A Multicriteria Multilevel Group Decision Method for Supplier Selection and Order Allocation

Abstract

Supplier selection is an integral part of supply chain management (SCM). It plays a prominent role in the purchasing activity of manufacturing and trading companies. Evaluation of vendors and procurement planning requires simultaneous consideration of tangible and intangible decision factors, some of which may conflict. A large body of analytical and intuitive methods has been proposed to trade off conflicting aspects of realism and optimize the selection process. In the large companies the fields of decision makers’ (DMs) expertise are highly distributed and DMs’ authorities are unequal. On the other hand, the decision components and their interactions are very complex. These facts restrict the effectiveness of using the existing methods in practice. The authors present a multicriteria decision analysis (MCDA) method which facilitates making supplier selection decisions by the distributed groups of experts and improves quality of the order allocation decisions. A numerical example is presented and applicability of the proposed algorithm is demonstrated in the Raiffeisen Westfalen Mitte, eG in Germany.

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Keywords: Multi-CriteriaDecisionAnalysis(MCDA),MultilevelGroupDecisionMaking(MLGDM),
OrderAllocation,SupplierSelection,SupplyChainManagement
INTRODUCTION
The formalization of complex decision prob-
lems requires comprehensive and accurate
modeling of the problem environment, its ele-
ments and their interactions. Selection of the
valid solution methods for such problems is a
very challenging task. Fictitious simplifica-
tions of decision situations lead to management
debacles and loss of profits. To avoid this, the
research efforts should be focused on the flex-
ible decision aiding framework which could
enable problem-oriented modularization of the
decision processes, their exhaustive analysis
by a set of appropriate and consistent methods
and generation of robust solutions. A variety
of empirical studies have been conducted to
improve decision making in teams. Still, the
complex nature of decision groups has been left
without proper attention in the analytical deci-
sion science. To fill this gap we first introduce
notions of Multilevel Group Decision Making
(MLGDM) to distinguish between the α, β and
γ decision makers (DMs). α-voting power is
A Multicriteria Multilevel Group
Decision Method for Supplier
Selection and Order Allocation
MariyaA.Sodenkamp,UniversityofPaderborn,Germany
LeenaSuhl,UniversityofPaderborn,Germany
ABSTRACT
Supplierselectionisanintegralpartofsupplychainmanagement(SCM).Itplaysaprominentroleinthe
purchasingactivityofmanufacturingandtradingcompanies.Evaluationofvendorsandprocurementplan-
ningrequiressimultaneousconsiderationoftangibleandintangibledecisionfactors,someofwhichmay
conict.Alargebodyofanalyticalandintuitivemethodshasbeenproposedtotradeoffconictingaspects
ofrealismandoptimizetheselectionprocess.Inthelargecompaniestheeldsofdecisionmakers’(DMs)
expertisearehighlydistributedandDMs’authoritiesareunequal.Ontheotherhand,thedecisioncomponents
andtheirinteractionsareverycomplex.Thesefactsrestricttheeffectivenessofusingtheexistingmethods
inpractice.Theauthorspresentamulticriteriadecisionanalysis(MCDA)methodwhichfacilitatesmaking
supplierselectiondecisionsbythedistributedgroupsofexpertsandimprovesqualityoftheorderallocation
decisions.Anumericalexampleispresentedandapplicabilityoftheproposedalgorithmisdemonstratedin
theRaiffeisenWestfalenMitte,eGinGermany.
DOI: 10.4018/jsds.2012010103

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proposed to elicit DMs’ contribution to criteria
prioritization; β-voting power is used to mea-
sure experts ability to evaluate performance
of alternatives with respect to the set of direct
decision criteria; γ-voting power index reflects
the DMs’ expertise in evaluation of auxiliary
decision components on indirect criteria.
Presented in this paper; the case study was
completed in cooperation with Raiffeisen West-
falen Mitte eG (also referred to as Raiffeisen),
an agricultural cooperative society operating in
Germany, Nord-Rhein Westfalen, since the 18th
century, with annual turnover exceeding 275
Mio. Euro in 2010. One of the largest trading
companies of crops, animal feed and fertilizers
also selling fuel oils is a significant aspect of
the company’s strategy. We have developed a
structured, multilevel group MCDA framework
to aggregate multiple objective factors and
group subjective expert judgments to enable
the strategic evaluation of fuel oil suppliers
and optimizing purchasing activity by align-
ing strategic priorities of the DMs with their
daily decisions.
PROPOSED ALGORITHM
AND ITS APPLICATION
Taking complex multicriteria decision, includ-
ing purchasing, is a consequent multistage pro-
cess. We designed the algorithm that includes
16 steps summarized below.
1. Identify Overall Purpose
of the Decision
A first step of MCDA is to establish a clear goal
pursued. Generally decision theory deals with
three main types of problems: choice, ranking
and classification (Zopounidis, 2002). Choice
is selection of the most appropriate alternative
or set of alternatives. Generally, organizations
have two approaches to supplier selection.
The first approach is to select the best single
supplier, which can meet all the requirements
(single sourcing). The second approach is to
select an appropriate combination of suppli-
ers (multiple sourcing) (Sanayei et al., 2008).
Ranking of suppliers is ordering of alternatives
based on measuring of their contribution to the
achievement of the stated decision objectives.
Classification is division of alternatives into
predefined homogeneous classes which are not
necessarily ordered, on the other hand in sorting
problems groups are ordered from the best to
worst (Zopounidis, 2002). The proposed multi-
level group framework is aimed at performing
the following analytical functions:
• Derive consensus based rankings of suppli-
ers in accordance with their strategic per-
formance. Rankings serve as a legitimate
and transparent foundation for establish-
ment of partnership strategies, selection
of long-term contractors and stimulation
of supplier development.
• Classification of vendors into the groups
reflecting their relative competitive advan-
tages and disadvantages.
• Support Just-In-Time (JIT) purchasing
decisions for trading activity based on
market-rate prices taking into consideration
compound strategic weights of vendors.
2. Form Decision Making Group
Once the goal is stated, a group comprised
of the people responsible for the successful
implementation of the decision must be formed.
Zeleny (2010) asserts that any DM makes
a decision either for himself or for others,
therefore a distinction between the decision
producer (or provider) and decisionconsumer
(or customer) has to be drawn. According to
the Crown copyright Multi-criteria analysis
manual (Crown, 2009) there are two main types
of DMs: stakeholders whose organization’s
values should find expression in the decision,
and key players who can make a useful and
significant contribution to the MCDA and
represent important perspectives on the subject
of the analysis. Numerical reviews in the field
of decision making have concluded that groups
learn faster, make fewer errors, recall better,
make better decisions, and are more productive,
with a higher-quality product than individuals

