Environmental impact assessment of manufacturing processes using a combinatorial mathematics based decision making method

Abstract

This paper presents a methodology for environmental impact assessment of manufacturing processes using a combinatorial mathematics based decision making method. An ‘environmental impact assessment index’ is proposed that evaluates and ranks the manufacturing processes for producing a given engineering product or component. The index is obtained from an ‘environmental impact assessment factors function’ considering environmental impact assessment factors and their relative importance for the considered application. An example is included to illustrate the approach.

Keywords:

• environmental impact assessment
• manufacturing process
• combinatorial mathematics
• decision making

1. Introduction

Recently there has been a strong move towards environmentally conscious manufacturing with an emphasis on life cycle assessment (LCA). The intention is that LCA should be integrated into a holistic or systemic approach to product design. Such an approach allows consideration of the total energy expended, the resources used and the waste created. Hence, it is very important to determine and minimise the entire environmental impact. Currently, design for environment (DFE) and LCA are the strategies to integrate environmental concerns into product design and process design. The design of the product, the environmental impact assessment and the manufacturing method are the critical factors causing impact on the environment.

A considerable amount of research on environmental impact assessment had been carried out in the past. Munoz and Sheng (1995) presented a model of the environmental impact of machining processes. The analytical model integrated aspects of the process mechanics, wear characteristics and lubricant flows. The quantifiable dimensions in the analysis included energy utilisation, process rate, work piece primary mass flow and secondary flow of process catalysts. Choi et al. (1997) established an assessment model for manufacturing processes in terms of environmental impact for quantitative evaluation of product design. An assessment methodology was developed on the basis of the ‘material balance’ of a process and the relationship among different processes. As a result, the amount of solid waste generated, the energy consumed, the waste water incurred as well as the level of noise were obtained. A case study of the production of a toy train with 12 scenarios was performed to illustrate and examine the assessment model.

Hanssen (1998) discussed environmental impacts of product systems in a life cycle perspective and surveyed five product types based on LCA studies. The author had summarised the results of 18 LCA studies on a variety of products from Norway and Sweden. Culaba and Purvis (1999) presented a methodology for the life cycle and sustainability analysis of manufacturing processes. The authors described a general methodology for the life cycle analysis of manufacturing processes taking into account the flexibility and decision making potential of knowledge base systems.

Karakoussis et al. (2001) presented the environmental impact of manufacturing planar and tubular solid oxide fuel cells. The authors examined the environmental impact of manufacturing two types of solid oxide fuel cell (SOFC) system. Ong et al. (1999) described the development of a semi‐quantitative pre‐LCA tool for assessing the environmental impacts of the production of a printer. The tool allows a designer to easily compute a total environmental impact value for each of the various alternative designs. In another work, Ong et al. (2001) used analytic hierarchy process (AHP) method to derive a single environmental score based on process emissions for each of the products or alternatives evaluated. Based on the environmental scores, the products could be ranked with respect to their environmental merits. The AHP method was incorporated into the Pre‐LCA tool to assign accurate environmental scores to products. The AHP method can efficiently deal with objective as well as subjective factors, especially where the subjective judgments of different individuals constitute an important part of the decision process. However, in some cases an unmanageable number of pair‐wise comparisons of factors with each other and that of the alternatives with respect to each of the factors may result.

Leão and Pashby (2004) presented a literature survey on the use of dielectric fluids that provide an alternative to hydrocarbon oil. It had been reported that water‐based dielectrics might replace oil‐based fluids in die sink applications. Socolof et al. (2005) presented final impact results from an industry‐wide environmental LCA of cathode ray tube (CRT) and liquid crystal display (LCD) computer monitors for 20 environmental impact categories. Zackrisson (2005) presented environmental aspects when manufacturing products mainly out of metals and/or polymers. Weighting or valuation methods often used in LCA were used to quantitatively compare and rank environmental aspects.

English et al. (2006) considered how a cold roll forming company could ensure that it was a sustainable and environmentally conscious manufacturer. Hussey and Eagan (2007) presented some insights from the use of structural equation modeling, which was used to evaluate the development of an environmental performance model for small and medium size enterprises (SMEs).

