Abstract
In a manufacturing organization, the term sustainability deals with the impact of production process and products on the environment and society, laying emphasis on preservation of scarce resources. In this article, the study concentrates on developing a Graph Theory model to measure the performance and inter-relationship between the sustainability enablers in an organization, thereby to quantitatively measure the extent to which ‘sustainable manufacturing’ practices are being followed in the organization. The objective of this study was to identify a set of sustainability enablers and attributes that impact a manufacturing organization. Digraphs were developed for the whole system and sub-systems depicting the inter-relationships and dependencies between various enablers and attributes to interpret the performance of the sustainability enablers in the case organization. Using the best case and worst case values, the level of sustainable manufacturing practices of the organization was found by Comprehensive Assessment Index. Based on the best case values, the relative significance of individual sustainability enablers are found and compared with worst case situations. The impacts of individual enablers on the overall sustainability level of the organization were also studied.
Nomenclature
| SM | = | sustainable manufacturing |
| VPM | = | variable permanent matrix |
| Pm | = | Permanent of a matrix |
| CAI | = | Comprehensive Assessment Index |
1. Introduction
Until recently, ‘attaining’ a certain level of productivity or performance was the key objective in a manufacturing system. But with the help of modern technology and allied resources, it became relatively easier to achieve such an objective. Since then, emphasis has been given to terms like ‘sustainability’ and ‘green’ environment, which have evolved due to the challenging atmosphere of diminishing natural resources and costly human resources arising out of the need for a higher standard of living (Yuan et al. Citation2012; Zubir et al. Citation2012; Andersson et al. Citation1998). Sustainability has evolved from being initially focused on issues such as environmental impact in terms of carbon footprint reduction and efficient use of energy resources, to including manufacturing products and using processes which are either eco- friendly or having less impact on the environment (Ghadimi et al. Citation2012; Deif Citation2011). This study focuses on measuring quantitatively the ‘sustainability’ of the products and processes used in a manufacturing organization, with the help of suitable sustainability enablers and criteria. The Graph Theory technique has been adopted for measuring the performance, correlation between each of the above mentioned enablers and criteria of the sustainability model. The advantage of using Graph Theory technique is that it measures the correlation between different enablers along with practice level and level of performance of each of these enablers in the manufacturing organization.
The main objectives of this study are
How well the existing manufacturing system ensures the sustainability of both the product and process, i.e. whether the current system will be able to meet the future requirements also?
How well each of the sustainability enablers perform in the current organization, their correlation among themselves and to identify which enablers need to be concentrated on future, to improve overall sustainability?
Therefore, the primary objective of this article is to measure overall sustainability performance of an organization with the help of performance measures of individual sustainability enablers. The advantage is that we get to measure the sustainability performance of an organization, in addition to measuring the relative performance of enablers from individual enabler scores.
The article is organized as follows. Section 2 briefs the literature review about sustainable manufacturing and Graph Theory; Section 3 deals with the methodology followed in this study; Section 4 presents the details about the case company and digraph development for sustainability enablers and criteria; Section 5 deals with the mathematical computation and sequence of Graph Theory calculations; Section 6 presents the results and discussions; Section 7 deals with the conclusions derived from the study.
2. Literature review
The literature was reviewed from perspectives of Graph Theory applications and sustainable manufacturing systems.
2.1 Review on Graph Theory
Dao and Mcphee (Citation2011) developed a Graph Theory based approach for the dynamic description of electrochemical systems. Apart from the usage of linear graphs for the system, Branch and Chord transformation techniques were used to generate equations used in the system. Modelling of nickel metal hydride battery was presented as an example. The authors suggested the use of Graph Theory procedure as it reduced the number of equations quite significantly, which in turn reduces complexity compared to the original model.
Tang (Citation2001) introduced a new methodology based on Graph Theory to compute the reliability of mechanical systems. The methodology consists of two parts. Using Graph Theory, the formula for reliability was found, which considers the inter relationship between the various subsystems. Then Boolean function was used to find out the physical interconnections between the components. An example was also provided which substantiates their findings.
Todd et al. (Citation2009) proposed the application of Graph Theory in cluster analysis and also developed GraphClus, a MATLAB code for its implementation. GraphClus can be applied in any case where the genetic relationship between the samples in a dataset exists. Also the algorithm was tested on natural geochemical and synthetic datasets, which denotes that the method performs better than the traditional cluster analysis methods.