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(Baron et al., 1992; Davis, 1969; Johnson &
Johnson, 2003; Laughlin & Early, 1982). The
decision group may include:
• Board members and CEOs having clear un-
derstanding of the organization’s strategy;
• Subject matter experts at various levels
having insight to evaluate organization
environment, functional design of the
company and specific areas of its activity,
including purchasing;
• Representatives who can properly define
what suppliers should be considered in the
decision process;
• Experts who can provide reasonable esti-
mates for proposed suppliers; and
• Operative managers who are deeply
involved with the issue at hand and will
implement the decision.
Group decision making does not mean that
all team members have to be involved in every
aspect of a decision; instead they are expected
to process data and apply their individual ex-
pertise to contribute to the outcome (Saaty &
Peniwati, 2008).
In the proposed decision analysis frame-
work is considered a group of
K
DMs
(k K=1 2, ,..., ). In the study conducted for
Raiffeisen was organized a decision group in-
cluding a Raiffeisen’s board member and
managers from purchasing department
(
K
=3).
3. Define, Describe and Structure
a Finite Set of Decision Criteria
In modern management, one needs to consider
many factors with the aim of developing a long-
term supplier relationship (Muralidharan et al.,
2006). Choosing the right suppliers involves
much more than scanning a series of price
lists, and choices will depend on a wide range
of factors which involve both quantitative and
qualitative (Ho et al., 2010). The multi-criteria
decision models allow the integration of both
objective and subjective criteria to produce an
aggregate performance measure (Akarte et al.,
2001). In the numerous scientific publications
it is clearly indicated that vendor selection has
a multi-objective nature implying that multiple
conflicting criteria need to be considered in
the supplier evaluation and selection process
(Dickson, 1966; Weber et al., 1991). These
criteria must be defined according to the corpo-
rate strategies and the company’s competitive
situation (Sanayei et al., 2008). According to
Bouyssou (1990), the criteria set must have two
key qualities; be readable (i.e., include a number
of criteria restricted enough so that it is possible
to reason on this basis and eventually to model
the inter and intra-criteria information required
to perform an aggregation procedure) and be
operational (i.e., be acceptable as a working
basis for the study). Even Swaps method (Ham-
mond et al., 1998) can be applied to simplify
the complex decision and reduce the number of
objectives in the consequences table.
In multi-criteria analysis decision factors
can be grouped into contradictory categories.
First classification approach for making trade-
offs among various indicators was outlined by
Benjamin Franklin in 1772 in his “Moral of
prudential algebra” and is known as method of
Pros and Cons (Hammond et al., 1998). Other
classification schemes include opportunities
and threats for evaluation of strategic courses
of action (Tavana & Sodenkamp, 2010), divi-
sion into benefits and costs (Triantaphyllou &
Baig, 2005), internal strength and weaknesses
along with external opportunities and threats
(SWOT) (Tavana et al., 2010; Ghazinoory et
al., 2011) or alternatively, consideration of ex-
isting benefits and opportunities and potential
costs and risks (BOCR) (Saaty & Sodenkamp,
2010). Performance of alternatives on positive
criteria has to be maximized and on negative
criteria minimized. When the number of fac-
tors is large, typically more than a dozen, they
may be arranged hierarchically (Saaty, 1977;
Triantaphyllou, 2000) or as a feedback net-
work (Saaty, 1996). Such structures allow for
a systematic grouping of metrics in complex
decision problems.
Proposed here, the supplier evaluation
model is based on the Pros&Cons classifica-

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tion, where each class contains a three-level
hierarchy of criteria. Let us define:
M
The total number of groups of factors;
(
m M
=1 2, ,..., )
N
The total number of decision criteria;
(
n N
=1 2, ,..., )
L
The total number of sub-criteria;
(l L=1 2, ,..., )
CPros (CCons ) The cluster “Pros” (“Cons”)
including subjective and objective positive
(negative) factors;
Cm
Pros (Cm
Cons ) The m-th group of factors within
the Pros (Cons) cluster; (m M Pros
=1 2, ,...,
(m MCons
=1 2, ,..., ))
MPros (MCons ) The number of groups of factors
within the Pros (Cons) cluster;
NPros (NCons ) The number of attributes within
the Pros (Cons) cluster;
LPros (L
Cons ) The number of sub-criteria
within the Pros (Cons) cluster;
NObj (NSbj ) The number of objective (subjec-
tive) decision criteria; (
n N=1 2, ,...,
)
L
Obj (LSbj ) The number of objective (subjective)
sub-criteria; (l L=1 2, ,..., )
Cmn
Pros (Cmn
Cons ) The n-th factor within the m-th
group of the Pros (Cons) cluster;
(m M Pros
=1 2, ,..., ; n Nm
Pros
=1 2, ,...,
(m MCons
=1 2, ,..., ; n Nm
Cons
=1 2, ,..., ))
Cmnl
Pros (Cmnl
Cons )The l-th sub-factor of factor
n within the m-th group of the
Pros (Cons) cluster;(m M Pros
=1 2, ,..., ;
n Nm
Pros
=1 2, ,..., ;l Lmn
Pros
=1 2, ,..., ;
(m MCons
=1 2, ,..., ; n Nm
Cons
=1 2, ,..., ;
l Lmn
Cons
=1 2, ,..., )
Based on the reviews of vendor selection
criteria (Dickson, 1966; Weber et al., 1991; Sen
et al., 2008; Inemak & Tuna, 2009) and inter-
views with Raiffeisen representatives we
identified 20 criteria (
N
=20 ) including 5
sub-factors (
L
=5) categorized into 6 groups
(
M
=6) and arranged them into the hierarchy.
The Pros category included 17 strategic
criteria allocated among the six groups
(MPros =6). The first group; Flexibility in-
cluded three criteria (NFlexibility
Pros =3) one of
which was comprised of three sub-criteria
(LFlexibility ProductMix
Pros
=3). The second group;
Service included three criteria ( NService
Pros =3)
one of which was divided into two sub-criteria
(LService GoodCommunicationSystem
Pros
=2). The other
three groups included 2 to 5 criteria each one
(NLogistics
Pros =3,NRelations
Pros =5,NFinancial
Pros =2)
without further division into sub-criteria. The
Cons category included one tactical negative
attribute and three strategic criteria allocated
among the two groups (
M
Cons
=2
), strategic
criteria in the group of Risks ( NRisks
Cons =3) and
the tactical criterion Price belonged to the group
Financial ( NFinancial
Cons =1).
The hierarchy of decision criteria for Raif-
feisen’s fuel suppliers is visualized in Figure 1
and description of individual criteria is given
in Table 1.
4. Define Decision Alternatives
The contemporary supply chain management
is to maintain long term partnership with sup-
pliers, and use fewer but reliable suppliers (Ho
et al., 2010). Aissaoui et al. (2007) stated that
today’s logistics environment requires a low
number of suppliers as it is very difficult to
manage high numbers. Therefore, inefficient
candidates should be not included into the
evaluation process. In Just-In-Time environ-
ment the majority of companies prefer to follow
a strategy of a single supplier or at least with
few suppliers (Ansari & Modarresss, 1986).
Quarly (1998) presented the factors of deter-
mining the policy of a single or multi supplier
selection. The elimination method is a useful
approach for suppliers pre-selection. The idea
is that suppliers who do not satisfy the mini-
mum level of key criteria are not accepted for
further consideration. Hammond et al. (1998)
stated that one may simplify a complex decision
by looking for the practical dominance in the
consequences table. This method reduces the

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number of alternatives and helps to focus only
on highly competitive options.
We consider a set { }
A
i of discrete elements
Ai denoting alternatives (
i I
=
1 2, ,...,
;
I≥2
).
The DMs from Raiffeisen selected eight
suppliers (
I=8
) for the evaluation process:
A1=GRG,A2=Atrian,A3=Certyoil,A4=Naro-
naft,A5=Vetic,A6=PetroliumNord,A7=West
PetrolGroup and A8=POSF.
5. Build Decision Hierarchy
Hierarchy is a fundamental tool of human think-
ing and the most common way to organize deci-
sion problems (Saaty & Peniwati, 2008). Saaty
(1994) suggests using the hierarchy containing
three basic levels of elements connected from
the top to the bottom; goal on the top, decision
criteria on the intermediate level and alternatives
on the bottom, as shown in Figure 2.
Figure1.HierarchyofRaiffeisen’ssupplierselectioncriteria