Ballester et al. (2007) discussed the environmental issues and proposed a methodology for determining the significance of environmental impacts based on comparative and sensitivity analyses using the ELECTRE TRI technique. An application of the methodology for the environmental assessment of a power plant project within the Valencian Region of Spain was presented. However, ELECTRE TRI method uses the concept of outranking relationship and the procedure is rather lengthy. As the number of alternatives increases, the amount of calculations rises quite rapidly and computational procedures are quite elaborate.

Neto et al. (2008) described a model (MIKADO) to analyse options to reduce the environmental impact of aluminium die casting. This model can be used as a decision‐support tool for the environmental management of a plant. MIKADO can be used to perform scenario analyses to analyse the impact on the environment of different strategies, while taking into account both economical and ecological consequences of decision‐making. The MIKADO approach was based on relevant parts of LCA, environmental systems management and multi‐criteria analysis. The model was developed for and applied to a specific aluminium die casting plant supplying car manufacturers with aluminium die casting products. However, the authors had mentioned certain limitations of their proposed MIKADO model in terms of the impact assessment methodology and non‐consideration of certain environmental issues. The model focuses primarily on pollution problems caused by the plant.

Even though a considerable amount of research had been carried out on environmental impact assessment in the past; only a few systematic decision making methods such as AHP, ELECTRE TRI and MIKADO were used. There is a need for a simple, systematic and logical scientific method or mathematical tool to guide user organisations in taking a proper environmental impact assessment decision related to the manufacturing processes. Establishing an assessment model for manufacturing processes in terms of environmental impact is necessary for quantitative evaluation of product design. The objective of assessment procedure is to identify the manufacturing process selection factors and obtain the most appropriate combination of these factors in conjunction with the real requirement. Thus, efforts need to be extended to determine factors that influence environmental impact of manufacturing processes, using a simple logical approach, to eliminate unsuitable manufacturing processes and select a proper manufacturing process or a combination of processes. This is considered in this paper using a combinatorial mathematics based decision making method in conjunction with AHP.

2. Environmental impact assessment factors matrix

Environmental impact assessment factor is defined as a factor that influences the selection of a manufacturing process (or a combination of manufacturing processes) for producing a given engineering product or component from an environment point of view. Environmental impact assessment factors matrix models the environmental impact assessment factors and their interrelationship. The size of the matrix is equal to the number of environmental impact assessment factors considered. To demonstrate environmental impact assessment factors matrix, an example of environmental impact assessment of manufacturing processes for a given engineering component is considered. Let the environmental impact assessment factors of interest be, solid waste (SW) generated, liquid waste (LW) generated, energy consumption (EC), waste water (WW), noise produced (NP) and gaseous emissions (GE). Environmental impact assessment factors matrix for the considered example is shown in Expression (1). This matrix is a 6×6 matrix and considers measures of all six factors (i.e. A_i) and their relative importance (i.e. a_ij). The matrix B is represented as:

where A_i is the value of i‐th environmental impact assessment factor and a_ij is the relative importance of the i‐th environmental impact assessment factor over the j‐th. The permanent of this matrix B, i.e. per (B), is defined as the environmental impact assessment factors function. The permanent is a standard matrix function and is used in combinatorial mathematics (Nijenhuis and Wilf 1975, Resta and Sburlati 2006, Liang et al. 2007). Application of permanent concept will lead to a better appreciation of environmental impact assessment factors. Moreover, using this no negative sign will appear in the expression (unlike the determinant of a matrix that contains both positive and negative signs) and no information will be lost.

The permanent function corresponds to the determinant of a matrix but considering all the determinant terms as positive terms. The permanent function is able to provide the total objective value when the numerical values for A_i and a_ij are substituted in the multinomial. Furthermore, permanent function is an invariant of the system. Owing to these reasons, researchers had used the permanent function of a matrix, which does not contain any negative terms, and thus provides the complete information without any loss (Gandhi and Agrawal 1994, Rao and Gandhi 2001, 2002, Grover et al. 2004, Rao and Padmanabhan 2006). Hence the permanent function is viewed relevant in this paper as the environmental impact assessment factors function.