Darvish et al. (Citation2009) recommended using Graph Theory methodology and Matrix methods as a decision support system in contractor selection for Construction procurement. They proposed to use the above methodologies as the method can consider both quantitative and qualitative contractor selection factors. They have also done a case study for the same. They proposed that the method can be extended to other applications including supplier selection.
2.2 Review on sustainable manufacturing systems
Sustainable manufacturing systems provide a wide scope in determining the inducement of sustainable manufacturing practices in contemporary organizations across all processes. A summarized list of literature review on sustainable manufacturing system has been discussed in Table .
Table 1 Summary of literature review.
The literature review indicated that no concrete study has been done on the application of Graph Theory methodology in sustainable manufacturing field. Hence the current case study is being conducted which focuses on the applying Graph Theory methodology in sustainable manufacturing considering the inter relationship between various enablers of sustainable manufacturing and the performance level of each enabler.
3. Methodology
The step by step procedure of conducting the study in a manufacturing organization is depicted in the below Chart-1.
Initially, the focus was to get some insight on the applications of Graph Theory technique in modelling scenarios. Graph Theory approach has certain advantages over the other techniques. Graph Theory approach includes diagrammatic representation of the whole system in terms of subsystems and their interactions, which can help in easily understanding the system, compared to other approaches like analytical hierarchy process. Also, these diagrammatic representations can be easily converted to matrix format, which can be used for mathematical computations, which cannot be done for other diagrammatic representations like flowcharts, cause and effect diagrams etc. Also, in Graph Theory technique, apart from measuring quantitatively the performance level or application level of a particular sustainability enabler, the inter relationship between various enablers can also be used to measure the overall sustainability. Hence, in this particular context, Graph Theory is the best approach that can be used to measure the overall sustainability of an organization because the individual sustainability enablers have high interdependencies among each other. Table shows the taxonomy of sustainability enablers.
Table 2 Taxonomy of sustainable manufacturing attributes.
The three major enablers of sustainable manufacturing system are explained as follows
3.1 Economic sustainability
Economic sustainability involves achieving the best economic results with an eye on the future use of scarce available resources. Investing in the future becomes much more significant as it underlines the motive of being sustainable. To attain such economic sustainability, all organizations looking forward to such an objective, need to properly plan for their economic future by adopting certain measures. Asset development measure tells about building the assets, by building the quality of employees and by other physical infrastructure like, offices, plant and machinery. Brand Development measure tells about development of the brand thereby adding to the intangible assets. Next, it asks to plan the money related matters, regarding the structure of their finances. Risk management measure tells about managing the risks related to finance management. Last measure tells about performing in an efficient, ethical and value based manner. An organization will not be successful in the societal and environmental fronts, if it lags behind in the economic sustainability performance.
3.2 Environmental sustainability
In the broader term of sustainable manufacturing, an organization is said to fulfil environmental sustainability, if it takes such decisions both in the process and the product, which will have least impact on the environment. In other words, it involves making decisions with utmost consideration on the impact on environment, with an eye on the existence of the system in future. The measures that manufacturers need to concentrate on are listed here. Effective measures should be taken by laying emphasis on energy management. Reduction in unit cost of energy results in both environmental and economic sustainability. Adopting waste reduction measures include investing more in Lean initiatives, which involves making the best use of existing resources and concentrating on reduction of wastes. Making the best use of latest technology is the last measure which involves the integration of Technology into sustainability thereby laying emphasis on innovative methods or process resulting in preservation of the environment through saving the resources.
3.3 Societal sustainability
Societal sustainability measures involve the population, both internal and external while making manufacturing decisions. The impact on all the stakeholders need to be highlighted, while making decisions regarding process and product, if the organization has to score high on sustainability front. It involves contributing to the human needs, apart from meeting the other targets. Corporate social responsibility (CSR) adds much to the societal sustainability objective. It involves making decisions that considers the human force, but may not be enforced by law. It involves different measures like adequate wages, incentives and benefits, apart from providing necessary safety measures which may cater to the internal population. This should also include other investments like health, education, housing and security initiatives for human resources, which will increase the societal sustainability score of the organization.
4. Case study
The case organization is a rotary-switch manufacturing company located in Tiruchirapalli, Tamil Nadu, India, relies mainly on the qualitative analysis of the sustainability study, to understand the economic, social and environmental impacts of both products and processes. The company manufactures load break switches, wiring ducts, terminal connectors, selector switches, ammeter switches, voltmeter switches, electromagnetic relays, DC disconnectors and magnetic wires. The model which is dealt with in this article will help in quantifying the sustainability performance and the interrelationship between various sustainability enablers.
