi and Searcy [15]. When a normal distribution is employed and the coefficients of variations of the involved factors
(i.e., the capacity and challenge variables) are less than 0.3, the probability of negative values will be negligible. Therefore,
the probability of negative variable(s) for the capacity and challenge factors under the normal distribution were deemed as
zero in the original model developed by Ahi and Searcy [15]. While limiting the probability of a negative random variable
under the normal distribution to zero has previously been used in modeling approaches [i.e., 74], it does not fully capture
all real-world possibilities. The use of log-normal distributions overcomes this issue.
The standard form of respective log-normal density functions (PDFs) for the capacity and challenge factors formulized in
Eq. (4), can be denoted as follows:

f c (c ) =

−
1
e
√
cσln c 2π

(ln c−μln c )2
2σ 2
ln c

(5)

(ln g−μln g )

2

f g (g ) =

1
√

gσln g 2π

e

−

2σ 2
ln g

,

(6)

where:

μln c
μln g
σ ln c
σ ln g

= Mean value of the variable ln c that is normally distributed
= Mean value of the variable ln g that is normally distributed
= Standard deviation of the variable ln c that is normally distributed

= Standard deviation of the variable ln g that is normally distributed.

By applying Eqs. (5) and (6) in Eq. (4), the SSC performance can be defined as:

SSCP =

∞
−∞

(ln c−μln c )2

−
1
e
√
cσln c 2π

2σ 2
ln c

⎡
⎣

(ln g−μln g )

2

c
−∞

−
1
e
√
gσln g 2π

2σ 2
ln g

⎤

d g ⎦d c

(7)

Eq. (7) therefore explicitly recognizes that whether a SSC moves toward sustainability is the probability that the SSC
under consideration can overcome the challenges imposed on it.
Since the log-normal density function is distorted positively, utilizing the respective median will be a better and more
convenient measure representing the central tendency for the log-normal distribution than the respective mean. With this
in mind, Eq. (7) may be simplified as follows: [73]

⎛

SSCP = 1 − ϕ

⎝−

⎞

ln c − ln g

σln2 c + σln2 g

⎠,

(8)

where:
c = Median value of variable c
g = Median value of variable g.
Therefore, the sustainability performance of supply chain can be estimated by applying Eq. (8) and using the standard
normal table.
Since one of the main purposes of this paper is to evaluate the performance of SSC over time, the proposed framework
has been designed to accommodate “p” number of designated periods (e.g., year), over which the sustainability analysis will
be carried out. The framework also recognizes that any SSC will have multiple capacity and challenge factors. Each of these
components can be comprised of “n” different types of variables (e.g., economic, environmental, social, and potentially other
factors). These variables will jointly form the capacity and challenge components in every designated period. In another key
departure from the (sustainability) model developed by Ahi and Searcy [15], which focused explicitly on 3 dimensions of the
triple bottom line sustainability perspective, the framework proposed in this research adopts an n-dimensional approach for
assessing SSC performance. The framework proposed in this paper thus addresses scenarios not contemplated in the study
of Ahi and Searcy [15] and provides greater flexibility for decision-making purposes.
Building on the discussion above, if X1t , X2t , X3t ,…, Xnt represent the independent factors affecting the capacity of the SSC
during period “t”, then the PDF for these factors may be denoted as f c (x1t ), fc (x2 t ), fc (x3t ), …, fc (xnt ), and the corresponding
CDF for the capacity of the SSC in period “t” can be defined as:

Fc (ct ) =

xˆ1t

xˆ2t

xˆ3t

−∞

−∞

−∞

...

xˆnt
−∞

fc (x1t , x2t , x3t , . . . , xnt )dx1t dx2t dx3t . . . dxnt

(9)

where fc (x1t , x2t , x3t , . . . , xnt ) is a multivariate PDF constructed from independent and identically distributed random variables xit (i.e., economic, environmental, social, and potentially other factors) that affect the capacity and jointly form the


