UNIVERSIDAD COOPERATIVA DE COLOMBIA
Bucaramanga
Facultad de Ciencias Administrativas y Económicas
BUSINESS ADMINISTRATION
OPERATION RESEARCH I (120301448)
Professor:
HÉCTOR FLORENTINO HERNÁNDEZ CÁRDENAS
Guidebook: OPERATIOS RESEARCH; Anand Sharma; Himalaya Publishing House, 2 printers, Daryaganj, New
Dalhi, 2.009
TRAINING UNIT #3
6. DECISION ANALYSIS AND DECISION TREE
6.1 INTRODUCTION
Basic functions of any manager in day-to-day performance of his job are planning, organising, monitoring and
controlling. In all these functions, he has to take a number of decisions, small or big. Thus, decision making
becomes an integral part of any management process. The decisions are based on the criteria decided by the
organisational objectives of business. Utility, minimisation of cost or time, maximisatioll of profits are some of
the criteria for good business decisions. Normally, there are combination of factors, which decide a particular
outcome of the decision and at times, these· may be in conflict. Adhering to high quality level may effect the
time and cost criterion, but credibility of the firm to secure future orders or to establish its market share with a
certain level of competitors may be very necessary and hence a trade off decision amongst time-costperformance parameters becomes a matter of utmost importance. There are large number of external factors
responsible to modify the decision and decision maker has to recognise factors like attitude or interest of stock
holders or employees and unions. Government policies or change in Regulatory framework may be a major
factor playing its cards in major decision making processes. Normally it is the change of decisions, when
problems are faced in business. Rationality of Decision making and their improvement bring out the best in a
Decision Maker. Hence, deep analysis of previous decisions and that of complexities of the given environment
help the process of coherent, and effective decision making. Quality of decision making depends on the input
qualitatively and quantitatively.
Often inputs or consequences are not fully known and uncertainty prevailing amongst the input parameter
creates complications for quality decision making. Decision theory provides a method for a rational decision
making under given circumstances.
In the previous chapters, we have described models with different parameters inter-reacting under different
environmental conditions. The models are formulated based on input information, where parameters are
known or are assumed to be known with certainty, while in others, uncertainty can prevail to varying degree.
Uncertain situations are dealt with by assuming parameters following various probability distribution functions.
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In this chapter, we are trying to work out a formal analytical framework for the decision maker, under
uncertainty conditions. Decision maker, in this case, has to make a choice among several courses of action
available to him. Due to uncertainty in decision variables relationship and environmental conditions being under
constant change as business and time proceeds, the best the decision maker can adopt is the best under the
circumstances. Uncertainty has to be tackled with certain amount of risk that the future is likely to materialize.
Calculated risk. therefore, becomes a handy tool to reach a worthwhile optimum decision. This analysis is
termed as Decision Analysis.
6.2 DECISION TABLES
The necessary quantitative data collected or known for a given problem can be arranged in the standard tabular
form known as Decision Table or Pay-off Table. The main objective of the pay-off table is to organize the given
known data in very structured format, so that its analysis becomes systematic. The decision table generally
contains the following elements:
1.
2.
3.
4.
Various alternatives or courses of action (finite)
The states of nature
The probabilities of the occurrences
The resultant pay-offs (conditional) or the outcome.
The tabulated form of this information is also given the name of Pay-off Matrix. A sample payoff table or
decision table or pay-off matrix is given below :
States of nature
Growth
Stagnation
Inflation
Alternatives
Stocks
7
10
3
Bonds
5
15
2
Fixed deposits
10
-5
7
6.3 DECISION MAKING PROCESS
As described under 12.1 and 12.2, the decision making process follows under given steps, for systematic analysis
of information in order to arrive at optimal business decision.
1. Identify all possible states of nature i.e., events available or affecting the decision.
2. List out various courses of action open to the decision maker. These finite number of courses of action
will facilitate the decision maker to decide under controlled parameters.
3. Identify the pay-offs for various strategic solutions under all known events or states of nature. Variation
of acts and events will be helpful to identify the outcomes or pay-off for various combinations.
4. Decision to choose from amongst these alternatives under given conditions with identified pay-offs. This
step may involve the judgment or any additional information helping the decision making process.
6.4 THE DECISION MAKING CATEGORIES
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Decision can be broadly divided into four major categories:
1. Strategic Decisions-These are those decisions which have the impact on the broad policy of the
organization and hence have long-term effects, such as decisions on type of market the business is
aimed at or the product mix to cater for the varieties of the product line.
2. Tactical Decisions-These are day-to-day decisions having impact on immediate business environment
and the resultant outcome.
3. Administrative Decisions - These are the decisions affecting the organizational structure of the firm for
optimization of its utility and performance. Selection of plant location, type of distribution system or
level of ma:t-machine ratio are termed as Administrative decisions.
4. Operating Decisions-These are the decisions taken to operate the organization at a particular
performance level and to keep the objectives well under control. Product pricing, Resources Scheduling
or Inventory decision such as re-order level or payment schedules are some of the operating decisions.
6.5 DECISION MAKING ENVIRONMENTS
Decision models are based on the type of input information available to the decision makers. Under the input
information umbrella, there are four types of decision environments, namely.