The case study is required to measure the level of performance of sustainability enablers in a quantified manner. The first step was to meet various stakeholders and provide with them the questionnaire that indirectly measures the various attributes of the sustainability enablers. The answers provided for those questions will be in the form of numerical scores in the scale 1–10 as given in Table . For example, to measure the financial performance attribute of the economic sustainability enabler, different indicators of financial performance are noted down and the organization's performance with regard to that particular indicator is reviewed in form of questionnaires. One such indicator will be profit of the company and the question – ‘How well the organization is performing with respect to increasing the profit of the company?’ The scores for all the questions will be noted down and the average score is obtained for a particular attribute. This average score is noted against each attribute as in Table .
Table 3 Scale values to investigate the performance of each sustainable manufacturing attribute.
Table 4 A sample checklist to measure ‘economic sustainability’ enabler attributes.
Similarly, the stakeholders are provided with the questionnaire to measure the level of inter-dependency between various sustainability enablers. For example, to measure the dependency of water resources on ‘end of life disposal policy’, each stake holder is provided with a question asking, ‘How the waste generated is disposed?’, ‘At any point, does the waste generated gets into contact with surrounding water resources?’, ‘If yes, in what quantity?’. The respondents will be asked to give their final answers in a scale as mentioned in Table . The average score will be score of interdependency between various enablers.
Table 5 Scale values to investigate the inter relationship or dependency of one sustainable manufacturing attribute on the other.
Before applying this technique, the organization has to make sure that the sustainability enablers which are being dealt with here are being taken care of and applied within the organization. Once the computation is done, it may help the organization to identify the focus areas and to develop required changes as may be needed for both product and process, to enable the respective sustainability criteria to get a better score. In Graph Theory approach, the interrelationship between various enablers is termed as Interdependency. Using this approach, one can easily measure the performance level of a particular sustainability criterion, and more importantly, can measure the interdependency among such criteria.
4.1 Preparation of digraphs
Digraph is a pictorial representation of the inter relationship between sustainability enablers and different criteria within each of these enablers. Figure shows the digraph for sustainability enablers. Sustainability enablers include economic sustainability (A1), environmental sustainability (A2) and societal sustainability (A3). The inter-relationship between the three enablers is shown in Figure . The inter-dependency is found using logical explanations and from the inputs by various experts in sustainability. The qualitative inputs are used to determine whether any interdependency exists between any two enablers. Consider A1, the arrow pointing from A1 to A2;a12 shows the inter-dependency of the second enabler on the first enabler, whereas, for the arrow pointing from A2 to A1,a21 shows the inter-dependency of the first enabler on the second enabler. In the same manner, A1 is also compared with A3. Similarly, the procedure is also performed for the other two enablers.
5. Development of mathematical model
The preparation of Graph Theory model is the first step in the measurement of sustainability in an organization. Now, the above Graph Theory model has to be transformed into a matrix, known as variable permanent matrix (VPM), which consists of values derived from the level of interdependency between various enablers and the level of performance of a particular enabler. The permanent value of the matrix is calculated, which forms the measured value of sustainability in an organization. The best case and the worst case values can be determined, by giving respective values in the matrix.
5.1 Developing VPM
The interrelationship between different sustainability enablers and the performance level of each of the three sustainability enablers are the prerequisites for developing a VPM. Equation (1) shows the matrix prepared for computing the permanent value, which forms the measured value A (Anand and Kodali Citation2010).
The elements of the matrix derive values from the digraph. The elements in the diagonal position represent the nodes of the digraph, which denote the performance level of each sustainability indicator. The non-diagonal elements denote the level of interrelationship between the sustainability indicators. The arrows in the digraph denote inter relationship between the sustainability enablers. If no arrow is present in the digraph, a value of zero is given for such relationships. The VPM is used to find the permanent value of the matrix which represents the quantified measured value of sustainability in any organization. The permanent value of the matrix is denoted as variable permanent function (VPF-SM). It can be computed manually using the same procedure for calculating the determinant, except that, for calculating the permanent value, positive sign is used everywhere, and no negative sign is used anywhere. Here, we have used MATLAB software for calculating the permanent value. The base formula for computing permanent (Pm) of a 3 × 3 matrix (matrix in Equation (1)) is shown as follows (Anand and Kodali Citation2010).
