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Assignment No.2
Quantitative Techniques
(5564)
Col MBA/MPA
DECISION THEORY
Fayyaz Ahmed Kayani
Roll No. AD593483
Semester: Autumn 2009
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ACKNOWLEDGEMENT
No one writes alone. So I would like to thanks all those who
helped and assisted a great source in completion of
assignment. Assigned topic was a new for me and it was not
possible to accomplish it without their magnificent support.
They have been a source of knowledge for me as they helped
me much in understanding the assigned Topic. I especially
thank to my honorable tutor who guided me in every juncture. I
also pay my gratitude to Department of Business
Administration, AIOU, Islamabad for their marvelous selection
of issues for MBA students through which they are gaining
treasure of knowledge after completion of given task for their
future.
DECISION THEORYF a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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INTRODUCTION
Every day we, are humans, make many decisions; and occasionally we make an
important decision that can have immediate and/or long-term effects on our lives.
Such decisions as where to attend school, whether to rent or buy, whether your
company should accept a merger proposal, and so on, are important decisions for
which we would prefer to make correct choice.
The success or failure that an individual or organization experiences, depends
to a large extent on the ability of making appropriate decisions. Making of a decision
requires an enumeration of feasible and viable alternatives (courses of action or
strategies), the projection of consequences associated with different alternatives,
and the measure of effectiveness (or an objective) to identify best alternative to be
used.
Everyone engages in the process of making decisions on a daily basis. Some of
these decisions are quite easy to make and almost automatic. Other decisions can be
very difficult to make and almost debilitating. Likewise, the information needed to
make a good decision varies greatly. Some decisions require a great deal of
information whereas others much less. Sometimes there is not much if any
information available and hence the decision becomes intuitive, if not just a guess.
Many, if not most, people make decisions without ever truly analyzing the situation
and the alternatives that exist. There is a subjective and intrinsic aspect to all
decision making, but there are also systematic ways to think about problems to help
make decisions easier. The purpose of decision analysis is to develop techniques to
aid the process of decision making, not replace the decision maker.
Earlier, the decisions were taken subjectively based on the skill, experience
and intuition of the decision maker. But in todays world of dynamism, the decision
making has become very complex, particularly in business, marketing and
management because they involve a number of interactive variables (factors) whose
values and relationships cannot be determined accurately. In such situations, mere
intuition and expertise of the decision maker are inadequate and we require well
considered judgment and analysis based on the use of several quantitative techniques
and even computers in solving problems. It is in this context that we need a full-
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fledged decision theory which provides a sound and scientific basis for improved
decision making.
Decision making is the essence of management. In general, the process of
making decisions calls for (i) identifying the alternatives, (ii) gathering all the
relevant information about them, and (iii) selecting the best alternative on the
basis of some criterion.The decision theory, also called the decision analysis, is used to determine
optimal strategies where a decision-maker is faced with several decision alternatives
and an uncertain, or risky, pattern of future events. To recapitulate, all decision-
making situations are characterized by the fact that two or more alternative courses
of action are available to the decision-maker to choose from. Further, a decision may
be defined as the selection by the decision-maker of an act, considered to be best
according to some pre-designated standard, from among the available options.
When analyzing the decision making process, the context or environment of the
decision to be made allows for a categorization of the decisions based on the nature
of the problem or the nature of the data or both. There are two broad categories of
decision problems: decision making under certainty and decision making under
uncertainty.
THEORETICAL QUESTIONS ABOUT DECISIONS
The following are examples of decisions and of theoretical problems that they give
rise to.
Shall I bring the umbrella today? The decision depends on something which I do not
know, namely whether it will rain or not.
I am looking for a house to buy. Shall I buy this one? This house looks fine, but
perhaps I will find a still better house for the same price if I go on searching. When
shall I stop the search procedure?
Am I going to smoke the next cigarette? One single cigarette is no problem, but if I
make the same decision sufficiently many times it may kill me.
The court has to decide whether the defendant is guilty or not. There are two
mistakes that the court can make, namely to convict an innocent person and to acquit
a guilty person. What principles should the court apply if it considers the first of these
mistakes to be more serious than the second?
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A committee has to make a decision, but its members have different opinions.
What rules should they use to ensure that they can reach a conclusion even if they are
in disagreement? Almost everything that a human being does involves decisions.
Therefore, to theorize about decisions is almost the same as to theorize about human
activities. However, decision theory is not quite as all-embracing as that. It focuses
on only some aspects of human activity. In particular, it focuses on how we use ourfreedom. In the situations treated by decision theorists, there are options to choose
between, and we choose in a non-random way.
Our choices, in these situations, are goal-directed activities. Hence, decision
theory is concerned with goal-directed behaviour in the presence of options.
A Truly Interdisciplinary Subject
Modern decision theory has developed since the middle of the 20th
century throughcontributions from several academic disciplines. Although it is now clearly an
academic subject of its own right, decision theory is typically pursued by researchers
who identify themselves as economists, statisticians, psychologists, political and
social scientists or philosophers. There is some division of labour between these
disciplines. A political scientist is likely to study voting rules and other aspects of
collective decision-making. A psychologist is likely to study the behaviour of
individuals in decisions, and a philosopher the requirements for rationality in
decisions. However, there is a large overlap, and the subject has gained from the
variety of methods that researchers with different backgrounds have applied to the
same or similar problems.
Normative and Descriptive Theories
The distinction between normative and descriptive decision theories is, in principle,
very simple. A normative decision theory is a theory about how decisions should be
made, and a descriptive theory is a theory about how decisions are actually made.
The should in the foregoing sentence can be interpreted in many ways. There is,
however, virtually complete agreement among decision scientists that it refers to the
prerequisites of rational decision-making. In other words, a normative decision theory
is a theory about how decisions should be made in order to be rational. This is a very
limited sense of the word normative. Norms of rationality are by no means the only
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or even the most important norms that one may wish to apply in decision-making.
However, it is practice to regard norms other than rationality norms as external to
decision theory. Decision theory does not, according to the received opinion, enter
the scene until the ethical or political norms are already fixed. It takes care of those
normative issues that remain even after the goals have been fixed. This remainder of
normative issues consists to a large part of questions about how to act in when thereis uncertainty and lack of information. It also contains issues about how an individual
can coordinate her decisions over time and of how several individuals can coordinate
their decisions in social decision procedures.
If the general wants to win the war, the decision theorist tries to tell him how to
achieve this goal. The question whether he should at all try to win the war is not
typically regarded as a decision-theoretical issue. Similarly, decision theory provides
methods for a business executive to maximize profits and for an environmentalagency to minimize toxic exposure, but the basic question whether they should try to
do these things is not treated in decision theory.
