Lesson Slides
MODULE A: DECISION-MAKING TOOLS
4 OCT 2018
Module A:Decision-Making Tools
• Break-even analysis (Chapter 7)
– Analysis to compare processes by finding the volume at which two pro
cesses have equal total costs.
• Preference matrix
– Table that allows managers to rate alternatives based on several perfor
mance criteria.
• Decision theory
– Approach when outcomes associated with alternatives are in doubt.
• Decision Tree
– Model to compare alternatives and their possible consequences.
Decision Theory
•
•
Decision theory is a general approach to decision making when
the outcomes associated with alternatives are in doubt
A manager makes choices using the following process:
1. List a reasonable number of feasible alternatives
2. List the events (states of nature)
3. Calculate the payoff table showing the payoff for each alternativ
e in each event
4. Estimate the probability of occurrence for each event
5. Select the decision rule to evaluate the alternatives
Decision making under uncertainty
Decision making under uncertainty. The manager can list the possible events but
cannot estimate probabilities.
1.Four decision rules
a.Maximin – (“best of the best”) For those pessimists who tend to
believe that the “worst case” event will certainly occur, this decision rule
chooses the alternative that has the best result, given the worst event
will occur.
b.Maximax – (“best of the best”) For those optimists who tend to
believe that the best possible event will certainly occur, this decision rule
chooses the alternative that has the best result, given the best event will
occur.
c.Equally Likely – (“the best weighted payoff”) For realists who tend to
believe that events tend to even out in the long run, this decision rule
places equal weight, or assumes equal probability, for each of the
possible events.
d.Minimax Regret – (“best worst regret”) This decision rule looks to
minimize the worst possible negative effect (regrets) associated with
making a wrong decision (and ignoring the positive effects of a good
decision).
Decision Making Under Certainty
•
•
The simplest solution is when the manager knows which e
vent will occur
Here the decision rule is to pick the alternative with the b
est payoff for the known event
IN CLASS EXAMPLES
MODULE A
DECISION MAKING TOOLS
4-oct-2018
Decisions Under Certainty
IN CLASS EXAMPLE 1
A manager is deciding whether to hire vendor A or vendor B. The decision much de
pends on the future demand. The demand may be small or large. Assume that pay
offs for each alternative are known with certainty. What is the best choice if future
demand will be low?
Possible Future Demand
Alternative
Low
High
Vendor A
200
270
Vendor B
160
800
0
0
Do nothing
Decision Making Under Uncertainty
Can list the possible events but can not estimate the probabilities
1. Maximin: The best of the worst, a pessimistic approach
2. Maximax: The best of the best, an optimistic approach
3. Equally Likely: The alternative with the best weighted pay
off assuming equal probabilities
4. Minimax Regret: Minimizing your regret (also pessimistic)
Decisions Under Uncertainty
IN CLASS EXAMPLE 2
Reconsider the payoff matrix in Example 1.
What is the best alternative for each decision rule?
SOLUTION
a. Maximin. An alternative’s worst payoff is the lowest number in
its row of the payoff matrix, because the payoffs are profits.
The worst payoffs ($000) are:
Alternative
Worst Payoff
Vendor A
200
Vendor B
160
Decisions Under Uncertainty
b. Maximax. An alternative’s best payoff ($000) is the highest number in its row
of the payoff matrix, or
Alternative
Best Payoff
Vendor A
270
Vendor B
800
c. Equally Likely. With two events, we assign each a probability of 0.5. Thus,
the weighted payoffs ($000) are
Alternative
Vendor A
Vendor B
Weighted Payoff
Decisions Under Uncertainty
d.
Minimax Regret.
 If demand turns out to be low, the best alternative is Vendor A and its
regret is
 Vendor B is hire when demand turns out to be low, the regret is
Regret
Alternative
Low Demand
High Demand
Maximum Regret
Vendor A
200 – 200 = 0
800 – 270 = 530
530
Vendor B
200 – 160 = 40
800 – 800 = 0
40
The column on the right shows the worst regret for each alternative.
To minimize the maximum regret, pick a Vendor B.
The biggest regret is associated with having only Vendor A and high demand.
IN CLASS EXAMPLE 3
Cheng (a realist), Mala (a pessimist), and Wani (an optimist) are joint owners
in a hotelier company. They must decide whether to build medium-sized hotel,
homestay-based hotel or budget hotel in Kundasang. The government is about
to issue a policy and recommendation on pioneer hoteliers that depends on
geographical nature and certain treaties are obtained. The policy is expected to
affect demand for the accommodations; however it is impossible at this time
to assess the probability of these policy “events.”
The following data are available:
Payoffs (Profits)
Alternative
Hill-side
Heavily hilly
Non-Hilly
Medium-size
$840,000
$440,000
$190,000
Homestay
$370,000
$220,000
$670,000
$25,000
$1,150,000
($25,000)
Budget
Solutions ICE3
Payoffs (Profits)
Alternative
Hill-side
Heavily hilly
Non-Hilly
Medium-size
$840,000
840-840=0
$440,000
$190,000
670-190=480
Homestay
$370,000
840-370=470
$220,000
$670,000
670-670=0
$25,000
$1,150,000
1150-1150=0
Budget
($25,000)
670-(-25)=695
 Cheng (realist – Equally Likely) would choose
Medium-size hotel.