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Real decision problems usually have a
more complex hierarchical structure than is
depicted by Saaty and involve criteria that
characterize alternatives not directly, but
through some external objects. The main reason
why such objects may have to be considered
as a part of decision hierarchy is the impossibil-
ity in some cases to provide direct assessment
of alternatives, according to a set of defined
decision criteria due to reflection by those
Table1.Decisioncriteriaandtheirdescription
Criterion Description Measurement
Unit
Volume Flexibility Supplier’s capabilities and readiness to increase/decrease the ordered quanti-
ties at short notice
Subjective scale
(SS)
Rush Order
Processing Possibility to purchase and deliver the products within a short time SS
Product Mix Purchased quantities of other products during the period Thousand litres
Business Hours Number of business hours during the week Hours
Information
Exchange
Information and forecasts regarding situation in the industry, market trends
and other relevant information e.g., advertising tactic SS
Number of
Contact Persons Number of contact persons authorized to take orders and to reply to inquiries Integer number
Responsiveness Speed of reaction and professionalism of contact persons SS
Number of
Loading Points Number of disposable loading stations Integer number
Quick Loading Possibility to load the goods quickly on the supplier’s terminals SS
Process Flexibility Well organized loading process on the stations; training programs for the drivers SS
Past Businesses Quantities of the product at hand purchased during the period Euro
Stabilized
Relationship
Long lasting relationships without pronounced negative incidents or contra-
dictions in the past SS
Supplier’s
Attitude Friendly and individual treatment; relationships beyond the business SS
Supplier’s
Desire to
Cooperate
Supplier’s attempts for sustainable partnership SS
Trust The expectations that the supplier’s future behaviour will remain within the
framework of common values and moral obligations SS
Bad Experience Negative incidents in the past, such as breaches of contracts or supplier defaults SS
Bad Reputation in
Industry
The supplier is not respected by its customers, suppliers or other groups of
interests SS
Supplier’s
Acquisition
Difficulties
Probability of lack of product in stock e.g., due to bad weather (frost, drought
or flood) SS
Terms of Payment Maximal provided payment period Days
Credit Limit The amount guaranteed by the supplier is high enough to satisfy your demand
for its product SS
Price Bid price of the product for 100 Litres Euro

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criteria of different aspects of the engaged
services, facilities or other external objects and
not of alternatives themselves. We shall further
call these external elements auxiliary decision
objects (ADOs). The indicators specifying
performance of the ADOs will be called indirect
criteria (C*). The attributes describing alter-
natives immediately will be referred to as direct
criteria. In Figure 3 is shown a decision hier-
archy including (M-1) direct criteria connected
to the alternatives, one indirect criterion describ-
ing the ADOs and relationships between the
alternatives and the ADOs.
Correspondence between the ADOs and
alternatives must be established in accordance
with Table 2 to enable tracking the influences
of indirect criteria on alternatives.
Raiffeisen’s suppliers do not own central-
ized facilities for warehousing and shipment of
fuels. Instead, each supplier leases space on the
large loading terminals. Moreover, several
competing suppliers can use service of the same
loading stations. The eight suppliers under
consideration share services of five (
T
=
5
)
loading terminals situated in Dortmund, Gelsen-
kirchen, Hamm, Lünnen and Üntrop. These
stations differ on two criteria from the group
Logistics: Quickloading (CPros
3 2 *) and Process
flexibility (CPros
3 3 *). The layout of suppliers on
the loading stations is profiled in Table 3.
Evaluated suppliers, shared by them ex-
ternal facilities, criteria and dependencies
among these elements yield the decision hier-
archy exhibited in Figure 4.
6. Identify the DM’s Alpha-Voting
Power for Assessment of Criteria
We assume that some DMs have more authority,
expertise, knowledge, or skills. Therefore each
voting member of the decision team is assigned
a voting power which is meant to reflect his or
her potential ability to influence the decision
outcome. Bodily (1979) indicated that these
weights may be assigned either through mutual
agreement of the decision team members or by
a “super decision maker” (benevolent dictator).
Top managers, CEOs or board members
may not be too deeply involved with the daily
(purchasing) decisions and evaluation of alter-
natives (vendors). But they usually have better
vision of strategic priorities and objectives of
their organization and its functional units than
lower level employees.
We introduce a coefficient α standing for
Alpha voting power to designate the relative
DMs’ impacts on the establishment of strategic
priorities expressed by importance weights of
the goals, objectives and criteria. The DMs re-
sponsible for criteria evaluation will be further
called α-level DMs.
Figure2.Athreelevelhierarchy

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We consider
K
αα-levelDMs, each with a
positive α-voting power index ±±
k, where
ak
k
K
α
α
α
=
∑=
1
1 (k K
α α
=1 2, ,..., ).
In the study conducted for Raiffeisen the
strategy group responsible for evaluation of
criteria included three α-levelDMs ( Kα=3)
with following α-voting power coefficients:
α10 5=,, α20 3=, and α30 2=,.
7. Elicit Importance
Weights of Criteria
This step includes the assessment of the relative
importance of identified criteria by the group of
α-levelDMs. The weight elicitation problem in
general is one of the most difficult problems in
MCDA, because MCDA methods are supported
by mathematical models and therefore the pref-
erences need to be expressed in mathematical
Figure3.Hierarchyincludingsetofauxiliarydecisionobjects
Table2.MatrixofconnectionsbetweenthealternativesandADOs
ADO, St Set of linked alternatives, {Ai(St)}
S1 {Ai(S1)}
… …
St {Ai(St)}
… …
ST {Ai(ST)}

International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012 89
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terms (Tervonen et al., 2007). Three factors are
usually considered to obtain the weights; the
variance degree of criteria, the independency of
criteria and the subjective preference of the DMs
(Wang et al., 2009). A number of approaches
have been proposed to define criteria weights.
Equal weights method (Dawes & Corrigan,
1974) requires minimal knowledge of the DM’s
priorities and minimal DM’s input and treat all
criteria as equally important. The simple multi-
attribute rating technique (SMART) (Edwards,
1977) is based on the idea of ranking the impor-
tance of the changes in criteria from the lowest
to the highest (best) levels, Edwards and Barron
(1994) presented an improved version of this
method called SMARTER which uses centroid
method to find the final rankings. SWING
(von Winterfeld & Edwards, 1986) is a direct
algebraic decomposed procedure based on the
ranking and scoring of criteria on a 100-point
scale. Simos (Figueira & Roy, 2002) is a method
where the user associates a “playing card” with
each criterion, then the user ranks the cards in
ascending order, according to the importance
he/she wants to ascribe to the criteria; the
white cards are used to determine the distance
between successive criteria, from which the
numerical attribute values are derived. The
objective weighting methods use the distance
metrics and include TOPSIS (Technique for
order preference by similarity to ideal solution)
(Hwang & Yoon, 1981), entropy (Srdjevic et
Table3.Allocationofsuppliersamongtheloadingstations
Loading Stations, St Suppliers, {Ai(St)}
Üntrop, t=1 Atrian, Certyoil, GRG, Petrolium Nord, POSF
Hamm, t=2 GRG, Vetic
Lünnen, t=3 Certyoil, GRG, Naronaft, Petrolium Nord, POSF
Dortmund, t=4 All
Gelsenkirchen, t=5 Atrian, GRG, West Petrol Group
Figure4.HierarchyforevaluationofRaifieisen’sfueloilsuppliers

