Environ. Sci. Technol. 1999, 33, 1495-1500
Application of Analytic Hierarchy
Process Techniques to Streamlined
Life-Cycle Analysis of Two Anodizing
Processes
PATRICK EAGAN*
Engineering Professional Development,
Mechanical Engineering, 432 North Lake Street,
University of WisconsinsMadison, Madison, Wisconsin 53706
LAURENCE WEINBERG
Boeing Company, P.O. Box 3707 (MS 7A-XC),
Seattle, Washington 98124-2207
New approaches and tools are needed to enable engineers
to assess and deal with the environmental attributes of
manufacturing processes. A special concern of adding
environmental attributes to products and processes is dealing
with the tradeoffs associated with those attributes. The
paper demonstrates the utility of the Analytic Hierarchy
Process (AHP) when applied to the environmental streamlined
life-cycle assessment (SLCA) of two manufacturing
processes (chromic acid and boric/sulfuric acid anodizing).
Two methods are detailed in the paper and the accompanying
Supporting Information. The application of AHP to
abridged matrix-based tools adds value to a SLCA approach
by providing logical consistency to valuing the matrix
cells and increasing the speed of analysis. AHP also provides
a built-in check on consistency that enables the user to
monitor the various comparison matrixes for logical
consistency in assigning numbers to the cells of the
matrixes.
Introduction
This paper describes an application of a streamlined lifecycle assessment matrix to an environmental analysis of two
aluminum anodizing processes. Analytic Hierarchy Process
(AHP) is a decision-making approach that has utility in the
emerging area of design for the environment (DFE). The
analysis will demonstrate the power, nuances, and sensitivity
of AHP when applied to streamlined life-cycle assessment
(SLCA). For the purposes of this paper, life-cycle analysis is
defined to be the analysis of a product, process, or facility’s
environmental benefits and burdens that occur during its
life-cycle (1-4). Specifically, this paper focuses on the
assessment of a manufacturing process. In addition, the use
of the terms SLCA and DFE is consistent with Graedel (5).
AHP is only one decision theory approach that can have
utility for environmental decision making. One of the
advantages of applying AHP to SLCA matrix analysis is its
flexibility. AHP can be used to establish the relative values
(or weighting) associated with each cell of a SLCA matrix or
to environmentally compare two or more processes or
products. When used in conjunction with a matrix-based
* Corresponding author phone: (608)263-7429; e-mail: Eagan@
engr.wisc.edu.
10.1021/es9807338 CCC: $18.00
Published on Web 03/26/1999
 1999 American Chemical Society
SLCA tool, AHP is relatively easy to use and in some
applications enhances the speed of analysis.
The application described in this paper was done at the
Boeing Company as a pilot test demonstration of the SLCA
technique. The analyses reported here and the development
of the SLCA matrixes were developed by a team of pollution
prevention process specialists. The analysis was carried out
to test the ease of application of the matrix technique and
the associated matrix cell questions.
An appendix, which appears as Supporting Information,
shows all the details of the analysis described in this paper.
Background
A critical aspect of environmental product or process design
is the analysis of its life-cycle. Most design-for-the-environment activities evaluate to one degree or another the
environmental impacts of various life-cycle stages. The
resulting tools are evolving. Ideally a method would identify
and account for all the environmental impacts of a product
or process. The Society of Environmental Toxicology and
Chemistry (SETAC) has formalized this methodology and
called it life-cycle analysis or LCA. Generally these LCAs have
been performed on “simple” products in the United States
and Europe. However, LCA has found limited application on
complex products. Extensive applications have been hampered by data sufficiency issues, costs, and balancing the
accuracy of analysis with decreasing utility associated with
that detail (2-4, 6).
Faced with the limited utility of life-cycle analysis for
complex products, several companies have developed SLCAs
or abridged LCA approaches for their design communities.
A useful type of SLCA is a matrix-based approach developed
by Graedel at AT&T (1, 5). Generic matrixes have been
developed for products (7), processes (8), facilities (9), and
materials (10). Other design matrixes have been developed
as well (11).
