Decision Analysis
Elements of decision problem
The objective
Examples: Maximize profit, minimize cost, choice of economical
operations, increase in market share.
The alternatives
A list of different actions and models available to chose from.
The uncontrollable events
The future events that are beyond the control of the decision maker.
Measurement of outcomes
Ways of measuring the outcome or payoff.
Select a decision criterion and make a decision
A decision criterion is a logical or rational method of choosing the
alternative that best meets the objective.
Classification of decision problems
Decision making under certainty
If we can identify with certainty which uncontrollable event
will apply.
Decision making under risk
If we do not know with certainty which of the uncontrollable
event will result, but we have probabilities of occurrence to
each event.
Decision making under uncertainty
If we don’t have probabilities for the uncontrollable events.
Example:
A company manufacturing computer games is faced with a sudden
growth in the sales volume. The management is considering expanding
the factory capacity or building a second plant, but there is no
guarantee that the rise in demand will continue. Thus, a third option is
to leave things as they are. What decision should be made to maximize
profit, if the costs for expanding the factory and to build new plant are
50000 and 100000 L.E/year, respectively. The estimated profits for no
expansion, expanding the factory and build new plant are 300000,
450000 and 540000 L.E per year respectively.
Solution:
The objective is to maximize profits.
The alternatives are:
1. Expand the factory
2. Build new plant
3. Nothing
The uncontrollable events:
1. Demand decreases
2. Demand stays at current level
3. Demand increases
Measurement of outcomes
Costs
No expansion zero cost
Expanding the factory 50000 L.E/year
New plant 100000 L.E/year
Profits
No expansion 300000 L.E/year
Expanding the factory 450000 L.E/year
New plant 540000 L.E/year
Selection of Decision Criterion
Decision making under certainty (DMUC)
If we know for sure that the demand will be at current level, then
expanding the factory will be the best decision, i.e the one with highest
profits of 450000 – 50000 = 400000 LE/year.
The profits for the other alternatives are:
300000 L.E/year (for no expansion)
450000 – 100000 = 350000 L.E/year (for building new plant).
Decision making under risk (DMUR)
Expected values criterion
Suppose for the that the probabilities of the demand decreases, stays at
current level, increases are 0.2, 0.45 and 0.35 respectively.
Measurement of outcomes
Costs
1. No expansion zero cost
2. Expanding the factory 50000 L.E/year
3. New plant 100000 L.E/year
Profits
Uncontrollable events 1. No expansion 300000 L.E/year
2. Expanding the factory 450000 L.E/year
Alternatives Demand Demand at Demand 3. New plant 540000 L.E/year
decrease current level increase
Expansion 300000-50000 = 450000-50000 = 450000-50000 =
250000 L.E/year 400000 L.E/year 400000 L.E/year
New plant 300000-100000 = 450000-100000 = 540000-100000 =
200000 L.E/year 350000 L.E/year 440000 L.E/year
Nothing 300000-0 = 300000-0 = 300000-0 =
300000 L.E/year 300000 L.E/year 300000 L.E/year
Prob. 0.2 0.45 0.35
Expected profit
Expanding the factory =0.2x250000+0.45x400000+0.35x400000
= 370000 L.E/year.
New plant =0.2x200000+0.45x350000+0.35x440000
= 351500 L.E/year.
No expansion =0.2x300000+0.45x300000+0.35x300000
= 300000 L.E/year.
The best decision according to the expected values criterion is to
expand the factory.
Measurement of outcomes
Costs
1. No expansion zero cost
2. Expanding the factory 50000 L.E/year
3. New plant 100000 L.E/year
Profits
1. No expansion 300000 L.E/year
2. Expanding the factory 450000 L.E/year
The opportunity loss 3. New plant 540000 L.E/year
Uncontrollable events
Alternatives Demand Demand at Demand
decrease current level increase
Expansion 50000 L.E/year 0 L.E/year 440000-400000 =
40000 L.E/year
New plant 100000 L.E/year 50000 L.E/year 0 L.E/year
Nothing 0 L.E/year 400000-300000 = 440000-300000 =
100000 L.E/year 140000 L.E/year
Prob. 0.2 0.45 0.35
Uncontrollable events
Alternatives Demand Demand at Demand
decrease current level increase
Expansion 50000 L.E/year 0 L.E/year 440000-400000 =
40000 L.E/year
New plant 100000 L.E/year 50000 L.E/year 0 L.E/year
Nothing 0 L.E/year 400000-300000 = 440000-300000 =
100000 L.E/year 140000 L.E/year
Prob. 0.2 0.45 0.35
Expected opportunity loss (EOL)
Expanding the factory =0.2x50000+0.45x0+0.35x40000
= 24000 L.E/year.
New plant =0.2x100000+0.45x50000+0.35x0
= 42500 L.E/year.
No expansion =0.2x0+0.45x100000+0.35x140000
= 94000 L.E/year.
The best decision according to the expected opportunity loss criterion
is to expand the factory.
Solution using decision trees
A decision tree is a practical way of organizing the three elements of a
decision problem:
1. Decision alternatives
2. Uncontrollable events
3. The outcome values
As well as permitting the calculation of expected profit, returns and
choosing the best alternative.
Thank you for your attention