90 International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012
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al., 2004), principal component analysis etc.
Combination of the objective and subjective
weights is implemented in the additive and
multiplicative synthesis (Wang et al. 2009).
The AHP is a subjective weighting method
that relies on the pairwise comparisons to de-
termine the weights of every decision criterion.
The AHP was proposed by Saaty (1977). In
the AHP pairwise comparisons are performed
using 1 to 9 Fundamental Scale (Saaty &
Sodenkamp, 2008).
Based on the pairwise comparison, matrices
weights of criteria can be derived. The geometric
aggregation rule should be used to avoid the
controversies associated with rank reversal
(Dyer, 1990; Harker & Vargas, 1990; Saaty,
1990b). After that, Consistency Ratio must be
calculated to assure accuracy and logicality of
provided subjective judgments.
The tree of attributes together with criteria
weights reflects the DMs’ value system for
decision at hand. Figure 5 illustrates a formal
scheme of assigning criteria weights by the
α-levelDMs.
Three α-levelDMs in the Raiffeisen study
used the AHP and Super Decisions software /
(http://www.superdecisions.com) indepen-
dently to derive individual weights of criteria
groups ( wm
kα), criteria (wmn
kα) and sub-criteria
(wmnl
kα). Tables 4 and 5 profile criteria importance
weights for two DMs on objective and subjec-
tive criteria respectively.
8. Identify DMs’ Beta-Voting Power
for Evaluation of Alternatives on
Subjective Direct Criteria
Once the set of decision alternatives is gener-
ated, the DMs’ will make their assessment based
upon subjective direct criteria should be se-
lected and differentiated according to their
ability to evaluate the alternatives. Performance
values of alternatives on the objective criteria
do not depend on the DMs’ opinion. We propose
to call the DMs responsible for evaluation of
alternatives on the subjective direct criteria
β-level DMs. The DMs may vary in the sense
of knowing decision alternatives to different
extents and having experience to evaluate them
rationally. In contrast to the Alpha-voting
power indices akα that indicate relative author-
ity or influence of the DMs in the process of
objectives or criteria weighting and establish-
ment of strategic priorities, the Beta-voting
power ββ
k
i ( ²²
²
²
k
i
k 1
K
1
=
∑=;k K
β β
=1 2, ,..., ;
i I
=1 2, ,..., ;
I
≥2) specifies the DMs’ rela-
tive ability to assess performance of alternatives
on the direct subjective criteria. Methods of
awarding the Alphavotingpower indices akα
can be also implemented to establish the Beta
votingpower components ββ
k
i .
Numerical values ββ
k
i for two Raiffeisen’s
β-levelDMs ( Kβ=2) are reflected in Table
6.
9. Collect Objective Data
The next step is collection of the hard data
describing performance of alternatives on quali-
tatively and objectively measurable criteria. The
performance values for the set of objectively
measurable factors do not depend on the DM’s
judgments and are equal for each individual.
The units of measurement have to be identical
for all the alternatives with respect to the same
criterion. Let’s denote;
pPros mnl
Obj i
( ) ( pCons mnl
Obj i
( ) ) Performance value of
the
i
-th alternative on the objectively
measurable Pros (Cons) l-th sub-criterion
of the n-th criterion within the m-th group;
(
i I
=1 2, , ..., ; l Lmn
=1 2, , ..., ;
m M=1 2, ,...,
; n Nm
=1 2, ,..., )
pPros mn
Obj i
( ) ( pCons mn
Obj i
( ) ) Performance value
of the
i
-th alternative on the objectively

International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012 91
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measurable n-th criterion within the
m-th group, if n does not contain sub-cri-
teria; (
i I
=1 2, ,..., ;
m M
=1 2, ,..., ;
n Nm
=1 2, ,..., )
Performance values of Raiffeisen’s suppli-
ers on the objective criteria are shown in Table 7.
10. Develop Scoring System for
Subjective Criteria and Assign
Scores to Alternatives on Direct
Soft Criteria
Intangible (soft) criteria can be defined in several
ways with scales varying both in definition and
in number of options. The type of scale, with
one definition on each end of the scale, gives
the respondent space for subjective judgment
while a scale with clearly defined alternatives
can result in more objective answers accord-
ing to the predefined alternatives. (Hartley &
Betts, 2010) A Likert scale is commonly used
in questionnaires to measure qualitative facts.
Rensis Likert invented the scale with the pur-
pose of using it within psychology and it can be
designed as a 5-, 7- or a 10-point scale. Typical
for a Likert scale is that the respondents specify
their level of agreement to a statement. By using
the Likert scale, the respondents can express
their strength of feeling on a scale consisting
of response categories.
Muralidharan et al. (2002) suggest guide-
lines for comparing supplier attribute. That is a
five-point rating scale with predefined descrip-
tions of each alternative. Judging whether a
supplier has met the company’s expectations,
or not is not always an easy task if there are no
clear statements declaring what the company’s
expectations are (Muralidharan, Anantharaman,
& Deshmukh, 2002). We adopted this scale to
the 10 grading points which is shown in Table 8.
The rating scale in Table 8 is appropriate
for the Pros criteria where the higher values
are preferred to the lower ones. For the Cons
criteria the scale values should be inverted so
that 1 is considered as the best value with
minimal negative impact and 10 as the worst
value with maximal negative impact, as speci-
fied in Table 9.
The scale grades for Pros should be
maximized and for Cons minimized. The per-
formance scores for the set of subjectively
Figure5.Assignmentofcriteriaweightbytheα-levelDMs

92 International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012
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Table4.WeightsofobjectivecriteriaderivedwiththeAHP
Groups,
Cm
Group
weights,
wm
kα
Criteria, Cmn
Citeria
weights, wmn
kα
Sub-criteria,
Cmnl
Sub-criteria
weights, wmnl
kα
DM 1 DM 2 DM 1 DM2 DM 1 DM 2
1.Flexibitity 0,100 0,060 1.3. Product Mix 0,249 0,194 1.3.1. HeatingOil 0,583 0,385
1.3.2. Gasoline 0,240 0,399
1.3.3.Motor Oils
/ Lubricants
0,177 0,216
2. Service 0,090 0,070 2.3.Good Communica-
tion System
0,302 0,181 2.3.1. Number of
Contact Persons
0,311 0,244
2.1. Business Hours 0,172 0,170
3. Logistics 0,060 0,050 3.1.Number of Loading
Pionts
0,241 0,146
4. Relations 0,130 0,080 4.1. Past Businesses 0,146 0,103
6. Financial 0,310 0,360 6.1. Term of Payment 0,320 0,300
6.3. Price 0,560 0,630
Table5.WeightsofsubjectivecriteriaderivedwiththeAHP

