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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 October 2015 Revised 30 June 2016 Accepted 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 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 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 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 A thorough discussion highlighting the implications of the proposed framework is provided in Section The conclusions and recommendations for future research are provided in Section 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 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 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 > ), (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 gˆ 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 ) = − e √ cσln c 2π (ln c−μln c )2 2σ ln c (5) (ln g−μln g ) f g (g ) = √ gσln g 2π e − 2σ 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 − e √ cσln c 2π 2σ ln c ⎡ ⎣ (ln g−μln g ) c −∞ − e √ gσln g 2π 2σ 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 = − 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 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 10158 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 ) SSCPt = ∞ −∞ √ ct σln ct 2π ⎛ SSCPt = − ϕ e − 2σ ln ct ⎡ ⎣ ct −∞ e √ gt σln gt 2π − (ln gt −μln gt ) 2σ ln gt ⎤ 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 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 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 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 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 10160 P Ahi et al / Applied Mathematical Modelling 40 (2016) 10153–10166 Table 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 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 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 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 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 and 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 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 Sustainability indicators representing challenge factors∗ SSCM characteristic yi j t t Economic focus Environmental focus Social focus Eﬃciency focus Performance focus 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 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 Calculated values∗ of the SSC’s capacity and challenge in years “1" to “4" t 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, 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, 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, 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, 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 contains calculated values for the capacity and challenge of SSC in years “1" to “4" Note that these values are hypothetical 10162 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 = − ϕ − −0.3376 − (−0.7547 ) 0.12222 + 0.41522 = − 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 = − 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 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 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 in Eqs (9) and (10), the numerical values for capacity and challenge of the SSC under evaluation in year (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 (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 (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, and were considered when the performance of the SSC under evaluation was estimated at the year 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 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 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 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Abrahamsson, Performance measurements in the greening of supply chains, Supply Chain Manage.:... 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
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