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: payman.ahi@ryerson.ca (P. Ahi).

http://dx.doi.org/10.1016/j.apm.2016.07.001

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

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

10159

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.

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

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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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: payman.ahi@ryerson.ca (P. Ahi).

http://dx.doi.org/10.1016/j.apm.2016.07.001

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

10154

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.

10156

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

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

10159

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.

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

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

10164

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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