International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012 93
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measurable attributes are different for the
K
β
β-levelDMs. Lets denote:
pos mnl
Sbj ik
( )Pr β(pCons mnl
Sbj ik
( ) β) Performance score
of the
i
-th alternative on the subjectively
measurable l-th Pros (Cons) sub-criterion
of the n-th criterion within the m-th group
assigned by
K
β the -th β-level DM;
(
i I
=1 2, ,..., ; k K
β β
=1 2, , ..., ;
l Lmn
=1 2, ,..., ;
m M
=1 2, ,..., ;
n Nm
=1 2, ,..., )
pos mn
Sbj ik
( )Pr β(pCons mn
Sbj ikb
( ) )Performance score of
the
i
-th alternative on the subjectively
measurable n-th Pros (Cons) criterion
within the m-th group, if n does not contain
sub-criteria, assigned by the kβ-th β-level
DM; (
i I=1 2, ,..., ;
k K
β β
=1 2, ,..., ;
m M=1 2, ,...,
; n Nm
=1 2, ,..., )
In Figure 6 is illustrated the process of as-
signing subjective scores to alternatives on one
direct criterion by the β-level DM.
11. Evaluate Auxiliary Decision
Objects on Indirect Criteria
Analogously to the directcriteria that reflect to
what extent alternatives meet the requirements
expressed by means of quantitative and qualita-
tive decision factors, indirectcriteria help to
Table6.BetavotingpowerofRaiffeisenDMs’
Table7.Objectiveperformancevaluesofalternatives
Criteria Sub-
criteria GRG Atrian Certyoil Naronaft Vetic Petrolium
Nord
West
Petrol
Group
POSF
1.3. Product Mix
1.3.1.
Heating Oil 4.354.915 1.579.919 1.098.650 122.618 760.851 0 252.841 3.301.832
1.3.2.
Gasoline 245.176 0 0 0 2.484.775 0 0 0
1.3.3.
Mineral
Oils/
Lubricants
26.920,28 0,00 90.219,65 0,00 0,00 0,00 0,00 456,45
2.1. Good
Communication
System
2.1.1.
Number
of Contact
Persons
5 2 2 2 5 1 1 3
2.3. Business Hours 45 39 45 45 45 45 39 50
3.1. Number of
loading points 5 3 3 2 2 3 2 3
4.1. Past
businesses 5.701.542 942.060 2.564.668 32.388 1.992.446 63.739 282.345 2.556.490
6.2. Payment period 20 20 20 20 20 20 30 20

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distinguish between the ADOs. The same as
directcriteria, indirect ones can be objective
(factual) or subjective (judgmental) merits.
Factual data characterizing the ADOs has to be
identified uniquely for each ADO and does not
depend on the DMs’ judgments. To formulate
this step algebraically lets define;
pPros mnl
Obj t
( ) *
(pCons mnl
Obj t
( ) *
)Performance value
of the
t
-th ADO on the objectively
measurable l-th Pros (Cons) sub-criterion
of the n-th criterion within the m-th
group(
t T=1 2, ,..., ;
l Lmn
=1 2, ,..., ;
m M
=1 2, ,..., ; n Nm
=1 2, ,..., )
pPros mn
Obj t
( ) *
(pCons mn
Obj t
( ) *
)Performance value of
the
t
-th ADO on the objectively measur-
able n-th Pros (Cons) criterion within the
m-th group, if n does not contain sub-cri-
teria;(
t T
=1 2, ,..., ;
m M
=1 2, ,..., ;
n Nm
=1 2, ,..., )
In contrast to the tangible characteristics,
intangible indirectindicators reflect the DMs’
opinions. Decision team responsible for evalu-
ation of the ADOs should include individuals
having appropriate expertise and knowledge.
Members of this group do not necessarily have
to be criteria evaluators (α-level DMs), nor
alternative assessors (β-levelDMs). The DMs
responsible for estimation of the ADOs on
subjective indirect criteria will be called γ-level
DMs. γ-level DMs may vary in the sense of
experience or authority to evaluate perfor-
mances of particular ADOs. The relative abil-
ity of γ-levelDMs to assess performance of the
ADOs on indirect subjective criteria will be
called γ-voting power. We considerKγγ-level
DMs, each with a positive γ-votingpower index
γγ
k
t, where
γγ
γ
γ
k
t
k
K
=
∑=
1
1 (k K
γ γ
=1 2, ,..., ;
t T=1 2, ,...,
).
Table8.RatingscaleforsupplierevaluationontheProscriteria
Point Grade Description
10 Exceptional Demonstrates substantially excellent performance,and has been at least in the excel-
lence category for last 12 months
7 Excellence Exceeds company’s and customers’ expectations, demonstrates extra effort
5 Good Meets the company’s expectations
3 Acceptable Meets company’s minimum requirements
1 Poor Does not meet company’s and customers’ minimum acceptable level
2,4,6,8,9 Annectent grades
Table9.RatingscaleforsupplierevaluationontheConscriteria
Point Grade Description
10 Poor Does not meet company’s and customers’ minimum acceptable level
7 Acceptable Meets company’s minimum requirements
5 Good Meets the company’s expectations
3 Excellence Exceeds company’s and customers’ expectations, demonstrates extra effort
1 Exceptional Demonstrates substantially excellent performance,and has been at least in the excel-
lence category for last 12 months
2,4,6,8,9 Annectent grades

International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012 95
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In order to evaluate the ADOs on subjec-
tive Pros and Cons a scoring system has to be
developed. For this purpose a 10-point verbal
scale with respective numerical values given in
Table 8can be applied for Pros, and an inverse
1 to 10 scale from the Table 9 can be adapted
for indirect Cons. Once the scale for subjective
scores has been defined evaluation of the ADOs
can begin. To formalize the process let us define:
pPros mnl
Sbj tk
( ) *
γ(pCons mnl
Sbj tk
( ) *
γ)Performance score
of the
t
-th ADO on the subjectively
measurable l-th Pros (Cons) indirect sub-
criterion of the n-th criterion within
the m-th group assigned by
the kγ-the γ-level DM;(
t T=1 2, ,..., ;
k K
γ γ
=1 2, ,..., ; l Lmn
=1 2, ,..., ;
m M
=1 2, ,..., ; n Nm
=1 2, ,..., )
pPros mn
Sbj tk
( ) *
γ(pCons mn
Sbj tk
( ) *
γ) Performance score
of the
t
-th ADO on the subjectively mea-
surable n-th Pros (Cons) indirect criterion
within the m-th group, if n does not contain
sub-criteria, assigned by the kγ-th γ-level
D M ; (
t T
=1 2, ,..., ; k K
γ γ
=1 2, ,..., ;
m M=1 2, ,...,
; n Nm
=1 2, ,..., )
The group of two purchasing managers
(γ-level DMs, Kγ=2) was formed to evalu-
ate five shared loading stations of Raiffeisen’s
suppliers on the subjective indirect criteria
Quickloading (CPros
3 2 *) and Processflexibil-
ity (CPros
3 3 *). The γ-votingpower indices and
performance scores assigned to the loading
points are given in Table 10.
12. Normalize All Objective
Performances and Subjective
Scores to Obtain Identical
Measurement Units
Next, we normalize variables with multiple
measurement scales to assure uniformity. The
literature reports on several normalization
methods. The selection of a specific normal-
ization method must be based on the problem
characteristics and model requirements (Tavana
& Sodenkamp, 2010). In this study, we use the
Figure6.Estimationofalternativesonthesubjectivecriteriabytheβ-levelDMs

