Decision support systems, Supplier selection, Information systems, Boolean algebra, Supply chain management, Multi criteria decision making, Decision modelsA new decision support system for supplier selection using boolean algebra

International Journal of Managing Public Sector Information and Communication Technologies (IJMPICT)
Vol. 5, No. 3, September 2014
A NEW DECISION SUPPORT SYSTEM FOR SUPPLIER
SELECTION USING BOOLEAN ALGEBRA
Nasina Jigeesh
Department of Operations & Systems, IBS Hyderabad, IFHE University, Dontanapalli,
Shankerpalli Road, Hyderabad – 501203, India.
ABSTRACT
For organizations operating with number of products/services and number of suppliers, to select the right
supplier meeting all their requirements will be a challenging job. Such organizations need a good
decision support system to evaluate the suppliers effectively. Several decision support systems have been
reported to deal with complex selection process to decide the right supplier. Many mathematical models
have also been developed. This paper presents a new method, named as Bit Decision Making (BDM)
method, which treats such complex system of decision making as a collection and sequence of reasonable
number of meaningful and manageable sub-systems by identifying and processing the relevant decision
criteria in each sub-system. Help of Boolean logic and Boolean algebra is taken to assign binary digit
values to the selection criteria and generate mathematical equations that correlate the inputs to the output
at each stage of decision making. Each sub-system with its own mathematical model has been treated as a
standardized decision sub-system for that phase of making decision in evaluating suppliers. The sequence
and connectivity of the sub-systems along with their outputs finally lead to selection of the best supplier. A
real-world case of evaluation of information technology (IT) tenders has been dealt with for application of
the proposed method. The paper discusses in detail the theory, methodology, application and features of
the new method.
KEYWORDS
Decision support systems, Supplier selection, Information systems, Boolean algebra, Supply chain
management, Multi criteria decision making, Decision models
1. INTRODUCTION
Decision-making environments formulate helpful mathematical models (linear programming,
nonlinear programming, etc.) with objective functions that specify the estimated consequences of
any combinations of decisions (Hillier and Lieberman, 2001). The descriptive theory of problem
solving and decision making is centrally concerned with how people cut problems down to size:
how they apply approximate, heuristic techniques to handle complexity that cannot be handled
exactly. Operations research and artificial intelligence are forging powerful new computational
tools; at the same time, a new body of mathematical theory is evolving around the topic of
computational complexity (Simon, 1986).
Several qualitative and quantitative decision making methods have been reported (Kepner and
Tregoe, 1981; Saaty and Kearns, 1985; Saaty, 1990; Edwards and Barron, 1994; Hooks, 1994;
Folger and LeBlanc, 1995; Saaty, 1995; Clemen, 1996; Goodwin and Wright, 1998; Hammond
et al, 1999; France et al, 2002; Sharma et al, 2004; Harris, 2006; Miah and Huth, 2011). Pros
and Cons analysis is a qualitative comparison method in which good things (pros) and bad things
(cons) are identified about each alternative and this method is suitable for simple decisions with
few alternatives (2 to 4) and few discriminating criteria (1 to 5) of approximately equal value. It
requires no mathematical skill and can be implemented rapidly. Kepner-Tregoe (K-T) decision
DOI : 10.5121/ijmpict.2014.5302 11

analysis is a quantitative comparison method in which a team of experts numerically score
criteria and alternatives based on individual judgements (assessments). Some practical
techniques applied to simple or complex decisions include T-Chart, PMI (Plus, Minus and
Interesting), Buriden’s Ass, Measured Criteria and Decision Matrix or Weighted Decision Table
(Harris, 2006).
France et al (2002) details the use of a multiple-objective decision-making methodology and an
integrative geographical information system-based decision-making tool developed to help
watershed councils prioritize and evaluate restoration activities at the watershed level. Sharma et
al (2004) presents a lexicographic goal programming (LGP) model for management decision-making
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in petroleum refinery industry for distribution of oil to the various depots.
The objective of supplier selection is to select appropriate suppliers that can provide faster
delivery, reduced cost and improved quality in order to increase corporate competitiveness and
additionally searching for those suppliers and continuously assessing their performance are
critical supply chain activities (Yang and Chen, 2006).
