The 21st International Conference on Multiple Criteria
Decision Making
13-17 June 2011, Jÿväskyla, Finland
Session MCDM models developed and used in Latin America
BALLAST WATER MANAGEMENT:
A COMPARATIVE ANALYSIS OF TODIM AND THOR
By Luiz Flavio Autran Monteiro Gomes1,3, Carlos Francisco
Simões Gomes1,2,3, Luiz Alberto Duncan Rangel2,3
1Ibmec/RJ, 2Universidade Federal Fluminense, 3MCDM
Research Group of Ibmec, Rio de Janeiro, Brazil. First
author’s e-mail address: autran@ibmecrj.br
1
Structure of the presentation
•
•
•
•
•
Problem definition
Structuring of the analysis
Choice of methods
Computations
Conclusions
2
Problem definition
3
This presentation addresses the problem of selecting a technology for
treating ballast water in ships. Ballast water poses a very serious, worldwide problem.
Slides 5 – 18 include a number of citations, figures and
tables taken from the vast litterature available on the
ballast water problem.
“A ballast tank is a compartment within a boat or ship that holds water. A
vessel may have a single ballast tank near its center or multiple ballast tanks
typically on either side. A large vessel typically will have several ballast tanks
including double bottom tanks, wing tanks as well as forepeak and aftpeak
tanks. Adding ballast to a vessel lowers its center of gravity, and increases
the draft of the vessel. Increase draft may be required for proper propeller
immersion.
The draft of a ship's hull is the vertical distance between the waterline and
the bottom of the hull), with the thickness of the hull included; in the case of
not being included the draft outline would be obtained. Draft determines the
minimum depth of water a ship or boat can safely navigate. The draft can
also be used to determine the weight of the cargo on board by calculating the
total displacement of water and then using Archimedes’ principle.” (Sources:
http://www.thefullwiki.org/Ballast_tank &
http://www.thefullwiki.org/Draft_(hull))
5
Scheme of a ship’s cross section. (Source:
http://www.thefullwiki.org/Ballast_tank)
6
Main ballast tanks and fuel ballast tanks. Source:
http://www.maritime.org/fleetsub/appendix/pages/figa-04.htm
7
“Ballast water is absolutely essential to the safe and efficient operation of
modern merchant ships, providing balance and stability to unloaded ships.
Ballast is any material used to weight and/or balance an object. One example
is the sandbags carried on conventional hot-air balloons, which can be
discarded to lighten the balloon's load, allowing it to ascend. Similarly, ballast
water is therefore water carried by ships to ensure stability, trim and
structural integrity. Ships have carried solid ballast, in the form of rocks, sand
or metal, for thousands of years. In modern times, ships use water as ballast.
However, ballast water may also pose a serious ecological, economic and
health threat due to invasive aquatic species.”
“Although current ballast water regulations recommend minimizing the
risk of introducing non-native species by exchanging ballast water in the
open ocean, this method has serious drawbacks. Even when it can be
used, organisms remaining inside the ballast tanks are discharged at a
later time into ports and harbors if the exchange fails to remove all
organisms.” (Sources: http://www.thefullwiki.org/Ballast_tank &
http://www.thefullwiki.org/Draft_(hull))
8
“With the introduction of steel-hulled vessels and pumping technology, water became the ballast
of choice. Water can be easily pumped in and out of ballast tanks, requires little manpower, and
as long as tanks are kept full, poses little to no stability problems.” (Source: IMO)
9
Sources: http://www.providence.edu/polisci/students/megaport/ballast.htm
& http://www.marinebiology.edu/Phytoplankton/ballast.htm
10
“Transfer of species in ballast water started as early as shipping trade. The
movement of some 3 to 12 billion tonnes of ballast water in ships
internationally each year has been responsible for the settlement of about
100 million tons of sediment. Its cleaning and the disposal of the ballast
sludge produced involve enormous costs, (approximately 30.000 € for a small
bulk carrier), as well as job hazards and time. Furthermore, as the sediment
cannot be removed, the freight capacity of the ship decreases with time and
stability problems arise.” (Source: http://www.bawapla.com/objectives.htm)
11
“Besides these economic aspects, ballast water has been recognised as a major
vector for the translocation of aquatic species across biogeographical boundaries.