1.
2.
3.
4.
Decision making under certainty
Decision making under uncertainty
Decision making under risk
Decision making under conflict.
Decision Making Under Certainty
Decision making under certainty are easiest to operate as information available is known with definite results.
Linear programming, Break even analysis, goal programming, Transportation and Assignment Models are some
examples of decisions under certainty. These have been described under relevant chapters already.
Decision Making Under Uncertainty
In the absence of past data, it is not possible to estimate the probabilities of occurrence of different states of
nature. The decision maker has no method of computing the expected payoff for any strategy. Launching a new
product with no information about action or strategy of the competitors falls under this category. The choice of
the strategy will have to be based on Company policy, experience and the judgment of the decision maker.
Following methods can be used for such situations :
(a)
(b)
(c)
(d)
(e)
(f)
Maximin criterion
Minimix criterion
Maximax criterion
Laplace criterion
Hurwicz Alpha criterion
Regret criterion
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The application of these methods has been illustrated in problem.
Decision Making Under Risk
Under this condition, the decision making is probabilistic and the person making decision cannot predict the
outcome of an event. By selecting a particular course of action, he can expect a variety of outcomes or a
combination of outcomes. Hence, the risk involved in taking a particular decision is large and this risk is reflected
in deciding possible occurrence of a state of outcome. In order to reach the best possible decision, probability
distribution of the occurrences will have to be decided based on past data and then the best course can be
decided based on largest expected profit value. Hence, the concept of Expected Monetary Value (EMV) is to be
understood and used as a criterion for decision making.
EMV (C i ) = ∑ P i O i ( i = 1 hasta n )
Where
C = Course of action i
P = probability of occurrence of outcome 0 i
n = number of possible outcomes
O i = the pay-off expected or outcome of action i
This can be understood from problems 12.2 and 12.3.
Decision Making Under Conflict
Conflict in decision making arises when there are more than one option open for optimality, due to the action of
others in the field . Thus decision making has to take into account the strategy of the competitor also, because
the outcome greatly depends not only on our own decisions but largely upon the action taken by the competitor
in the similar field. Thus Games theory comes into play and will be discussed separately in chapter.
6.6 SOME IMPORTANT CONCEPTS
Expected Value of Perfect Information (EVPI)
When the situation is probabilistic, there is no control on the occurrences of a given state. of nature. If the
decision maker had exact information, the situation would be entirely different i.e., with more authentic and
exact information available, the decision quality would improve. Thus, the expected value with perfect
information will be the expected or the average outcome of the states of nature of the level of informatiop.
Therefore, we can calculate the expected value of perfect information (EVPI) with the help of the best
alternatives for each state of nature and multiply the pay-off with its probability of occurrence.
Thus, Expected Value with Perfect Information (EVPI).
= (Best outcome of first state of nature) x (Probability of first state of nature) + (Best outcome of second state of
nature) x (Probability of second state of nature) +........+ (Best outcome of the last state of nature) x (Probability
of last state of nature).
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This expected value with Perfect Information will, thus be the additional or improved value achieved due to
perfect information
Thus
EVPI = EPPI - EMV
where
EPPI = Expected Profit with Perfect Information
and
EMV = Expected Monetary Value
In the relationship described above, the Expected Profit with Perfect Information (EPPI) would mean the
maximum obtainable expected monetary value based on perfect information. Let us take the case of increase in
the price of a given product. If we anticipate the possibility of price increase and if we know what the competitor
would do, then decision made will be easier with more confidence. The manufacturer will be able to adopt the
optimal course of action with certainty, if he knows that the competitor would not raise the price, if he acted to
raise the price of his manufactured product. This is possible due to completely reliable or perfect information.
Expected Opportunity loss (EOl)
There is yet another method of maximising the monetary value. This is the way of minimising the expected
opportunity loss or expected value of regret. This is obtained by using the difference between the pay-off value
of the most favourable course of action and some other course of action. This is considered loss of opportunity
by not choosing the most useful or favourable course of action. From a given state of data (information) we can
calculate the opportunity loss by subtracting all outcomes from the maximum obtainable payoff or outcome for
all states of nature. The opportunity loss for each course of action, then, is termed as conditional opportunity
loss and expected opportunity loss for any course of action would be the conditional opportunity loss multiplied
by its probability of occurrence. These concepts have been used in problem 12.4.
REFERENCES AVAILABLE IN ebrary
Sharma, Anand. Operations Research.
Mumbai, IND: Global Media, 2009. p 459.
http://site.ebrary.com/lib/ucooperativa/Doc?id=10415322&ppg=42
Copyright © 2009. Global Media. All rights reserved.
Ramamurthy, P.. Operations Research.
Daryaganj, Delhi, IND: New Age International, 2007. p 716.
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http://site.ebrary.com/lib/ucooperativa/Doc?id=10367718&ppg=2
Copyright © 2007. New Age International. All rights reserved.
Mishra, D.N.; Agarwal, S.K.. Operation Research.
Lucknow, IND: Global Media, 2009. p 274.
http://site.ebrary.com/lib/ucooperativa/Doc?id=10416937&ppg=2
Copyright © 2009. Global Media. All rights reserved.
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