OPERATIONAL RESEARCH IN
DECISION MAKING
GROUP C BACF/19A/FT
AUTHORED BY:
APPALASAMY MANISHA
1903_19143
BOODOO KRISHNA
1903_19147
BUNDHOO JYOTEE
1903_19150
GROODOYAL PREEYAKSHA 1903_19154
JOLICOEUR MEGANE
1903_19159
RENOTEE RASHIKA
1903_19173
APPALASAMY MANISHA -DECISION UNDER RISKS
BOODHOO KRISHNA
-GAME THOERY
BUNDHOO JYOTEE
-DECISION UNDER CERTAINTY
GROODOYAL PREEYAKSHA-INTRODUCTION,CONCLUSION,FUTUREWORK
JOLICOEUR MEGANE
-PAYBACK ANALYSIS
RENOTEE RASHIKA DEVI
-DECISION TREE ANALYSIS
1
ACKNOWLEDGEMENT
We would like to express our deepest appreciation to all those who have
provided us with the possibility to complete this assignment. A special thanks
to our lecturer, MR RAJIV CHOORAMUN, whose contribution in encouraging us
and giving us suggestions, helped us to coordinate our project.
Last but not the least, many thanks to our team member who have invested
their time in achieving the goal.
2
CONTENTS
ACKNOWLEDGEMENT
ABSTRACT
METHODOLOGY
INTRODUCTION
MODELS OF DECISION MAKING
PRINCIPLES OF DECISION MAKING
CONCLUSION
FUTUREWORK OF OPERATIONAL RESEARCH
IN DECISION MAKING
3
CONCLUSION
FUTUREWORK OF OPERATIONAL RESEARCH IN
DECISION MAKING
APPENDIX
REFERENCES
4
ABSTRACT
RESEACHER:
PRESENTATION TITTLE: DECISION MAKING PROCESS
RESEARCH FOCUS:
SCHOOL:
STUDENT LEVEL:
ABSTRACT
Decision making
5
METHODOLOGY
Most formula has been derived from paper or book:
DECISION TREE ANALYSIS
EXPECTED VALUES=OUTCOMESXPROBABILITY
NET EXPECTED VALUES=EXPECTED VALUES-OUTCOME
PAYBACK ANALYSIS
BAYES’ RULE
6
INTRODUCTION
Operational research is an analytical method of problem-solving and decision-making that is
useful in managing organizations. In other words, Operational Research is the study of how
to make decisions efficiently.
It provides the necessary data to analyst to be able to take decisions and means to apply
scientific, systematic, technical and mathematical methods for taking the appropriate
decision and solve the issue.
There are various techniques that a business can use while taking decisions. For example,
quantitative techniques enable businesses to take decision objectively and efficiently.
The different operational research models and decision-making principles can be seen
further below.
7
Advantages of Operations Research in Decision Making
 Better co-ordination and Management
The operational research techniques are very efficient and effective for planning.
 Efficient Control
Managing organizations can be really complicated and expensive. This is why there is
a need for proper supervision and control. Thus, Operations research may provide
the manager a better help in identifying the area of problem.
 Better and Analytical Decisions
Operational research models help to make better decisions.
 Maximize profits and Minimize losses
 Efficient systems
 Increased Business Productivity
 Better Decision Making
8
Limitations of Operations Research in Decision Making
 Difficulties in Implementation
Implementing decisions is a delicate task.
 More time consuming and costly
 Dependence on an Electronic Devices
 Distance between Manager and Operations Researcher
 Solve only quantitative issues
 Complex
9
MODELS OF OPERATIONAL RESEARCH
The process of decision making contains various methods. Quantitative techniques of
decision-making help make these methods simpler and more efficient.

MODEL 1: GAME THOERY
What Is Game Theory?
Game theory was introduced in 1944 by mathematicians John Von Neumann and
John Nash, as well as economist Oskar Morgenstern.
It is the study of social situations among competing players.
Any time we have a situation with two or more players that involves known payouts
or quantifiable consequences, we can use game theory to help determine the most
likely outcomes.