It is estimated that as many as 10,000 alien species of plants and animals are
transported per day in ships around the world. As ships travel faster and world
trade grows, organisms are better able to survive the journey, using the settled
sediments as a substrate, and the threat of invasive species from ballast water
increases. Thus with a reduction of sediment settlement in ballast tanks, a
significantly reduced danger of alien organisms can be expected.” (Source:
http://www.bawapla.com/objectives.htm)
“At July 2005, eight countries (Argentina, Australia, Brazil, Finland, Maldives,
The Netherlands, Spain and Syrian Arab Republic) have signed the Ballast
Water Management Convention, subject to ratification.” (Source:
http://www.imo.org)
12
“Options being considered include:
• Mechanical treatment methods such as filtration and separation.
• Physical treatment methods such as sterilization by ozone, ultra-violet light,
electric currents and heat treatment.
• Designing ships that do not have structural supports and odd corners in the
ballast tanks that trap organisms and ballast water.
• Chemical treatment methods such adding biocides to ballast water to kill
organisms.
Various combinations of the above.
Treatment options must not interfere unduly with the safe and economical
operation of the ship and must consider ship design limitations. Any control
measure that is developed must meet a number of criteria, including:
•It must be safe.
• It must be environmentally acceptable.
• It must be cost-effective.
• It must work.”
(Source: http://globallast.imo.org/index.asp?page=ballastw_treatm.htm&menu=true. Here is a
useful reference on BW treatment technologies: http://www.lr.org/Images/BWT0210_tcm155175072.pdf)
13
“Unlike other forms of marine pollution, such as oil spills, where
ameliorative action can be taken and from which the environment will
eventually recover, the impacts of invasive marine species are most often
irreversible
In essence, ballast water is a major pathway of biological invasion
throughout the world. A promising way to prevent the introduction of
bioinvaders that cause ecological and economic harm is to remove
organisms from ballast water. No one method has yet been proven to
remove all organisms from ballast water and therefore more research
must be conducted in this area.”
(Source:
http://globallast.imo.org/index.asp?page=ballastw_treatm.htm&menu=true.
Here is a useful reference on BW treatment technologies:
http://www.lr.org/Images/BWT0210_tcm155-175072.pdf)
14
Source: Australian Quarantine & Inspection Service 1993. Ballast Water Management.
Ballast Water Research Series Report No. 4 AGPS Canberra.
15
“The dead weight tonnage (DWT) is also called loaded displacement. It is
equal to the difference in volume between the displacement of water by the
ship when fully loaded (loaded draft) and the displacement considering the
weight of the hull, all equipment, machinery, and boilers (ballast draft). In
other words, DWT is a measure of the weight the ship is designed to carry.”
(Source: Australian Quarantine & Inspection Service 1993. Ballast Water
Management. Ballast Water Research Series Report No. 4 AGPS Canberra)
16
Clam life cycle
Prawn life cycle
Source: http://globallast.imo.org/problem.htm
“Countries have tried to control the problem by requiring incoming ships to
flush their ballast tanks in the open ocean. Governments are preparing to
impose tougher standards on discharged ballast water.
In response, several companies have developed systems to kill organisms in
ballast tanks. Studies are going on in order to minimize the problem.”
IMO Assembly Resolution A.868(20) - “Guidelines for control and
management of ships’ ballast water to minimize the transfer of harmful
aquatic organisms and pathogens”.
17
“Even considering that inland water navigation in Brazil is still far from being used in
its full capacity a number of invasive aquatic species have been discovered in the
most important river and sea ports of that country.” (Source: Management of Ballast
Water in Brazil, presented at ICBWM 2008, by N.N. Pereira, R.C. Botter, M.M. Henrique)
18
“In Brazil, for example, it is verified that an invasion of the golden mussel
“Limnosperma fortunei”, proceeding from the ships’ ballast water has ocurred. This is
a native species from Chinese rivers and arroyos and from the Asian Southeast. Only
recently, for unknown reasons, it comes expanding its distribution around the world.