Although the scope of the normative is very limited in decision theory, the
distinction between normative (i.e. rationality-normative) and descriptive
interpretations of decision theories is often blurred. It is not uncommon, when you
read decision-theoretical literature, to find examples of disturbing ambiguities and
even confusions between normative and descriptive interpretations of one and thesame theory. Probably, many of these ambiguities could have been avoided. It must
be conceded, however, that it is more difficult in decision science than in many other
disciplines to draw a sharp line between normative and descriptive interpretations.
This can be clearly seen from consideration of what constitutes a falsification of a
decision theory. It is fairly obvious what the criterion should be for the falsification
of a descriptive decision theory.
ELEMENTS OF DECISION MAKINGDecision Maker: The entity responsible for making the decision. This may be a single
person, a committee, company, and the like. It is viewed here as a single entity, not
a group.
Alternatives: A finite number of possible decision alternatives or courses of action
available to the decision maker. The decision maker generally has control over the
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specification and description of the alternatives. These alternatives are also called
courses of action (actions, acts or strategies) and are known to the decision-maker.
States of Nature: The scenarios or states of the environment that may occur but are
not under control of the decision maker. These are the circumstances under which a
decision is made. The states of nature are mutually exclusive events and exhaustive.
This means that one and only one state of nature is assumed to occur and that all
possible states are considered.
Payoff or Outcome: Outcomes are the measures of net benefit, or payoff, received
by the decision maker. This payoff is the result of the decision and the state of
nature. Hence, there is a payoff for each alternative and outcome pair. The measures
of payoff should be indicative of the decisions makers values or preferences. The
payoffs are generally given in a payoff matrix in which a positive value represents net
revenue, income, or profit and a negative value represents net loss, expenses, or
costs. This matrix yields all alternative and outcome combinations and their
respective payoff and is used to represent the decision problem.
General form of payoff matrix
1 2 n
1
2
Courses of Action
(Alternatives)
States of Nature Probability S S S
N
N
L
1 11 12 1n
2 21 22 2n
m m m1 m 2 mn
p p p p
p p p p
N p p p p
L
L
M M M M L M
L
STEPS OF DECISION MAKING PROCESS
The decision making process involves the following steps:
1. Identify and define the problem.
2. Listing of all possible future events, called states of nature, which can occur in
the context of the decision problem. Such events are not under the control of
decision-maker because these are erratic in nature.
3. Identification of all the courses of action (alternatives or decision choices)
which are available to the decision-maker. The decision-maker has control over
these courses of action.
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4. Expressing the payoffs resulting from each pair of course of action and state of
nature. These payoffs are normally expressed in a monetary value.
5. Apply an appropriate mathematical decision theory model to select best course
of action from the given list on the basis of some criterion (measure of
effectiveness) that results in the optimal (desired) payoff.
TYPES OF DECISION-MAKING ENVIRONMENTSTo arrive at a good decision it is required to consider all available data, an exhaustive
list of alternatives, knowledge of decision environment, and use of appropriate
quantitative approach for decision-making. In this section four types of decision-
making environments: Certainty, uncertainty, risk and conflict have been described.
The knowledge of these environments helps in choosing appropriate quantitative
approach for decision-making.
Type 1 - Decision-Making under Certainty
The process of choosing an act or strategy when the state of nature is completely
known is called decision making under certainty. The decision-maker has the
complete knowledge (perfect information) of consequence of every decision choice
(course of action or alternative) with certainty. Obviously, he will select an
alternative that yields the largest return (payoff) for the known future (state of
nature). In such situation, each act will only result in one event and the outcome of
the act can be predetermined with certainty. Hence, such situations are also termed
as deterministic situations. For example, the decision to purchase either National
Saving Certificate (NSC); or deposit in National Saving Scheme is one in which it is
reasonable to assume complete information about the future because there is no
doubt that the Pakistani government will pay the interest when it is due and the
principal at maturity. In this decision-model, only one possible state of nature
(future) exists.
Type 2 - Decision-Making under Risk
In this case the decision-maker has less than complete knowledge with certainty ofthe consequence of every decision choice (course of action) because it is not
definitely known which outcome will occur. This means there is more than one state
of nature (future) and for which he makes an assumption of the probability with
which each state of nature will occur. For example, probability of getting head in the
toss of a coin is 0.5. Decision-making under risk is a probabilistic decision situation, in
which more than one state of nature exists and the decision-maker has sufficientF a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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information to assign probability values to the likely occurrence of each of these
states. The probabilities of various outcomes may be determined objectively from the
past data. Knowing the probability distribution of the states of nature, the best
decision is to select that course of action which has the largest expected payoff
value. The expected (average) payoff of an alternative is the sum of all possible
payoffs of that alternative weighted by the probabilities of those payoffs occurring.However, past records may not be available to arrive at the objective probabilities. In
many cases the decision-maker may, on the basis of his experience and judgment, be
able to assign subjective probabilities to the various outcomes. The problem can then
be solved as decision problem under risk.
Under conditions of risk, the most popular decision criterions for evaluating the
alternative is the expected monetary value/expected opportunity loss of the
expected payoff.
(i) Expected monetary value (EMV)
More generally, the decision-making in situations of risk is on the basis of the
expectation principle, with the event probabilities assigned, objectively or
subjectively as the case may be, the expected pay-off for each strategy is
calculated by multiplying the pay-off values with their respective probabilities
and then adding up these products. The strategy with the highest expected
pay-off represents the optimal choice. It goes without saying that in problems
involving pay-off matrix in terms of costs, optimal strategy is that
corresponding to which the expected value is the least.
(ii) Expected Opportunity Loss (EOL)
An alternative approach to maximizing expected monetary value (EMV) is to
minimize the expected opportunity loss (EOL), also called expected value of
regret. The EOL is defined as the difference between the highest profit (or
payoff) for a state of nature and the actual profit obtained for the particular
course of action taken. In other words, EOL is the amount of payoff that is lostby not selecting the course of action that has the greatest payoff for the state
of nature that actually occurs. The course of action due to which EOL is
minimum, is recommended.
Since EOL is an alternative decision criterion for decision-making under
risk, therefore, the results will always be the same as those obtained by EMV
criterion discussed earlier.F a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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The steps for calculating EOL are summarized as follows:
(a) Prepare a profit (cost) table for each course of action and state of nature
combination along with the associated probabilities.
(b) For each state of nature calculate the opportunity loss (OL) values by
subtracting each payoff from the maximum payoff for that outcome. (For
each state of nature calculate the opportunity loss (OL) values bysubtracting the minimum payoff for that outcome from each payoff.)
(c) Calculate EOL for each course of action by multiplying the probability of
each state of nature with the OL value and then adding the values.
(d) Select a course of action for which the EOL value is minimum.