It is a strategy where at least an optimal decision-making of independent and
competing players in a strategic process.
10
The Basics of Game Theory
The focus of game theory is the game, which serves as a model of an interactive
situation among rational players.
The key to game theory is that one player's payoff is contingent on the strategy
implemented by the other player. That is, the actions and choices of all the
participants affect the outcome of each.
The game identifies the players' identities, preferences, and available strategies and
how these strategies affect the outcome. Depending on the model, various other
requirements or assumptions may be necessary.
11
The Prisoner's Dilemma
The Prisoner's Dilemma is a famous example of game theory. Consider the example
of two criminals arrested for a crime. Police have no hard evidence to convict them.
However, to gain a confession, officials remove the prisoners from their solitary cells
and question each one in separate chambers. Neither prisoner has the means to
communicate with each other.
1. If both confesses, they will each receive a five-year prison sentence.
2. If prisoner 1 confesses, but Prisoner 2 does not, Prisoner 1 will get three years
and Prisoner 2 will get 10 years.
3. If prisoner 2 confesses, but Prisoner 1 does not, Prisoner 1 will get 10 years, and
Prisoner 2 will get three years.
4. If neither confesses, each will serve two years in prison.
 The most favorable strategy is to not confess.
 However, neither is aware of the other's strategy and without certainty that
one will not confess, both will likely confess and receive a five-year prison
sentence.
12
The Nash Equilibrium
Nash Equilibrium is an outcome reached that, once achieved, means no player can increase
payoff by changing decisions. It can also be thought of as "no regrets," in the sense that
once a decision is made, the player will have no regrets concerning decisions considering
the consequences.
And in this Prisoner's Dilemma example, the Nash equilibrium suggests that both players
will make the move that is best for them individually but worse for them collectively.
13
Limitations of Game Theory
The biggest issue with game theory is that, like most other economic models, it relies on the
assumption that people are rational actors that are self-interested and utility-maximizing.
Of course, we are social beings who do cooperate and do care about the welfare of others,
often at our own expense.
Game theory cannot account for the fact that in some situations we may fall into Nash
equilibrium, and other times not, depending on the social context and who the players are.
14
MODEL 2: DECISION TREES ANALYSIS
One model for performing decision tree analysis was
created by J.ROSS QUINLAN at the University of Sydney
in 1975.
Decision tree analysis is a general, predictive
modelling tool that has applications spanning
a number of different areas. In general,
decision trees are constructed via an
algorithmic approach that identifies ways to
split a data set based on different conditions.
Decisions trees are a form of multiple effect
analyses. All forms of multiple variable
analyses allow us to predict , explain ,describe
or classify an outcome. This multiple variable
analysis capability of decision trees enables us
15
to go beyond simple one-cause, one-effect
relationships and to discover and describe
things in the context of multiple influences.
Multiple variable analysis is particularly
important in current problem-solving because
almost all critical outcomes that determine
success are based on multiple factors.
16
DECISION TREE USING FLOWCHART
1. The Oval
An End or a Beginning
Oval
The oval is used to represent the start and end of a process. Use the symbol to
begin flowchart. Use the same symbol again to show that your flowchart is complete.
2.The Rectangle
A Step in the Flowcharting Process
Rectangle
The rectangle is your go-to symbol. It represents any step in the process flow you’re
diagramming and is the workhorse of the flowchart diagram.
3. The Arrow
Directional Flow
17
Arrow
The arrow is used to guide the viewer along their flowcharting path. And while there
are many different types of arrow tips to choose from, we recommend sticking with
one for your entire flowchart. It’s less confusing and generally more aesthetically
pleasing.
4.The Diamond
Call for a Decision
Diamond
The diamond symbolizes that a decision needs to be made. If there are only two
choices, you can draw arrows directly from the diamond to the next step (example on
the left). If there are more than two choices, you can draw them neatly by copying
the example on the right.
18
A decision tree is a flowchart like a diagram that shows
the various outcomes from a series of decisions. It can
be used as a decision making tool ,for research analysis
or planning strategy. A primary advantage for using a
decision tree is that it is easy to follow and understand.