From Bacia do Prata’s estuary, it has expanded quickly for the superior stretches of
Paraná River’s Basin, invading, mainly, the great rivers, on a speed about 240 km/year.
In 2001, its presence was reported in Itaipu’s plant, and, in 2002, it was found in the
hydroelectric plants of Porto Primavera and Sérgio Motta, down Paraná River, in São
Paulo. The entrance of this species in this system of rivers must have occurred through
the intense navigation and transposition of boats used in the fishery. The impact of the
golden mussel in Brazil has been great and has caused public health problems; clogging
of tubulations, filters of hydroelectric plants and water sucking bombs; degradation of
the native species; and, also, problems related to the fishery.” (Source: Management of
Ballast Water in Brazil, presented at ICBWM 2008, by N.N. Pereira, R.C. Botter, M.M. Henrique)
19
Structuring of the analysis
20
A group of Brazilian of scientists and engineers comprising fifteen civilian and four
military experts and including members of the Brazilian delegation to IMO’s
International Conference on Ballast Water Management for Ships was asked to
demonstrate the feasibility of evaluating alternative ballast water treatment
technologies and to produce a ranking of those by using Multicriteria Analysis. The
technical leadership was one of the authors of this paper; their first challenge was
to design the evaluation process.
These analysts took the experience of IMO and decided to follow the following
steps:
Step 1: identify alternative ballast water management technologies according to
the experience of IMO Member States;
Step 2: same for evaluation criteria;
Step 3: obtain consensus about the alternatives to be evaluated and about the
criteria set;
Step 4: identify the importance to criteria by their relative weights;
Step 5: rank the alternatives by an acceptable multicriteria method;
Step 6: run a sensitivity analysis;
Step 7: produce a recommendation for potential users.
The multicriteria methods to be used should allow incorporating their value
judgment based on their experiences as well as the experiences of IMO
Member States. The evaluation process should be taken as a learning process.
Finally, it should also provide a recommendation for selecting the best ballast
water exchange and treatment methods.
21
After a carefully, first screening three competitive, alternative ballast water
management technologies were identified. The nineteen professionals participated
full-time in that first screening, that took two weeks (in IMO). The studies in Brazil
took more then five months (before IMO). The alternatives to be analyzed were then
named Management Method 1, Management Method 2, and Management Method
3. Although they were hypothetical alternatives their characteristics are quite typical
of existing technologies.
In order to apply Multicriteria Analysis to the problem the following
clusters of criteria were thus identified:
•Practicability
•Biological effectiveness (including pathogens)
•Cost/benefit
•Time frame within which the IMO standards could be practically
implemented
•Environmental impact of the sub-products from the use of each
technology.
One week of extensive discussions lead the experts to agree on the
following evaluation criteria. Those criteria were considered
exhaustive, non redundant and operational:
22
a) Practicability
a.1) Quantitative criteria
C1 - what ballast flow rate range is the system applicable? (m3/hour) (specify the minimum and maximum
flow rate)
C2 - what is the ship tonnage that the system can be applied to? (DWT) (specify the minimum and
maximum tonnage)
C3 - what is the additional workload on board? (man/hours)
C4 - what is the highest sea state (in the Beaufort, 0 – 12, wind scale) on which the system can operate?
C5 - what is the increase in tank's sediment caused by the system? (specify percentage)
a.2) Questions that need to be answered by a nominal scale, subject to association to a numerical scale of
intervals or by a yes/no answer
C6 - does the system present any risks to the ship's crew safety or to the crew? (-3, high risk; -2, medium
risk; -1, low risk; 0, no risk)
C7 - does the system affect the tanks' corrosion rate? (-2, increases the rate; -1, does not increase the rate;
0, reduces the rate)
C8 - does the system dispense with the need to keep chemical products on board? (Yes or No)
C9 - can the system be used in short voyages (up to 12 h)? (Yes or No)
C10 - can the system be operated without complete re-circulation of the ballast water? (Yes or No)
C11 - is the system unaffected by incrustation that could lead to a drop in pressure and/or to a reduction in
the flow rate? (Yes or No)
C12 - is the system being applicable to existing ships? (Yes or No)
C13 - are the ship's other functions independent from the system's operation? (Yes or No)
a.2) Questions that require detailed answers
C14 - does the system present any occupational hazard to the operator? Describe and quantify. (-3, high; -2,
medium; -1, low; 0, no hazard)
23
b) Biological effectiveness (including pathogens)
b.1) Quantitative Criteria
C15 - how effective is the system in relation to the removal, elimination and
inactivation/neutralization of aquatic organisms, apart from pathogens (according to the various
taxonomic groups)? (quantify in terms of percentage, size and/or concentration of organisms)
C16 - same as 15 for pathogens.