A special concern of adding environmental attributes to
products and processes is dealing with the tradeoffs associated with those attributes. Some environmental attributes
come at the expense of others. Is it better to minimize the
use of water in Arizona for production at the expense of
volatile air emissions? Is it better to locate a manufacturing
plant near a source of energy or near a source of production
materials? Design engineers when faced with shrinking design
cycle times and time pressures will answer these complex
questions, and a prioritization process takes place. How
to identify those values, assign corresponding weights, and
make the values explicit are important and sometimes
difficult to perceive. SETAC recognized these issues and
outlined a number of methods to deal with valuation, including decision analysis using Multi-Attribute Utility Theory
(MAUT), Analytic Hierarchy Process (AHP), and Impact
Analysis Matrix (IAM) (12). Design tools that are in a matrix
format lend themselves to an AHP approach. This paper will
focus only on AHP.
What Is AHP?
AHP is a flexible method that assigns weights to various factors
in a hierarchical structure by making pairwise comparisons.
The method permits comparison of alternatives with respect
to multiple attributes. It is particularly useful for complex
problems and when values are involved. An AHP user
identifies an objective to be attained and alternatives to meet
this objective, creates a hierarchy of factors that influence
the objective, and populates a sequence of pairwise comparison matrixes using AHP scoring rules. This is illustrated
and discussed below and in the Supporting Information. The
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FIGURE 1. Process matrix.
method has been used in a variety of problems and settings
(13, 14) to establish a structured approach for decision
making. These include risk analysis (15), cost/benefit studies
(16), and conflict resolution (17) to name a few.
The AHP approach has a number of features. AHP can be
used for sensitivity analysis to see what happens when
different values are prioritized. It can be used by individuals
or groups. AHP also allows professionals to revisit and refine
problem definition and values over time as well as to examine
the tradeoffs and values represented by the analysis.
The AHP approach assumes that each of the factors under
assessment is independent. In practice this is difficult to
achieve, but the method can still be applied when there is
some degree of interdependence. Saaty has addressed this
question of independence in his work (pp 89-90 of ref 14).
When the objective is the comparison of two alternative
processes using an SLCA matrix, the user has two options.
The first consists of computing a weighted, scored matrix for
each process and then comparing the resulting matrixes (the
Matrix Question Approach). This option permits each process
to be examined by itself and may indicate areas of potential
process improvement. This approach also could be considered when detailed quantitative information is available for
the alternative processes. Another way to attack the problem
is to create another level in the AHP structure and to use the
AHP methodology to directly compare the two processes
(the Direct Comparison Approach). The second option is
often faster to apply because it does not require effort where
the processes are equivalent in their impact. When less is
known about the processes, as is often the case during the
early stages of design, the Direct Comparison Approach still
permits useful analysis. Direct comparison also addresses
some of the problems associated with the use of relative
magnitude terms when using the Matrix Question Approach.
(See SLCA Matrix Description section below.)
AHP Example Application
This paper compares two alternative anodizing processes
for the treatment of aluminum. Both processes involve
running a current through a bath in which the aluminum
part is submerged. Alternative A involves the use of chromic
acid as the bath, while alternative B uses a boric/sulfuric
acid bath. The principal reason for alternative B is the
elimination of chromium chemistry in the anodizing process.
Chromium (as chromium VI) is a regulated material with
significant environmental and health impacts due to its
hazardous nature. Alternative A operates at a lower temperature (with possible cooling requirements) than alterna1496
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tive B, indicating that alternative B may have energy
advantages. However, it turns out that alternative B requires
better temperature control (it operates in a smaller temperature range), which would tend to favor alternative A with
respect to energy considerations. For purposes of this
analysis, these two factors cancel each other out; the processes
are considered to be equal with respect to infrastructure
energy considerations. Discussions with process experts
suggested that both processes contributed equally to the
weight of products passing through the processes. Hence
the impact to energy consumption during the product lifecycle stage (lc6 in Figure 1) was considered to be the same
for each process. It is in these seemingly difficult comparisons
that decision theory can be helpful. AHP lends itself to
performing “what-if” scenarios.
SLCA Matrix Description
Figure 1 shows the process matrix, the life-cycle stages, and
the environmental concerns arrayed in a six by six matrix (8,
18). Designers using a streamlined matrix approach answer
a series of questions associated with each cell of the matrix.