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STEPS TO DRAW DECISION TREE ANALYSIS
1.Drawn from left to right.
2.The tree starts with a decision point , a
node, so start the tree with a square.
3.Add the chance nodes, the probabilities and
the outcomes.
4.Calculate the expected values.
5.Calculate the net expected value.
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EXAMPLE OF DECISION TREE ANALAYIS
THE PROPERTY OWNER
QUESTION:
A property owner is faced with a choice of:
(a) A large-scale investment (A) to improve her flats. This could produce a substantial payoff in terms of increased revenue net of costs but will require an investment of
£1,400,000. After extensive market research it is considered that there is a 40% chance
that a pay-off of £2,500,000 will be obtained, but there is a 60% chance that it will be
only £800,000.
(b) A smaller scale project (B) to re-decorate her premises. At £500,000 this is less costly
but will produce a lower pay-off. Research data suggests a 30% chance of a gain
of £1,000,000 but a 70% chance of it being only £500,000.
(c) Continuing the present operation without change (C). It will cost nothing, but neither
will it produce any pay-off. Clients will be unhappy and it will become harder and harder to
rent the flats out when they become free.
How will a decision tree help the taking of the decision?
SOLUTION:
Process:
1. Draw the decision tree representing the options open to the property owner.
The tree starts with a decision point, a node, so start the tree with a square.
Three lines radiate from this, representing the three options. Label them carefully.
21
2. Add the chance nodes, the probabilities and the outcomes. The options end with possible
outcomes, so mark with a circle. In this case there are two possible outcomes for the
investment options, and only one for the 'as is' option. Add all the data to this diagram.
3. Calculate the expected values. Now start to calculate, starting from the right. Multiply
the outcomes by the relevant probability, and then add the answers together for each
option. Put answer above the appropriate circle.
4. Calculate the net expected value. The final stage is to adjust for the costs of the
options. Now subtract the costs of each option from the expected value, and mark the
calculation on the diagram. Reject the options with the lowest net expected value.
22
ADVANTAGES
DISAVANTAGES
Easy to understand.
May suffer from overfitting.
Useful in data exploration.
Calculations can become complex when
there are many class labels.
Less data cleaning required.
Decision tree often involves higher time
to train the model.
APPLICATIONS OF DECISION TREE ANALYSIS
Classification algorithms being used in Data Mining and
Machine Learning. Example applications include:
· Evaluation of brand expansion opportunities for a business
using historical sales data
· Determination of likely buyers of a product using demographic
data to enable targeting of limited advertisement budget
· Prediction of likelihood of default for applicant borrowers
using predictive models generated from historical data
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· Help with prioritization of emergency room patient treatment
using a predictive model based on factors such as age, blood
pressure, gender, location and severity of pain, and other
measurements
· Decision trees are commonly used in operations research,
specifically in decision analysis, to help identify a strategy most
likely to reach a goal.
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MODEL 3: PAYBACK ANALYSIS
Payback Analysis
There are numerous methods of making decisions with the help of quantifiable data,
and payback analysis is one of these. A decisionmaker will use this method to
determine the viability of a project, that is which project to accept and which to
reject.
Therefore, the payback period has to be calculated for the projects. A payback
period is the time required to recover the money invested in an asset from its net
cash flows. It is represented in terms of years. The decision-maker will choose the
project with the less or shortest payback period so as to earn back the amount
invested faster and the money is at risk for a shorter period of time.
The payback period can be calculated using this formula:
Payback period=Initial Investment ÷ Net cash flows from a project
Advantages of payback period:
1. Easy to calculate.
2. It is more objective as cash flows are used instead of profits.
3. Risks related to time are lessened as the shortest payback is chosen.
It promotes a policy of caution as it helps to evaluate risks of different projects.
4. It increases a company’s liquidity.
Disadvantages of payback period:
1. In case of only 1 project, it may be difficult to determine the maximum acceptable
payback period.