b.2) Questions for which the answers should be either Yes or No
C17 - does the system eliminate cysts (e.g. toxic dinoflagellate cysts, producers of toxins)?
C18 - does the system allow the elimination of organisms when the water enters the tank?
C19 - is the system adequate for the elimination of all species or life stages that may present a
hazard to the environment?
c) Cost-benefit
c.1) Quantitative criteria
C20 - what is the purchase cost? (US$)
C21 - what is the cost of installation? (US$)
C22 - what is the operational cost? (US$/ton)
C23 - what is the cost variation per ship size? (US$/ton)
C24 - what is the increase of fuel or oil consumption that is introduced by the use of this system on
board? (percentage)
24
d) Time frame within which the standards could be practically implemented
d.1) Quantitative criteria
C25 - within which time frame could the standards be practically implemented? (no. of months)
e) Influence of the system's sub-products on the environment
e.1) Question for which the answer should be either Yes or No
C26 - is the system free from generating sub-products that can have an impact on the environment?
Observation: Undesirable outcomes are taken with negative values as well as those that have a
negative impact with higher absolute values. According to that: i) In criteria C3, C5, C20-C25, negative
values are assigned to the lowest desirable features; ii) In criteria C8-C13, C17-C19 and C26, where the
answers should be either "Yes" or "No", a value of 1 was assigned to a "Yes" answer (desirable) and a
value of 0 to a "No" answer (undesirable); and iii) In criteria C6, C7 and C14, verbal (or nominal) scales
associated to a numerical scale have been created for checking purposes.
In the multicriteria analyses all criteria should be considered as having
the same weight due to difficulties in achieving consensus about the
weights. The nineteen experts considered the 26 criteria relevant
enough to be jointly considered in the structuring of the analysis. That
family of evaluation criteria reflected the convergence of a number of
technical, environmental, and political opinions and positions.
25
One parentheses: where does politics enter into the game? One example
follows:
• Relatively cheap methods exist for treating BW, one of them being the
exchange for lifeless water. Lifeless water can be normally found at 20 km
far from coastal areas and in places with more than 2,500 m of depth.
This is a method for treatment that can be used by countries such as
Brazil. It cannot be used in countries formed by many islands neither by
say European countries with relatively small sea areas.
• Some countries such as Brazil would have therefore lower costs for
treating BW than other countries . Vetoing the exchange for lifeless water
would be something natural from these countries. Besides, it may happen
that some countries would like to impose treatment technologies
produced by local companies instead of accepting a wide diversity of
solutions.
• The application of Multicriteria Analysis to the problem helped in
providing for a much broader view of the problem. It also contributed to
overpass the monocriterion perspective of pure politics.
26
In the multicriteria analyses all criteria should be considered as having
the same weight due to difficulties in achieving consensus about the
weights. The nineteen experts considered the 26 criteria relevant
enough to be jointly considered in the analysis. That family of evaluation
criteria reflected the convergence of a number of technical,
environmental, and political opinions and positions.
On the conceptual side we followed Milan Zeleny’s thinking when he
says, referring to three alternatives A, B, and I: “Because the choice
between A and B is influenced by the position of I (and therefore by
some of the remaining alternatives) observe that the independence of
irrelevant alternatives axiom has no place in describing human decision
making. So-called “irrelevant “ alternatives are actually very relevant and
human preferences are a function of the available alternatives and
change as these alternatives vary.” (Zeleny, M. HSM Integrating
Knowledge, Management and Systems. Singapore: World Scientific
Publishing, 2005, p. 273)
27
Three existing ballast water management technologies were considered in
the analysis: Management Methods 1, 2, and 3. The evaluation matrix below
was filled by experts.