These questions are intended to measure the degree of
environmental impact arising from the “life stage” in the
area of concern. For the process matrix, a typical question
for the first row, first column cell would be “Are large
quantities of water required to control process under analysis
(PUA) process equipment temperature?” Answers to the
questions make it possible to identify and score the various
environmental aspects of the process in each cell on a 0-5
scale (note that the choice of scale is arbitrary). The sample
question also illustrates one of the challenges of this
technique, the use of a relative magnitude term like the word
“large”. A user should define what will constitute “large” in
the context of the application. Other terms such as “significant” or “major” present similar difficulties. Direct comparisons of alternatives can help address this type of semantic
problem.
The process matrix is intended to be generic and to be
applicable to a wide range of processes. However, users
should modify the matrix to meet their needs by revising the
life-cycle stages, the areas of impact, or both. The meaning
of the life-cycle stages used in the Boeing process matrix can
be found in ref 8.
Environmental scores for processes can be quantified by
summing all of the cells in the matrix or showing them as
row or column sums. These matrixes can then be used to
improve process design, compare design alternatives, or
allocate resources to problem areas.
FIGURE 4. Second-level or tier 2 factors.
FIGURE 2. Matrix question approach.
FIGURE 5. Final tiersalternatives.
FIGURE 3. First-level or tier 1 factors.
Given the raw cell scores based on a series of questions,
it is desirable to assign weights to the cells in the matrix with
respect to each other. By not assigning weights, the user
implies that each cell is equally important. Equal cell valuation
has a consequence. For example, the user is implicitly treating
the importance associated with nonhazardous materials
choices for process infrastructure equal to that associated
with energy impacts during process termination. While
treating all cells equally may be of interest in a straight
comparison of processes, it is not as useful when engineering
or managerial decisions need to be made. As a management
device, varying the weights for each cell permits management
to transmit a vision of importance for process improvement.
For example, management may want to emphasize energy
reduction and assign higher weights to the cells in the energy
column.
Figure 2 represents the Matrix Question Approach. Each
cell’s unweighted (raw) score is multiplied by the corresponding cell weight to arrive at the cell’s weighted score
(the final weighted score). This is not matrix multiplication
as it is usually defined.
It is in this valuation approach that AHP can be used,
consistently and transparently, to develop a weighting factor
for each cell with respect to the other cells. The other benefit
to this kind of approach is that it makes the values of the tool
designers reflect managerial or expert opinion in a very cellspecific, visible way.
Conversion from the Matrix Format to an AHP Hierarchy
AHP will be used in the two approaches introduced earlier.
Both involve the comparison of two alternative processes.
The Matrix Question Approach will use AHP to value the
cells in the process matrix of Figure 1 with respect to anodizing
type processes. This information will then be combined with
the results of individually scoring the matrix for the two
alternative anodizing processes to compare these two
processes. In the second, the Direct Comparison Approach,
the two alternative anodizing processes are compared directly
using AHP. This second application will build upon the
analysis done for the first application.
The first step in the use of AHP is to determine a goal or
objective. The authors selected the following objective:
Determine the (process) design option with the least adverse
environmental impact over the life of the process.
The manufacturing process example chosen involves a
metal finishing operation (anodizing of aluminum) with a
choice between two types of anodizing methods described
earlier. The relative valuation of life-cycle steps and areas of
environmental concern reflect the choices and values of those
applying the tool, as well as the operating conditions that
characterize manufacturing at the site. The notation in Figure
3 will be used.
For each of these factors, the next level (second level or
tier 2) consists of the environmental impact categories shown
FIGURE 6. Process matrix hierarchy.
in Figure 4. The final tier consists of the two alternatives
shown in Figure 5. Figure 6 represents the hierarchical
structure.
The selection of the life-cycle stages as the tier 1 factors
is not pre-ordained. Using the environmental concerns as
the first tier and the life-cycle stages as the second tier in the
hierarchy is valid. The user needs to determine which order
seems most natural to the analysis.
In the analysis that follows, the comparisons were
structured so that a higher degree of importance indicated
greater adverse environmental impact. Thus, the alternative with the lower score is the preferred choice. This approach avoids semantic problems caused by double negatives.