Linear-weighting (LW) models were used to evaluate potential suppliers using several equally
weighted factors, and then allow the desion-maker to choose the supplier with the highest total
score (Timmerman, 1986). Mathematical-programming (MP) models can also be used to select
the suppliers by creating an objective function to be maximized (for example, profit) or
minimized (for example, costs), that is, performing optimization, by varying the values of the
variables in that objective function. According to De Boer et al (1998) and Ghodsypour and
O’Brien (1998), LW models do not include quantitative factors, whereas the MP models have the
disadvantage of not including qualitative factors in selecting suppliers.
Analytic hierarchy process (AHP) is a quantitative comparison method used to select a preferred
alternative by using pair-wise comparisons of the alternatives based on their relative performance
against the criteria. The basis of this technique is that humans are more capable of making
relative judgements than absolute judgements. AHP technique was used in designing evaluation
models for various applications (Yang and Chen 2006, Ghodsypour and O’Brien 1998).
Ghodsypour and O’Brien (1998) proposed an integrated AHP and linear programming model as
a decision support system for selecting supplier. Yang and Chen (2006) proposed an integrated
evaluation model by combining the AHP and grey relational analysis (GRA) to select the
suppliers. Multi-attribute utility theory (MAUT) is a quantitative comparison method used to
combine dissimilar measurement of costs, risks, and benefits, along with individual and
stakeholder preferences, into high-level aggregated preferences. Min (1994) used the multi-attribute
utility approach to deal with the problem of selection of international suppliers using the
criteria described as financial, quality, risks, service, partnerships, cultural and communication,
and trade restrictions. Paulus and Riemann (2013) proposed to use a company-specific value-creation
for the cloud-affinity and the cloud-usability of a business process in public sector.
They considered specific challenges of addressing processes in cloud services. They also
considered all relevant security criteria alongside the process lifecycle and formulates the
process-security management requirements derived from each single life-cycle phase.
In this paper, a new decision making system, named as Bit Decision Making (BDM) method has
been proposed to simplify the decision process in complex systems. BDM method is based on
both qualitative and quantitative factors in assigning and processing the scores of suppliers to
select the right supplier. In this method, a complex system is divided into reasonable number of
sub-systems and each sub-system is described with some criteria items based on its special
characteristics and objectives and scores of either ‘1’ or ‘0’ (binary digits) are assigned to those
criteria items. By applying Boolean logic and simple Boolean algebra, the method automates the
decision process in each sub-system and the filtered quality entities pass on to the next sub-

system in a hierarchical order to be awarded scores based on the special criteria items adopted
therein. This process continues till the single final entity is selected. The proposed method is
unique in methodology when compared to existing decision making methods. This paper
elaborates the method to strengthen its scope of application. As an example, the BDM method
has been applied to the case of evaluation of IT tenders covering different stages of tender
evaluation, namely, ‘Invitation to tender’, ‘Business strengths’, “Technical’, ‘Financial
quotation’ and ‘Final evaluation’. The proposed method is user-friendly in terms of its simplicity
to input either ‘1’ or ‘0’ based on the policy framed by the user/organization. The result of set of
input binary digits for each alternative will also be worked out by a suitable binary relationship
between the inputs and the probable output.
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2. CASE STUDY
The present study proposes an evaluation model as a decision support system to select a supplier.
To demonstrate the model, a real-world case study was carried out during 1997-2000 relating to
evaluation of IT tender bids received by a government technical consulting agency, ABS Ltd. (to
maintain confidentiality, the name of the organization is herewith referred to as ABS Ltd.) for
computerization of different government organizations in a Southern Indian state. That was the
time when India, especially the said state government was very aggressive in initiating and
implementing various prestigious IT projects to enable the whole state fully computerize its
administration. Many state government organizations were directed to approach ABS for its
consultancy for computerization of whole or partial organizational activities by procuring
hardware, office automation, various software packages and development of relevant software
solution(s). ABS is a wholly owned state government corporation focusing on e-Governance, by
providing consultancy, procurement services and implementation support to the government
entities for their Information and Communications Technology initiatives. ABS evolved
different evaluation methods to select the right suppliers for the right work requested by any
government organization. The case study deals with the role of ABS in calling for IT tender bids
and the way ABS evaluated them and finalized the right vendor/supplier to do the specified IT
job proposed. To maintain confidentiality, the mostly adopted common process of evaluation of
IT tender bids for state government organizations and various stages of such evaluation process
along with evaluation criteria has been highlighted in this paper without mentioning the name of
a specific state government department. But, the needful description of the evaluation process is
presented without any gaps or misunderstandings.