The environmental impact assessment factors function for matrix Expression (1) is written as:

Expression (2) is the complete expression for the considered environmental impact assessment problem, as it considers the presence of all factors and all of the possible relative importance between the factors. The terms are the sets of distinct diagonal elements and loops of off‐diagonal elements of different sizes (i.e. a_ija_ji, a_ija_jka_ki, etc.). As explained, this expression corresponds to the determinant of a 6×6 matrix but considering all the terms as positive terms. Thus, the environmental impact assessment factors function characterises the considered environmental impact assessment problem as it contains all possible factors and their relative importance.

A computer program, PERMAN, is developed in this paper using C⁺⁺ language for calculating the value of permanent function of a square matrix of M×M size.

3. Environmental impact assessment index

Environmental impact assessment index (EIAI) is a measure of degree or extent by which a manufacturing process (or a combination of processes) can be successfully selected for producing a given engineering product or component in an environmental‐friendly manner. The environmental impact assessment factors function defined above, i.e. Expression (2) contains measures of factors and their relative importance and is used for evaluation of the EIAI. The numerical value of the environmental impact assessment factors function is called the EIAI. As the environmental impact assessment factors function contains only the positive terms, therefore higher values of A_i and a_ij will result in increased value of EIAI. To calculate this index, the required information are the values of A_i and a_ij.

3.1 Value of factor

The value of A_i should preferably be obtained from available or estimated data. When quantitative values of the factor are available, normalised values of a factor assigned to the alternatives are calculated by v_i/v_j, where, v_i is the measure of the factor for i‐th alternative and v_j is the measure of the factor for the j‐th alternative which has a higher measure among the considered alternatives. This ratio is valid for beneficial factors only. A beneficial factor means its higher measures are more desirable for the given application. Whereas, a non‐beneficial factor (e.g. energy consumption) is the one, whose lower measures are desirable and the normalised values assigned to the alternatives are calculated by v_j/v_i. In this case, v_j is the measure of the factor for the j‐th alternative which has a lower measure among the considered alternatives.

In the case of a qualitative factor (i.e. a quantitative value is not available), a ranked value judgment on a fuzzy conversion scale is adopted. By using fuzzy set theory, the value of the factors can be first decided as linguistic terms, converted into corresponding fuzzy numbers and then converted to the crisp scores. Cheng and Hwang (1992) had proposed a numerical approximation system to systematically convert linguistic terms to their corresponding fuzzy numbers. It contains eight conversion scales and in the present work, an 11‐point scale is considered. Rao and Padmanabhan (2006) had used a similar approach in their work. Table 1 shows the environmental impact assessment factor on a qualitative scale using fuzzy logic, corresponding to the fuzzy conversion scale as shown in Figure 1, and helps the users in assigning the values of A_i. For more details about the fuzzy conversion scale, one may refer to the work of Cheng and Hwang (1992). Once a qualitative factor is represented on a scale then the normalised values of the factor assigned for different alternatives are calculated in the same manner as that for quantitative factors.

Table 1. Values of environmental impact assessment factor.

Qualitative measures of environmental impact assessment factor	Assigned values
Exceptionally low	0.045
Extremely low	0.135
Very low	0.255
Low	0.335
Below average	0.410
Average	0.500
Above average	0.590
High	0.665
Very high	0.745
Extremely high	0.865
Exceptionally high	0.955

Figure 1 Linguistic terms to fuzzy numbers conversion(11‐point scale).

3.2 Relative importance of factors

The relative importance between two factors (i.e. a_ij) is assigned a value on the scale proposed by Saaty (2000) in his AHP method. The main procedure to assign the relative importance and to check the consistency made in the judgments is as follows:

	Construct a pair‐wise comparison matrix using a scale of relative importance. The judgments are entered using the fundamental scale of the AHP proposed by Saaty (2000). A factor compared with it is always assigned to value 1, so all diagonal entries of the pair‐wise comparison matrix are equal to 1. The numbers 3, 5, 7 and 9 correspond to the verbal judgments ‘moderate importance’, ‘strong importance’, ‘very strong importance’ and ‘absolute importance’ (with 2, 4, 6 and 8 for compromise between the previous values). Assuming M factors, the pair‐wise comparison of factor i with factor j yields a square matrix A1M×M where aij denotes the comparative importance of factor i with respect to factor j. In the matrix, aij = 1 when i = j and aji = 1/aij.
	Find the relative normalised weight (wj) of each factor by (i) calculating the geometric mean of i‐th row and (ii) normalising the geometric means of rows in the comparison matrix. This can be represented as: and The geometric mean method of AHP is used to find out the relative normalised weights of the factors because of its simplicity and easiness to find out the maximum Eigen value and to reduce the inconsistency in judgments. Hence, in the present work the geometric mean method of AHP is also used to find out the relative normalised weights of the factors.
	Calculate matrices A3 and A4 such that A3 = A1×A2 and A4 = A3/A2, where A2 = [w1, w2, ..., wj]T. A4 matrix is the result of dividing A3 matrix by A2 matrix.
	Find out the maximum Eigen value λmax (i.e. the average of matrix A4).
	Calculate the consistency index CI = (λmax−M)/(M−1). The smaller the value of CI, the smaller is the deviation from the consistency.
	Obtain the random index (RI) for the number of factors used in decision making (Saaty 2000).
	Calculate the consistency ratio CR = CI/RI. Usually, a CR of 0.1 or less is considered as acceptable and it reflects an informed judgment that could be attributed to the knowledge of the analyst about the problem under study.

A computer program, REL‐IMP, is developed in the present work and it includes the above steps and checks for the consistency made in the judgments. It may be mentioned that one may choose any scale for A_i and a_ij. But the final ranking will not change, as these are relative values. It is, however, desirable to choose a lower scale for A_i and a_ij to obtain a manageable value of EIAI.

The EIAI for different alternative manufacturing processes is evaluated using expression (2) and substituting the values of A_i and a_ij. Manufacturing process, for which the value of EIAI is the highest, is the best choice for producing the given engineering product or component.

4. Methodology

The main steps of the methodology are as follows:

Step‐I:

Once the product has been identified, identify the manufacturing processes and the environmental impact assessment factors for producing the given engineering product or component and short‐list the manufacturing processes on the basis of the identified factors satisfying the requirements. A quantitative or qualitative value or its range may be assigned to each identified factor as a limiting value or threshold value for its acceptance for the considered application. A manufacturing process with each of its factor, meeting the criterion, may be short‐listed.

Step‐II:

	After short‐listing the manufacturing processes, find out the relative importance (aij) relationships between the factors and normalise the values of factors (Ai) for different alternative manufacturing processes.
	Develop the environmental impact assessment factors matrix. This will be an M×M matrix with diagonal elements of Ai and off‐diagonal elements of aij.
	Obtain the environmental impact assessment factors function for the environmental impact assessment factors matrix.
	Substitute the values of aij and normalised values of Ai, obtained in Step‐I, in environmental impact assessment factors function to evaluate the environmental impact assessment index for the considered manufacturing processes.
	Arrange the manufacturing processes in descending order of EIAI. The manufacturing process having the highest value of EIAI is the best choice for producing the given engineering product or component.

Step‐III:

Take a final decision keeping in view the practical considerations. All possible constraints likely to be experienced by the user are looked into during this stage. These constraints include management constraints, political constraints, economical constraints, etc. However, compromise may be made in favour of a manufacturing process with a higher EIAI.

5. Example

Now, to demonstrate and validate the application of proposed combinatorial mathematics based decision making method for environmental impact assessment of manufacturing processes, a case study presented by Choi et al. (1997) is considered.

Choi et al. (1997) established an assessment model for manufacturing processes in terms of environmental impact for quantitative evaluation of product design. An assessment methodology was developed on the basis of the ‘material balance’ of a process and the relationship among different processes. As a result, the amount of solid waste generated, the energy consumed, the waste water incurred as well as the level of noise were obtained. A case study of the production of a toy train with 12 scenarios was performed to illustrate and examine the assessment model. The aim of the case study was to give an assessment of the product in terms of securing less environmental damage by changing the following:

1. one component of the product being produced by different manufacturing processes;

2. the recycling concept being introduced into the product;

3. the design of the product being altered.