 Mala (pessimist – Maximin) would choose
Homestay-based hostel
 Wani (optimist – Maximax) would choose
Budget hotel
 The Minimax Regret solution is Medium-size hotel
(Smallest biggest regret $710,000)
Decisions Under Risk
• The manager can list the possible events and estimate their
probabilities
• The manager has less information than decision making under
certainty, but more information than with decision making
under uncertainty
• The expected value rule is widely used
• This rule is similar to the Equally Likely decision rule, except th
at the events are no longer assumed to be equally likely
Decisions Under Risk
IN CLASS EXAMPLE 4
Reconsider the payoff matrix in Example 1 & Example 2. For the expected value
decision rule, which is the best alternative if the probability of small demand is
estimated to be 0.4 and the probability of large demand is estimated to be 0.6?
SOLUTION
Possible Future Demand
The expected value for each alternative
is as follows:
Alternative
Vendor A
Vendor B
Alternative
Small (0.4)
Large (0.6)
Vendor A
200
270
Vendor B
160
800
Expected Value
IN CLASS EXAMPLE 5
For Cheng (a realist), Mala (a pessimist), and Wani (an optimist), find the best decision
using the expected value rule. The probabilities for the events are given below.
What alternative has the best expected results?
Payoffs (Profits)
Alternative
Medium-size
Homestay
Budget
Heavily hilly
Non-Hilly
Medium-size
$840,000
$440,000
$190,000
Homestay
$370,000
$220,000
$670,000
$25,000
$1,150,000
($25,000)
Budget
Alternative
Hill-side
Hill-side (0.50)
Heavily hilly (0.30)
Non-hilly (0.20)
Expected
Value
Decision Trees
• Are schematic models of available alternatives and possible consequences
• Are useful with probabilistic events and sequential decisions
 Square nodes represent decisions
 Circular nodes represent events
 Events leaving a chance node are collectively exhaustive
• Conditional payoffs for each possible alternative-event combination sh
own at the end of each combination
• Draw the decision tree from left to right
• Calculate expected payoff to solve the decision tree from right to left
Decision Trees
E1 & Probability
E2 & Probability
E3 & Probability
Payoff 1
Payoff 2
Payoff 3
Alternative 3
1
1st
decision
2
Alternative 5
Possible
2nd decision
E2 & Probability
= Event node
Alternative 4
E3 & Probability
Payoff 1
Payoff 2
Payoff 3
Payoff 1
Payoff 2
= Decision node
Ei = Event i
P(Ei) = Probability of event i
FIGURE A.2 – A Decision Tree Model
Decision Tree: ICE 6
A firm is deciding between two alternatives: to introduce a new product or to
keep the existing product. Introducing a new product has uncertain outcomes in
dependence on the demand.
If the demand is high, the resulting profit of the firm will be 140.
The low demand will be result in the profit 80.
The firm estimates the probabilities of a high and low demand 0.7 and 0.3,
respectively.
If the firm keeps the existing product, its profit will be 110.
SOLUTION
• For the chance node 2, we calculate the expected value of the profit
(0.7*140 + 0.3*80 = 122) and write this value over the node 2.
• At the decision node 1, we select the decision alternative with the higher
expected profit. Because max (122;110) = 122, introducing the new product
is profitable. We write the maximum expected profit over the node 1 and
draw double lines through the branch representing the inferior (worse)
decision alternative.
DECISION TREE: ICE7
A company faces a decision with respect to a product (codenamed M997) developed by one
of its research laboratories. It has to decide whether to proceed to test market M997 or
whether to drop it completely. It is estimated that test marketing will cost £100K.
Past experience indicates that only 30% of products are successful in test market.
If m997 is successful at the test market stage then the company faces a further decision
relating to the size of plant to set up to produce m997. A small plant will cost £150K to build
and produce 2000 units a year whilst a large plant will cost £250K to build but produce 4000
units a year.
The marketing department have estimated that there is a 40% chance that the competition
will respond with a similar product and that the price per unit sold (in £) will be as follows
(assuming all production sold):
Large Plant
Small Plant
Respond to competition
20
35
Not respond to competition
50
65
Assuming that the life of the market for M997 is estimated to be 7 years and that the yearly
plant running costs are £50K (both sizes of plant - to make the numbers easier!) should the
company go ahead and test market M997?
ICE8
A developer must decide how large a luxury sports complex to build – small,
medium, or large. The Profitability of this complex depends upon the future
level of demand for the complex
• States of nature: the states of nature could be defined as low demand and
high demand
• Alternatives: could decide to build a small, medium, or large complex
• Payoffs: the profit for each alternative under each Potential state of nature
is going to be determined
Payoff in Millions of Dollars
Alternative
Low (0.3)
High (0.7)
Small
8
8
Medium
5
15
-11
22
Large