Expected value of perfect information (EVPI)
The expected profit with perfect information is the expected return, in the
long run, if we have perfect information before a decision is made. The
Expected Value of Perfect Information (EVPI) may be defined as the maximum
amount one would be willing to pay, to acquire perfect information as to which
event would occur. EPPI represents the maximum obtainable EMV with perfect
information as to which event will actually occur (as calculated before
information is received). If EMV represents the maximum obtainable EMV
without perfect information, perfect information would increase expected
profit from EMV up to the value of EPPI, so the amount of that increase would
be equal to EVPI. Thus, we have
EVPI = EPPI EMV
Type 3 - Decision-Making under Uncertainty
In this case the decision-maker is unable to specify the probabilities with which
the various states of nature (futures) will occur. However, this is not the case of
decision-making under ignorance, because the possible states of nature are known.
Thus, decisions under uncertainty are taken even with less information than decisionsunder risk. For example, the probability that Mr. X will be the prime minister of the
country 15 years from now is not known.
The decision situations where there is no way in which the decision-maker can
assess the probabilities of the various states of nature are called decisions under
uncertainty. In such situations, the decision-maker has no idea at all as to which of
the possible states of nature would occur nor has he a reason to believe why a givenF a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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state is more, or less, likely to occur as another. With probabilities of the various
outcomes unknown, the actual decisions are based on specific criteria. The several
principles which may be employed for taking decisions in such conditions include (i)
Laplace Criterion, (ii)Maximin or Minimax Criterion, (iii)Maximax or Minimin
Criterion, (iv)Savage Criterion, (v)Hurwicz Criterion (or Criterion of Realism).
Such situations are frequent in business and management. Will the new plant orindustrial unit be successful? Will the new product be able to compete with others in
the market? How much to produce and stock to get maximum returns?
(i) Optimism (Maximax (Profit) or Minimin (Cost)) Criterion
In this criterion the decision-maker ensures that he should not miss the
opportunity to achieve the largest possible profit (maximax) or lowest possible
cost (minimin). Thus, he selects the alternative (decision choice or course of
action) that represents the maximum of the maxima (or minimum of the
minima) payoffs (consequences or outcomes). The working method is
summarized as follows:
(a) Locate the maximum (or minimum) payoff values corresponding to each
alternative (or course of action), then
(b) Select an alternative with best anticipated payoff value (maximum for
profit and minimum for cost).
Since in this criterion the decision-maker selects an alternative with largest (or
lowest) possible payoff value, it is also called an optimistic decision criterion.
(ii) Pessimism (Maximin (Profit) or Minimax (Cost)) Criterion
This principle is adopted by pessimistic decision-makers who are conservative
in their approach. Using this approach, the minimum pay-offs resulting from
adoption of various strategies are considered and among these values the
maximum one is selected. It involves, therefore, choosing the best (the
maximum) profit from the set of worst (the minimum) profits.
When dealing with the costs, the maximum cost associated with eachalternative is considered and the alternative which minimizes this maximum
cost is chosen. In this context, therefore, the principle is used minimax-the
best (the minimum cost) of the worst (the maximum cost).
The working method is summarized as follows:
(a) Locate the minimum (or maximum in case of profit) payoff value in case of
loss (or cost) data corresponding to each alternative, thenF a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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(b) Select an alternative with best anticipated payoff value (maximum for
profit and minimum for loss or cost).
Since in this criterion the decision-maker is conservative about the future and
always anticipates worst possible outcome (maximum for profit and minimum
for loss or cost), it is called a pessimistic decision criterion. This criterion is
also known as Walds criterion.(iii) Equal probabilities (Laplace) Criterion
Since the probabilities of states of nature are not known, it is assumed that all
states of nature will occur with equal probability, i.e. each state of nature is
assigned an equal probability. As states of nature are mutually exclusive and
collectively exhaustive, so the probabilities of each of these must be
1
number of states of nature. The working method is summarized as follows:
(a) Assign equal probability value to each state of nature by using the formula:
1
number of states of nature.
(b) Compute the expected (or average) payoff for each alternative (course of
action) by adding all the payoffs and dividing by the number of possible
states of nature or by applying the formula:
(Probability of state of nature j) (Payoff value for the combination of alternative, i
and state of nature j)
(c) Select the best expected payoff value (maximum for profit and minimum
for cost).
This criterion is also known as the criterion of insufficient reason because,
except in a few cases, some information of the likelihood of occurrence of
states of nature is available.
(iv) Coefficient of optimism (Hurwicz) Criterion
This criterion suggests that a rational decision-maker should be neither
completely optimistic nor pessimistic and, therefore must display a mixture of
both. Hurwicz, who suggested this criterion, introduced the idea of a
coefficient of optimism (denoted by ) to measure the decision-makers degree
of optimism. This coefficient lies between 0 and 1, where 0 represents a
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In the case of costs, the principle works like this.
(a) From the given payoff matrix, develop an opportunity loss (or regret)
matrix as follows:
(i) Find the worst payoff corresponding to each state of nature, and
(ii)Subtract all other entries (payoff values) corresponding to each state of
nature from this value.(b) For each course of action (strategy or alternative) identify the best or
minimum regret value. Record this number in a new row.
(c) Select the course of action (alternative) with the greatest anticipated
opportunity loss value.
Type 4 - Decision-Making under Conflict
In many situations, neither states-of-nature are completely known nor are they
completely uncertain. Partial knowledge is available and therefore it may be termed
as decision-making under partial uncertainty. An example of this is the situation of
conflict involving two or more competitors marketing the same product.
Some Examples related to Different Decision-Making Environments
Example 1: A food product company is contemplating the introduction of a
revolutionary new product with new packaging or replace the existing product atmuch higher price (S1) or a moderate change in the composition of the existing
product with a new packaging at a small increase in price (S2) or a small change in the
composition of the existing product except the word New with a negligible increase
in price (S3). The three possible states of nature or events are: (i) high increase in
sales (N1), (ii) no change in sales (N2) and (iii) decrease in sales (N3). The marketing
department of the company worked out the payoffs in terms of yearly net profits forF a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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each of the strategies of three events (expected sales). This is represented in the
following table:
States ofNature
Strategies
S1 S2 S3N1 7,00,000 5,00,000 3,00,000
N2 3,00,000 4,50,000 3,00,000
N3 1,50,000 0 3,00,000
Which strategy should the concerned executive choose on the basis of the following?
(a) Maximin criterion (b) Maximax criterion
(c) Minimax regret criterion (d) Laplace criterion
Solution: The payoff matrix is rewritten as follows:
(a) Maximin Criterion
States of Nature Strategies
S1 S2 S3N1 7,00,000 5,00,000 3,00,000
N2 3,00,000 4,50,000 3,00,000N3 1,50,000 0 3,00,000
Column (minimum) 1,50,000 0 3,00,000 MaximinThe maximum of column minima is 3,00,000. Hence, the company should adopt
strategy S3.
(b) Maximax Criterion
States of Nature Strategies
S1 S2 S3N1 7,00,000 5,00,000 3,00,000
N2 3,00,000 4,50,000 3,00,000N3 1,50,000 0 3,00,000
Column (maximum) 7,00,000
Maximax
5,00,000 3,00,000
The maximum of column maxima is 7,00,000. Hence, the company should adopt
strategy S1.