Criteria
C1
Alternatives
Management Method 1
Management Method 2
Management Method 3
m3/h
m3/h
Maximum 13,000 m3/h
Minimum 300 m3/h
Maximum 15,000
Minimum 100 m3/h
Maximum 14,000
Minimum 200 m3/h
C2
Maximum 450,000 DWT
Minimum 450 DWT
Maximum 350,000 DWT
Minimum 350 DWT
Maximum 250,000 DWT
Minimum 450 DWT
C3
-90 man/h
-80 man/h
-90 man/h
C4
7
8
10
C5
-10 %
-12 %
-5 %
C6
-1
-2
-3
C7
-2
-1
-3
C8
1
1
0
C9
1
1
0
C10
1
1
0
C11
0
1
1
C12
0
1
1
C13
0
0
1
C14
0
-1
-2
C15
93 %
92 %
90 %
C16
90 %
88 %
91 %
C17
1
0
1
C18
1
0
0
C19
0
1
1
C20
-US$ 200,000.00
-US$ 210,000.00
-US$ 220,000.00
C21
-US$ 10,000.00
-US$ 21,000.00
-US$ 1,000.00
C22
-0.02 $/ton
-0.03 $/ton
-0.04 $/ton
C23
-US$ 9
-US$ 8
-US$ 6
C24
-3 %
-8 %
-1 %
C25
-6 months
-8 months
-9 months
C26
0
1
0
28
Choice of methods
29
Although a wide variety of tools could be used, the analysts decided to use
two multicriteria methods that have been conceived and developed by
Brazilian researchers. For this reason TODIM and THOR were chosen as
analytical tools.
Characteristics of the two methods:
• While TODIM has elements from the North American as well as the
European School, THOR is based on the ELECTRE family of methods and
takes care of imprecision both by fuzzy and rough set theoretical
modelling
• Both are non compensatory methods
30
The TODIM Method:
• The TODIM (an acronym in Portuguese for Interactive and Multicriteria
Decision Making) method is a discrete multicriteria method founded on
Prospect Theory (PT)
• The multiattribute value function of TODIM is built in parts, with their
mathematical descriptions reproducing the gain/loss function of PT. The
global multiattribute value function of TODIM aggregates all measures of
gains and losses over all criteria; that function is based on Tversky’s idea
of an additive difference function
• Being founded on PT, TODIM can either use a status quo, reference
alternative or the concept of a floating reference alternative
• Getting the weights of criteria (all equal in this application)
• Choosing a reference criterion
• Valuation of the alternatives in relation to each criterion, with
normalization by dividing each weight by largest weight for each
criterion
• Computing a matrix of relative dominance
• Calculation of the measurements of the overall desirability of each
alternative
• Sensitivity analysis
• An Excel®-based spreadsheet for calculations and for producing graphs
31
Measure of relative dominance of each alternative i over another
alternative j:
m
 (i, j)    c (i, j ),
(i, j)
c 1
Variables and parameters of TODIM:
(i,j) – dominance measurement of an alternative i in relation to
another alternative j
c (i, j) – measure of value of alternative I as compared against
alternative j according to criterion c
arc – substitution rate for criterion c as compared against criterion r
wic and wjc – valuations of alternatives i and j according to criterion c
 – attenuation factor, applicable to the segment of the value function
in the negative quadrant
 i – overall desirability of each alternative
32
Gain, No gain & no loss, and Loss parts of the value function:
 a rc (wic  w jc )

if wic  w jc  0

c a rc




Φ c (i, j)  0
if wic  w jc  0



( a rc )(w jc  w ic )
 1
c
if wic  w jc  0

a rc

 θ
33
Other mathematical formulations that have been tested for representing the
loss and gain sections of the prospect theoretical value function:
• Tanh and the shifted tanh
• Cumulative PT
34
Desirability of each alternative:

i
n
n
j 1
j 1
 (i, j)  min  (i, j).