The value computed using the above equation is known as ‘Comprehensive Assessment Index’ (CAI) or Permanent (SM).
5.2 Evaluation of diagonal elements of VPM-SM
Each of the diagonal elements in the VPM, which represent the nodes of the digraph, is a high-level attribute which can be computed only by considering it as a group of interrelated low-level attributes. Here, we consider each of the sustainability enablers as a high-level attribute which in turn consists of several low-level attributes. Each of the low-level attributes under a particular enabler can be represented as where superscript I denotes the corresponding sustainability enabler and subscript i denotes the low-level attribute under the particular enabler. To find out (AI)’s and aij's in the VPM, the following procedure is followed
Digraphs should be developed for each of the sustainability enablers with the low-level attributes as the nodes, in the same manner as the high level digraph was drawn with sustainability enablers as its nodes.
The lower-level digraphs help to find the performance level of a particular enabler and the degree of inter-relationship between various attributes within an enabler. The various diagraph at sub system level are shown in Figures .Figures show the digraphs for sustainability enablers economic sustainability (A1), environmental sustainability (A2) and societal sustainability (A3). Economic sustainability enabler consists of five attributes: Financial Health (
), economic performance (
Figure 2 Digraph for the ‘economic sustainability’ enabler. 
Figure 3 Digraph for ‘environmental sustainability’ enabler. 
Figure 4 Digraph for ‘societal sustainability’ enabler. 
Using the sequential steps in this section, the VPM for subsystems are represented as VPM-
Likewise, the VPM for all three sub-systems, VPM-
The non-diagonal values within VPM of each of the sustainability enabler, which represent the level of inter relationship of each of the sustainability attribute with any other attribute can be evaluated using another scale as follows.
From the above 2 scales, all values of permanent matrix can be found out and the final matrix can be developed. Matrix 3–5 shows the permanent matrices for three individual sustainability enablers.
6. Results and discussions
The Permanent values of the above matrices were computed using MATLAB. The results are presented as follows:-
The above values form the diagonal elements of the final sustainability matrix, VPM-SM. The non-diagonal elements are dependent on the inter relationship between various enablers of sustainability, which are found out with the help of sustainability experts and industrial applications. Matrix 6 shows the VPM-SM for the case organization. From this, CAI was computed.
The permanent function of the above VPM-SM matrix was computed using MATLAB. The resultant value denotes the level to which the sustainability enablers perform in an organization or in other words, how well the organization has practiced sustainable manufacturing.
The log value of CAI can be used to reduce the complexity
The range where the CAI lies can be identified using two cases namely best and worst situation.
6.3 Practical best case
Practically, in the best case scenario, the diagonal elements of the lower level matrices of individual enablers take the maximum possible value of 9, keeping the non-diagonal values unchanged. Matrix 7 shows a sample permanent matrix for ‘economic sustainability’ enabler, for the practically best case scenario.
The permanent value of economic sustainability enabler in the practically best case situation is as follows:
Likewise, the permanent values for the other individual enablers in the practically best case situation are also calculated. The permanent values of other individual enablers in the practically best case situation are as follows:
The Comprehensive Assessment Index = VPM-SM = 1.0276 × 1016. The logarithmic value corresponding to the best case value is log 10 (1.0276 × 1016) = 16.01. The result also shows that the sustainability enabler, environmental sustainability has the maximum role in determining the sustainability of a manufacturing organization whereas societal sustainability has the minimum role, in the manufacturing organization.
6.4 Practical worst case
In the practically worst case scenario, diagonal elements of the lower level matrices of individual enablers take the minimum possible value of ‘1’, keeping the other values unchanged. Matrix 8 shows a sample permanent matrix for ‘economic sustainability’ enabler, for practically worst case scenario.
The permanent value obtained after computation for the Economic sustainability enabler for the practically worst case scenario is shown below
Likewise, the permanent values for other individual enablers in the practically worst case situation are also calculated. The permanent values of other individual enablers in the practically worst case situation are as follows:
CAI = VPM-SM = 2.3029 × 1012. The logarithmic value corresponding to the worst case value is log10 (2.3029 × 1012) = 12.362. For the case organization, the calculated CAI is 15.82 which is very close to the practical best case value of 16.01, which shows that the organization has well practiced sustainable manufacturing system. In other words, the sustainability enablers perform very well in the organization. Table shows the complete permanent values for all practical case situations.