(c) Minimax Regret Criterion (opportunity loss in case of profits)
States ofNature
Strategies
S1 S2 S3
N1 7,00,000
7,00,000 =0 7,00,000
5,00,000 =2,00,000 7,00,000
3,00,000 =4,00,000
N2 4,50,000 3,00,000 =1,50,000
4,50,000 4,50,000 =0
4,50,000 3,00,000 =1,50,000
N3 3,00,000 1,50,000 =1,50,000
3,00,000 0 =3,00,000
3,00,000 3,00,000 =0
Column(maximum)
1,50,000
Minimax regret
3,00,000 4,00,000
Hence, the company should adopt minimum opportunity loss strategy, S1.
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(d)Laplace Criterion
Since, we do not know the probabilities of states of nature, assume that they are
equal. For this example, we would assume that each state of nature has a probability
1/3 of occurrence. Thus,
Strategy Expected Return (Rs)
S1 (7,00,000 + 3,00,000 + 1,50,000)/3 = 3,83,333.33
S2 (5,00,000 + 4,50,000 + 0)/3 = 3,16,666.66S3 (3,00,000 + 3,00,000 + 3,00,000)/3 = 3,00,000
Since, the largest expected return is from strategy S1; the executive must select
strategy S1.
Example 2:A Super Bazaar must decide on the level of supplies it must stock to meet
the needs of its customers during Eid days. The exact number of customers is not
known, but it is expected to be in one of the four categories; 300, 350, 400 or 450
customers. Four levels of supplies are thus suggested with level j being ideal (from
the viewpoint of incurred costs) if the number of customers falls in category j.
Deviations from the ideal levels results in additional costs either because extra
supplies are stocked needlessly or because demand cannot be specified. The table
below provides these costs in thousands of rupees.
Customer categorySupplies level
A1 A2 A3 A4E1 7 12 20 27
E2 10 9 10 25E3 23 20 14 23
E4 32 24 21 17
(a) Which level of inventory is chosen on the basis of (i) Laplace criterion (ii) minimax
criterion (iii) minimin criterion?
(b) Now consider payoff matrix as profit matrix then which level of inventory is
chosen on the basis of Hurwicz criterion
Solution: (a) (i) Laplace Criterion
Since, we do not know the probabilities of states of nature, assume that they areequal. For this question, we would assume that each state of nature has a probability
1/4 of occurrence. Thus,
Strategy Expected Return (Rs)
A1 (7 + 10 + 23 + 32)/4 = 18
A2 (12 + 9 + 20 + 24)/4 = 16.25
A3 (20 + 10 + 14 + 21)/4 = 16.25
A4 (27 + 25 + 23 + 17)/4 = 23
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Since, the lowest expected return is from strategy A2 and A3; the executive must
select strategy A2 or A3.
(ii)Minimax Criterion
States of Nature Strategies
A1 A2 A3 A4E1 7 12 20 27
E2 10 9 10 25E3 23 20 14 23
E4 32 24 21 17
Column(maximum)
32 24 21
Minimax27
The minimum of column maxima is 21. Hence, the company should adopt strategy A3.
(iii) Minimin Criterion
States of Nature Strategies
A1 A2 A3 A4E1 7 12 20 27
E2 10 9 10 25E3 23 20 14 23
E4 32 24 21 17
Column(minimum)
7
Minimin
9 10 17
The minimum of column minima is 7. Hence, the company should adopt strategy A1.
(b) In the context of profit data, Hurwicz Criterion, HC = (Max Value) + (1 ) (Min
Value). Its value for various strategies is as follows:
State ofNature
Profit from optimal Course of Action(thousand Rs)
(1) (2) (3) (4) (5) (6) (7) (8)
A1 A2 A3 A4 Profit (Max incolumns (1, 2,3 & 4))
0.5 x(5)
Profit (Min incolumns (1, 2,3 & 4))
0.5x (7)
(6) +(8)
E1 7 12 20 27 32 16 7 3.5 19.5
E2 10 9 10 25 24 12 9 4.5 16.5
E3 23 20 14 23 21 10.5 10 5 15.5
E4 32 24 21 17 27 13.5 17 8.5 22Since, maximum is 22, so, it is optimal to adopt strategy A4.
Example 3: Al Abbas Ltd has installed a machine costing Rs 4 lacs and is in the
process of deciding on an appropriate number of a certain spare parts required for
repairs. The spare parts cost Rs 4000 each but are available only if they are ordered
now. In case the machine fails and no spares are available, the cost to the companyF a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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of mending the plant would be Rs 18000. The plant has an estimated life of 8 years
and the probability distribution of failures during the time, based on experience with
similar machines, is as follows:
No. of failures during 8-yearly period 0 1 2 3 4 5
Probability 0.1 0.2 0.3 0.2 0.1 0.1
Ignoring any discounting for time value of money, determine the following:
(a) The expected number of failures in the 8-year period.
(b) The optimal number of units of the spare part on the basis of Hurwicz principle
(taking =0.7).
(c) EVPI.
Solution: Since the availability of number of spares at the time of the failure of any
machine is under the control of decision-maker, no. of spares per year is considered
as course of action (decision choice) and the no. of failures of machines is uncertain
and only known with probability, therefore, it is considered as a state of nature(event).
Let S be the quantity (number of spares to be available). And F is the no. of failures
within one year. It is given that cost of storing a spare is Rs. 4000. Cost of not storing
the spare is Rs. 18000.
Cost function =4,000S, S F
4,000S + 18000 (F S), S < F
(a) The expected number of failures in the 8 year period, is given by
6
i i
i 1
E(F) p F 0.1 0 0.2 1 0.3 2 0.2 3 0.1 4 0.1 5 2.3=
= = + + + + + =
State ofNature(F)
Probability Cost (thousand Rs) Due to Courseof Action (purchase)
Expected Cost (thousand Rs) Due toCourse of Action
(1) (2) (3) (4) (5) (6) (7) (1) x(2)
(1) x(3)
(1) x(4)
(1) x(5)
(1) x(6)
(1)x(7)
0 1 2 3 4 5 0 1 2 3 4 5
0 0.10 0 4 8 12 16 20 0 0.4 0.8 1.2 1.6 2
1 0.20 18 4 8 12 16 20 3.6 0.8 1.6 2.4 3.2 42 0.30 36 22 8 12 16 20 10.8 6.6 2.4 3.6 4.8 6
3 0.20 54 40 26 12 16 20 10.8 8 5.2 2.4 3.2 4
4 0.10 72 58 44 30 16 20 7.2 5.8 4.4 3 1.6 2
5 0.10 90 76 62 48 34 20 9 7.6 6.2 4.8 3.4 2
Expected Cost (EC) 41.4 29.2 20.6 17.4 17.8 20
(b) In the context of cost data, Hurwicz Criterion, HC = (Min Value) + (1 ) (Max
Value). Its value for various strategies is as follows:
Stateof
Probability Cost (thousand Rs) Due toCourse of Action
Cost from optimal Course ofAction(thousand Rs)
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Nature
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
0 1 2 3 4 5 Cost (Minin columns(2, 3, 5, 6& 7))
0.7x (8)
Cost (Maxin columns(2, 3, 5, 6& 7))
0.3x(10)
(9) +(11)
0 0.05 0 4 8 12 16 20 0 0 90 27 27
1 0.10 18 4 8 12 16 20 4 2.8 76 22.8 25.6
2 0.20 36 22 8 12 16 20 8 5.6 62 18.6 24.2
3 0.30 54 40 26 12 16 20 12 8.4 48 14.4 22.84 0.20 72 58 44 30 16 20 16 11.2 34 10.2 21.4
5 0.15 90 76 62 48 34 20 20 14 20 6 20
Since, minimum is 20, so, it is optimal to keep 5 spare parts.