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P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

variable “ ct ”, which represents the capacity of SSC in the period “t”, xˆit is the maximum value for xit , i (i.e., 1, 2, 3, …, n) is
the index of respective sustainability indicators representing capacity and challenge factors, and t (i.e., 1, 2, 3, …, p) is the
index of designated periods.
Similarly, if Y1t , Y2t , Y3t , …, Ynt represent the independent challenge factors imposed on the SSC in period “t”, then the
PDF for these factors may be denoted as fg (y1t ), fg (y2t ), fg (y3t ), …, fg (ynt ), and the corresponding CDF for the challenge to

the SSC in period “t” can be defined as:

Fg (gt ) =

yˆ1t

yˆ2t

yˆ3t

−∞

−∞

−∞

...

yˆnt
−∞

fg (y1t , y2t , y3t , . . . , ynt )dy1t dy2t dy3t . . . dynt

(10)

where fg (y1t , y2t , y3t , . . . , ynt ) is a multivariate PDF constructed from independent and identically distributed random variables yit that jointly form the variable “ gt ”, which represents the challenge to the SSC in the period “t”, yˆit is the maximum
value for yit , and i and t are as defined above.
By applying Eqs. (9) and (10), the capacity and challenge of the SSC under consideration in period “t” can be calculated.
Considering all of the above and based on assumptions that all of the factors comprising the SSC’s capacity and challenge
are log-normally distributed, Eqs. (7) and (8) can now be written as:

(ln ct −μln ct )

2

SSCPt =

∞
−∞

1
√

ct σln ct 2π

⎛
SSCPt = 1 − ϕ

e

−

2σ 2
ln ct

⎡
⎣

ct
−∞

1

e
√
gt σln gt 2π

−

(ln gt −μln gt )
2σ 2
ln gt

2

⎤

dgt ⎦dct

(11)

⎞

⎝− ln ct − ln gt ⎠,
σln2 ct + σln2 gt

(12)

where:
SSCPt = Sustainable supply chain performance in the period “t”

ct = Median value of the variable ct
gt = Median value of the variable gt
σln ct = Standard deviation of the variable ln ct
σln gt = Standard deviation of the variable ln gt .
By calculating the related capacity and challenge components for different periods of “t” and applying the results in
Eq. (12) in conjunction with the use of the standard normal table, the performance of the SSC under consideration can be
estimated for each period of interest, separately.
3. Illustrative application
The comprehensive framework developed in this research provides a solid foundation for assessing the performance of
SSC. Its ability to incorporate any number of key challenge and capacity factors that may be involved in SSCM makes it
particularly promising. To illustrate the broad applicability of the framework an illustrative example will be provided that is
modeled on the definition of SSCM suggested by Ahi and Searcy [4]. Based on this definition, SSCM is characterized jointly
by the key characteristics of business sustainability and SCM. The 13 key characteristics of business sustainability and SCM
are listed as economic, environmental, social, volunteer, resilience, long-term, stakeholder, flow, coordination, relationship,
value, efficiency, and performance focuses. Building on this definition, the analysis and assessment of SSC performance can
be carried out in an integrated 13-dimensional approach. Detailed descriptions and example indicators addressing the key
characteristics are presented in Table 2.
It is necessary to note that many representative indicators focusing on a triple bottom line perspective (i.e., highlighting
only economic, environmental, and social focuses) have been provided in detail by Ahi and Searcy [15]. Some other representative indicators that can be utilized in a triple bottom line approach have also been introduced in a study by Tajbakhsh
and Hassini [14]. A comprehensive list of performance indicators applied in SSCM is provided by Ahi and Searcy [76]. That
paper also analyzes the indicators according to the 13 key characteristics of SSCM used in this paper.
There are several factors that complicate the use of a real-world example for SSCM performance measurement. Measuring SSC performance requires that relevant data is available at the supply chain level. However, the majority of reported
sustainability indicators are based on information that addresses a single entity within the chain. For example, consider that
the Global Reporting Initiative (GRI) [77] (i.e., the world’s most widely-used sustainability reporting guidelines) has recognized such a requirement, however, sustainability indicators that address suppliers are still limited. Only 15 out of a total
of 91 performance indicators recommended by the GRI address supply chain issues [77, p. 86], and yet, they do not offer
much guidance on how to collect data at the supply chain level. It should be noted that data availability is a fundamental
requirement for successful application of any SSC performance measuring tool. Unfortunately, there is little real-world data
available that is reported at the supply chain level [17]. Most publicly-disclosed sustainability performance indicators (e.g.,
emissions, energy and/or material use) are reported at the level of a single entity in a chain rather than the whole supply

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Table 2
Descriptions and example indicators of the key SSCM characteristics.
SSCM
characteristic

Descriptiona

Example indicatorb ,c

Economic focus

“The definition includes language related to the economic
dimension of sustainability.”