When any state government organization approaches ABS for selecting supplier for a specific IT
activity, ABS first performs a preliminary investigation of requirements and availability of funds
of the user organization. When the project is feasible, ABS notifies the request for proposal
(RFP) and invites the tender bids as an open tender process. Different suppliers/vendors from all
over India will submit both the technical and financial bids separately. The bids received after
the due date will be rejected. To evaluate the accepted tender bids and select the right supplier
out of them, ABS follows several phases of evaluation with specific criteria issues in each phase.
The phases include Preliminary evaluation phase, Business strengths evaluation phase, Technical
(Demonstration) evaluation phase, Financial Quotation evaluation phase and Final evaluation
phase.
Preliminary evaluation phase starts with the activity of checking the bids whether they have
satisfied the mandatory requirements of the bid process, in this case, making appropriate earned
money deposit (EMD) and providing evidence of specified business (information technology)
line. Here, the ‘bidder’ means the vendor/supplier organization, which sends its authorized
people as their representative(s) to participate in the bidding process. For a bidder, if any of
these two criteria items is assigned negative score, that bidder will be disqualified and eliminated

from further evaluation process. The bidders qualified in the preliminary phase will be
evaluated in the second phase, that is, Business strengths evaluation phase, in terms of their past
performance in the business. For this purpose, the business performance for the last three
financial years, technical staff and available infrastructure will be treated as evaluation criteria
issues. In this case, lot of assumptions could be made to pass or fail those bidders who failed to
generate profits in any one or two of the past three financial years based on right analysis and
analogy. The help of scores gained in the remaining two criteria items, namely, technical staff
and infrastructure would also be taken to evaluate the bidder. Of course, the bidder who ran in
losses in the last three consecutive financial years would be naturally disqualified.
For the technical evaluation phase, the bidders passed in the second phase would be authorized to
visit the client organization for a short duration to develop a prototype application for a specific
activity based on their preliminary study on the organization’s requirements. The prototype
application developed by the bidders will be evaluated in terms of their understanding and
analysis of requirements, technical skills to develop the application accordingly and expressing
and presenting the problem and solution in a clear and convincing manner. All these issues
would be treated as the evaluation criteria issues in this phase, based on which the bidder would
assign scores appropriately. The bidders who successfully pass this phase would be promoted to
the next phase, that is, Financial Quotations evaluation phase. Like in most organizations, ABS
opens the financial quotations submitted by the bidders at the beginning of the tender bids along
with the technical bid. The financial bids of the bidders who passed the previous phase would be
opened in the presence of all the bidders and the estimated cost quoted by them for the specified
work would be announced openly. ABS used to consider two major issues in this phase, namely,
the score obtained by a bidder in the previous technical phase and the cost quoted by that bidder
in the financial quotations phase and if the bidder is found to be technically sound among all the
rest, but quoted highest price, that bidder might be negotiated over the price or further services or
both. If the bidder is rigid on the price, there may be chances to consult another bidder who
obtained next better score in the technical evaluation. Therefore, based on the score of technical
evaluation phase and the price quote and tendency for further negotiations on price and services,
the bidders would be evaluated in this final phase. A single successful bidder would be finalized
in this phase and the work order would be placed on that bidder.
Following the objectives and evaluation criteria of each phase, the BDM method involves
development of a truth table by listing the criteria items and assigning Binary values (0 or 1) to
each criteria item for each vendor/supplier and at the end of each phase, a mathematical model
by correlating the output with the inputs will be generated. The mathematical model thus created
for each phase of evaluation would be treated as an evaluation standard to evaluate bidders for
that particular phase.