(c)
State of Nature
Probability Cost (thousand Rs) Due to Course ofAction
Cost from optimal Course ofAction(thousand Rs)
(1) (2) (3) (4) (5) (6) (7) (8) (1) x (8)
0 1 2 3 4 5 Cost (Min in (2, 3,5, 6 & 7))
WeightedCost
0 0.05 0 4 8 12 16 20 0 0
1 0.10 18 4 8 12 16 20 4 0.8
2 0.20 36 22 8 12 16 20 8 2.4
3 0.30 54 40 26 12 16 20 12 2.4
4 0.20 72 58 44 30 16 20 16 1.6
5 0.15 90 76 62 48 34 20 20 2
Expected Cost with Perfect Information (ECPI) 9.2
Now, EVPI = EC* ECPI
= 17.4 9.2
= 8.2 thousand rupees
Example 4:An investor is given the following investment alternatives and percentage
rates of return.Investmentalternatives
State of Nature (Market Conditions)
Low Medium High
Regular Shares 7% 10% 15%
Risky Shares -10% 12% 25%
Property -12% 18% 30%
Over the past 300 days, 150 days have been medium market conditions and 60 days
have had high market increases. On the basis of these data, state the optimum
investment strategy for the investment.
Solution: According to the given information, the probabilities of low, medium and
high market conditions would be 0.30 (300 (150 + 60) = 90/300), 0.50 (150/300) and
0.20 (60/300) respectively. The expected pay-offs for each of the alternatives are
calculated and shown in the table below:
MarketConditions
Probability Profit (Rs) Due to Course ofAction
Expected Payoff (Rs) Due to Courseof Action
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(1) (2) (3) (4) (1) x (2) (1)x (3) (1) x (4)
Regularshares
Riskyshares
Property Regularshares
Riskyshares
Property
Low 0.30 0.07 0.10 0.15 0.021 0.03 0.045
Medium 0.50 0.10 0.12 0.25 0.05 0.06 0.125
High 0.20 0.12 0.18 0.30 0.024 0.036 0.06
Expected monetary value (EMV) 0.053 0.126 0.230
Since the expected return of 23% is the highest for property, the investor shouldinvest in this alternative.
Example 5:A company manufactures goods for a market in which the technology of
the product is changing rapidly. The research and development department has
produced a new product which appears to have potential for commercial exploitation.
A further Rs 60,000 is required for development testing.
The company has 100 customers and each customer might purchase at the most one
unit of the product. Market research suggests that a selling price of Rs 6000 for each
unit with total variable costs of manufacturing and selling estimate are Rs 2,000 for
each unit.
From previous experience, it has been possible to derive a probability distribution
relating to the proportion of customers who will buy the product as follows:
Proportion of customers 0.04 0.08 0.12 0.16 0.20
Probability 0.10 0.10 0.20 0.40 0.20
Determine the expected opportunity losses, given no other information than that
stated above, and state whether or not the company should develop the product.
Solution: If p is the proportion of customers who purchase the new product, the profit
is:
(6,000 2,000) x 100p 60,000 = Rs (4,00,000p 60,000).
Let Ni (I = 1, 2, , 5) be the possible states of nature, i.e. proportion of the customers
who will buy the new product and S1 (develop the product) and S2 (do not develop the
product) be the two courses of action.
The profit values (payoffs) for each pair of N is and Sjs are shown in the following
table:
State of Nature Ni(Proportion ofCustomers, p)
Probability
Profit = Rs(4,00,000p 60,000)Course of Action
Opportunity Loss (Rs) (1) x(2)
(1) x(3)
(1) (2) (3)
S1 S2 S1 S2 S1 S20.04 0.1 44,000 0 0 (44,000) = 44,000 0 0 = 0 4,400 0
0.08 0.1 28,000 0 0 (28,000) = 28,000 0 0 = 0 2,800 0
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0.12 0.2 12,000 0 0 (12,000) = 12,000 0 0 = 0 2,400 0
0.16 0.4 4,000 0 4,000 4,000 = 0 4,000 0 = 4,000 0 1,600
0.20 0.2 20,000 0 20,000 20,000 = 0 20,000 0 = 20,000 0 4,000
Expected Opportunity Loss (EOL) 9,600 5,600
(Note: All the entries of column S2 would be 0. Since, we are not developing anything
then no profit will be earned)
Since, the company seeks to minimize the expected opportunity loss, the company
should select course of action S2 (do not develop the product) with minimum EOL.
Example 6:A retailer purchases cherries every morning at Rs 50 a case and sells them
for Rs 80 a case. Any case remaining unsold at the end of the day can be disposed of
next day at a salvage value of Rs 20 per case (thereafter they have no value). Past
sales have ranged from 15 to 18 cases per day. The following is the record of sales for
the past 120 days:
Cases sold 15 16 17 18Number of days 12 24 48 36
Find how many cases the retailer should purchase per day to maximize his profit.
Solution: Since number of cherries (in cases) purchased is under the control of
decision-maker, purchase per day is considered as course of action (decision choice)
and the daily demand of the cherries is uncertain and only known with probability,
therefore, it is considered as a state of nature (event).
Let P be the quantity (number of cases of cherries to be purchased). And D is the
demand within a day.
Profit = (80-50) P, D>=P
(80-50)D (50-20) (P-D), D < P
The resulting profit values and corresponding expected payoffs are computed in the
following table:
States ofNature D(Demandper week)
Probability Profit (Rs) Due to Courses ofAction P (Purchase per day)
Expected Payoff (Rs) Due to Courses ofAction (Purchase per Day)
15 16 17 18 15 16 17 18
(1) (2) (3) (4) (5) (1)x(2) (1)x(3) (1)x(4) (1)x(5)15 12/120 =
0.1450 420 390 360 45 42 39 36
16 24/120 =0.2
450 480 450 420 90 96 90 84
17 48/120 =0.4
450 480 510 480 180 192 204 192
18 36/120 =0.3
450 480 510 540 135 144 153 162
Expected monetary value (EMV) 450 474 486 474
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Since the highest EMV of Rs 486 is corresponding to course of action 17, the retailer
must purchase 17 cases of cherries every morning.