Ü Sustainability cost
Ü Total supply chain cost
Ü Operational revenues

Environmental
focus

“The definition includes language related to the
environmental dimension of sustainability.”

Ü Air emissions

Ü Energy use
Ü Waste reduction

Social focus

“The definition includes language related to the social
dimension of sustainability.”

Ü Social welfare
Ü Percent of employment sourced from local communities
Ü Lost time injury frequency

Volunteer focus

“The definition includes reference to the voluntary nature
of business sustainability.”

Ü Participation in voluntary programs
Ü Number of individual volunteering
Ü Volunteer hours

Resilience focus

“The definition includes reference to resilience, defined as
“an ability to recover from or adjust easily to misfortune or
change” [75]. Note that indicators specifically addressing
risk were considered to address this focus as well.”

Ü Risk reduction
Ü Total perceived risks

Ü Risk exposure

Long-term focus

“The definition includes reference to the long-term nature
of sustainability. Reference to end-of-life management,
reuse, product recovery, reverse logistics, the closed-loop
supply chain, and the product life cycle were taken as
indications of a long-term focus.”

Ü Quantity of non-product output returned to process by
recycling or reuse
Ü Number of products that can be re-used or recycled
Ü Reuse rate

Stakeholder focus

“The definition includes explicit reference to stakeholders,
including (but not limited to) customers, consumers, and
suppliers.”

Ü Customers’ satisfaction
Ü Customer returns
Ü Customer complaint level

Flow focus

“The definition includes language related to the flows of
materials, services, or information. Reference to the supply
chain was considered to implicitly refer to this focus area.”

Ü Total flow quantity of scrap
Ü Capacity to manage reverse flows
Ü Managing reverse material flows to reduce transportation

Coordination
focus

“The definition includes reference to coordination within
the organization or between organizations. Reference to
the supply chain, the product life cycle, or activities across
channels was considered to implicitly refer to this focus
area.”

Ü Cooperation with our suppliers for eco-design
Ü Increasing the level of coordination of planning decisions and
flow of goods with suppliers including dedicated investments
(e.g. information systems, dedicated capacity/tools/equipment,
dedicated workforce)
Ü Improving opportunities for reducing waste through
cooperation with other actors

Relationship
focus

“The definition includes reference to the networks of
internal and external relationships. This includes
mentioning the coordination of inter-organizational
business processes.”

Ü After sales service rate
Ü Collaborative relationships
Ü Interaction and harmony co-exist with natural systems on
production and consumption systems

Value focus

“The definition includes reference to value creation,
including increasing profit or market share and converting
resources into usable products.”

Ü Market share growth
Ü Net present value
Ü Gross value added

Efficiency focus

“The definition includes reference to efficiency, including a
reduction in inputs.”

Ü Resource efficiency
Ü Overall efficiency achieved by means of sustainable production
practices
Ü Productivity/efficiency

Performance
focus

“The definition includes reference to performance,
including applying performance measures, improving

performance, improving competitive capacity, monitoring,
and achieving goals.”

Ü Operational performance
Ü Capacity utilization
Ü Increasing competitiveness

Notes: a Adopted from Ahi and Searcy [4].
b
Adopted from Ahi and Searcy [76].
c
Indicators could address multiple characteristics.

chain level. Therefore, the troublesome issue of incomplete data collection (i.e., overwhelmingly focused on single entities
within supply chains [12,17,18,78–81], and the lack of regular public disclosures by corporations (i.e., such disclosures are
almost entirely within the discretion of individual companies), all make the examining of sustainability performance frameworks and/or models with real world data very challenging.