In order to automate the application of this method, a Microsoft Excel spreadsheet has been
developed to automatically calculate the outputs for each vendor as per the input scores assigned
for every phase of evaluation. This methodology can be customizable for other industries also
with simple modifications. The method stresses the need of effective integration of specialized
knowledge and experience of the evaluators with the objectives and policies of the organization
in dividing the complex decision-making system into reasonable number of meaningful and
manageable sub-systems, identifying the right decision criteria or attributes with proper
guidelines and assumptions to assign the binary scores for different entities in each sub-system
and completing the process with final wholesome decision.
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3. BIT DECISION MAKING (BDM) METHOD
A disciplined and transparent decision-making process employing credible evaluation methods
will provide: structure to approach complex problems; rationale for decisions; consistency in the
decision making process; objectivity; documented assumptions, criteria, and values used to make
decisions; and decisions that are repeatable, reviewable, revisable, and easy to understand (Baker
et al, 2001).
The main objectives of BDM method are to (i) breakdown the complex decision system into as
many smaller and manageable sub-systems as possible and (ii) apply Boolean logic and Boolean
algebra to the decision process in each such sub-system. A complex system will be broken down
into reasonable number of meaningful and manageable small sub-systems and each sub-system
consists of some relevant decision criteria. Each criterion is assigned a value of either ‘1’ or ‘0’,
that is, a binary number, to represent either ‘yes’ or ‘no’, either ‘true’ or ‘false’, either ‘correct’
or ‘incorrect’, ‘either ‘on’ or ‘off’, etc. The group of possible alternative values of a criterion
forms a pattern of binary values. Hence, different patterns of binary digits are possible from all
the relevant criteria of a particular sub-system. The set of binary values of all the criteria will
result an output, which will represent the decision to be made in that particular case. Similarly,
the output is also treated as a binary digit, which is decided by the decision-maker.
In order to make the whole decision system consisting of binary digits and each variable equated
to a bit value (either ‘1’ or ‘0’), the output derived from two or more input values is limited only
to a single bit, which is the last bit, by suppressing the carrier, if any. For example, if an output
is a result of addition of two input bit values, the addition 1+0 results ‘1’, but 1+1 results only ‘0’
(the carrier ‘1’ is suppressed) to limit the output value to a single bit. Thus, the Boolean logic
represented by a binary digit is implemented in the BDM method for both input and output
values.
It is the user (decision maker) that decides to assign either ‘1’ or ‘0’ to the selected decision
criterion based on the analogy and the logic the user weighs, adopts and treats correct. The
decision maker may either be an individual expert or a group of experts. After assigning binary
digits to different criteria in a sub-system, the user has to again decide the result of their output,
i.e., either to assign ‘1’ or ‘0’ based on the strategy under implementation. This method of
assigning binary values to inputs and outputs generates different sets of combinations in different
sub-systems and each combination of inputs has an output. The analogy and logic that is followed
for a sub-system should be treated as a standard for that system and a standard mathematical
equation can be generated using Boolean algebra by correlating the inputs to their respective
output. Any change in the analogy results changes in the assignment of binary values to the inputs
and the outputs and thereby leads to changes in the correlation equation. Thus, a sub-system with
fixed mathematical model (correlation equation) can be treated as a standardized decision system.
Figure 1 represents the process of decision making and mathematical modeling in BDM method.

Mathematical
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Output
as a Binary
value
Inputs
as Binary
Criteria Decision
process
Analyse
and Apply
Correlate
Inputs to
Outputs
Figure 1. BDM evaluation model
model
as Binary
expression
logic
BDM method can be applied to any simple or complex decision systems. In the case of complex
systems, the system should be divided into a reasonable number of independent, meaningful and
manageable sub-systems and each such sub-system is treated with the above procedure and a
unique mathematical correlation equation can be derived for it. This needs thorough study and
analysis of the total system, its break-down into different sub-systems and the various decision
criteria possible in each sub-system.
The method is having both quantitative and qualitative dimensions. Quantitative is in the sense
that Boolean values are assigned to each criteria item and processed in the form of mathematical
equations. Qualitative is in the sense of identifying the right and potential criteria items and
assigning values appropriately in each sub-system of evaluation.