Example 7:A company needs to increase its production beyond its existing capacity.
It has narrowed the alternatives to two approaches to increase the production
capacity: (a) expansion, at a cost of Rs 8 million, or (b) modernization at a cost of Rs5 million. Both approaches would require the same amount of time for
implementation. Management believes that over the required payback period,
demand will either be high or moderate. Since high demand considered being
somewhat less likely than moderate demand, the probability of high demand has been
set at o.35. If the demand is high, expansion would gross estimated additional Rs 12
million but modernization only additional Rs 6 million, due to lower maximum product
capability. On the other hand, if the demand is moderate, the comparable figures
would be Rs 7 million for expansion and Rs 5 million for modernization.
(a) Calculate the profit in relation to various action and outcome combinations and
states of nature.
(b) If the company wishes to maximize its EMV, should it modernize or expand?
(c) Calculate the EVPI.
(d) Construct the conditional opportunity loss table and also calculate EOL.
Solution: Defining the states of nature: high demand and moderate demand (over
which the company has no control) and courses of action (companys possible
decisions): Expand and Modernize.
Since the probability that the demand is high estimated at 0.35, the probability of
moderate demand must be (1 0.35) = 0.65. The resulting profit values,
corresponding expected payoffs and Expected Opportunity Loss (EOL) values are
computed in the following table:
Stateof
Nature(Demand)
Probabilit
y
Profit (millionRs) Due to
Course of Action
ExpectedPayoff
(million Rs)Due to Courseof Action
Profit fromoptimal Course
ofAction(millionRs)
OpportunityLoss (million
Rs) Due toCourse of Action
(1) x(5)
(1) x(6)
(1) (2) (3) (1) x(2)
(1) x(3)
(4) (1) x(4)
(5) (6)
Expand(S1)
Modernize(S
2)
Expand (S1)
Modernize(S2)
Profit(Max in(2 &3))
WeightedProfit
S1 S2 S1 S2
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HighDemand
(N1)
0.35 12 8 =4
6 5 =1
1.4 0.35 4 1.40 4 4 =0
4 1= 3
0 1.05
ModerateDemand
(N2)
0.65 7 8 =1
5 5 =0
0.65 0 0 0 0(1) =1
0 0= 0
0.65 0
Expected monetary value (EMV) 0.75 0.35Expected Profit with Perfect Information (EPPI) 1.40Expected Opportunity Loss (EOL) 0.65 1.05
(b) Since the highest EMV of Rs 0.75 million is corresponding to course of action
Expand, the company must expand it.
(c) EVPI = EPPI EMV
=1.40 0.75
= Rs. 0.65 Million
(d)Since, the company seeks to minimize the expected opportunity loss (EOL), the
company should select course of action S1 (Expand).
Example 8:A toy manufacturer is considering a project of manufacturing a dancing
doll with three different movement designs. The doll will be sold at an average of Rs
10. The first movement design using gears and levels will provide the lowest tooling
and set up cost of Rs 1,00,000 and Rs 5 per unit of variable cost. A second design with
spring action will have a fixed cost of Rs. 1, 60,000 and variable cost of Rs 4 per unit.
Yet another design with weights and pulleys will have a fixed cost of Rs. 3, 00,000 and
variable cost of Rs 3 per unit. One of the following demand events can occur for the
doll with the probabilities:Demand (units) Probability
Light demand 25,000 0.10
Moderate demand 1,00,000 0.70
Heavy demand 1,50,000 0.20
(a) Construct a payoff table for the above project.
(b) Which is the optimum design?
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(c) How much can be decision-maker afford to pay to obtain perfect information
about the demand?
Solution: Payoff (Profit) = Revenue Cost
= (Selling Price x no. of units demanded) (fixed cost + variable cost)
= (Selling Pricexno. of units demanded)(fixed cost+(no. of units demandedxper unit
cost))
State of
Nature
(Demand)
Probability Profit (Rs) Due to Course of Action Expected Payoff (Rs) Due to Course
of Action
(1) (2) (3) (4) (1) x (2) (1) x (3) (1) x (4)
Gears &
Levels
Spring
Action
Weights &
Pulleys
Gears &
Levels
Spring
Action
Weights &
Pulleys
Light 0.10 25,000 10,000 1,25,000 2,500 1,000 12,500
Moderate 0.70 4,00,000 4,40,000 4,00,000 2,80,000 3,08,000 2,80,000
Heavy 0.20 6,50,000 7,40,000 7,50,000 1,30,000 1,48,000 1,50,000
Expected monetary value (EMV) 4,12,500 4,55,000 4,17,500
Since, EMV is largest for spring action, it must be selected.
State of Nature
(Demand)
Probability Profit (Rs) Due to Course of Action Profit from optimal Course of
Action(Rs)
(1) (2) (3) (4) (4) (1) x (4)Gears &
Levels
Spring
Action
Weights &
Pulleys
Profit (Max in
(2, 3 & 4))
Weighted
Profit
Light 0.10 25,000 10,000 1,25,000 25,000 2,500
Moderate 0.70 4,00,000 4,40,000 4,00,000 4,40,000 3,08,000
Heavy 0.20 6,50,000 7,40,000 7,50,000 7,50,000 1,50,000
Expected Profit with Perfect Information (EPPI) 4,60,500
The maximum amount of money that the decision-maker would be willing to pay to
obtain perfect information regarding demand for the doll will be EVPI = EPPI EMV
=4,60,000 4,55,000 = Rs 5,500
DECISION TREE ANALYSIS
Decision-making problems discussed so far have been limited to a single
decision over one period of time, because the payoffs, states of nature, courses of
action and probabilities associated with the occurrence of states of nature are not
subject to change.
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However, situations may arise when a decision-maker needs to revise his previous
decisions on getting new information and make a sequence of several interrelated
decisions over several future periods. Thus he should consider the whole series of
decisions simultaneously. Such a situation is called a sequential or multi period
decision process.
Decision tree is a network which exhibits graphically the logical relationshipbetween the different parts of the complex decision process. It is a graphic model of
each combination of various acts and states of nature {S i, Aj}; (I = 1, 2, , m; j = 1, 2,
, n) along with their payoffs, the probability distribution of the various states of
nature and the EMV or EOL for each act.
Decision tree is a very effective device in making decisions in various
diversified problems relating to personnel, investment, portfolios, project
management, new project strategies, etc.
Each combination (Si, Aj) is depicted by a distinct path through the decision
tree. An essential feature of the decision tree is that the flow should be from left to
right in a chronological order.