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P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166
Table 3
Sustainability indicators representing capacity factors∗ .
SSCM characteristic

Economic focus

Environmental focus

Social focus

.
.
.
.
.
.
Efficiency focus

Performance focus

xi j t

x11t
x12t
x13t
x14t
x21t
x22t
x23t
x24t
x31t
x32t
x33t
x34t

T
1

2

3

4

xˆ111
xˆ121
xˆ131
xˆ141
xˆ211
xˆ221
xˆ231
xˆ241
xˆ311
xˆ321
xˆ331
xˆ34

xˆ112
xˆ122
xˆ132
xˆ142
xˆ212
xˆ222
xˆ232
xˆ242
xˆ312
xˆ322
xˆ332
xˆ34

xˆ113
xˆ123
xˆ133
xˆ143
xˆ213
xˆ223
xˆ233
xˆ243
xˆ313
xˆ323
xˆ333
xˆ34

xˆ114
xˆ124
xˆ134
xˆ144
xˆ214
xˆ224
xˆ234
xˆ244
xˆ314
xˆ324
xˆ334
xˆ34

1

2

3

4

.
.
.
.
.
.

.
.
.
.
.
.

.
.
.
.
.
.

.
.
.
.

.
.

.
.
.
.
.
.

x121t
x122t
x123t
x124t
x131t
x132t
x133t
x134t

xˆ1211
xˆ1221
xˆ1231
xˆ1241
xˆ1311
xˆ1321
xˆ1331
xˆ134

xˆ1212
xˆ1222

xˆ1232
xˆ1242
xˆ1312
xˆ1322
xˆ1332
xˆ134

xˆ1213
xˆ1223
xˆ1233
xˆ1243
xˆ1313
xˆ1323
xˆ1333
xˆ134

xˆ1214
xˆ1224
xˆ1234
xˆ1244
xˆ1314
xˆ1324
xˆ1334
xˆ134

1

2

3

4

Notes: ∗ For the purpose of simplicity, equal weights are considered for all the involved sustainability indicators.
xi j t = The sustainability indicator representing SSCM characteristic that affects the capacity in
period “t”.
xˆi jt = Numerical value for the sustainability indicator representing SSCM characteristic that affects the capacity in period “t”.
i = Index of the involved SSCM key characteristic (i.e., 1, 2, …, 13).
j = Index of the sustainability indicator relevant to the SSCM key characteristic involved.
t = Index of designated periods (i.e., 1, 2, 3, 4).

To demonstrate these difficulties, consider the public sustainability disclosures of the world’s largest corporation by revenue [82], Walmart. Walmart has an extensive supply chain sustainability program that has been the subject of widespread
media coverage [see e.g., 83]. However, assessing SSC performance for Walmart is not possible based on publicly available
data, largely for the reasons listed above. Walmart has disclosed a commendable amount of information on its supply chain
sustainability and has worked toward the development of a sustainability index for several years [84,85]. However, despite
these very substantial efforts, data is not publicly available for all key players across the supply chain. The ongoing development of the program indicates that there are likely numerous gaps in data, even where it is not publicly disclosed.
Moreover, further complications are embedded due to the likely differences in data quality throughout the supply chain.
This brief example demonstrates the difficulty of relying on real-world data to demonstrate the application of the model
developed in this paper.
Building on the above and also the complications and difficulties that exist around the fundamental issues of data collection, data allocation, and data reporting at the supply chain level detailed in Ahi and Searcy [15], a theoretical example is
provided to demonstrate the application of the proposed multidimensional framework. Accordingly, it is necessary to make
the following assumptions to better highlight the applicability of the framework. Assume that 4 sustainability indicators are
considered for any of the 13 key characteristics of SSCM that represent the respective capacity and challenge factors. The
results of this assumption are summarized in Tables 3 and 4.
It should be noted that in the assumptions outlined in the Tables, xˆi j and yˆi j are the numerical values for sustainability
t

t

indicators representing the SSCM characteristics that affect the capacity and challenge in period t, respectively. Also, i (i.e.,

1, 2, …, 13) represents the index of the key SSCM characteristics (i.e., economic, environmental, social, …, efficiency, and
performance focus), j represents the index of the sustainability indicator relevant to the involved key characteristic, and t
(i.e., 1, 2, 3, and 4) represents the index of designated periods (i.e., years).
Building on the above assumptions and applying Eqs. (9) and (10), the involved variables will jointly develop respective
capacity and challenge components of the SSC in each of 4 consecutive years. In other words, by applying the numerical
values of sustainability indicators representing SSCM characteristics in Eqs. (9) and (10), the numerical values of respective
capacity (i.e., c1 , c2 , c3 , c4 ) and challenge (i.e., g1 , g2 , g3 , g4 ) can be calculated for each year, separately. Accordingly, when


P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

10161

Table 4
Sustainability indicators representing challenge factors∗ .
SSCM characteristic

yi j t

t
1

Economic focus

Environmental focus

Social focus

.
.