4. PROCESS OF EVALUATION OF INFORMATION
TECHNOLOGY (IT) TENDER BIDS
Clients are able to get a minimum price by putting out the contract to competitive bid and
advertising an invitation for bid that lists customer requirements usually results in low bids [7,9].
The IT tender bids cover development of an IT product or service, sub-contracting part or total of
project work, purchase of software, hardware, stationery, related tools and peripherals, etc. The IT
tender process generally consists of many stages like (1) Invitation to tender, (2) Preliminary phase
of evaluation (evaluation of mandatory requirements), (3) Evaluation of business strengths of
bidders, (4) Evaluation of technical strengths of bidders, (5) Evaluation of financial quotations
submitted by bidders and (6) Finalization of successful bidder.
The ‘invitation to tender’ documents the customer requirements, needs, terms and conditions and
also the eligibility of the bidder in different aspects like resources, business and technical
capabilities. Responding to the invitation to tender openly, in general, many suppliers will submit
their tender bids.
Tender bid normally consists of mandatory and desired requirements of the contractor. If any
tender bid does not meet the mandatory requirements, that proposal will be immediately rejected.
Examples for mandatory requirements are payment of earnest money deposit (EMD) for
participation in tender, matching business of the bidder, etc. The evaluation criteria involved in

this preliminary phase of tender process are to check whether the bidder has paid the EMD amount
and whether the bidder is in the same business line to handle the proposed work.
The bids, that pass in the preliminary evaluation phase, are eligible for the next stages of
evaluation, namely, Business strengths, Technical, Financial quotation and Final evaluations. The
number of phases of evaluation process can be modified depending on the user’s criteria, choices,
resources, requirements and vision.
In the business strengths evaluation phase, evaluation is focused on the business turnover of the
bidder, for example, the business turnover in the last three financial years, that is, whether the
business is running in profit or loss. Evaluation of other business strengths like availability of
resources (both manpower and infrastructure), etc. may also be considered. For this purpose, the
bidders or their representatives may be interviewed and their development sites even be visited.
The technical (demonstration) phase may include the evaluation criteria such as supplier’s level of
analysis of the requirements of user, development skills, and presentation skills. For this
evaluation phase, the bidders who are successful in the previous phase will be invited to give
demonstration on their study and analysis of user requirements, any prototype application
developed, etc.
Evaluation of financial quotations depends mainly on the price quoted by the bidder in the
financial bid, which is submitted in a separate sealed cover along with the tender bid. This phase
may also include another decision criterion, the bidder’s flexibility for negotiations on price and
service. For this evaluation phase, the bidders qualified in the technical phase will be considered
and their financial bids opened in the presence of those bidders.
The last phase, called the Finalization of successful bidder, evaluates the performance of the
bidders in the technical phase in comparison with their financial quotes and the subsequent
negotiations held on price and services and finally selects the successful bidder to award the work
or purchase order.
When all the above phases of evaluation are managed properly, the task of evaluation of tender
bids will become successful.
5. APPLICATION OF BDM METHOD TO EVALUATE INFORMATION
TECHNOLOGY TENDERS
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The application of BDM method to all the phases of IT tender evaluation process starting from
preliminary phase is detailed below.
5.1. Preliminary phase
The evaluation process in this phase is to check whether the bidder has satisfied the mandatory
requirements of the tender, like paying the EMD amount and continuing in the same line of
business. Hence the two issues, namely, EMD payment (X1) and same business line (X2) can be
treated as two decision criteria in this phase of evaluation. Following BDM method, if ‘1’ is
assigned to X1 for positive response, i.e., EMD is paid, ‘0’ will be assigned to the negative
response, i.e., EMD is not paid. In the same way, ‘1’ is to be assigned to X2, if the bidder is in the
same line of business or else ‘0’ is to be assigned. Assigning bit values in this way forms
maximum four possible combinations (A, B, C, D) of input and output values. A truth table, Table
1, can be developed using these inputs and their result.