The product structure was described below along with the related manufacturing processes:

	Engine funnel (two pieces): the product was a plastic one and hence the injection moulding process was employed so that machining operations and the electrical discharge machining (EDM) process were required for the production of the tooling and the mould set.
	Engine boiler (sheet metal): this was produced by the drawing process and drilling operations. With regard to the drawing process, the machining operation was employed to produce the mould set.
	Engine cabin (zinc): this was produced by the die‐casting process and drilling operations. In regard to die casting, machining operations and the EDM operation were employed to produce the mould set.
	Steel pin (3 pieces, mild steel): this was produced by turning operations.
	Base (zinc): this was produced by die‐casting process and drilling operations. With regard to die casting, machining operations and the EDM operation were employed to produce the mould set.
	Bush (6 pieces, mild steel): these were produced by turning and drilling operations.
	Wheel (6 pieces, mild steel): this was also produced by turning and drilling operations.
	Screw (6 pieces, mild steel): these were produced by turning operations.
	Cover: as this was a plastic product, the injection moulding process was employed, so that the machining operation and EDM process were required for the production of the tooling and the mould set.

On the basis of the above information, the assessment of the toy train was carried out for the different scenarios shown in Table 2, and the results were shown in Table 3.

Table 2. Assessment of the toy train for 12 different scenarios (Choi et al. 1997).

Scenario	Description of assessment
1	The original toy train model
2	Based on ‘1’, but the production method of the wheel was changed from machining to die casting
3	Based on ‘1’, but the production method of the wheel was changed from machining to injection moulding
4	Based on ‘1’, all bushes and screws were removed and three shafts were added
5	Based on ‘4’, but the production method of the wheel was changed from machining to die casting
6	Based on ‘4’, but the production method of the wheel was changed from machining to injection moulding
7	Based on ‘1’, the concept of recycling was introduced. This meant if any material can be reused or recycled, no solid waste was involved
8	Based on ‘7’, but the production method of the wheel was changed from machining to die casting
9	Based on 7, but the production method of the wheel was changed from machining to injection moulding
10	Based on ‘4’, the concept of recycling was introduced. This meant if any material can be reused or recycled, no solid waste was involved.
11	Based on ‘10’, but the production method of the wheel was changed from machining to die casting
12	Based on ‘10’, but the production method of the wheel was changed from machining to injection moulding

Table 3. Assessment results for the toy train for 12 different scenarios (Choi et al. 1997).

Scenario	Solid waste (mm^3)	Energy consumption (kWh)	Waste water (m^3)
1	476,743	1.252	0.879
2	458,449	0.892	0.524
3	473,311	0.892	0.524
4	457,146	0.815	0.526
5	438,852	0.455	0.172
6	453,714	0.455	0.172
7	51,023	1.252	0.879
8	30,593	0.892	0.525
9	30,617	0.892	0.525
10	31,426	0.815	0.526
11	10,996	0.455	0.172
12	11,020	0.455	0.172

Now, to demonstrate and validate the proposed combinatorial mathematics based decision making, various steps of the methodology, proposed in Section 4, are carried out as described below:

Step‐I:

In the present work, the factors considered are the same as that of Choi et al. (1997), and these are SW, EC, WW and noise level (N). However, Choi et al. (1997) had shown that the values of the noise factor are equal ( = 100 dB(A)) for all the alternative scenarios. Hence this factor is not considered in this paper. Had the values of noise been shown differently for different scenarios by Choi et al. (1997), those values would have been considered in this paper.

Step‐II:

(1) The quantitative values of the factors, which are given in Table 3, are to be normalised. All three factors considered are non‐beneficial factors and lower values are desirable. Values of these factors are normalised following the procedure suggested in the first paragraph of Section 3.1 and are given in Table 4 in the respective columns.

Table 4. Normalised assessment results for the toy train for 12 different scenarios.