.
.
.
.
Efficiency focus

Performance focus

2

3

4

yˆ111
yˆ121
yˆ131
yˆ141
yˆ211
yˆ221
yˆ231
yˆ241
yˆ311
yˆ321
yˆ331
yˆ34

yˆ112
yˆ122
yˆ132

yˆ142
yˆ212
yˆ222
yˆ232
yˆ242
yˆ312
yˆ322
yˆ332
yˆ34

yˆ113
yˆ123
yˆ133
yˆ143
yˆ213
yˆ223
yˆ233
yˆ243
yˆ313
yˆ323
yˆ333
yˆ34

yˆ114
yˆ124
yˆ134
yˆ144
yˆ214
yˆ224
yˆ234

yˆ244
yˆ314
yˆ324
yˆ334
yˆ34

.
.
.
.
.
.

.
.
.
.
.
.

.
.
.
.
.
.

.
.
.

.
.
.

.
.
.
.
.
.

y121t
y122t
y123t
y124t
y131t
y132t
y133t
y134t

yˆ1211
yˆ1221
yˆ1231
yˆ1241
yˆ1311
yˆ1321
yˆ1331
yˆ134

yˆ1212

yˆ1222
yˆ1232
yˆ1242
yˆ1312
yˆ1322
yˆ1332
yˆ134

yˆ1213
yˆ1223
yˆ1233
yˆ1243
yˆ1313
yˆ1323
yˆ1333
yˆ134

yˆ1214
yˆ1224
yˆ1234
yˆ1244
yˆ1314
yˆ1324
yˆ1334
yˆ134

y11t
y12t
y13t
y14t

y21t
y22t
y23t
y24t
y31t
y32t
y33t
y34t

1

2

1

3

2

4

3

4

Notes: ∗ For the purpose of simplicity, equal weights are considered for all the involved sustainability indicators.
yi j t = The sustainability indicator representing SSCM characteristic that affects the
challenge in period “t”.
yˆi j t = Numerical value for the sustainability indicator representing SSCM characteristic that affects the challenge in period “t”.
i = Index of the involved SSCM key characteristic (i.e., 1, 2, …,13).

j = Index of the sustainability indicator relevant to the SSCM key characteristic involved.
t = Index of designated periods (i.e., 1, 2, 3, 4).

Table 5
Calculated values∗ of the SSC’s capacity and challenge in
years “1" to “4".
t
1
2
3
4

ct
0.5926
0.6815
0.7827
0.7455

ln ct
−0.5232
−0.3835
−0.2450
−0.2937

gt
0.2712
0.3947
0.7089
0.5456

ln gt
−1.3049
−0.9296
−0.3440
−0.6059

Note: ∗ All the presented values for ct and gt are hypothetical
scores utilized only for the purposes of illustration.

c1 , c2 , c3 and c4 are the calculated numerical values of SSC’s capacity for the years 1, 2, 3 and 4, respectively, c4 will represent the numerical value of their median and ln c4 signifies the numerical value for the natural logarithm of that median.
Moreover, taking c1 , c2 , c3 and c4 as the numerical values of SSC’s capacity calculated for the years 1, 2, 3 and 4, respectively,
ln c1 , ln c2 , ln c3 and ln c4 are representing the numerical values of their respective natural logarithms, and σln c4 represents
the numerical value of their standard deviation.
Similarly, given g1 , g2 , g3 and g4 are the calculated numerical values of SSC’s challenge for the years 1, 2, 3 and 4, respectively, g4 will represent the numerical value of their median and ln g4 indicates the numerical value of the natural logarithm
of that median. Further, taking g1 , g2 , g3 and g4 as the numerical values of SSC’s challenge calculated for the years 1, 2, 3
and 4, respectively, ln g1 , ln g2 , ln g3 and ln g4 are representing the numerical values of their respective natural logarithms,
and σln g4 represents the numerical value of their standard deviation.
Drawing on the above, and solely for the purposes of illustration, assume that Table 5 contains calculated values for the
capacity and challenge of SSC in years “1" to “4". Note that these values are hypothetical.