2. It ignores the total profits of the projects.
3. It ignores time value of money.
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 EXAMPLE
Excel ltd is considering the purchase of a new machine. Two different
machines will suit the company’s purpose. The cash flows are given:
Year 1
Year 2
Year 3
Year 4
Machine A
Cost Rs210000
Estimated cash flows
70000
80000
90000
90000
Machine B
Cost Rs180000
Estimated cash flows
70000
70000
80000
80000
Required: Calculate the payback period for each of the two machines.
Answer:
• Machine A The initial outlay will be paid back partway through Year 3. (Rs70000
Year 1+ Rs80000 Year 2+ Rs60000 partway through Year 3)
Specifically,60000/90000th through the third year Machine A payback is two and
60/90th years=2.67 years.
• Machine B The initial outlay will also be paid partway through Year 3. (Rs70000+
Rs70000+ Rs40000 partway through Year 3) Specifically,40000/80000th through Year
3.Machine B payback is two and 40/80th years=2.5 years.
Excel ltd should buy machine B.
Note: Payback uses cash flows not profits. It is therefore recommended to convert
Profit into cash.
26
Example 2
Given below are details of two capital expenditure projects which the Board of
Development Ltd has under consideration. Project 1 and project 2 has an initial cost
of Rs14000000 and Rs12000000 respectively, but because of shortage of funds, only
one of the projects can be undertaken. The following information is available for two
proposed projects:
Project 1
Expected profit
generated
Year 1
Year 2
Year 3
Year 4
Project 2
RS 000
RS 000
3500
5000
8000
10000
3500
4000
5500
6500
The profit for each project has been calculated after providing for annual
depreciation as follows:
Project 1
RS 000
1500
Project 2
RS 000
1200
Calculate the payback period.
Cash flows
Year 0
Year 1
Year 2
Year 3
Project 1
Rs 000
(14000)
(3500+1500)5000
(5000+1500)6500
9500
• Project 1
Payback=2 + 2500/9500=2.26 years
• Project 2
Payback=2 + 2100/6700=2.31 years
Project 1 should be undertaken-it has the shorter payback
Period.
27
Project 2
Rs 000
(12000)
4700
5200
6700
PRINCIPLES OF DECISION MAKING
Types of decision making
Decision Making is very important in any kind of business.
The decisions are taken in different types of environment and are classified by their degree
of certainty. The decision makings environments are:
1) Decision Making Under Certainty
2) Decision Making Under Uncertainty
3) Decision Making Under Risks
 Decision Making Under Certainty
Under this condition, it is assumed that all information is available. That is, the decisionmaker knows exactly the state of nature that will occur and the alternatives and outcomes
associated with the alternatives. The decision-maker has full control on the events and
situations. Under this situation the most desirable consequence dictates the decision
alternative to be chosen although conditions of certainty are very rare especially when
significant decisions are involved.
A simple example of decision making under certainty: If I have Rs50000 and I want to invest,
then I would like to open a bank’s saving account which will give me more interest. Like I
have the options of 8% annually, 9% annually and 12% annually. So, I would automatically
choose 12%.
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 Decision Making Under uncertainty
SUMMARY
In decision under uncertainty individual decision makers have to choose one of a set
number of alternatives with complete information about their outcomes but in the absence
of any data or information about the probabilities of the various state of nature.
INTRODUCTION
Normally, personal and professional decisions can be made with some difficulty. Either the
best course of action is clear or the varieties of the decision are not enough to require a
great amount of attention. Occasionally, decision arise where the things are not clear and it
is necessary to take time and effort to devise a systematic method of analyzing the various
courses of action. With decisions under uncertainty, the decision maker should:
1. Take an inventory of all viable options available for gathering information, for
experimentation and for action.