96 International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012
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approach where the normalized value is the
quotient of the initial value divided by the sum
of the values of all alternatives/ADOs on that
criterion. Normalized objective performances
on direct, as well as on indirect Pros and Cons
criteria can be defined by the expressions
(1) - (4):
pp
p
Pros mnl
Obj i Pros mnl
Obj i
Pros mnl
Obj i
l
'( ) ( )
( )
=∑ (1.a)
pp
p
Pros mn
Obj i Pros mn
Obj i
Pros mn
Obj i
n
'( ) ( )
( )
=∑ (1.b)
pp
p
Cons mnl
Obj i Cons mnl
Obj i
Cons mnl
Obj i
l
'( ) ( )
( )
=∑ (2.a)
pp
p
Cons mn
Obj i Cons mn
Obj i
Cons mn
Obj i
n
'( ) ( )
( )
=∑ (2.b)
pp
p
Pros mnl
Obj t Pros mnl
Obj t
Pros mnl
Obj t
l
'( ) ( )
( )
*
*
*
=∑ (3.a)
pp
p
Pros mn
Obj t Pros mn
Obj t
Pros mn
Obj t
n
'( ) ( )
( )
*
*
*
=∑ (3.b)
pp
p
Cons mnl
Obj t Cons mnl
Obj t
Cons mnl
Obj t
l
'( ) ( )
( )
*
*
*
=∑ (4.a)
pp
p
Cons mn
Obj t Cons mnl
Obj t
Cons mn
Obj t
n
'( ) ( )
( )
*
*
*
=∑ (4.b)
Normalized subjective scores on direct
and on indirect Pros and Cons criteria can be
defined by the expressions (5) - (8):
pp
p
os mnl
Sbj ik os mnl
Sbj ik
os mnl
Sbj ik
l
'( ) ( )
( )
Pr
Pr
Pr
β
β
β
=∑ (5.a)
pp
p
os mn
Sbj ik os mn
Sbj ik
os mn
Sbj ik
n
'( ) ( )
( )
Pr
Pr
Pr
β
β
β
=∑ (5.b)
pp
p
Cons mnl
Sbj ik Cons mnl
Sbj ik
Cons mnl
Sbj ik
l
'( ) ( )
( )
β
β
β
=∑ (6.a)
pp
p
Cons mn
Sbj ik Cons mn
Sbj ik
Cons mn
Sbj ik
n
'( ) ( )
( )
β
β
β
=∑ (6.b)
pp
p
os mnl
Sbj tk os mnl
Sbj tk
os mnl
Sbj tk
'( ) ( )
( )
Pr *
Pr *
Pr *
γ
γ
=γγ
l
∑ (7.a)
pp
p
os mn
Sbj tk os mn
Sbj tk
os mn
Sbj tk
n
'( ) ( )
( )
Pr *
Pr *
Pr *
γ
γ
γ
=∑ (7.b)
Table10.VotingpowerandscoresofRaiffeisenγ-levelDMs
Shared loading facilities, t
Dortmund, t=1 Gelsenkirchen, t=2 Hamm, t=3 Lünnen, t=4 Üntrop, t=5
γ-level DMs, kγDM1,
kγ=1
DM2,
kγ=2
DM1,
kγ=1
DM2,
kγ=2
DM1,
kγ=1
DM2,
kγ=2
DM1,
kγ=1
DM2,
kγ=2
DM1,
kγ=1
DM2,
kγ=2
γ-voting power 0,5 0,5 0,7 0,3 0,4 0,6 0,75 0,25 0,5 0,5
Qu ick l oa din g,
C32*
10 10 10 5 7 5 4 7 5 8
Process flexibility,
C33*
10 10 3 5 7 9 7 8 6 8

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pp
p
Cons mnl
Sbj tk Cons mnl
Sbj tk
Cons mnl
Sbj tk
'( ) ( )
( )
*
*
*
γ
γ
=γγ
l
∑ (8.a)
pp
p
Cons mn
Sbj tk Cons mn
Sbj tk
Cons mn
Sbj tk
n
'( ) ( )
( )
*
*
*
γ
γ
γ
=∑ (8.b)
Normalized values of Raiffeisen’s suppliers
on objective factors are calculated using formula
(1) and are presented in Table 11.
Normalized scores of the Raiffeisen’s
loading points are calculated using equation (4)
and are demonstrated in Table 12.
14. Integrate All Voting Power
Indices, Criteria Weights, Tangible
and Intangible Estimates
After the normalization process, we use an
integration procedure to combine the following
elements into one pair of values for Pros and
Cons of each decision alternative;
• Voting power coefficients αα
k, ββ
k
i and
γγ
k
t;
• K± sets of
M
criteria group weights
(wm
kα),
N
attribute weights (wmn
kα) and
L
sub-criteria weights (wmnl
kα);
• NObj and L
Obj normalized performances
of
I
alternatives and
T
ADOs on the
direct and indirect objective Pros and Cons
criteria ( pPros mnl
Obj i
'( ) , pPros mn
Obj i
'( ) ,
pPros mnl
Obj t
'( ) , pPros mn
Obj t
'( ) , pCons mnl
Obj i
'( ) ,
pCons mn
Obj i
'( ) , pCons mnl
Obj t
'( ) and pCons mn
Obj t
'( ) );
•
K
β sets of normalized scores of
I
alterna-
tives on the direct subjective Pros and Cons
criteria ( pos mnl
Sbj ik
'( )Pr
β, pos mn
Sbj ik
'( )Pr
β,
pCons mnl
Sbj ik
'( ) βand pCons mn
Sbj ik
'( ) β); and
• Kγ sets of normalized scores of
T
ADO’s
on the indirect subjective Pros and Cons
criteria ( pos mnl
Sbj tk
'( )P r *
γ, pos mn
Sbj tk
'( )P r *
γ,
pCons mnl
Sbj tk
'( ) *
γand p'( )Cons mn *
Sbj tk³).
14.1. Combination of the
Group Criteria Weights
For the first step of the integration procedure
it is necessary to find combined among the
α-level DM’s, weights of criteria groups
(wm), criteria (wmn ) and sub-criteria (wmnl ).
w w
mkm
k
k
K
= ⋅
=
∑( )αα
α
α
α
1
(9.a)
w w
mn kmn
k
k
K
= ⋅
=
∑( )αα
α
α
α
1
(9.b)
w w
mnl kmnl
k
k
K
= ⋅
=
∑( )αα
α
α
α
1
(9.c)
14.2. Prioritization of the ADOs
In the second step of the integration procedure
we calculate the group rankings of the ADO’s
in order to incorporate this information into
the decision matrix later for evaluation of the
alternatives.
Aggregated group Pros and Cons of the
each ADO must be derived taking into account
γ-voting power indices ³³
k
t using formulas
(10)-(11) respectively:
p pos mnl
Sbj t
k
tos mnl
Sbj tk
k
K
( ) '( )Pr *Pr *
= ⋅
=
∑γγ
γ
γ
γ
1
(10.a)
p pos mn
Sbj t
k
tos mn
Sbj tk
k
K
( ) '( )Pr *Pr *
= ⋅
=
∑γγ
γ
γ
γ
1
(10.b)
p pCons mnl
Sbj t
k
tCons mnl
Sbj tk
k
K
( ) '( )
* *
= ⋅
=
∑γγ
γ
γ
γ
1
(11.a)
p pCons mn
Sbj t
k
tCons mn
Sbj tk
k
K
( ) '( )
* *
= ⋅
=
∑γγ
γ
γ
γ
1
(11.b)
We use weighed-sum aggregation method
and equations (12)-(13) to calculate the total