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P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

Taking the information presented in Table 5, c4 = 0.7135 and g4 = 0.4702 are the median values, ln c4 = −0.3376 and
ln g4 = −0.7547 are natural logarithms of median values, and σln c4 = 0.1222 and σln g4 = 0.4152 are standard deviations of
natural logarithms for the related capacity and challenge components calculated for the years “1" to “4", respectively. By
plotting these values in Eq. (12), the respective SSCP4 can be estimated as:

SSCP4 = 1 − ϕ −

−0.3376 − (−0.7547 )
0.12222 + 0.41522

= 1 − ϕ (− 0.9637 )

Using the standard normal table ϕ (− 0.9637 ) is approximated at 0.1685, and therefore, the performance of SSC under
evaluation for the year “4" may be estimated as:

SSCP4 = 1 − 0.1685 = 0.8315 or 83.15%
This calculated value for SSCP4 implies that with the probability of 83.15%, the SSC under investigation was successful
in overcoming the imposed challenges, and hence progressed toward sustainability in the year “4". It is important to note
that progress can also be assessed at the level of individual capacity and challenge factors. The example here focused on
an integrated assessment of sustainability performance. This was based on an aggregation of the scores for the individual
factors. However, the disaggregated scores for each capacity and challenge factor are also available. Assessments of these
disaggregated scores may be particularly important for factors where performance is poor or where there is strong regulatory or stakeholder attention. For instance, the overall score of 83.15% in the example provided above (i.e., the level of
progress toward sustainability in the particular period of interest), might imply that the SSC under investigation has been
improving and overcoming most of the challenges imposed. However, it could also conceal very poor performance for a
particular factor(s) involved. Such factor(s) could have been expressed by an indicator of zero or a performance score that
is quite low. Factors with very poor performance would almost certainly require additional managerial attention. Therefore,
it is imperative to be able to investigate the disaggregated numbers, in addition to the composite score, in order to ensure
these important issues are not overlooked. Accordingly, the proposed composite score of SSCPt provides a meaningful basis
not only for evaluating the overall progress of SSC in the particular period of interest, but also for tracing back and investigating the individual performance indicator(s) involved (e.g., signifying the 13 key characteristics of SSCM used) within the
same period of interest.
4. Discussion
Building on Eq. (12), if the sustainability capacity and challenges involved in the supply chain under evaluation are
fluctuating in a similar pattern (i.e., increasing or decreasing correspondingly), not much progress toward sustainability may
be seen. On the other hand, if the SSC’s capacity is increasing while the challenges are decreasing, i.e., where the difference
between the respective natural logarithms of median values for the involved capacity and challenge components is getting

wider, the performance of the SSC under evaluation will exhibit improved results (i.e., values closer to 1 or 100%).
The framework will provide a solid basis for comprehensively evaluating the fluctuations in SSC performance over time.
This feature is similar to that of Ahi and Searcy [15], though the framework presented here comes with an increased capability to handle any number of factors. Accordingly, building on the process outlined in the illustrative example presented,
the SSC performance can be efficiently calculated for any subsequent period of interest (i.e., year 5, 6, …). For instance,
by plotting the numerical values for sustainability indicators representing the SSCM characteristics that affect the capacity
and challenge in year 5 in Eqs. (9) and (10), the numerical values for capacity and challenge of the SSC under evaluation
in year 5 (i.e., c5 and g5 ), and the subsequent numerical values of their natural logarithms (i.e., ln c5 and ln g5 ) can be
calculated, respectively. Next, by considering all the respective calculated values of capacity (i.e., c1 , c2 , c3 , c4 ) and challenge
(i.e., g1 , g2 , g3 , g4 ) for the previous years (i.e., years 1, 2, 3, and 4) alongside c5 and g5 , their respective median values at
the year 5 (i.e., c5 and g5 ) and also their respective natural logarithms (i.e., ln c5 and ln g5 ) can be computed, consequently.
Then, by employing all the values of natural logarithms for the respective calculated values of capacity (i.e., ln c1 , ln c2 , ln c3 ,
ln c4 ) and challenge (i.e., ln c1 , ln c2 , ln c3 , ln c4 ) for the previous years (i.e., years 1, 2, 3, and 4) alongside ln c5 and ln g5 ,
their respective standard deviation values at the year 5 (i.e., σln c5 and σln g5 ) can also be calculated. Finally, by plotting
the calculated values of ln c5 , ln g5 , σln c5 and σln g5 in Eq. (12) and using the standard normal table, the performance of
SSC under evaluation for the year “5" can be estimated. The methodology outlined above can be employed to estimate the
performance of the SSC under evaluation over any period of interest.
As highlighted above, it is necessary to emphasize that the proposed framework permits that computations of capacity
and challenge components from all the previous periods are taken into account when estimating the performance of SSC
at any designated period of interest (e.g., all the capacity- and challenge-related calculations from years 1, 2, 3 and 4 were
considered when the performance of the SSC under evaluation was estimated at the year 5 in the example presented above).
Accordingly, existing modeling approaches often focus on short time horizons with little focus on cumulative effects [86–88].
In light of this, the proposed framework provides a unique ability to assess the performance of the SSC under evaluation at
any designated time while also possessing the ability to consider the cumulative impact of the involved factors in all the
previous periods.