Standard symbols are used in drawing a decision tree.
(i) A square ( ) is used to represent a decision point or decision node at which
the decision maker has to decide about one of the various acts or alternatives
available to him.
(ii) Each act or alternative is shown as a line, representing a branch of the tree
emanating from the square.
(iii) A circle ( ) is used to represent a chance event or chance node at which
various events or states of nature are represented by lines, which depict the
sub-branches of the tree emanating from the circle.
(iv) Each branch of the tree (corresponding to each act or strategy) has as
many sub-branches as the number of events or states of nature.
(v) Along the branches/sub-branches are also shown the probabilities of variousstates of nature and the payoffs for each combination (Si, Aj); I = 1, 2, , m; j =
1, 2, , n along with the EMV or EOL for each act.
(vi) As a branch can sub-branch again, we obtain a tree like structure, which
represents the various steps in a decision problem.
Roll Back Technique of Analyzing a Decision Tree
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Produc
tX
-30000
ProductY-50000
HighDem
and(0.4)
75000
Medium Demand (0.4)
55000LowDemand(0.2)
35000
HighDem
and(0.3)
100000
Medium Demand (0.4)
80000
LowDemand(0.3)7
Example 2:A businessman has two independent investments A and B available to him
but he lacks the capital to undertake both of them simultaneously. He can choose to
take A first and then stop, or if A is successful then take B, or vice versa. The
probability of success for A is 0.7 while for B it is 0.4. Both investments require aninitial capital outlay of Rs. 2000; and both return nothing if the venture is
unsuccessful. Successful completion of A will return Rs. 3000 (over cost), and
successful completion of B will return Rs. 5,000 (over cost). Draw and evaluate the
decision tree by the roll back technique and determine the best strategy.
Solution:
Net Payoff (Rs.) Expected Payoff (Rs.)75000-30000=45000 450000.4=1800055000-30000=25000 250000.4=1000035000-30000=5000 50000.2=1000Total 29000 (EMV)
100000-50000=50000 500000.3=1500080000-50000=30000 300000.4=1200070000-50000=20000 200000.3=6000Total 33000 (EMV)
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AcceptA
(Cost2
000)
Do Nothing
AcceptB
EMV = 2060
EMV = 1400
Succ
ess
Failure
Stop
EMV = 800
EMV = 1500
(Cost2000)
(0)D1
Succ
ess
Succ
ess
Success
Failu
Failure
Failure
Stop
AcceptA
(Cost2000)
(Cost2000)AcceptB
-2000
(0.3)
3000
(0.7)
5000
(0.4)
-2000
3000(0.7)
5
(0.
-200(0.6
D2
D3
Decision Node Event Probability
(p)
Conditional Payoff (in
Rs.) P
Expected Payoff (Rs.)
p PD3 (i) Accept A Succes
s
0.7 3000 2100
Failure 0.3 -2000 -600
EMV = 1500
(ii) Stop 0
D2 (i) Accept B Succes
s
0.4 5000 2000
Failure 0.6 -2000 -1200
EMV = 800
(ii) Stop 0
D1 (i) Accept A Succes
s
0.7 3000 + 800 = 3800 2660
Failure 0.3 -2000 -600
EMV = 2060
(ii) Accept B Succes 0.4 5000 + 1500 = 6500 2600F a y y a z A h m e d K a y a n i R o l l N o . 5 9 3 4 8 3
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s
Failure 0.6 -2000 -1200
EMV = 1400
(iii)Do Nothing 0
From the above table we conclude that the best strategy is to accept investment A
first and if it is successful, then accept the investment B.
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PRACTICAL STUDY OF THE ORGANIZATION
WITH RESPECT OF THE TOPIC
ORGANIZATION: GLAXOSMITHKLINE Pakistan Limited
SYSTEM STUDIED: RISK MANAGEMENT SYSTEM
In GSK, the Risk Management System is used as proactive approach to eliminate /
reduce the potential risks associated with their business. Decision theory is used
extensively in Risk Management System for scoring the risks on the basis of likelihood
and consequences.
Note : This is only the overview of Risk Management System. Original documents
could not be part of assignment due to their confidentiality.
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COMPANY INTRODUCTION
GlaxoSmithKline Pakistan Limited was created on January Ist 2002 through the
merger of SmithKline and French of Pakistan Limited, Beecham Pakistan (Private)
Limited and Glaxo Wellcome (Pakistan) Limited- standing today as the largest
pharmaceutical company in Pakistan.
As leading international pharmaceutical company they make a real difference
to global healthcare and specifically to the developing world. Company believes this is
both an ethical imperative and key to business success. Companies that respond
sensitively and with commitment by changing their business practices to address such
challenges will be the leaders of the future. GSK Pakistan operates mainly in two
industry segments: Pharmaceuticals (prescription drugs and vaccines) and consumer
healthcare (over-the-counter- medicines, oral care and nutritional care).
GSK leads the industry in value, volume and prescription market share.
Company is proud of their consistency and stability in sales, profits and growth. Some
of their key brands include Augmentin, Panadol, Seretide, Betnovate, Zantac and
Calpol in medicine and renowned consumer healthcare brands include Horlicks,
Aquafresh, Macleans and ENO.
In addition, company is also deeply involved with our communities and
undertakes various Corporate Social Responsibility initiatives including working with
the National Commission for Human Development (NCHD) for whom GSK was one of
the largest corporate donors. GSK consider it their responsibility to nurture the
environment we operate in and persevere to extend their support to our community
in every possible way. GSK participates in year round charitable activities which
include organizing medical camps, supporting welfare organizations and donating to /
sponsoring various developmental concerns and hospitals. Furthermore, GSK maintainsstrong partnerships with non-government organizations such as Concern for children,
which is also extremely involved in the design, implementation and replication of
models for the sustainable development of children with specific emphasis on primary
healthcare and education.
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GSKs MISSION STATEMENT
Excited by the constant search for innovation, we at GSK undertake our quest
with the enthusiasm of entrepreneurs we value performance achieved with
integrity. We will attain success as a world class global leader with each and every
one of our people contributing with passion and an unmatched sense of urgency.
Our mission is to improve the quality of human life by enabling people to do more,
feel better and live longer.
Quality is at the heart of everything we do-from the discovery of a molecule to the
development of a medicine.
RISK MANAGEMENT SYSTEM
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Risk management is an essential component of the system of internal control and
governance and is regarded as good management practice throughout GSK. A
systematic, standardized and effective approach to risk management is required in
order to:
Establish a common language and protocols for communicating risks in order to
take right decisions at right time.
Ensure that responsibilities for managing risks are clearly stated, understood
and accepted.
Establish appropriate mechanisms for communication, reporting and escalation
of risks.
Ensure that business objectives are achieved.