98 International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012
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Pros (pPros t
( )*) and Cons (pCons t
( )*) scores of T
ADOs.
* *
* * *
( ) ( ( '( )
( ) ) '( ) ( ) )
t Obj t
Pros Pros
mn mn mnl mnl
l
Sbj t Obj t Sbj t
Pros Pros Pros
mnl mn mn
l n n
p w w p
p p p
= ⋅
+ + +
∑
∑ ∑ ∑ (12)
* *
* * *
( ) ( ( '( )
( ) ) '( ) ( ) )
t Obj t
Cons Cons
mn mn mnl mnl
l
Sbj t Obj t Sbj t
Cons Cons Cons
mnl mn mn
l n n
p w w p
p p p
= ⋅
+ + +
∑
∑ ∑ ∑ (13)
In the Raiffeisen study integrated group
rankings of the five shared loading terminals
were obtained using formulas (10) and (12),
the results are shown in Table 13.
14.3. Derive Values of the
Alternatives on the Indirect Criteria
Once positive and negative ratings of all ADO’s
have been calculated, impacts of indirect cri-
teria on the decision alternatives have to be
measured taking into consideration correspon-
dence between the ADO’s and alternatives as
defined in Table 2. To calculate performance
level of decision alternatives Ai on the indirect
criteria C* for contradictory classes Pros and
Cons formulas 14(a) and 14(b) can be applied
Table11.Normalizedperformancesofalternativesonobjectivecriteria
Groups of
criteria,
C
m
Criteria, Cmn
Sub-criteria,
Cmnl
Alternative suppliers,
A
i
GRG Atrian Certyoil Naronaft Ventic Petrolium
Nord
West
Petrol
Group
POSF
1.Flexibility 1.3.
Product Mix
1.3.1.
Heating Oil 0,380 0,138 0,096 0,011 0,066 0,000 0,022 0,288
1.3.2.
Gasoline 0,090 0,000 0,000 0,000 0,910 0,000 0,000 0,000
1.3.3.Motor
Oils/
Lubricants 0,229 0,000 0,767 0,000 0,000 0,000 0,000 0,004
2. Service 2.1. Business Hours 0,238 0,095 0,095 0,095 0,238 0,048 0,048 0,143
2.3. Good
Communication
System
2.3.1.
Number of
Contact
Persons 0,127 0,110 0,127 0,127 0,127 0,127 0,110 0,142
3. Logistics 3.1. Number of Loading Points 0,217 0,130 0,130 0,087 0,087 0,130 0,087 0,130
4. Relations 4.1. Past Businesses 0,403 0,067 0,181 0,002 0,141 0,005 0,020 0,181
6. Financial 6.1. Term of Payment 0,125 0,125 0,125 0,125 0,125 0,125 0,125 0,125
6.3. Price 0,126 0,121 0,122 0,128 0,129 0,125 0,122 0,127
Table12.Normalizedscoresoftheloadingstations
Indirect criteria, Cmn*
Shared loading facilities, t
Dortmund, t=1 Gelsenkirchen, t=2 Hamm, t=3 Lünnen, t=4 Üntrop, t=5
DM1 DM2 DM1 DM2 DM1 DM2 DM1 DM2 DM1 DM2
Quick loading, C32*0,278 0,286 0,278 0,143 0,194 0,143 0,111 0,200 0,139 0,229
Process flexibility, C33*0,303 0,250 0,091 0,125 0,212 0,225 0,212 0,200 0,182 0,200

International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012 99
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respectively. The numbers obtained can then
be incorporated into the process of alternatives
evaluation together with direct criteria.
p
p
T
Pros mn
i
Pros mn
t
t
Ti
i
( )
( )
*
*
==
∑
1
(14.a)
p
p
T
Cons mn
i
Cons mn
t
t
Ti
i
( )
( )
*
*
==
∑
1
(14.b)
where Ti stands for number of ADOs related
to alternative i.
Raiffeisen’s loading point information and
suppliers’ integrated group performance scores
on the indirect criteria are collected in Table 14.
14.4. Calculate Group Weights of the
Alternatives on Each Criterion
The normalized subjective group scores on
direct factors must be merged with β-voting
power magnitudes to derive consensus bases
rankings of alternatives.
p pos mnl
Sbj i
k
ios mnl
Sbj ik
k
K
( ) '( )Pr Pr
= ⋅
=
∑ββ
β
β
β
1
(15.a)
p pos mn
Sbj i
k
ios mn
Sbj ik
k
K
( ) '( )Pr Pr
= ⋅
=
∑ββ
β
β
β
1
(15.b)
p pCons mnl
Sbj i
k
iCons mnl
Sbj ik
k
K
( ) '( )
= ⋅
=
∑ββ
β
β
β
1
(16.a)
p pCons mn
Sbj i
k
iCons mn
Sbj ik
k
K
( ) '( )
= ⋅
=
∑ββ
β
β
β
1
(16.b)
14.5. Combine All Direct Pros and
Cons Weights For Each Alternative
Then we apply the weighed-sum aggregation
to calculate combined objective and subjective
Pros ( pPros i
( ) ) and Cons ( pCons i
( ) ) of I alterna-
tives on the directcriteria.
( ) ( ( '( )
( ) ) '( ) ( ) )
i Obj i
Pros Pros
mn mn mnl mnl
l
Sbj i Obj i Sbj i
Pros Pros Pros
mnl mn mn
l n n
p w w p
p p p
= ⋅
+ + +
∑
∑ ∑ ∑
(17)
( ) ( ( '( )
( ) ) '( ) ( ) )
i Obj i
Cons Cons
mn mn mnl mnl
l
Sbj i Obj i Sbj i
Cons Cons Cons
mnl mn mn
l n n
p w w p
p p p
= ⋅
+ + +
∑
∑ ∑ ∑
(18)
14.6. Find a Pair of Total Pros
and Cons for Each Alternative
On the final step of our integration procedure
the total Pros ( pPros i
( ) ) and Cons ( pCons i
( ) )
values are calculated for each alternative as
added weighed estimates on the direct and in-
direct criteria:
*
1
( ) ( ( ( ) ( ) ))
M
i i i
Pros Pros Pros
m mn mn
m
p w p p
=
= ⋅ +
∑
(19)
*
1
( ) ( ( ( ) ( ) ))
M
i i i
Cons Cons Cons
m mn mn
m
p w p p
=
= ⋅ +
∑
(20)
The Pros and Cons of Raiffeisen’s suppliers
are presented in Table 15.
Table13.Groupratingsoftheloadingstations
Loading terminals, St Dortmund, t=1 Gelsenkirchen,
t=2 Hamm, t=3 Lünnen, t=4 Üntrop, t=5
Weights of terminals, p(Pros)t0,226 0,134 0,150 0,143 0,153