2. List all events that may occur.
3. Arrange all pertinent information and choices/assumptions made.
4. Rank the consequences resulting from the various courses of action.
5. Determine the probability of an uncertain event occurring.
For decision-making under uncertainty, we have;
• Wald’s Maximin criterion
• Hurwicz’s criterion
• Maximax criterion
• Savage’s minimax regret criterion
• Laplace’s insufficient reason criterion
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HURWICZ’S OPTIMISM-PESSIMISM CRITERION
The most well - known criterion is the Hurwicz criterion, suggested by Leonid Hurwicz in
1951, which selects the minimum and the maximum payoff to each given action x. The
Hurwicz criterion attempts to find a middle ground between the extremes posed by the
optimist and pessimist criteria. Instead of assuming total pessimism or pessimism, Hurwicz
incorporates a measure of both by assigning a certain percentage weight to optimism and
the balance to pessimism. However, this approach attempts to strike a balance between the
maximax and the maximin criteria. It suggests that the minimum and the maximum of each
strategy should be averaged using a and 1 - a as weights. a represents the index of
pessimism and the alternative with the highest average selected.
The index selected a reflects the decision maker’s attitude towards risk taking. A cautious
decision maker will set a = 1 which reduces the Hurwicz criterion to be the maximin
criterion. An adventurous decision maker will set a = 0 which reduces the Hurwicz criterion
to the maximax criterion.
A weighted average can be computed for every action alternative with an alpha - weight a,
called the coefficient of realism. “Realism’’ here means that the unbridled optimism of
maximax is replaced by the attenuated optimism as denoted by the a. An a = 1 denotes
absolute optimism (Maximax) while a = 0 indicates absolute pessimism (Maximin). The a is
selected subjectively by the decision maker.
Selecting a value for a simultaneously produces a coefficient of pessimism 1 - a , which
reflects the decision maker’s aversion to risk. A Hurwicz weighted average H can now be
computed for everyaction alternative Ai in A as follows:
Hurwicz decision rule is followed:
1. Select a coefficient of optimism value a.
2. For every action alternative compute its Hurwicz weighted average H.
3. Choose the action alternative with the best H as the chosen decision (‘’Best’’ means Max
{H} for positive-flow payoffs, and Min {H} for negative-flow payoffs).
We can therefore use an example to illustrate it as follows; An investor wants to decide in
which of the 3 company to invest. The profits are dependent on the state of the economy
boom, steady and recession rate. Assuming degree of optimism a = 0.6 and therefore 1-a =
0.4, the value of h is calculated in the table:
ALTERNATIVE
MAXIMUM
PAYOFF
MINIMUM
PAYOFF
30
h
Company A
8000
2000
5600
Company B
5000
3500
4400
Company C
5000
4000
4600
The maximum value is 5600 so this criterion selects company A.
STATE OF NATURE
Alternatives
Boom
Steady
Recession
Company A
8000
4500
2000
Company B
3500
4500
5000
Company C
5000
5000
4000
Maximax criterion
31
The Maximax criterion is an optimistic approach. It suggests that the decision maker
examine the maximum payoffs of alternatives and choose the alternative whose outcome is
the best. This criterion appeals to the adventurous decision maker who is attracted by high
payoffs. This approach may also appeal to a decision maker who likes to gamble and who is
in the position to withstand any losses without substantial inconvenience.
It is possible to model the optimist profile with the Maximax decision rule ( when the
payoffs are positive – flow rewards, such as profits or revenue. When payoffs are given as
negative – flow rewards, such as costs, the optimist decision rule is Minimum. Note that
negative – flow rewards are expressed with positive numbers.)
Maximax decision rule is followed:
1. For each action alternative (matrix row) determine the maximum payoff possible.
2. From these maxima, select the maximum payoff. The action leading to this payoff is the
chosen decision.
Maximax criterion:
Refer from the table we observe that maximum payoff for each are 8000, 5000, and 5000
respectively. Maximum among these is 8000 corresponding to company A. Therefore, this
strategy chooses company A.
Wald’s Maximin Criterion
32
The decision – theoretic view of statistics advanced by Wald had an obvious interpretation
in terms of decision – making under complete ignorance, in which the maximin strategy was
shown to be a best response against natures’ minimax strategy. Wald’s criterion is
extremely conservative even in a context of complete ignorance, through ultra –
conservatism may sometimes make good sense (Wen and Iwamura, 2008). The Maximin
criterion is a pessimistic approach. It suggests that the decision maker examines only the
minimum payoffs of alternatives and chooses the alternative whose outcome is the least
bad. This criterion appeals to the cautious decision maker who seeks ensurance that in the
event of an unfavourable outcome, there is at least a known minimum payoff. This
approach may be justified because the minimum payoffs may have higher probability of
occurrence or the lowest payoff may lead to an extremely unfavourable outcome.