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Table 1: Truth table for the Preliminary phase
Decision Criteria Possible patterns
A B C D
X1 (EMD payment) 1 1 0 0
X2 (same business
line)
1 0 1 0
Output 1 0 0 0
The assignment of digits in the above table and the output drawn up will be through application of
simple logic by the user. For example, in pattern C, when EMD is not paid means the bidder is not
at all eligible to participate in the tender even though the bidder is in the same business line. Hence
the output is ‘0’. Similarly, payment of the EMD alone does not qualify the bidder unless the
bidder is in the same business line. This case is represented by pattern B.
From the above possible combinations, the mathematical equation correlating the output Y1 to the
inputs X1 and X2, can be generated using Boolean algebra as,
Y1 = AND(X1, X2). …..(1)
In the above equation, simple Boolean ‘AND’ operation has been used between the two variables,
X1 and X2; that means X1. X2.
5.2. Business Strengths evaluation phase
In this case, the decision criteria considered are the turnover for the last three financial years,
strength of technical staff, and infrastructure availability. For the last three years, the business
turnover of each year is to be checked, i.e., whether profit or loss. If it is profit, assign ‘1’,
otherwise, assign ‘0’. So there are three input criteria elements for the turnover of the last three
years – X3, X4, and X5. Here, a constraint of having profit at least once during the last three
financial years may be laid down to consider such bidders. That means, a bidder having no profit
at least once during the last three years can be eliminated. For the criterion of strength of technical
staff (X6), if it is satisfactory, assign ‘1’ or else assign ‘0’. Similar process is followed in the case
of infrastructure availability (X7). Thus, Table 2 is the resultant truth table for this phase.
Table 2: Truth table for the Business Strengths phase
A B C D E F G H I J K L
X3 (1st year business) 1 1 1 1 1 1 1 1 1 1 1 1

X4 (2nd year business) 1 1 1 1 1 1 1 1 0 0 0 0
X5 (3rd year business) 1 1 1 1 0 0 0 0 0 0 0 0
X6 (Technical staff) 1 1 0 0 1 1 0 0 1 1 0 0
X7 (Infrastructure) 1 0 1 0 1 0 1 0 1 0 1 0
Output 1 1 1 0 1 1 1 0 1 0 0 0
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(Constraint: There should be profit at least once during the last three financial years)
The patterns include the bidders having profit in every year, twice and only once during the last
three years respectively along with their strengths in manpower and infrastructure. The important
constraint used for evaluation regarding turnover is added at bottom of the table.
The way the output is derived is through applying strategy and logic, which may be quite difficult
in some cases like patterns, J and K. There, even though the bidder is having profit at least once
during the last three years, the bidder has failed in having either satisfactory strength of technical
people or infrastructure, which may not be acquired immediately due to financial losses for the last
two years if the bidder is awarded the work. In the case of patterns F and G wherein the bidder is
in profit for two years, it is assumed that the bidder is financially capable to strengthen either
infrastructure facilities or technical staff. Regarding the pattern I, even though the bidder has profit
only once in the last three years, the bidder is having good strengths of technical staff and
infrastructure and hence it is assumed that the bidder can wipe out the losses if the work is
awarded. Based on the above strategy, the output is assigned a value ‘1’ for those bidders to be
considered. The ultimate correlation equation derived from the truth table is
Y2 = OR(AND(OR(AND(X3,X4),AND(X4,X5),AND(X3,X5)),OR(X6,X7)),
AND(X6,X7)) …..(2)
The above Boolean expression is equivalent to [(X3. X4 + X4. X5 + X3. X5). (X6 + X7) + X6 .
X7].
If the logic and strategy as explained above is changed, the assignment of bit values also changes
leading to change in the correlation equation. Hence, it is the duty of decision maker(s) to evolve
proper logic and strategy.
5.3. Technical evaluation phase
The bidders qualified in the above two phases may be asked to demonstrate their product(s) if the
purpose of tender is to purchase product(s), or to develop a prototype application according to the
requirements of the user if the purpose of the tender is to develop an application or service. Here,
three criteria items may be considered, based on the bidder’s capabilities in analysis of user’s
requirements (X8), development (X9) and presentation (X10). Let us assume to consider a bidder
who passes in at least two out of the three evaluation criteria issues (X8, X9, X10). Table 3 is the
resultant truth table.