100 International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012
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15. Rank Alternatives Based on
their Euclidean Distance to the
Ideal Point
Zeleny (1982) suggested using the Euclidean
measure to compare alternatives among them-
selves and with the ideal one. This approach
was implemented in numerous researchers
(Tavana & Sodenkamp, 2010; Tavana et al.,
2010) and by practitioners. The ideal Pros
value ( pPros* ( ) ) is the highest Pros weight
among the set of {pPros i
( ) } and ideal Cons
value ( pCons* ( ) ) is the lowest Cons weight
among the set of { pCons i
( ) }. To find the Euclid-
ean distance of each alternative from the ideal
one we extract the quadratic root of summarized
squared differences between the ideal and the
i
-th indices of the Pros and Cons. Lets define:
EPros i
( ) ( ECons i
( ) )The distance from the ideal
positive (negative) merit for the i-th alter-
native;
(
i I
=
1 2, ,...,
)
E
i Euclidean distance from the ideal point for
the i-th alternative; (
i I
=
1 2, ,...,
)
E
Mean Euclidean distance for the alternatives;
p Max pPros Pros i
* ( ) { ( ) }= (21.a)
p Min pCons Cons i
* ( ) { ( ) }= (21.b)
2 2
( *( ) ( ) ) ( * ( ) ( ) )
i i i
Pros Pros Cons Pros
E p p p p= − + −
(22)
We then sort alternatives
A
i from the best
to the worst one based on the values
E
i and
form a set {
A
Ord }. Ar
i
indicates that
i
-th al-
ternative has
r
-th rank in the ordered set
{AOrd }, where
r I=1, ...,
.
The highest Pros value among the set of
Raiffeisen’s suppliers is
p
Pros* ( ) ,=0 056 ,
whereas the lowest Cons value is
pCons* ( ) ,=0 015 . The Raiffeisen fuel oil
suppliers’ distances to the ideal point, together
with ranks based on Euclidean distance are
shown in Table 16.
16. Choose the Optimal
Alternative(s) and Assign Order
Quantities
To solve the choice decision problem the
maximal efficiency can be achieved if the al-
ternative Ar
i
=1 with the highest rank will be
selected. In purchasing management this kind
of supplier selection is called single sourcing
and it is used if one supplier can satisfy all the
buyer’s needs.
If decision goal is formulated in terms of
selection of several best options, the required
number Q (Q I≤) of alternatives must be
defined by the decision group. The desire of
purchasing managers to split orders among
Table14.Suppliers’loadingstationsinformation
Suppli-
ers, Ai
GRG,
i=1
Atrian,
i=2
Certyoil,
i=3
Naronaft,
i=4
Vetic,
i=5
Petrolium
Nord, i=6
West Petrol
Group, i=7
POSF,
i=8
Number of
Loading
Stations, Ti
5 3 3 3 2 3 2 3
Loading
stations, St
Dortmund,
Gelsenkirchen,
Hamm, Lünnen,
Üntrop
Dortmund,
Gelsenkirch-
en, Üntrop
Dort-
mund,
Lünnen,
Üntrop
Dortmind,
Hamm,
Lünnen
Dortmund,
Hamm
Dortmund,
Lünnen,
Üntrop
Dortmund,
Gelsen-
kirchen
Dortmund,
Lünnen,
Üntrop
Total scores
on indirect
criteria,
pPros mn
i
( ) *
0,161 0,171 0,174 0,173 0,188 0,174 0,180 0,174

International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012 101
Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
vendors may arise for a variety of reasons,
including inability of suppliers to satisfy all of
the buyer’s requirements or intentionally creat-
ing an environment of competitiveness. In such
case, Q first elements from the ordered set {
A
Ord } must be selected to assure highest ef-
ficiency of Q alternatives. The selected alter-
natives are Aq
i
with q Q=1, ..., .
Raiffeisen follows the policy of risks
minimization and multiple sourcing. To pur-
chase fuels the DMs select three
Q
=3 vendors
with highest ranks
r
. These are GRG (Aq
i
=
=
1
1),
Vetic ( Aq
i
=
=
2
5) and POSF ( Aq
i
=
=
3
8). Then order
quantities oq(
q Q
=1, .. ) have to be allocated
among the selected suppliers proportionally to
the normalized relative weights
w
q
' of se-
lected alternatives within set {Q}.
1
1
i
q
qQ
i
q
q
E
w
E
=
= −
∑
(23)
where Eq
i is Euclidean distance for the q-th
selected alternative and E E
q
i i
=.
1
' q
qQ
q
q
w
w
w
=
=
∑
(24)
Assuming that d is demand of the product
to purchase, the order quantities for vendors
are:
'
q
q
o w d= ⋅ (25)
Normalized weights of the suppliers se-
lected by Raiffeisen, and assigned to them
order quantities for
d
=72 000 (liters) are
presented in Table 17.
CONCLUSION
The research presented in this study promotes
explicit and comprehensive modeling of
extremely complex decisions and systematic
evaluation and selection of alternatives based
on their contribution made throughout the
organization. When real decision processes do
not fit into the typical hierarchy “goals-criteria-
alternatives” due to involvement of the external
Table15.Suppliers’overallProsandCons
Suppliers, Ai
Merits
GRG,
i=1
Atrian,
i=2
Certyoil,
i=3
Naronaft,
i=4
Vetic,
i=5
Petrolium
Nord, i=6
West Petrol
Group, i=7
POSF,
i=8
Pros, pPros i
( ) 0,056 0,037 0,040 0,029 0,050 0,036 0,036 0,049
Cons, pCons i
( ) 0,015 0,020 0,043 0,016 0,016 0,037 0,018 0,029
Table16.Suppliers’distancestotheidealandfinalranks
Supplier, Ai GRG,
i=1
Atrian,
i=2
Certyoil,
i=3
Naro-
naft,
i=4
Vetic,
i=5
Petrolium
Nord, i=6
West Petrol
Group, i=7
POSF,
i=8
Euclidean
Distance, Ei0,000 0,019 0,032 0,026 0,006 0,029 0,019 0,015
Rank, r1 4 (tied) 8 6 2 7 4 (tied) 3

102 International Journal of Strategic Decision Sciences, 3(1), 81-105, January-March 2012
Copyright © 2012, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited.
services or other intermediate units, connections
between the decision elements become more
intricate and standard methods are no longer
applicable. We demonstrate a supplier selection
problem including indirect influences of deci-
sion criteria on the vendors and formulate ap-
propriate step-by-step assessment framework.
All relevant objective information, together
with the expert judgments regarding criteria
importance; performance scores of alternatives
and auxiliary objects are captured consistently
in the evaluation procedure. Principal distinc-
tion is drawn between the three types of DMs;
strategy determination group (α-level DMs),
alternatives evaluation group (β-level DMs)
and ADOs assessment group (γ-level DMs).
Moreover, different grades of DMs influence
inherent to real decision teams are expressed
by voting power coefficients and then included
into the aggregation procedure, aimed to reveal
consensus based supplier priorities. Sensitivity
analysis can be performed in order to under-
stand impacts of particular parameters on the
final result and to examine robustness of the
proposed solution.
Systematic holding of non-anonymous
assessment sessions with our method makes
significant contributions to the decision process
transparency. Moreover, the MLGDM process
can be used as a tool for DMs’ learning and
dynamic monitoring of strategic and tactical
purchasing decisions on different organizational
layers.
ACKNOWLEDGMENTS
The authors would like to thank the anonymous
reviewers and the editor for their insightful
comments and suggestions. All the suppliers’
names are changed to protect their anonymity.
The data presented in this study is significantly
reduced to allow a meaningful illustration of
the method.
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LeenaSuhlhasbeenaprofessorofBusinessInformationSystems,especiallyOperationsResearch
andDecisionSupport,attheUniversityofPaderbornsince1995.SheholdsaMScdegreein
engineering,aPhDfromHelsinkiUniversityofTechnology,Finland,andhabilitatedinBerlin
UniversityofTechnology.ResearchintheworkinggroupofProf.Suhlfocusesondecisionsup-
portsystems,optimizationandsimulationsystemsforbusinessplanningprocessesaswellas
applicationsin supplychainplanning,transportation,traffic,andlogistics systems.Dr.Suhl
workedasavisitingresearcheratIBMThomasJ.WatsonResearchCenter,YorktownHeights,
USAandhasbeenavisitingprofessorinFinland,theUSA,ChinaandPoland.Prof.Suhlisco-
ordinatorofnumerousprojectsfundedbyDFG,EU,BMBF,NRWorindustryaswellasmember
oftheexecutiveboardofGesellschaftfürOperationsResearch(GOR).Shehaspublishedover
100reviewedarticlesandismemberoftheeditorialboardofseveralinternationaljournals.