SCOPE OF RISK MANAGEMENT PROCESS
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PROCESS STEP ACTIVITIES
Following are the different steps involved in the risk management system:
Establish the Risk Management Organization for the risk assessment area.
Identify, Record and Priorities Scored Risks.
Confirm and Approve Risk Mitigation plans.
Implementation, monitoring and of risk mitigation plans.
Governance and Maintenance.
Figure Risk Management Process
Decision Theorycomes into play when a risk is going to be scored (Analyse the
risks). Risks are scored on the basis of likelihood and consequences.
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A Risk is the basic record.
Risk requirements now split into three components.
Mandated requirements to progress risks through workflow.
A number ofRisk Mitigation Plans may be attached to Risk. A Risk must have at
least one Risk Mitigation Plan.
A number ofAction Plans may be attached to each Risk Mitigation Plan. A Risk
Mitigation Plan must have at least one Action Plan.
The diagram below depicts the structure of a Risk Record.
RISK SCORING
Risk scoring is subjective there is no right or wrong answer it is based on personal
judgment or consensus.
Review the consequence of a risk first and only when this is agreed review the
associated likelihood of the scored consequence.
The subjectivity on assessment of likelihood is inherently higher than that for
consequence and influenced by individual perception, background, and local
objectives a team based approach is always used to reach consensus on
likelihood.
The key requirement for the risk management process is that the significant risks
are identified and managed appropriately the precise scoring is a secondary
consideration.
It is essential that risks assessment area are consistently scored and prioritized and
a group view is required by the Quality management process to avoid personal bias
in scoring.
The scoring supports the prioritization of risks but, even then, judgment is
required where several risks all have the same score and decisions are required in
terms of resource allocation.
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The scoring supports the prioritisation of risks but, even then, judgment is
required where several risks all have the same score and decisions are required in
terms of resource allocation.
Comparisons of numbers of risks on aggregation of risk assessment areas are of
little value any analysis and trending should focus on topics and not scores.
Differences in number and ratings of risks across risk assessment areas should be
explored in terms of processes, resources and approach to generate them.
As with risk description, scoring is based on the current environment taking into
account all controls.
A control can impact the consequence or likelihood. A control should be
considered as something which impacts how severe a risk can become and not be
limited to physical controls, written procedures or failsafe controls.
Risks should be assessed and scored from a GSK perspective. Hence, the
consequence and likelihood Matrix has been changed, to focus on the impact of
the Regulators detecting risks e.g. observations.
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RISK MANAGEMENT SYSTEM (HOME PAGE)
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RISK MANAGEMENT SYSTEM
WORKFLOW
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RISK IDENTIFICATION TOOLS
5 Whys
Brainstorming
Surveys
Interviews
FMEA (Failure Mode Effect Analysis)
SWOT (Strengths, Weaknesses, Opportunities & Threats) Analysis
PEST (political, Economic, Socio-Cultural, Technological) Analysis
Kaizen (Continuous Improvement)
GEMBA (Go and See)
Affinity & Fishbone diagrams
Reality Trees
Process flowcharts
Potential Problem Analysis (Kepnor Tregoe)
Benchmarking
Mind maps
IPO
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REFERENCES
1. Quantitative Techniques (AIOU)
2. www.infra.kth.se/~soh/decisiontheory.pdf
3. en.wikipedia.org/wiki/Decision_theory
4. www.answers.com/topic/decision-theory
5. www.mendeley.com/.../decision-theory-a-brief-introduction
6. books.google.com
7. www.stat.tamu.edu/~hart/632/Bayes2
8. www.rapidmore.com/rapidshare.php?...decision+theory...brief+introduction
9. darwin.eeb.uconn.edu/eeb310/lecture.../decision/decision.html
10.www.morehouse.edu/facstaff/ajohnson/ai.../6.825-lecture-19.pdf
11.www.springerlink.com/index/R456425111457PK7.pdf
12.www.cse.unr.edu/~bebis/CS679/Handouts/DHS2.11Revised.pdf
13.www.envisionsoftware.com/.../Normative_Decision_Making_Theory.html
14.economics.stanford.edu/.../normative-decision-theory
15.home.ubalt.edu/ntsbarsh/opre640a/partix.htm
16.www.mindtools.com Decision Making
17.www.businessdictionary.com/definition/decision-theory.html
18.encyclopedia2.thefreedictionary.com/decision+theory
19.Lectures delivered by worthy Tutors in the class
http://www.infra.kth.se/~soh/decisiontheory.pdfhttp://www.answers.com/topic/decision-theoryhttp://www.mendeley.com/.../decision-theory-a-brief-introductionhttp://www.stat.tamu.edu/~hart/632/Bayes2http://www.rapidmore.com/rapidshare.php?...decision+theory...brief+introductionhttp://www.morehouse.edu/facstaff/ajohnson/ai.../6.825-lecture-19.pdfhttp://www.springerlink.com/index/R456425111457PK7.pdfhttp://www.cse.unr.edu/~bebis/CS679/Handouts/DHS2.11Revised.pdfhttp://www.envisionsoftware.com/.../Normative_Decision_Making_Theory.htmlhttp://home.ubalt.edu/ntsbarsh/opre640a/partix.htmhttp://www.google.com/url?url=http://www.mindtools.com/pages/main/newMN_TED.htm&rct=j&ei=3mXeS4DwJYv80wSVyZHIBw&sa=X&oi=breadcrumbs&resnum=10&ct=result&cd=1&ved=0CCsQ6QUoAA&q=decision+analysis+problems&usg=AFQjCNFP6VJVi1dR1dZYfZLDZFrY6pKi-ghttp://www.businessdictionary.com/definition/decision-theory.htmlhttp://www.infra.kth.se/~soh/decisiontheory.pdfhttp://www.answers.com/topic/decision-theoryhttp://www.mendeley.com/.../decision-theory-a-brief-introductionhttp://www.stat.tamu.edu/~hart/632/Bayes2http://www.rapidmore.com/rapidshare.php?...decision+theory...brief+introductionhttp://www.morehouse.edu/facstaff/ajohnson/ai.../6.825-lecture-19.pdfhttp://www.springerlink.com/index/R456425111457PK7.pdfhttp://www.cse.unr.edu/~bebis/CS679/Handouts/DHS2.11Revised.pdfhttp://www.envisionsoftware.com/.../Normative_Decision_Making_Theory.htmlhttp://home.ubalt.edu/ntsbarsh/opre640a/partix.htmhttp://www.google.com/url?url=http://www.mindtools.com/pages/main/newMN_TED.htm&rct=j&ei=3mXeS4DwJYv80wSVyZHIBw&sa=X&oi=breadcrumbs&resnum=10&ct=result&cd=1&ved=0CCsQ6QUoAA&q=decision+analysis+problems&usg=AFQjCNFP6VJVi1dR1dZYfZLDZFrY6pKi-ghttp://www.businessdictionary.com/definition/decision-theory.html