The Matrix Question Approach
Using the AHP methodology, one can create a series of
comparison matrixes to display the relative importance of
one level of the hierarchy with respect to each of the factors
in the levels above. For the anodizing example, the AHP
structure of Figure 6 results in one 6 × 6 matrix (for the six
life-cycle stages) and six (for the six life-cycle stages), 6 × 6
matrixes (for the six impact areas with respect to each lifecycle stage). These matrixes will be used to generate the
weights to be assigned to each cell of the process matrix of
Figure 1. In the Direct Comparison Approach, the user would
create an additional 36 (for the 36 life-cycle stage/impact
area combinations) 2 × 2 matrixes (for the two alternative
processes). These matrixes can be found in the Supporting
Information.
The AHP approach requires a comparison of the factors
and their relationship to the impact on the goal. The user
performs this comparison by assigning an integer ranging
from 1 to 9 or the reciprocal of such an integer to each cell
of the matrix to measure the relative importance of the factors
that characterize the cell. The cells along the diagonal are
given the value 1. The precise description of this scoring
mechanism is given in the Supporting Information. If at any
stage the user wishes to avoid the admittedly difficult process
of comparing factors, then one can assign ‘1’ to every cell,
i.e., treat all factors as having equal importance. The user,
however, must realize that this choice is itself a statement
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FIGURE 7. Sample AHP matrixes.
of relative value. The values inserted into the matrix will
depend on the particular processes being examined, the site
where the processes are being implemented, and other similar
factors. Although the example involves two alternative
processes, AHP will easily accommodate two to seven
alternatives. The rationale behind the limitation of seven
alternatives is discussed by Saaty (pp 55-57 of ref 19).
Figure 7 illustrates two of the AHP matrixes for the
anodizing process described above. The entries represent
values assigned by the individual or team carrying out the
analysis. During the comparison of the life-cycle stages, two
factors were kept in mind while doing the pairwise comparison. These were the designer’s ability to influence the
life-cycle step and the relative extent of environmental impact
of the life-cycle step. In addition, some heuristic rules are
provided in the Supporting Information to help compare
the various life-cycle stages.
From the first matrix in Figure 7, it can be seen that the
life-cycle of products that pass through the process under
analysis (PUA) was considered to be the most important
factor. This reflects the fact that products that pass through
the PUA have extended lives. The PUA itself is considered
the next most important factor. The pre- and post-PUA
manufacturing steps are considered to be of intermediate
importance, while the infrastructure and termination steps
are considered to be of least importance. The infrastructure
stage was given a low level of importance relative to the
other life-cycle stages because the process was chemical
rather than mechanical in nature, the existing equipment
could be used for both processes, and the equipment has a
long useful life. Of the six, second tier matrixes, only one is
shown in Figure 7.
For the infrastructure stage (lc1), energy and solid waste
were considered to be the two dominant environmental
factors. The Supporting Information shows that the matrixes
for the manufacturing stages (lc2, lc3, and lc4) are similar to
each other, with energy, hazardous materials, and air
emissions as the dominant factors and with energy and air
taken as the most important. (Note: Because anodizing
process B represents a significant improvement in the area
of hazardous material choice, this relative ranking will tend
to downplay the advantage of B over anodizing process A.)
For process termination, lc5, the residues and energy use are
taken to be the major factors, with solid waste as the principal
factor. For lc6, energy use is the predominant factor, followed
by hazardous materials and the residues.
At this point, the AHP pairwise comparison matrixes at
the tier 1 and tier 2 levels are complete. The next step is to
apply mathematical algorithms to extract the appropriate
eigenvalues and eigenvectors that are used to determine the
weights to be assigned to the various factors. These weights,
in turn, can be used to assign weights to each of the cells in
the Boeing process matrixes. If a process is being evaluated
by itself, the cells are scored from 0 to 5 and then multiplied
by the cell weight as shown in Figure 2. If two processes are
being evaluated, each matrix can be analyzed, and the
resulting matrixes compared. The user can total scores or
add up the sum of the weighted cells. Figure 8 represents the
final cell weighting for the anodizing-type processes. The
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FIGURE 8. Anodizing process matrix cell weights.
FIGURE 9. Chromic acid raw scores.
FIGURE 10. Boric/sulfuric acid raw scores.
FIGURE 11. Product of the chromic acid raw scores and the cell
weightings (Figure 8).
FIGURE 12. product of the boric/sulfuric acid raw scores and the
cell weightings (Figure 8).
numbers 0.054, 0.149, 0.290, 0.133, and 0.141.233 represent
the column sums from Figure 8. The highest weighted
environmental area of concern was energy, corresponding
to the value of 0.290 associated with the energy column.