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Table 3: Truth table for the Technical phase
A B C D E F G H
X8 (Analysis) 1 0 1 0 1 0 1 0
X9 (Development) 0 0 1 1 1 1 0 0
X10 (Presentation) 1 1 0 0 1 1 0 0
Output 1 0 1 0 1 1 0 0
The equation correlating the output to the inputs is as follows,
Y3 = OR(AND(X8,OR(X9,X10)),AND(X9,X10)) …..(3)
The above Boolean expression is similar to [X8. (X9 + X10) + X9. X10.
5.4. Financial Quotation evaluation phase
The bidders who get through successfully from the third phase of evaluation will be invited to
attend the event of opening of their financial bids. After opening the financial bids, the rates
quoted by different bidders are displayed to start further evaluation exercise. This phase of
evaluation includes checking the price quoted (X11) by the bidder for the product or service and
testing the bidder’s flexibility for negotiations on price or services (X12). From the list of prices,
if the price quoted by a bidder is considerably high, ‘0’ is to be assigned to the criteria item, X11,
or if the price quoted is reasonable or considerably low , ‘1’ is to be assigned to X11. If the bidder
is ready for negotiations, 1 is to be assigned to the variable, X12, and 0 otherwise. Let us assume
that even though a bidder quotes high price, the bidder can be considered on the grounds of
flexibility for negotiations. Following this strategy, Table 4 will be the resultant truth table.
Table 4. Truth table for the Financial quotes phase
Criteria item Possible patterns
A B C D
X11 (quoted price) 1 1 0 0
X12 (flexibility for negotiations) 1 0 1 0
Output 1 1 1 0
From the possible combinations of inputs and outputs as shown in the table, the resultant
correlation equation is
Y4 = OR(X11,AND(NOT(X11),X12)) …..(4)
___

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The above Boolean expression is similar to [X11 + X11. X12].
5.5. Final evaluation phase
This is a critical phase because of finalizing the successful one from the competing bidders and for
this purpose the decision maker(s) may evolve their own strategy or use a general strategy. The
decision maker may also combine the results of both third (technical) and fourth (financial) phases
of evaluation to take a consolidated decision. For example, the customer may pick up the bidders
who have scored ‘1’ for all the criteria items under the technical phase and check whether they
have passed in the financial phase. If more bidders are found passed in this way, the bidders who
have scored ‘1’ for the two criteria items in the financial phase can be considered. Even then, if a
number of competing bidders are resulted, a bidder can be finally selected based on the
negotiations held on price and services.
A simple Microsoft Excel spreadsheet has been developed to validate all the Boolean algebraic
expressions presented in the form a mathematical models. The results are exactly coinciding
with the results obtained through application of administrative analogy and the organizational
policies and procedures. This case is an application to show how a complex decision system can
be divided among different phases of decision making process and appropriate mathematical
models using Boolean algebra can be developed by covering the contribution of various salient
variables that influence the system at different stages.
The Microsoft Excel spreadsheet developed to implement the BDM method is shown in the
figure, Figure 2.
Figure 2. Spreadsheet showing application of BDM method for making decision

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6. FEATURES OF BDM METHOD
From the theory and methodology and results of application of BDM method, the following
features of the method have been summarized:
Granularity: In BDM method, a complex system can be divided into a reasonable number of
independent, meaningful and manageable sub-systems or phases to ease the decision making
process. The size of the resulting grain of the system will be decided by the concerned decision
maker(s) and their implementation of logic and strategy.
Flexibility: Based on the decision criteria useful for making decisions in each phase, possible
patterns of combination of input values and the ultimate output value are created. The patterns
with the same input values need not result the same output value in different phases. This is due to
the difference in using specific logic, strategy and analogy in different phases. This is evident from
the truth tables, Table 1 and Table 4, wherein the same input patterns are present but with different
outputs. In addition to the changes in the logic and values of the inputs and outputs, the correlation
equation will also change accordingly. This way, the BDM method provides a lot of flexibility to
change decision criteria, their values and the ultimate output values depending upon the strategy
and logic the user wants to implement in a particular evaluation phase.