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10163

Furthermore, as implied earlier, all of the sustainability indicators representing SSCM characteristics involved in the illustrative example were assumed to be equally weighted. This was done for the purposes of simplicity. However, this does
not always need to be the case. Since every supply chain may have its own priorities and circumstances, different decisionmakers may wish to assign different weights to different factors involved. In this light, the employment of priority assignments would be entirely dependent on the supply chain’s unique circumstances. In such cases, there is a number of
priority assignment approaches available. These approaches may be broadly classified as participatory methods and statistically driven techniques. The budget allocation process, Delphi models, and analytical hierarchy process represent some of
the participatory methods, while data envelopment analysis, factor analysis, and unobserved components models highlight
some of the statistically driven techniques [89]. Nevertheless, it is noteworthy to emphasize that, in order to provide insight
into how various weights may affect their overall SSC performance measurement, decision-makers may choose to analyze
the impacts of employing different priority assignment approaches.
Moreover, the framework proposed in this paper shares some additional similar themes to the study by Ahi and Searcy
[15], notably consideration of context-dependent supportive and hindering factors involved in SSC and the use of nondeterministic, variable characteristics of SSC functions. As emphasized earlier, this paper assumes that a ratio scale provides a
meaningful approach for evaluating SSC performance. This is needed to normalize the data, given that the factors considered may have different units of measurement (including, potentially, in qualitative terms as well). Similar to Ahi and Searcy
[15], all sustainability indicators in this paper were thus represented as percentages. This further underscores the probabilistic nature of the proposed framework. Note that the significance of employing the ratio scale mechanism in sustainability
analysis has already been emphasized in the literature [see e.g., 90].
Drawing on the above, both frameworks proposed in the current paper and in the earlier study by Ahi and Searcy
[15] also face the same challenges and limitations (i.e., scarcity of regulated and standardized systems for meaningful data
collection, data allocation, and data reporting activities). However, the framework proposed in this paper is a substantial
extension of the earlier model and thus possesses a number of additional benefits. To alleviate the effects and possibility
of having any negative values for the involved variables, the framework proposed in this paper employs the log-normal
distribution for the capacity and challenge factors. The ability to accommodate these situations potentially provides a more
realistic stochastic assessment of SSC performance. Furthermore, while the earlier study by Ahi and Searcy [15] had an explicit triple bottom line approach and was thus limited to a 3-dimensional perspective of SSC performance, the framework
developed in this paper is capable of accommodating an n-dimensional approach. It can therefore comprehensively accommodate any number of characteristics that may be involved in assessing SSC performance. The framework developed in this
paper, therefore, provides superior flexibility for decision-making purposes.
The illustrative example further shows that implementing the proposed framework in practice will require improvements
in data availability and quality. As previously argued by Ahi and Searcy [15], this might be achieved through enhanced
reporting and standardization of data collection procedures utilized among all the key players within the SSC. Developing
mechanisms for allocating impacts to specific chains is also a key challenge that will need to be resolved. Given that many
existing sustainability indicators do not lend themselves to being applied in stochastic modeling approaches, there is also
a need for the collection of data which can eventually be used in stochastic measurement approaches [15]. Moreover, it
is important to note that many of the sustainability indicators available in the peer-reviewed literature were not originally
designed to be utilized in a supply chain context [17]. Additional research on tailoring existing indicators to the supply chain
context is needed.