n
n
j 1
j 1
max   (i, j )  min   (i, j )
35
36
THOR:
•
•
•
•
•
•
A multicriteria decision support system based on ELECTRE methods:
weights of criteria (all equal in this application)
preference and indifference thresholds for each criterion
concordance and discordance thresholds
fuzzy and rough set theoretical resources for tackling imprecision
a module that allows a group of decision makers to reach a decision
through the exchange of views of group members, from which
negotiation around the acceptable proposals starts
37
The THOR software is an implementation of the algorithm in Delphi 7.0
(Dbase in Firebird) and it allows:
• Conducting analyses of sensibility by changing weights, level of
uncertainties involved, etc, etc
• Comparing the three types of ranking rules; and
• Eliminating irrelevant criteria
38
When using THOR, 3 different situations in terms of ranking rules may be
used and are shown below. S3 is less strict that S1 and S2 and therefore can
lead to more dominances of one alternative over another. S1 allows a
greater number of ties that S3. S2 is an intermediate situation between S1
and S3.
- S1 :
n
 (w
j 1
n
j
| aPj b)   (wJ | aQj b  aI j b  aRj b  bQj a  bPj a)
j 1
- S2 :
n
 (w
j 1
n
| aPj b  aQj b)   ( wJ | aI j b  aR j b  bQj a  bPj a)
j
j 1
- S3 :
n
 (w
j 1
n
j
| aPj b  aQj b  aI j b)   (wJ | aRj b  bQj a  bPj a)
j 1
39
Some characteristics of the use of THOR:
• When using THOR the alternatives could be compared according to the
three different situations, S1, S2, and S3.
• Veto criterion – the candidate ballast water treatment technology should
not present any unacceptable restrictions.
• Undesirable outcomes were considered as having negative values side-byside with outcomes having a negative impact with higher absolute values.
According to that:
• In criteria C3, C5, C20-C25, negative values are assigned to the lowest
desirable features
•In criteria C8-C13, C17-C19 and C26, where the answers should be either "Yes"
or "No", a value of 1 was assigned to a "Yes" answer (desirable) and a
value of 0 to a "No" answer (undesirable)
• In criteria C6, C7 and C14, verbal (or nominal) scales associated to a
numerical scale have been created for checking purposes.
40
Some publications on TODIM, THOR and extensions:
•
•
•
•
•
•
CHEN, F.-d.; ZHANG, X.; Kang, F.; FAN, Z.-p. and CHEN, X. A Method for Interval Multiple
Attribute Decision Making With Loss Aversion. 2010 International Conference of
Information Science and Management Engineering, IEEE Computer Society, 453-456,
2010.
GOMES, L. F. A. M. ; RANGEL, L.A.D. An Application of the TODIM Method to the
Multicriteria Rental Evaluation of Residential Properties. European Journal of
Operational Research, v. 193, p. 204-211, 2009.
GOMES, L. F. A. M. ; RANGEL, L.A.D.; MARANHÃO, F. J. C. Multicriteria Analysis of
Natural Gas Destination in Brazil: An application of the TODIM Method . Mathematical
and Computer Modelling, v. 50, p. 92-100, 2009.
GOMES, C. F. S. ; XAVIER, L.H.; VALLE, R. Multicriteria Decision Making Applied to Waste
Recycling in Brazil. Omega, v. 36, p. 395-404, 2008.
GOMES, L.F.A.M.; LIMA, M.M.P.P. From Modelling Individual Preferences to Multicriteria
Ranking of Discrete Alternatives: A Look at Prospect Theory and the Additive Difference
Model. Foundations of Computing and Decision Sciences, v. 17, p. 171-184, 1992.
GOMES, L.F.A.M.; LIMA, M.M.P.P. Todim: Basics and Application to Multicriteria Ranking
of Projects with Environmental Impacts. Foundations of Computing and Decision
Sciences, v. 16, p. 113-127, 1992.