At this point, the weights are applied to the cell scores,
as determined by the responses to the corresponding cell
questions. Each process is now rated, and a user can identify
areas for process improvement from an environmental
perspective. Figures9 and 10 show the raw scores for the
two anodizing processes. Multiplying the raw scores
with the cell weights as shown in Figure 8 produces the
weighted scores for the two processes shown in Figures11
and 12.
A total of the cell scores from Figure 9 (chromic) yields
an unweighted score of 87.5. The boric/sulfuric option
unweighted score is 73.7. Thus, the boric/sulfuric option has
the lower perceived adverse environmental score. If the user
FIGURE 13. Anodizing process comparison process scores combined
with tier 2 weights.
Matrix Question Approach. Part of this difference is attributable to different groups carrying out the two different
analyses. In addition the Direct Comparison Approach
permitted a more refined comparison of the two processes.
For example, the Matrix Question Approach offers only a
yes/no choice with respect to the use of hazardous materials
in the PUA, while the Direct Comparison Approach allows
for a greater degree of comparison.
FIGURE 14. Final comparison of anodizing processes A and B.
Matrix Computations
normalizes the scores so that they sum to 1, the corresponding
figures become 0.543 (chromic) and 0.457 (boric/sulfuric).
Summing and normalizing the weighted scores from
Figures 11 and 12 show the scores for the two processes.
Chromic acid scored 0.554, and boric/sulfuric scored 0.446.
Thus, the weighting scheme has tended to raise the chromic
score somewhat and to lower (improve) the boric/sulfuric
score, thus increasing the preference for the boric/sulfuric
option.
In many applications, however, the user is more interested
in directly comparing two or more alternative processes rather
than analyzing each process separately in a stand-alone mode
as done above. In such a case, AHP offers a convenient
method to carry out this comparison.
With the advent of user-friendly computational programs
such as MatLab and Mathcad, which make use of matrix
notation, it is useful to frame the AHP technique as applied
to streamlined LCA in the language of matrixes. This is done
in the Supporting Information. Other available software
includes Expert Choice and Criterium Decision Plus from
Infoharvest.
The Direct Comparison Approach
Building on the first and second tier weights developed under
the Matrix Question Approach, the user now proceeds to
directly compare the two anodizing processes against one
another with respect to the tier 2 factors for each of the tier
1 factors. This results in a series of 36 2 × 2 matrixes. These
matrixes can be found in the Supporting Information. As
before, the eigenvalues and eigenvectors for these matrixes
can be computed using available software or by developing
appropriate computer algorithms, and from these data,
weights can be determined for the alternatives. Conceptually,
it may be easier to look at the vector of weights for the
alternatives as an allocation of points between alternatives.
In other words, the user allocates one point between the
alternatives for the corresponding life-cycle stage/area of
concern. The weighted matrix from the Matrix Question
Approach part of the paper can be used to look at the vector
weights. It is also possible to build up the final ‘score’ for the
alternatives by constructing the appropriate matrixes and
using matrix multiplication to calculate this score. It is
important to remember that the scores are relative, and they
should not be taken as absolute values associated with each
alternative. The matrix construction including the application
of AHP to allocate points between the two anodizing
processes can be found in the Supporting Information.
After assigning weights to the Tier 1 and Tier 2 factors and
using AHP to compare the alternative processes (see Supporting Information), the alternatives can be ranked with
respect to each other. Recall that these are relative, not
absolute, rankings. Figure 13 shows a summation of the lifecycle rows.
Recalling that a higher score indicates greater adverse
environmental impact, a user can see that alternative A
(chromium acid anodize) is less environmentally acceptable
for each life-cycle stage, or at best, the same as the alternative
boric/sulfuric acid anodize. Using weights for the tier 1 factors
with respect to the objective, the final matrix (vector)
compares the two process alternatives (see Figure 14. On the
basis of these two analyses, from the environmental lifecycle aspect, the boric/sulfuric acid process is the better
choice.
The authors, using the Direct Comparison Approach, gave
the boric/sulfuric option greater preference over the chromic
process than the pollution prevention team did using the
Discussion
The paper demonstrates the utility of AHP in the assessment
of two manufacturing processes, chromic acid versus boric/
sulfuric acid anodizing. AHP also provides a built-in check
on consistency that enables the user to monitor the various
comparison matrixes for logical consistency in assigning
numbers to the cells of the matrixes.