From the above example that have been used we can say that Maximin criterion selects
company C.
Savage’s Minimax Regret
33
The Savage Minimax Regret criterion examines the regret, opportunity cost or loss resulting
when a particular situation occurs and the payoff of the selected alternative is smaller than
the payoff that could have been attained with that particular situation. The regret
corresponding to a particular payoff Xij is defined as Rij = Xj(max) – Xij where Xj(max) is the
maximum payoff attainable under the situation Sj. This definition of regret allows the
decision maker to transform the payoff matrix into a regret matrix. The minimax criterion
suggests that the decision maker looks at the maximum regret of each strategy and selects
the one with the smallest value. This approach appeals to cautious decision makers who
want to ensure that the selected alternative does well when compared to other alternatives
regardless of the situation arising. It is particularly attractive to a decision maker who knows
that several competitors face identical or similar circumstances and who is aware that the
decision maker’s performance will be evaluated in relation to the competitors. This criterion
is applied to the same decision situation and transforms the payoff matrix into a regret
matrix.
The Minimax Regret criterion focuses on avoiding the worst possible consequences that
could result when making a decision. Although regret is an emotional state (a psychological
sense of loss) which, being subjective, can be problematic to assess accurately, the
assumption is made that the regret is quantifiable in direct (linear) relation to the rewards
Rij expressed in the payoff matrix. This means that an actual loss of, say, a euro (an
accounting loss) will be valued exactly the same as a failure to take advantage of the
opportunity to gain an additional euro (an opportunity loss, which is disregarded in financial
accounting). In other words, the Minimax regret criterion views actual losses and missed
opportunities as equally comparable.
Laplace’s criterion
34
The Laplace’s insufficient reason criterion postulates that if no information is available
about the probabilities of the various outcomes, it is reasonable to assume that they are
likely equally. Therefore, if there are n outcomes, the probability of each is 1/n. This
approach also suggests that the decision maker calculate the expected payoff for each
alternative and select the alternative with the largest value. The use of expected values
distinguishes this approach from the criteria using only extreme payoffs. This characteristic
makes the approach similar to decision making under risk.
The Laplace’s criterion is the first to make explicit use of probability assessments regarding
the likelihood of occurrence of the states of nature. As a result, it is the first elementary
model to use all of the information available in the payoff matrix.
The Laplace’s argument makes use of Jakob Bernoulli’s Principle of insufficient Reason. The
principle, first announced in Bernoulli’s posthumous masterpiece, Ars conjectandi (The Art
of Conjecturing, 1713), states that “in the absence of any prior knowledge, we should
assume that the events have equal probability’’. It means that the events are mutually
exclusive and collectively exhaustive. Laplace posits that, to deal with uncertainty rationally,
probability theory should be invoked.This means that for each state of nature (Sj in S), the
decision maker should assess the probability of Pj that Sj will occur. This can always be done
– either theoretically, empirically or subjectively. Laplace decision rule is followed:
1. Assign Pj = P(Sj) = 1/n to each Sj in S, for j = 1,2....,.
2. For each Ai (payoff matrix row), compute its expected value:
E(Ai) = summation of j Pj(Rij).
3. Select the action alternative with the best E(Ai) as the optimal decision.
Using the example above we can calculate for the Laplace criterion as follows;
Assign equal probabilities i.e. 1/3. The expected payoff is calculated for each alternative:
ALTERNATIVES
BOOM
STEADY
RECESSION
COMPANY A
COMPANY B
COMPANY C
1/3(8000)+
1/3(3500)+
1/3(5000)+
1/3(4500)
1/3(4500)
1/3(5000)
+1/3(2000)
+1/3(5000)
+1/3(4000)
Hence this criterion also selects company A.