Table 6 Permanent values for the case organization – current value, best case and worst case situation.
6.5 Theoretical best case and worst case values – for any organization
The theoretical best case and worst case values are computed not for the case organization, but for any organization. This computation is done in order to find the range of values, which any organization can take, depending on its inter-relationships. If an organization is totally unaware of the sustainability enablers, it can take the least value. However, the probabilities of such cases are very low.
In the theoretically best case scenario, the diagonal elements of the lower level matrices of individual enablers take the maximum possible value of 9, and also the non-diagonal values also take the maximum value of 5. Matrix 9 shows the permanent matrix of ‘economic sustainability’ enabler, for theoretically best case scenario.
The permanent values of individual enablers in the theoretically best case situation are as follows:
CAI = VPM-SM = 2.2837 × 1017. The logarithmic value corresponding to the theoretically best case value is log10 (2.2837 × 1017) = 17.35.
In the theoretically worst case scenario, the diagonal elements of the lower level matrices of individual enablers take the minimum possible value of 1, and also the non-diagonal values also take the maximum value of 1. Matrix 10 shows the permanent matrix of ‘economic sustainability’ enabler, for theoretically worst case scenario.
The permanent values of individual enablers in the theoretically worst case situation are as follows:
CAI = VPM-SM = 446673. The logarithmic value corresponding to the theoretically worst case value is log10 (446673) = 5.65
6.6 Sustainability measurement scale
Sustainability measurement scale is a diagrammatic representation of sustainability scores, based on the above values for theoretically best case and theoretically worst case situations, which shows the range of values for any organization. The practically best case and worst case values are also designated in the scale (Figure ).
6.7 Practical implications
The study of the practically best case situation implies that environmental sustainability has the highest impact on the overall performance of sustainability in an organization. In order to achieve a greater degree of performance in environmental sustainability, both the product and the production process should be developed in such a way that there is least impact on the environmental attributes, like land resources, water resources, energy and mineral resources etc.; measures like cutting down the material wastes by adopting lean methodologies, lowering the energy spent per unit produced by reducing wastes like idle time and by using improved designs, the adverse impact on environment can also be reduced significantly.
The other two enablers, namely economic and societal sustainability, have relatively lesser significance, when compared to Environmental sustainability. But those two areas cannot be neglected, as all the three enablers are dependent upon each other. The performance of the organization under societal sustainability area can be improved by ways of different measures like getting stakeholders confidence before taking any significant decisions, by way of providing adequate wages and salaries and satisfying external population by means of measures like CSR initiatives. The performance in the economic front can be improved by right investments, building assets and better risk management.
The study proved the practical feasibility of such approaches, to analyse and review the production process and the layout of the organizations production area it was feasible to eliminate excess movement, materials and tooling for a more streamlined product flow. A series of process improvements were carried out as a result of this study to reduce hazardous and solid wastes, reduce wastewater discharges and energy consumption. Production improvements included reduced lead time, defects, and material loss and damage. Improving products to reduce impact in use and at the end of life were also considered for future products by the design community of the organization.
7. Conclusions
The modelling of sustainable systems is a complex task and it involves interrelationship between sustainability enablers and criteria. First, the focus was to identify a set of sustainability enablers and attributes that impact a manufacturing organization, after the literature review, which showed that no study has been done so far which adopted the Graph Theory methodology in finding the impact and performance of sustainability enablers in a manufacturing organization. After that, digraphs were developed for the whole system and sub-systems which depicts the inter-relationships and dependencies between various enablers and attributes. Then, those digraphs were transformed into matrices and calculations were performed for finding the permanent values of those matrices, which were used to interpret the performance of the sustainability enablers in the case organization. Using the best case and worst case values, the practice of sustainable manufacturing in the organization was found. Based on the best case values, the relative significance of individual sustainability enablers are found out. It has been found that environmental sustainability has the highest significance and societal sustainability has relatively lower significance among the sustainability enablers. The study measures overall sustainability performance of an organization with the help of performance measures of individual sustainability enablers. The findings derived from the study enabled the benchmarking of the case organization with other best in class organizations. The research can be done further in detail for each of the three sustainability indicators by further disintegrating the current attributes into much lower level attributes, for which detailed research needs to be done.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1. Email: [email protected].
2. Email: [email protected].
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