41
Computations
42
In the evaluation matrix undesirable outcomes were considered with
negative values as well as those that have a negative impact with higher
absolute values. According to that: i) In criteria C3, C5, C20-C25, negative
values are assigned to the lowest desirable features; ii) In criteria C8-C13,
C17-C19 and C26, where the answers should be either "Yes" or "No", a
value of 1 was assigned to a "Yes" answer (desirable) and a value of 0 to a
"No" answer (undesirable); and iii) In criteria C6, C7 and C14, verbal (or
nominal) scales associated to a numerical scale have been created for
checking purposes.
All values in the evaluation matrix were transformed into maximization
criteria and normalized for the use of the TODIM method. The THOR
method used data as shown in that matrix.
43
The application of TODIM took into consideration three possible situations: (i)
attenuation factor θ equal to 1.0 (less risk proneness); (ii) θ equal to 10.0
(greater risk proneness); and (iii) θ equal to 5.0 (an intermediate value between
the two previous extreme situations). Results from the computations are
presented in the table below. This table shows that MM1 ≻ MM2, MM3
Alternatives
Management
Method 1
Management
Method 2
Management
Method 3
 for θ = 1.0
 for θ = 5.0
 for θ = 10.0
1.000
1.000
1.000
0.808
0.000
0.000
0.000
0.210
0.425
Performance of the three alternatives
computed by the TODIM method
44
TODIM for  = 1
Value function for TODIM, θ = 1
1,5
1
0,5
0
-1,5
-1
-0,5
0
0,5
1
1,5
-0,5
-1
-1,5
Losses and gains
45
TODIM for  = 5
Valuefunction
functionfor
forTODIM,
TODIM,θθ==55
Value
1,5
1
0,5
0
-1,5
-1
-0,5
0
0,5
1
1,5
-0,5
-1
-1,5
Losses and gains
Losses and gains
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TODIM for  = 10
Value function for TODIM, θ = 10
1,5
1
0,5
0
-1,5
-1
-0,5
0
0,5
1
1,5
-0,5
-1
-1,5
Losses and gains
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In other words, thanks to the mathematical expressions for the gain and
the loss parts of its value function results from applying the TODIM
method to input data are consistent with the prospect theoretical value
function.
This has suggested that TODIM is indeed one of the very
few discrete multicriteria analytical methods founded on PT.
Criteria and alternatives in the THOR software
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An output from THOR
50
By using THOR it could be seen that Management Method 1 ranked
higher that the two other alternatives, being slightly better than
Management Method 3. There was indeed an ordinal agreement in the
outputs from TODIM and THOR when θ was made equal to 5.0 and to
10.0. Both methods then produced the following rank:
MM1≻MM3≻MM2. When θ was equal to 1.0, however, there was a
discordance between TODIM and THOR concerning the last two
alternatives: MM1≻MM2≻MM3 from TODIM and MM1≻MM3≻MM2 from
THOR. Nevertheless, since this was a problem in technology choice, for
practical purposes it was concluded that the two methods produced a
similar results. Taking into account the computations from TODIM for θ
equal to 5.0 and to 10.0 as well as the outputs from using THOR, it was
clear that MM2 could be ignored. Therefore if a rank were to be
produced only MM1 and MM3 would be in that rank. The final results is
that MM1 should be taken as the best choice.
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Conclusions
52
The multicriteria analysis demonstrated that the choice of an overall best
treatment should also be based on technical criteria and not merely on
political grounds.
It is worth noting that although the two methods rely on different bases
they produced in essence quite similar results. Other applications of
both TODIM and THOR have confirmed the convergence of results in
spite of the conceptual and technical differences between the two
methods: while TODIM is founded on the paradigm of Prospect Theory
and data are aggregated by means of building an additive value
function, THOR relies on the notion of outranking and does not take
into account the attitude of a decision maker facing risk. The fact that
they produce similar results suggests that structuring a decision
problem in a comprehensive way and applying a method correctly may
be at least as important as the technical characteristics of the method
per se.
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Acknowledgements:
This work was partially supported by CNPq through Research Projects No.
310603/2009-9 and 502711/2009-4.
Thank you!
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