If the data-related issues and challenges can be navigated, the integrated multidimensional framework developed in this
paper will provide a flexible, straightforward, and practical approach for comprehensive assessment of SSC performance.
This could permit evaluations of SSC within or between supply chains over time. However, it is necessary to note that the
integrity and realistic application of such comparison(s) will be rooted in the consistent collection, allocation, and reporting
of data within and between supply chains.
5. Conclusion
The growing integration of sustainability into supply chains has established an evolving interface that highlights a requirement for devising appropriate and meaningful aggregation measurement tools [13,14,17,19]. In this research, a multidimensional framework was developed to comprehensively assess the performance of SSC. By taking as many characteristics
as may be involved in managing a SSC, the framework developed in this paper can be employed as an integrative, multidimensional sustainability tool to analyze the interactions and trade-offs among such characteristics. Given its stochastic
nature, the proposed framework can envelop the involved uncertainty behaviors, and at the same time, it can incorporate
the cumulative impacts required for the long-term focus of SSC. In the proposed framework, the performance of a SSC in
each designated period of interest can be approximated, as can the cumulative effects of the involved factors in all previous
periods.
The multidimensional framework developed in this research makes a number of important contributions. It explicitly
addresses the requirement highlighted in the literature for the development of stochastic theories, models, and frameworks
for assessing SSC performance [13,15,19]. Such approaches are essential as stochastic models and/or frameworks are capable of accommodating the complexities as well as the uncertainties inherent in SSC performance modeling. Furthermore,
the developed framework provides a straightforward method for comprehensively assessing the performance of SSCs over


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P. Ahi et al. / Applied Mathematical Modelling 40 (2016) 10153–10166

time. It explicitly addresses the need underscored in the literature for sustainability measurement tools that focus on the
long-term, and hence, cumulative effects of the factors involved [86–88]. Accordingly, the proposed framework provides a
genuine foundation for evaluating the performance of SSC while the cumulative impact of all the involved factors in all the
entailed periods is taken into account. Lastly, by considering as many SSCM characteristics as may be involved, the proposed framework can be employed as a practical tool by decision-makers who aim to effectively highlight and/or manage
the required reference points, when identifying the available opportunities and challenges for improving their SSC performances. The developed framework may also provide opportunities for making performance comparisons between various
SSCs, provided that the entailed required data are collected, allocated, and reported in the same way across all the SSCs
under comparison. Most importantly, the framework presented in this paper can accommodate any number of sustainability
measurement characteristics and include both positive and negative indicator values.

Note that for the purposes of simplicity, all factors representing the involved SSCM characteristics were considered
equally weighted in this paper. However, as emphasized earlier, different decision-makers may wish to assign different
priorities to different factors involved. Therefore, the inclusion of respective importance coefficients (i.e., weights) in the
developed framework is recommended for the future research. A probabilistic weighting scheme is of particular interest.
Moreover, all the capacity and challenge factors involved in the proposed framework were considered as the variables acting independently. In this light, development of a sustainability model that incorporates dependent capacity and challenge
variables is further recommended for the future research. Research could also focus on improving measurement at the level
of the individual capacity and challenge factors. This could be particularly important in cases where priorities differ among
the various factors involved. Such research could be useful to decision-makers to assign organizational and/or managerial
responsibilities to particular metrics where is needed. These complementary lines of research will provide additional opportunities to assess the performance of SSC under evaluation. Finally, the authors reiterate that having the real supply chain
data would have made it easier to visualize how the proposed framework would be operationalized and how to identify
the challenges an organization may encounter in implementing such framework. Accordingly, future research could focus on
identifying the challenges and opportunities in making more supply chain data publicly available.
Acknowledgments
The authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for supporting
their research. The authors also thank the Editor-in-Chief and the reviewers for their valuable and constructive comments
that we believe have significantly improved the paper.
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