35
EXPECTED
PAYOFF
=4833
=4333
=4666
 Decision making under risk
It is defined as the choice of an optimal action based upon the probabilities of occurrence of
various states of nature. In this case the decision maker knows the probabilities of the
various outcomes or alternatives then will take the decision while considering the risk.
Decision process
• The problem is defined and all feasible alternatives are taken into account. The possible
outcomes for each alternative are assessed.
• Outcomes are discussed based on their monetary payoffs or net gain in reference to
assets or time.
• Various uncertainties are quantified in terms of probabilities.
• The quality of the optimal strategy depends upon the quality of the judgments. The
decision-maker should identify and examine the sensitivity of the optimal strategy with
respect to the crucial factors.
The decision making under risk with probability is divided into in two methods, these are:
1. Expected monetary criterion: this is used to calculate expected monetary value for each
activity using probabilities. In this case the activity which has the maximum value is selected.
2. Expected opportunity loss criterion: this method will require calculation of expected
opportunity loss for each activity using probabilities. The activity with the minimum value is
chosen.
The decision making under risk process is as follows:
a. Use the information you have to assign your beliefs (called subjective probabilities)
regarding each state of the nature, p(s),
b. Each action has a payoff associated with each of the states of nature X(a,s),
c. We compute the expected payoff, also called the return (R), for each action R(a)
Sums of [X(a,s) p(s)],
d. We accept the principle that we should minimize (or maximize) the expected payoff,
e. Execute the action which minimizes (or maximize) R(a)
The choice of an optimal action is based on The Bayesian Decision Criterion according to
which an action with maximum Expected Monetary Value (EMV) or minimum Expected
Opportunity Loss (EOL) or Regret is regarded as optimal.
36
Example
The payoffs (in Rs) of three Acts A1, A2 and A3 and the possible states of nature S1, S2 and
S3 are given below;
Expected Monetary Value (EMV)
A1
PS
S1
S2
S3
0.3
-35
250
550
A2
A3
0.4
120
-350
650
EMV
0.3
-100
220
700
(0.3x-35) +(0.4x250) +(0.3×550) =254.5
(0.3×120) +(0.4×-350) +(0.3×650) =91
(0.3×-100) +(0.4×220) +(0.3×700) =260
From the table shown above the maximum value is 260 that is A3 is said to be optimal. On
the other hand, the problem can be solved by calculating the minimum Expected
opportunity loss. Before doing the Expected opportunity loss table it is required to do a
regret table.
REGRET TABLE
S1
S2
S3
P(S)
0.3
0.4
0.3
A1
[120-(-35)] =155
250-250=0
700-550=150
A2
120-120=0
250-(-350) =600
700-650=50
37
A3
120-(-100) = 220
250-200=50
700-700=0
EXPECTED OPPORTUNITY LOSS(EOL)
PS
S1
S2
S3
A1
A2
A3
0.3
155
0
150
0.4
0
600
50
0.3
220 (0.3x155)+(0.4x0)+(0.3x150)=91.5
50 (0.3x0)+(0.4x600)+(0.3x50)=255
0
(0.3x220)+(0.4x50)+(0.3x0)=86
FUTURE WORK OF OPERATIONAL RESEARCH IN DECISION
MAKING
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While operational research mainly involves mathematical analysis, its principles also apply
to many other real-world issues, like in promotion and selling if products, in economy and in
military and so on.
 The Economy
It is the duty of every government to do proper planning for the economic development of
the country. Thus, the government can make use of the operational research techniques to
establish a profit plan.
 Engineering
In the field of Industrial Engineering, there is a claim of problems, starting from the
pro­curement of material to the dispatch of finished products. Hence in order to provide
decision on scientific basis, O.R. study team con­siders various alternative methods and
their effects on existing system.
 Agriculture
With the sudden increase of population and resulting shortage of food, every country is
facing many problems such as Optimum allocation of land to a variety of crops as per the
climatic conditions. Therefore, a good quantity of work using operational research
techniques can be done in this direction.
 Marketing
With the use of OR techniques a marketing administrator can make decisions about:
-Where to allocate the products for sale so that the total cost of transportation is set to be
minimum
-The minimum per unit sale price
-The size of the stock to come across with the future demand
 Management
A personnel manager can utilize OR techniques to appoint the highly suitable person on
minimum salary or to know the best age of retirement for the employees.