Scenario	Solid waste (mm^3)	Energy consumption (kWh)	Waste water (m^3)
1	0.02306	0.3634	0.1957
2	0.0240	0.51	0.3282
3	0.0232	0.51	0.3282
4	0.02405	0.5583	0.3270
5	0.02505	1	1
6	0.02423	1	1
7	0.2155	0.3634	0.1957
8	0.3594	0.51	0.3276
9	0.3591	0.51	0.3276
10	0.3499	0.5583	0.3270
11	1	1	1
12	0.9978	1	1

Relative importance of factors (a_ij) is assigned the values as explained in Section 3. Let the decision maker make the following relative importance assignments among SW, EC and WW:

In this example, the decision maker has assigned comparatively higher importance to SW, high importance to EC and low importance to WW (using AHP method). For example, SW is considered to be moderately more important than EC in environmental impact assessment of manufacturing processes. Hence a relative importance of 3 is assigned to SW over EC. Similarly, other relative importance relations can be explained. However, it may be added that, in actual practice, these values of relative importance can be judiciously decided by the decision maker depending on the requirements. The assigned values in this paper are for demonstration purpose only. Furthermore, it may be added that the relative importance values are independent of the quantitative and/or qualitative values of the factors.

(2) Environmental impact assessment factors matrix of this graph is written based on Expression (1).

(3) Environmental impact assessment factors function is written. However, it may be added that as a computer program is developed for calculating the permanent function value of a matrix, this step can be skipped.

(4) Environmental impact assessment index is calculated using the values of A_i and a_ij for each alternative manufacturing process. The a_ij values represent the relative importance of the attributes and remain the same in the matrix for different alternatives while calculating EIAI. However, the values of diagonal elements A_i will be different for different alternatives.

(5) The calculated values of EIAI for different manufacturing processes are given below in descending order:

Table

Scenario 11:	6.3552
Scenario 12:	6.3508
Scenario 5:	4.4054
Scenario 6:	4.4038
Scenario 10:	3.6544
Scenario 9:	3.6121
Scenario 8:	3.6116
Scenario 4:	3.2691
Scenario 2:	3.2216
Scenario 3:	3.2207
Scenario 7:	3.1453
Scenario 1:	2.9392

Thus, the proposed method using combinatorial mathematics based method in conjunction with AHP suggests scenario 11 as the most environmental‐friendly. Scenario 12 is next to scenario 11 in this regard and scenario 1 is the least environmental‐friendly. Choi et al. (1997) also suggested scenario 11 as the first, scenario 12 as the second and scenario 1 as the last choice from an environmental impact point of view. However, the proposed method is superior to the method used by Choi et al. (1997) in that it enables a more critical analysis since any number of quantitative and qualitative factors can be considered. Also, the proposed method in this paper can take care of the environmental impact assessment factor on a qualitative scale using fuzzy logic. Such a provision is missing in the method suggested by Choi et al. (1997). Furthermore, the proposed method assigns the values of relative importance based on AHP method, whereas Choi et al. (1997) had not considered this aspect and used simple mathematics to analyse the environmental impact of manufacturing processes. The use of permanent concept helps in better appreciation of the factors and it characterises the considered environmental impact assessment problem as it contains all possible factors and their relative importance (from a combinatorial point of view).

It may be noted that the proposed combinatorial mathematics based method in conjunction with AHP is used for assessing 12 scenarios involving three assessment factors in this present example. However, the proposed approach, in general, can consider any number (e.g. M) of quantitative and qualitative factors. The computer program developed in this paper for calculating the permanent function of a matrix of M×M size can be used for that purpose.

6. Conclusions

Even though a considerable amount of research on environmental impact assessment of manufacturing processes had been carried out in the past, only a few systematic decision making methods were used. In this paper, a simple and logical decision making method based on combinatorial mathematics is suggested which helps in selection of a suitable environmental‐friendly manufacturing process (or a combination of manufacturing processes) from among a large number of available alternative manufacturing processes for producing a given engineering product or component. The measures of the environmental impact assessment factors and their relative importance are considered together to rank the alternative manufacturing processes and hence it provides a better accurate evaluation of the alternative manufacturing processes.

The proposed EIAI evaluates and ranks manufacturing processes that leads to selection of a suitable manufacturing process (or a combination of manufacturing processes) for producing a given engineering product or component.

The proposed method is a general method and can consider any number of quantitative and qualitative environmental impact assessment factors simultaneously and offers a more objective and simple environmental impact assessment approach. Furthermore, the suggested methodology can be used for any type of assessment and selection problem involving any number of factors.

Acknowledgement

The author acknowledges the financial support of the Council of Scientific and Industrial Research (CSIR), New Delhi to carry out the present work.