The AHP technique enables the user to make explicit the
values that are embedded in the analysis and thereby provides
the reviewer of the analysis with important data on “where
the analyst was coming from” when the streamlined LCA
was performed. The technique can be applied in a reasonably
short period of time, on the order of several hours if speed
is required, making it usable in a design environment. AHP
is certainly not the only technique that is available to assign
weights to the cells of a streamlined life-cycle matrix or to
compare alternatives with respect to environmental impact,
but anyone who proposes to work in this area should consider
the methods described in this paper as possible tools.
The application of AHP to abridged matrix-based DFE
tools has a number of benefits. These include increased
sophistication of establishing weighting values for the matrix
cells of an SLCA. The method allows a rational process where
panels of external or company environmental experts can
set weights in a relatively objective, internally consistent,
transparent way. Comparisons of processes can be done very
quickly, as is shown in the previous examples. All of these
factors add value to the SLCA approach to improving the
environmental attributes of products and manufacturing
processes.
Supporting Information Available
A detailed look at the analyses of the two anodizing processes
including a list of the heuirstic rules, the AHP matrix
computations, and a description of the necessary matrix
manipulations using matrix notation (16 pages). This material
is available free of charge via the Internet at http://
pubs.acs.org.
Literature Cited
(1) Graedel, T. E.; Allenby, B. R. Industrial Ecology; Prentice-Hall:
Engelwood Cliffs, NJ, 1995.
(2) Curran, M. A.; Young, S. Int. J. Life Cycle Assess. 1996, 1 (1),
57-60.
(3) Ehrenfeld, J. R. J. Ind. Ecol. 1997, 1 (2).
(4) Owens, J. W. J. Ind. Ecol. 1997, 1 (1), 37-49.
(5) Graedel, T. E. Streamlined Life-Cycle Assessment; Prentice-Hall:
Englewood Cliffs, NJ, 1998.
(6) White, A.; Shapiro, L. K. Environ. Sci. Technol. 1993, 27 (6),
1016-1017.
(7) Graedel, T. E.; Allenby, B. R.; Comrie, P. R. Environ. Sci. Technol.
1995, 29 (3), 143A.
VOL. 33, NO. 9, 1999 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
9
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(8) Eagan, P. D.; Weinberg, L. Development of a Streamlined, Lifecycle Design for the Environment Tool for Manufacturing
Process Modification: A Boeing Defense and Space Group Case
Study. Presented at the International Symposium of Electronics
and the Environment, Part of the Conference Record, San
Francisco, CA, May 5-6, 1997.
(9) Weinberg, L. The Development of a Streamlined, Environmental
Life-Cycle Analysis Matrix for Facilities. Presented at the
International Symposium of Electronics and the Environment,
Part of the Conference Record, Oak Brook, IL, May 4-5, 1998.
(10) Allenby, B. R. Environ. Qual. Manage. 1996, 5 (4).
(11) Veroutis, A.; Aelion, V. Environ. Qual. Manage. 1996, 5 (4).
(12) Society of Environmental Toxicology and Chemistry and SETAC
Foundation of Environmental Education Inc. A Conceptual
Framework for Life-cycle Impact Assessment; SETAC: 1993.
(13) Saaty, T. L. The Analytic Hierarchy Process: RWS Publications:
1990.
1500
9
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 33, NO. 9, 1999
(14) Saaty, T. L. Decision Making for Leaders: RWS Publications:
1995.
(15) Mustafa, M.; Al-Bahar, J. F. IEEE Trans. Eng. Manage. 1991, 38
(1).
(16) Willett, K.; Sharda, R. Socio-Econ. Planning Sci. 1991, 25 (2),
103-112.
(17) Saaty, T. L. Int. J. Conflict Manage. 1990, 1 (1), 47-68.
(18) Weinberg, L.; Eagan, P. D. Environ. Qual. Manage. 1997, 7 (1).
(19) Saaty, T. L. Multicriteria Decision Making; RWS Publications:
1996.
Received for review July 20, 1998. Revised manuscript received December 8, 1998. Accepted December 8, 1998.
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