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1.Game theory
 Game: Any set of circumstances that has a result dependent on
the actions of two or more decision-makers (players).
 Players: A strategic decision-maker within the context of the
game.
 Strategy: A complete plan of action a player will take given the
set of circumstances that might arise within the game.
 Payoff: The payout a player receives from arriving at a
particular outcome
 Equilibrium: The point in a game where both players have
made their decisions and an outcome is reached
 Social situation: It includes any situation in which you and at
least 1 other person are present.
 Optimal decision: A decision that leads to at least as good a
known or expected outcome as all other available decision
options.
2.Decision making under uncertainty
 Uncertainty – a situation in which something is not known, or
something that is not known or certain
 Substantial – of considerable importance
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 Systematic – according to an agreed set of methods or
organized plan
 Viable – able to work as intended or able to succeed
 Pertinent - relating directly to the subject being considered
 Optimist – the quality of being full of hope or a belief that
something good will happen
 Pessimist – a person who thinks that bad things are more likely
to happen or who emphasizes the bad
 part of a situation
 Unbridled – not controlled or limited
 Aversion – (thing that causes) a feeling of strong dislikes
 Postulates – to suggest a theory, idea as a basic principle from
which a further idea is form or developed
 Elementary – relating to the early stages of studying a subject
 Posthumous – happening after a person’s death
 Conjecturing – a guess about something based on how it seems
and not on proof
 Empirically – in a way that is based on what is experienced or
seen rather than on theory

Payoff – the result of a set of actions, or an explanation at the
end of something Quantifiable – able to measured
3.DECISION TREE ANALYIS
Node: A node is a point of intersection/connection within a
network. In an environment where all devices are accessible
through the network, these devices are all considered nodes.
Planning strategy: Strategic planning is an organizational
management activity that is used to set priorities, focus energy
and resources, strengthen operations, ensure that employees
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and other stakeholders are working toward common goals,
establish agreement around intended outcomes/results, and
assess and adjust the organization’s direction in response to a
changing environment.
Expected values: It gives a way to include the missing piecethe probability of each alternative in decision making.
4.PAYBACK ANALYSIS
Time value of money: Money received or paid in the future
does not have the same value as money received or paid
today.
Depreciation: Loss in value of a non-current assets.
Cashflow: Amount of money transferred into and out of a
business.
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CONCLUSION
As a final analysis, it can be said that indeed, in its recent years of organized development,
O.R. has solved successfully many cases of research for military, the government and
industry.
But its execution depends on the various mathematical methods and calculations. The
Operation Research may be considered as a tool which is employed to raise the efficiency of
management decisions. OP seeks the optimum state in all spheres and thus provides
optimum solution to organizational problems. It is of considerable value in Production
Management also.
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REFERENCES
1.Decision tree: http://textbook.stpauls.br/Business_Organization/page_105.htm
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2. Decision Making under uncertainty: Wen, M., Iwamura, K. (2008): Fuzzy facility locationallocation problem under the Hurwicz criterion. European Journal of Operational Research
184: 627-635.
: http://terpconnect.umd.edu/~sandborn/courses/808S_projects/reynolds.html
3.Decision under risk:
https://webcache.googleusercontent.com/search?q=cache:RPXspohnUIIJ:https://www.soa.
org/globalassets/assets/files/resources/essays-monographs/2009-erm-symposium/mono2009-m-as09-1-damghani.pdf+&cd=2&hl=en&ct=clnk&gl=mu&client=firefox-b-d
Future work of OP in Decision Making:




B., L. Rigby, S. Lasdon and A. D. Waren, "The Evolution of Texaco's Blending Systems:
From OMEGA to StarBlend’’
R. C. Leachman, R. F. Benson, C. Liu and D. J. Raar, "IMPReSS: An Automated
ProductionPlanning and Delivery-Quotation System at Harris Corporation Semiconductor Sector,"
kalyan-city.blogspot.com
whatis.techtarget.com
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