Standardization: Once the equations correlating the inputs to the output are derived for each sub-system,
they will act as evaluation-model standards to automate the decision making process. Any
change in either the criteria items or their resultant output value in any sub-system leads to change
the mathematical correlation equation of that sub-system. A sub-system with a fixed mathematical
model can be treated as a standardized decision system, which automates the decision process with
any number of cases. This way of standardizing decision making in each sub-system leads to the
formulation of a standard decision making system for the whole complex system.
Integration: Once the whole process is described along with different phases and their sequence,
the output pertaining to an entity in one phase decides whether to go it to next phase or not. The
entities that pass one phase will move to next phase and this continuity will be maintained till the
last phase. Last phase deals with those entities that successfully passed all the phases and
decides the best one out of them.
Linear programming methods help the organizations to have optimization solution with a set of
most-feasible values for the variables under consideration subject to the given constraints. This
is one time solution for a problem of selected variables and constraints. In the case of AHP, it
starts with a problem, identify subsequent criteria and sub-criteria at different levels and work
with their data for each pair of alternatives available. Let us take the same problem of selection
of a bidder from a set of bidders who submitted the bids. To select the bidder, in AHP, there will
be some criteria established by the organization, for example, price, service, reputation,
expertise, etc. Under each criteria, there may be different sub-criteria items and so on, depending
upon the attributes of processes and participants. The bidders will be treated as alternatives and
the scores will be awarded to each criteria and subsequent sub-criteria by pair-wise comparisons
of alternative bidders. Even though the BDM method is also a phased approach like AHP, it
concerns with the criteria items related to a particular phase based on the policies and procedures
of the organization. The movement to other phase will be possible once the current phase has
been completed and the alternatives are filtered out. This is just like a system development life
cycle (SDLC) or simply the water-fall method.

23
7. CONCLUSIONS
There are systems where a firm decision, i.e., either ‘yes’ or ‘no’ is to be taken for each criteria
issue present therein and there will not be any scope for weighing the item in between those
extreme decision points, just like in fuzzy logic systems. The number of such decision criteria
varies differently in different systems and in big and complex systems there may be large number
of such criteria. The method (BDM) presented in this paper assumes that a complex system can
be divided into a reasonable number of independent, meaningful and manageable sub-systems or
phases arranged in sequence to ease the decision making process. The BDM method has many
important features like granularity, flexibility, standardization, and integration. It uses Boolean
logic and simple Boolean operations (‘OR’, AND, and NOT) and derives mathematical model
for each sub-system. The system with a specific mathematical model can be treated as a
standardized decision system and any changes made in either the decision criteria or their
resultant output lead to change in the mathematical model. A real world case study, the
evaluation of IT tenders in one public-sector company, is given as an example of application of
BDM method so as to provide a wide scope for the method to be applied to other areas and other
fields to simplify the complex decision process. The same method can be applied to evaluate the
performance of the selected suppliers in performing their assigned supply tasks from time to time
in different dimensions like quality, cost, delivery/shipping and reduction of cycle time, etc.
Following this method, a Microsoft Excel spreadsheet can be created as a decision support
system to feed the Boolean values for each and every evaluation criterion and get the decision-result
for each entity and for that whole system automatically.
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Author: Dr. Nasina Jigeesh
Dr. N.Jigeesh, Ph.D (Physics), Ph.D. (Management Science) working as a
Professor & Head of the Department of Operations & Systems, IBS-Hyderabad,
which is a constituent of the ICFAI Foundation for Higher Education (IFHE)
University. He has above 25 years of experience in both Industry and Academia.
His experience includes Administration, Management, Teaching and Research.
Published several papers in both International and National Journals and in
Conferences as well. Teaching the subjects of Project Management, Information
Systems for Managers, Enterprise-wide Systems for Managers, DBMS, Data
Mining & Data Warehousing, e-Business, Business Intelligence & Business
Analytics. He guided one Ph.D. work and is guiding several other Ph.D. students
in the area of Mangement Science. His research interests include Project
Management, Knowledge Management and
Information Technology/Systems.

Decision support systems, Supplier selection, Information systems, Boolean algebra, Supply chain management, Multi criteria decision making, Decision modelsA new decision support system for supplier selection using boolean algebra

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